Nicole Dostaler - Fourth Grade - Fractions Unit

ED569C – Math for Grades 4-6

Fun with Fractions,

A Grade Four Math UnitA Grade Four Math Unit

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Fun with Fractions

Unit Plan Summary

Teacher(s) Nicole Dostaler

Grade Level Grade 4

Unit of Study Mathematics – Fractions

Duration of the Unit 5 Lessons

Learning Goal

The Learning Goal(s) for this unit is as follows:

The fourth grade students will—

recognize fractions and construct unit wholes using various manipulatives,

including geoboards, pattern blocks and fraction strips.

identify and construct equivalent fractions to one-sixteenth (1

16) using various

manipulatives, including geoboards, pattern blocks and fraction strips.

Summary of the Unit

The students will participate in a unit entitled, “Fun with Fractions”, which is an

introductory group of lessons that builds upon previous student knowledge of fractions and

builds a strong foundation for future experiences. In the one-week series of five lessons,

students will be exploring fractions largely in relationship to the concept of “one whole”.

The students will gain the knowledge and skills necessary to observe, construct and create,

investigate, and communicate their understanding of the presented concepts. They will be

constructing whole units from given fractions and breaking down whole units into fractions.

They will work with story problems, begin practice in writing addition fraction number

sentences, find equivalent fractions, and build their understanding and recognition of ½ and

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¼. Their experiences will be very concrete and grow more abstract as they utilize a wide-

range of manipulatives, such as fraction strips, geoboards, and pattern blocks, to support

their understanding of fractional concepts.

Summary of the Lessons

Lesson 1: Problem Solving Fractions

Objective: The fourth grade students will be able to visually and numerically

represent fractions to one-eighth (18

) using problem solving strategies and fraction pies.

In this lesson, students will explore the concept of sharing equally and fairly to

review their knowledge of fractions. Students will learn how to divide objects (example:

slices of pie, pizza, cake, etc.) between individuals using fraction pie manipulatives.

They relate sharing portions of these objects to numeral fraction values after reviewing

the vocabulary terms: numerator and denominator. The students complete a

performance task where they use problem solving strategies to answer a fractional story

problem, draw a picture, and explain how they received their answer. The students will

be assessed by a formative 3-point rubric in the areas of problem solving,

communication/visual representation, reasoning, connections, and number sense.

Lesson 2: Exploring and Adding Equivalent Fractions

Objective: The fourth grade students will be recognize equivalent fractions to one

whole by writing corresponding addition number sentences using fraction strips to the

one-sixteenth (1

16).

In this lesson, students will be creating their own fraction strip manipulatives to

learn about equivalent fractions. Students recognize that strips divided into a different

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numbers of parts can represent the same whole. They explore which size fractions are

similar and different from one another from 1 to 1

16. Students work to find various

combinations of smaller fraction strips that “cover” up their one whole (1 or 11

) fraction

strip. They write these findings on their recording sheet in the form of related addition

number sentences. The students will be assessed by the teacher during their exploration

by the use of an informal formative observational checklist in the areas of problem

solving, representation, connections, and number sense.

Lesson 3: Pattern Block Fractions

Objective: The fourth grade students will be recognize and generate equivalent

fractions using pattern blocks, while understanding that different models can show one

whole.

In this lesson, students will explore the concept “one whole” and equivalent

fractions. Students learn that different shapes can be considered “one whole” and

explore how different fractions can name the same amount. They will represent

fractions visually using pattern blocks. Using a model other than fraction strips helps

students realize that any shape can be a “whole”. The students will complete a

performance task game with a partner where they use pattern blocks to represent rolls of

a fraction cube in relationship to a provided whole shape. The students will be assessed

by a formative 3-point rubric to determine whether they meet or exceed the objectives

of the task, partially meet the objectives of the task, or do not meet the objectives of the

task. The students are expected to properly tally their game play, accurately draw their

pattern blocks, demonstrate recognition of specific fractions, and explain their

understanding of equivalent fractions.

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Lesson 4: Visualizing Halves and Fourths

Objective: The fourth grade students will construct different regions to demonstrate

one-half (12

) or one-fourth (14

) and construct the whole unit when given a region

representing one- half (12¿ or one-fourth (

14

) with the use of geoboards.

In this lesson, students will explore the concept halves and fourths as they explore

dividing (portioning) and constructing whole units. Students will integrate fractions,

measurement, and geometry during this investigation. As students experiment with

finding different ways to show halves and fourths of shapes, they think visually and

explore the idea that different shapes can cover the same area. The students will create

and divide shapes using geoboards. The students will complete a self-assessment to

make them responsible for completing the performance task sheet, create their fractional

quilt squares, and explain their understandings or misunderstandings faced during this

investigation.

Lesson 5: Summing up Fractions

Objective: The fourth grade students will recognize and construct unit wholes and

equivalent fractions to one-sixteenth (1

16) using manipulatives, including geoboards,

pattern blocks and fraction strips.

In this lesson, students will be review and be assessed on their understanding of

fractions, “one whole”, and equivalent fractions. Students will complete a carousel

brainstorming activity to organize and summarize their knowledge on the concepts of

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“Fractions”, “Whole”, and “Equivalent”. During the performance task, the students will

work in a variety of centers that utilize geoboard, fraction strip, and pattern block

manipulatives as they complete a “Summing Up Fractions” Recording Packet. Students

will explore and apply their knowledge of the units’ concepts by constructing them out

of the manipulatives and recording their findings and explanations in the packet. The

students will be assessed by an observational performance rubric for their behaviors

during the task, as well as by a summative scoring tool of a corrected “Summing Up

Fractions” Recording Packet. This scoring tool is a copy of the original packet, but

provides the correct potential answers for the teacher to use as a reference to evaluate

the students’ responses. They will receive a score out of 45 points. They should receive

a score above 34 to be considered as meeting the goals for the unit. Students can receive

11 points in Center A with pattern blocks, 6 points in Center B utilizing geoboards, 10

points in Center C as they explore fractional notation, and 18 points in Center D using

fraction strips.

Content Standards

National Standards (NCTM, 2002, p. 148)

In grades 3-5, students should develop understanding of fractions as parts of

unit wholes, as parts of a collection, as locations on number lines, and as

divisions of whole numbers; use models, benchmarks, and equivalent forms to

judge the size of fractions; and recognize and generate equivalent forms of

commonly used fractions.

In grades 3-5, students should create and use representations to organize,

record, and communicate mathematical ideas; select, apply, and translate

among mathematical representations to solve problems; and use

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representations to model and interpret physical, social, and mathematical

phenomena.

Connecticut State Standards (CT State Department of Education, 2010, p. 32-35)

1.3 Use operations, properties and algebraic symbols to determine

equivalence and solve problems.

o GLE4. Represent possible values by using symbols (variables) to

represent quantities in expressions and number sentences. Use

number sentences (equations) to model and solve word problems.

2.1 Understand that a variety of numerical representations can be used to

describe quantitative relationships.

o GLE7. Construct and use pictures and models to determine and

identify equivalent ratios and fractions.

o GLE8. Locate, label and estimate (round) fractions with like and

unlike denominators of two, three, four, five, six, eight and ten by

constructing and using models, pictures and number lines.

o GLE9. Construct and use models, pictures and number lines to

compare and order fractional parts of a whole and mixed numbers

with like and unlike denominators of two, three, four, five, six, eight

and ten.

o GLE10. Construct and use models, pictures and number lines to

identify wholes and parts of a whole, including a part of a group or

groups, as simple fractions and mixed numbers.

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2.2 Use numbers and their properties to compute flexibly and fluently, and

to reasonably estimate measures and quantities.

o GLE20. Use models and pictures to add and subtract fractions with

like and unlike denominators of two, three, four, five, six, eight and

ten and match number sentences or equations to the problems.

o GLE21. Identify or write number sentences to solve simple

problems involving fractions, decimals (tenths) and mixed numbers

o GLE22. Write contextual problems involving the addition and

subtraction of fractions with like denominators, decimals (tenths)

and mixed numbers; solve the problems and justify the solutions.

o GLE23. Estimate a reasonable answer to simple problems involving

fractions, mixed numbers and decimals (tenths).

Process Skills (NCTM, 2002, pp. 182, 188, 194, 195, 200, 280)

Instructional programs from grades 3-5 should enable all students to—

o Problem Solving

Build new mathematical knowledge through problem solving

Solve problems that arise in mathematics and in other contexts

Apply and adapt a variety of appropriate strategies to solve problems

Monitor and reflect on the process of mathematical problem solving

o Reasoning and Proof

Recognize reasoning and proof as fundamental aspects of mathematics

Make and investigate mathematical conjectures

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Select and use various types of reasoning and methods of proof

o Communication

Organize and consolidate their mathematical thinking through

communication

Communicate their mathematical thinking coherently and clearly to peers,

teachers, and others

Analyze and evaluate the mathematical thinking and strategies of others

Use the language of mathematics to express mathematical ideas precisely

o Connections

Recognize and use connections among mathematical ideas

Understand how mathematical ideas interconnect and build on one another

to produce a coherent whole

Recognize and apply mathematics in contexts outside of mathematics

o Representation

Create and use representations to organize, record, and communicate

mathematical ideas

Select, apply, and translate among mathematical representations to solve

problems

Use representations to model and interpret physical, social, and

mathematical phenomena

References:

Connecticut State Department of Education. (2010). Connecticut Prekindergarten—Grade 8

Mathematics Curriculum Standards. Hartford, CT: Bureau of Curriculum & Instruction.

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<http://www.sde.ct.gov/sde/lib/sde/pdf/curriculum/math/PK8_MathStandards_GLES

_Mar10.pdf>.

NCTM (2002). Reflecting on Principles & Standards in Elementary and Middle School

Mathematics, Readings from NCTM’s School-Based Journals. (2002). Reston, VA: The

National Council of Teachers of Mathematics, Inc.

<http://nctm.org/standards/content.aspx?id=3182>.

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Master of Arts in Teaching ProgramDivision of EducationQuinnipiac University

PROBLEM SOLVING FRACTIONS

Student Teacher Nicole DostalerGrade/Subject 4 th Grade/Mathematics – Problem Solving/Fractions Date of Lesson November 2010

Content Standards:

In grades 3-5, students should develop understanding of fractions as parts of unit wholes, as

parts of a collection, as locations on number lines, and as divisions of whole numbers; use

models, benchmarks, and equivalent forms to judge the size of fractions; and recognize and

generate equivalent forms of commonly used fractions. (NCTM, 2002, p. 148)

In grades 3-5, students should create and use representations to organize, record, and

communicate mathematical ideas; select, apply, and translate among mathematical

representations to solve problems; and use representations to model and interpret physical,

social, and mathematical phenomena. (NCTM, 2002, p. 148)

1.3 Use operations, properties and algebraic symbols to determine equivalence and solve

problems. (CT Department of Education, 2010, p. 32)

2.1 Understand that a variety of numerical representations can be used to describe quantitative

relationships. (CT Department of Education, 2010, p. 33-34)

o GLE10. Construct and use models, pictures and number lines to identify wholes and

parts of a whole, including a part of a group or groups, as simple fractions and mixed

numbers.

2.2 Use numbers and their properties to compute flexibly and fluently, and to reasonably

estimate measures and quantities. (CT Department of Education, 2010, p. 34-35)

o GLE21. Identify or write number sentences to solve simple problems involving

fractions, decimals (tenths) and mixed numbers.

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Learner Background:

The third grade students:

o Understand the vocabulary terms: “whole”, “half”, “share”, “evenly”, “equivalent”, &

“equal”.

o May have previously heard the terms: “numerator” and “denominator”.

o Know how to accurately use addition and subtraction of one-digit whole numbers.

o Know how to divide a whole object into half from previous grade levels, and will get more

practice in this lesson for students who may have struggled or need a review of the concept.

o Know how to divide a set of objects evenly using whole numbers from previous grade levels.

o Know how to solve story problems.

o Have experience using mathematics manipulatives, including fraction pies in previous grades.

o Have experience devising reasonable estimates.

o Have experience with fractions in previous grade levels, including part-whole or part-set.

o May have previous experience with division, but is not necessary for success in this lesson.

Student Learning Objectives(s): The fourth grade students will be able to visually and numerically

represent fractions to one-eighth (18


Assessment: The teacher will evaluate the students’ “Sharing a Pizza” Task Sheet in accordance with

the attached rubric for problem solving, communication/visual representation, reasoning,

mathematical connections, and number sense. The students’ task sheets should state the method they

used, that they applied this use to solve the story problem and explained how they solved using this

strategy, which had the ability to result in a majority of accurate answers. The students should have

represented these amounts with numbers, drawn a picture to make a visual representation, and labeled

the aspects of the picture with words. Lastly, the students should have answered the questions at the

bottom of the task sheet using the information and data they found in their representations. In doing

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this task sheet, the students would be able to see the numerical and visual connection between fraction

concepts. (See the assessment section at the end of the lesson plan.)

Materials/Resources:

Scrap Paper (One sheet for each student.)

Stack of six papers (or other items) for the initiation

Pencils (One for each student.)

“Sharing a Pizza” Task Sheet (One for each student.)

Paper circles for manipulative use

Fraction pies (12

, 14

, and 18

)

Scissors

Pizza Fractions 3-Point Rubric

Learning Activities:

Initiation:

o Ask the students: “What is sharing?”

o “When we share, we take a part of the whole group we have and give a part of it to others.

For example, if I wanted to share my six papers with you. I could give a piece to you and you

and you. (Demonstrate this by passing out some of the papers to the three students. Keep

three for yourself.) How many pieces of paper does each of you have? (One.) I have three. “

o “What would I have to do if I wanted to share all of my paper with them? How could I fairly

share them with these friends so they each have the same amount of paper and I have none?”

o “Today, we are going to learn how to evenly and fairly share objects with our friends. We

are going to determine how to separate what we have and share them between everyone in the

group equally. We are going to find various ways to represent what we are thinking and

write about what we thought about when we shared.”

Lesson Development:

Whole class/Partnered instructional grouping

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o Choose four students to stand at the front of the room. “What would happen if I went to a

bakery to get some desserts and I bought a pie? I want to give all four of my friends here

some of the pie. How do you think I could do that?” Ask the students to share some of their

responses.

o After responses are shared, use physical manipulatives and scissors (paper circles) to

represent the pie. Act out some of the students’ solutions by passing them out to the actors.

o Address any responses that say that to simply cut them out any sized piece. Explain that we

have to share the entire pie evenly and fairly between them all so there is no pie left over.

What could we do to make this happen?

o Physically cut the manipulative into fourths. “How many pieces do we have? How many

friends do we have? Are there any leftover pie slices if we pass them out to each friend? Are

there any friends without this piece of the pie?” Physically hand out the pieces to each student

and have the students hold them so they are visible.

o “How many pie slices does each friend have?” Have students hold up their pieces. Count

each piece each student has to check with the whole class. “Does each friend have the same

amount of the pie? Now that everyone has the same amount, we have shared with them

evenly. When we divide the pie between each person, they need to be EQUAL and that

means to have the SAME amount each.”

o Tell the students that fractions have two parts: A numerator and denominator. “The

numerator is the number on top, and the denominator is the number on the bottom. If you

remember that the ‘d’ stands for "down," it can help you which one the denominator is.”

o “How many pieces our pie was cut into. Show me by holding up the correct number of

fingers.” Look to make sure each student is holding up four fingers.

o Draw the circle model of the circle divided into four sections on the board, and then write the

number four as the denominator. Explain that this number tells how many parts are in the

whole. In this case, how many parts the circle is made up of.

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o Explain that the top number of a fraction, or numerator, tells you how many parts are left in

the whole after some are removed. Take away one section of the fraction pie drawn on the

board. Write the number 3 on top of the fraction. Tell the students that in this pie, there are

only 34

of it left. Review the fractions for each portion of the circle as pieces are removed

one by one and that 44

is the same as 1 because there is one whole pie.

Model :

o “Now, I went the bakery and bought a chocolate cake for dessert. This cake was already cut

at the store and has eight slices. I have four people coming to my party. How many slices of

pie would we all get to eat if I do not want any leftovers?”

o Use the think aloud strategy to explain what I am thinking to the students by speaking out

loud. This is helpful to organize thoughts so then students can see how it relates to the

written explanation of the answer.

o Model using the manipulative 18

fraction pies. Use students to represent the people coming to

the party and demonstrate to the class how to distribute the pieces of cake to each of the

people coming to the party. How many pieces would each person get? What fraction is this

if I wrote this with numbers?

o Draw the objects on the board in a visual representation of the physical manipulatives.

o Write about my thinking and why I chose to “share” in this way on the board. Use full

sentences and proper grammatical structure.

o Repeat with another example (2 pizzas with 8 slices and 4 guests or 1 cake with 6 slices and 3

guests, etc.) and draw the pictorial representation on the board. Show how the shapes are

represented by the symbol numeral amounts.

o Ask the students if there are any other ways they can represent the sharing.

Guided Practice :

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o Pass out scrap paper and one set of fraction pie manipulatives to the students.

o Do another example with the students where the result will cause the students to receive

fourths in their fraction responses. (Example: 2 pies and 8 people)

o “How could I split these two pies between eight friends so that I have no leftovers and

everyone gets one piece of pie?”

o Have students work on scrap paper drawing pictures and writing responses as they work

alongside the teacher’s examples on the board to practice before the independent practice.

o Model drawing the objects in a visual representation on the board. Have the students guide

what you are drawing.

o Allow students to share their responses on how they solved how many objects to share. Write

three to four student responses on the board verbatim to show how students will write about

their thinking on their task sheets.

Independent Practice : Individual instructional grouping – Students working alone at desks

o Pass out the “Sharing a Pizza” Task Sheet to students, along with scrap work paper and more

circle manipulatives.

o Read the open-ended question to the students, “For dinner, you went to a pizzeria with three

friends. You are going to order a large pizza with eight slices. Two of your friends want

cheese pizza, one of your friends wants pepperoni, and you want sausage on it. How many

slices of the pizza will have each topping?

o Explain to the students that they will have to determine how pieces have each topping of the

pizza will have. Using the information they find, they will have to answer the two questions at

the bottom of the paper and state how many slices each topping has and what the fraction is.

o In the box, explain that they will have to show how they got their answer. This could be a

drawing that includes both pictures and numbers to show their thinking. It could show

another visual representation or a mathematics equation.

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o Under the box, explain to the students that they will write about how they divided up the

pizza toppings. They need to write in full sentences to explain their thinking.

o Allow students to use physical manipulatives to represent the pizza slices as they problem

solve. Explain that they will have to represent what they physically do with the

manipulatives in their picture in the box if used.

o As students work, walk around and assist any students that have questions or difficulties.

o When students are finished, invite some students to share their answers, display their pictures

they drew, and explain the reasoning behind their answers to the class. Compare results and

explanations between students.

o Collect their task sheets and assess their understanding of the concept according to the rubric.

Closure:

o “Now that you all are finished with your task sheets, I want to review what we accomplished

today. In the lesson, we learned how to evenly share objects. Who can tell me what sharing

is? Who can tell me how we evenly shared when there were not enough whole items to be

given to each person? (‘We had to cut them into pieces/halves/fourths/eights, etc.’) How do

we write this when we use numbers? Why is it important that we share evenly? You all did a

great job today counting, dividing and sharing the different items we bought with friends!”

Differentiated Instruction:

Tyler

Identified Instructional Need: Tyler typically can be found completing his mathematics work

earlier than the rest of the students because of his advanced understanding of the material. He

has a distinct ability to grasp the concepts quickly and is able to apply them to his class work.

Differentiation Strategy: Tyler may be asked to create his own story problem for the classmates

to solve that would result in a fractional answer. He would be provided with a blank version of

the task sheet the other students are using where he would have to show his thinking and his

answers, including how others would go about solving his story problem.

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Michelle

Identified Instructional Need: Michelle has a hearing impairment that fluctuates in severity.

Differentiation Strategy: Michelle is slightly below grade level with her mathematics ability and

seems to demonstrate the ability to meet grade level expectations with more focused instruction.

Differentiation should help improve her skills. Michelle will have hearing support by the use of a

microphone that I will wear, so that she can hear me at a higher level in her hearing aids. She also

sits near the front of the classroom. The visual demonstration of the lesson on the board

(equations, pictorial representations, etc.) will assist Michelle in understanding the concept being

taught. The presented fractions and manipulatives will be written/drawn on the board or on an

individualized task sheet for her to see, in order to ensure that she knows what the class is

working on. She can also ask her math partner for support and explanation during class

instruction. She will be pulled into a small work group with other students that need to improve

certain mathematical concepts.

References:




_Mar10.pdf>.

NCTM (2002). Reflecting on Principles & Standards in Elementary and Middle School Mathematics,

Readings from NCTM’s School-Based Journals. (2002). Reston, VA: The National Council of

Teachers of Mathematics, Inc. <http://nctm.org/standards/content.aspx?id=3182>.

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Name: ____________________ Pizza Fractions Rubric Date: ____________

Objective: The fourth grade students will be able to visually and numerically represent fractions to one-

eighth (18


Low Competency

1

Medium Competency

2

High Competency

3

Problem Solving

Student showed great difficulty (or no attempt) determining how to solve the problem or used poor planning, which resulted in an inaccurate answer.

Student had a partially correct plan based on

some use of sharing/dividing equally concepts. There may be some small errors that

resulted in an inaccuracy.

Student had a correct plan to solve the problem that utilized sharing/dividing equally concepts, which could lead to an accurate

answer.

Communication/ Visual

Representation

Student did not explain using words, pictures, or numbers. They may have

shown representations with great inaccuracies.

Student explained ideas only using some words,

pictures, or numbers. There may be some small

errors in the representation.

Student explained ideas using words, pictures, & numbers. Drawings are

clear and accurately represent their answer.

Reasoning

Student provides no explanation of their

reasoning about how they split up the pizza. There may also be evidence of gross misunderstanding.

Student provides an explanation about the way they split up the pizza as well as some justification

of their reasoning.

Student provides accurate, insightful and/or creative

explanation about the justification behind their

reasoning.

Connections

Student shows little to no evidence of numerical

computation or there are great errors.

Student shows some evidence of numerical computation, but there

may be some minor flaws.

Student shows accurate evidence of numerical

computation and integrates the connection in their representation.

Number Sense

Students showed great difficulty using fraction

and whole number concepts. Student may

use inappropriate number concepts to answer the

question.

Student shows use of fraction and whole

number understanding. There may be some minor

flaws in application.

Student shows insightful and/or creative use of

fraction and whole number understanding.

Assessment:

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Name: ____________________ Pizza Fractions Rubric Date: _ _11/8/10______

Objective: The fourth grade students will be able to visually and numerically represent fractions to one-

eight (18


Low Competency

1

Medium Competency

2

High Competency

3

Problem Solving

Student showed great difficulty (or no attempt) determining how to solve the problem or used poor planning, which resulted in an inaccurate answer.

Student had a partially correct plan based on some use of fractional

concepts. There may be some small errors that

resulted in an inaccuracy.

Student had a correct plan to solve the problem that

utilized fractional concepts, which could

lead to an accurate answer.

Communication/ Visual

Representation

Student did not explain using words, pictures, or numbers. They may have

shown representations with great inaccuracies.

Student explained ideas only using some words, pictures, or numbers in the box. There may be

some small errors in the representation.

Student explained ideas in the box using words, pictures, & numbers.

Drawings are clear and accurately represent their

answer.

Reasoning

Student provides no explanation of their

reasoning about how they split up the pizza. There may also be evidence of gross misunderstanding.

Student provides an explanation about the way they split up the pizza, as well as some justification

of their reasoning.

Student provides accurate, insightful and/or creative

explanation about the justification behind their

reasoning.

Connections

Student shows little to no evidence of numerical

computation or there are great errors.

Student shows some evidence of numerical computation, but there

may be some minor flaws.

Student shows accurate evidence of numerical

computation and integrates the connection in their representation.

Number Sense

Students showed great difficulty using fraction

and whole number concepts. Student may

use inappropriate number concepts to answer the

question.

Student shows use of fraction and whole

number understanding. There may be some minor

flaws in application.

Student shows insightful and/or creative use of

fraction and whole number understanding.

Example of completed rubric:

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Name: ___________________________________________ Date: __________________________

Sharing a Pizza

For dinner, you went to a pizzeria with three friends. You are going to order a large

pizza with eight slices. Two of your friends want cheese pizza, one of your friends

wants pepperoni, and you want sausage on it. How many slices of the pizza will have

each topping?

What will you do to solve it? _______________________________________________

Show how you got your answer.

Explain what you did and what you noticed that helped you find the answer.

__________________________________________________________________________________

__________________________________________________________________________________

__________________________________________________________________________________

How many slices will each topping have? ___________________________________________

__________________________________________________________________________________

What fraction of the pizza is each topping? __________________________________

__________________________________________________________________________________

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Example of completed task sheet:

Name: _______Madison___________________________ Date: _____November

8__________

Sharing a Pizza

For dinner, you went to a pizzeria with three friends. You are going to order a large

pizza with eight slices. Two of your friends want cheese pizza, one of your friends

wants pepperoni, and you want sausage on it. How many slices of the pizza will have

each topping?

What will you do to solve it? __I will make a

drawing.___________________________

Show how you got your answer.

2 4

2

Explain what you did and what you noticed that helped you find the answer. I drew a circle with eight slices on it, since that’s how many slices it said it had.

Then I colored in one slice of what topping everyone wanted. I saw there was four

slices left, so I did that again and the pizza was full!

________________________________

How many slices will each topping have? _______Cheese will have 4 slices.

Pepperoni will have 2 slices and sausage will have 2

slices._____________________________________

Cheese

Pepperoni

Sausage

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What fraction of the pizza is each topping? ___Cheese is 48 . Sausage is

28 and

pepperoni is 28

.

___________________________________________________________

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EXPLORING & ADDING EQUVALENT FRACTIONS

Student Teacher Nicole DostalerGrade/Subject 4 th Grade/Mathematics – Fractions Date of Lesson November 2010

Content Standards:









1.3 Use operations, properties and algebraic symbols to determine equivalence and solve

problems. (CT Department of Education, 2010, p. 32)

o GLE4. Represent possible values by using symbols (variables) to represent quantities

in expressions and number sentences.



o GLE7. Construct and use number lines, pictures and models to determine and identify

equivalent ratios and fractions.

o GLE9. Construct and use models, pictures and number lines to compare and order

fractional parts of a whole with like and unlike denominators of two, three, four, five,

six, eight and ten.

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parts of a whole, including a part of a group or groups, as simple fractions.



o GLE20. Use models and pictures to add and subtract fractions with like denominators of

two, three, four, five, six, eight and ten.

Learner Background:

The fourth grade students:

o Understand the vocabulary terms: “numerator”, “denominator”, and “equivalent”.

o Know how to add whole numbers.

o Have experience using mathematics manipulatives, such as Unifix cubes and Cuisenaire

rods, which assisted in comparing lengths.

o Have experience working with linear fraction models largely in previous grade levels.

o Have experience working with symbolic forms of fractions largely in previous grade

levels, but several need more practice with this concept and will receive it in the lesson.

o Have experience representing quantities that have the same value with an equal sign.

o Have some previous experience working with fractions to the 1

16, but largely in non-

standard formats.

o Have some previous experience with addition of fractions in previous grade levels, but

the majority of the students have not vast formal experience within a classroom.

Student Learning Objectives(s): The fourth grade students will be recognize equivalent fractions to

one whole by writing corresponding addition number sentences using fraction strips to the one-

sixteenth (1

16).

Dostaler 28

Assessment: The teacher will evaluate the students using informal observations as they are working.

The teacher will score the students on an observational checklist for problem solving, number sense,

mathematical connections, and representations. On the recording sheet, the students must write an

addition sentence using fractions that equal one. The student should have first demonstrated the

addition sentence in a physical representation by using their fraction strips. They should compare their

strips to the “whole” strip to verify their answers. Lastly, they should have symbolically written the

fraction amounts in the correct box as an addition sentence, which should usually result in the

accurate answer. They should attempt to not repeat any combination of addition statements. In doing

this task sheet, the students would be able to see the numerical and visual connection between fraction

strips and the symbolic representation of their addition sentence. The teacher will observe the

students completing this task by walking around and possibly conferencing with several students

throughout the independent practice. The teacher will check off and make notes on the skills that they

see the students’ representing. The students should master at least two of these categories during this

lesson. (See the assessment section at the end of the lesson plan.)


3” x 18” Strips of paper in red, navy, light blue, brown and purple. (One strip of each color for

each student.)

Scissors (One for each student.)

Envelope (One for each student.)


“Make a One” Recording Sheet (One for each student.)

Markers

Pack of gum with 5 strips inside

Observational Checklist


Initiation: Whole class instructional grouping

Dostaler 29

o Bring a pack of gum. Ask the students: “What is this that I am holding up?” (“A pack of

gum!”) “How many packs of gum do I have? (“One!”)

o “This pack of gum is made up of 5 strips of gum inside.” Take out the pieces one by one and

count them out loud. “These 5 strips make up the 1 pack of gum. If I eat a piece of gum, I

can write a fraction that shows what part of the 5-pack of gum that I chewed.” Write 15

on

the board.

o Ask the students: “What do you think the six refers to? What do you think the one stands

for? Why does this mathematical notation make sense? What could I write to show the

fractional part of the rest of the 5-pack that I didn’t chew yet?” Take student responses and

write related explanations on the board.

o Continue through the pack of gum reviewing the concepts of 25

, 35

,45

, and 55

.Be sure to note

that the whole pack of gum is represented by 55

.

o “Today, we are going be working with fractions. We will each be creating our own set of

fraction strips out of paper to use when we work with them. They will help us visually

represent one-whole in a variety of ways. It is important that we understand fractions

because we interact with them every day…just like you saw with the pack of gum or even

when we want to share our food with a friend. We will use the strips we make to explore

creating addition number sentences of our fractions. We will write all of the different ways

we can make a one on a task sheet that I will pass out to you all later in the lesson. First,

we’re going to have some fun folding and cutting paper to make our fraction sets.”

Lesson Development:

Whole class instructional grouping

o Pass out a series of paper strips to each student so they all have one of each color. Provide

each student with a marker and a pair of scissors.

Dostaler 30

o Walk the students through the steps to fold, cut, and label each strip properly. Model each

step:

“On the navy strip, write11

. If this strip is staying whole, why do we write 11

? What

does the 1 on top represent?” (“Numerator: This top number counts. It tells how

many parts we have in our portion.”) “What does the bottom 1 represent?”

(“Denominator: The bottom number tells us what is being counted. It tells us how big

the part is.”)

“On the red strip, fold it in half perfectly. Cut on that fold. On each piece write 12

.

The whole strip has been divided into two pieces of the same size. Each piece is one

of the two pieces. The 1 on top represents that right now I am holding one of the two

pieces total. The 2 on the bottom represents the total number of red pieces.

“With the light blue strip, fold it in half perfectly. Cut on that fold. Now take each of

the two pieces and fold them in half perfectly. Cut on those folds. How many pieces

do you have now?” (“Four!”) “On each piece, write 14

. Right now, I am holding up

one of the pieces, so the 1 is on top. However, there are 4 of the pink pieces in total

and causes us to put the 4 on the bottom.”

“With the brown strip, fold it in half perfectly. Cut on that fold. Now take each of the

two pieces and fold them in half perfectly. Cut on those folds. Take each of the four

pieces and fold them in half. Cut on their folds. How many pieces do I now have?

(“Eight.”) “What do you think we will write on each of these pieces? ( {1} over {8} )

“What does the top number represent? What number will we write on the bottom?”

(“An eight because there are eight pieces of brown paper total!”)

“With the purple strip, fold it in half perfectly. Cut on that fold. Now take each of the

two pieces and fold them in half perfectly. Cut on those folds. Take each of the four

pieces and fold them in half. Cut on their folds. Now, you need to take each of the

Dostaler 31

eight pieces, fold them in half evenly and cut on their folds! Phew! How many

pieces do I now discover?” (“Sixteen.”) “What do you think we will write on each of

these pieces?” ( {1} over {16} )“Do you see a pattern? What does the top number

represent? What number will we write on the bottom?” (“A sixteen because there are

sixteen equal pieces of purple paper total!”)

o “I’d like you to now label the backs of all of your pieces with your initials so we don’t lose

any of the pieces.” Write your name on the back of some to model for the students. “We

need to be careful and keep all of our pieces together. I will give you all an envelope at the

end of the lesson to store your fraction strips in.

o “Can you all line up your strips on your desk? I’d like the whole strip on the top and next

the ½ strip underneath that, so on and so forth.”

o Ask the students: “What do you notice about the pieces?” (Possible answers include: The

pieces get smaller and smaller. Each piece is half of the one before it. The strips are the

same length.)

o Provide some students with some time just to explore with their new fraction strips.

Model

o “First, I’d like all of your eyes up here, while you watch me demonstrate how to work with

our fraction strips. Like I said previously, today we are going to find as many ways as we can

to make a one. To do this, I am going to take my 11

strip. This strip represents one whole.

We will place our smaller fraction strips on this strip to see what combinations we can use to

fill it up.” (If magnetic fraction strips are available, utilize these manipulatives on the board.)

o Use the think aloud strategy to explain thoughts on how to find one way to fill the strip up

with other strips. Take the 12

and 12

strips and lay them over the 11

strip for the students.

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Show them how these two strips completely cover the 11

strip. “I know that 12

and 12

make

one because my 11

strip is completely covered evenly. There are no extras over hanging it.”

o Model using the manipulatives. Move them around and project them onto a larger screen if

possible so that all the students can see.

o Show how the shapes are represented by the symbol numeral amounts written on them.

“Since I know that 12

and 12

make 11

, which means 1, I can write that as 12

+ 12

= 1.”

o Pass around the “Make a One” Task Sheet for the students to write the equation upon.

Guided Practice

o “I’d like you all to try to work with your fraction strips and make a one with me. Can you all

take your 12

strips and line them up over your 11

strip?” Walk around to observe the students

lining the strips up properly.

o Ask the students: “How can we verify that our strips are the same size? What do we know

about them before we made our fraction set?”

o Have students work with the fraction strips to uncover a new way to cover the 11

strip.

Prompt the students to explore using only the 14

strips. Ask the students: “How many 14

strips do you think it will take to cover up the 11

?”

o Model doing this for the students, preferably using an overhead projection. “How many 14

strips do you see lying on top of my 11

strip? Were your answers correct? Why/why not?”

Dostaler 33

o Have students come up to the board to write 14

for every strip that is present lying on their 11

strip. “We know that 14

and 14

and 14

and 14

make 11

or 1. They are the same amount. We

have four of the 14

strips on our 1 strip. What can we write then to make an addition

sentence, like the one I made previously?” (“14

+ 14

+ 14

+ 14

= 1”)

o Hold a discussion to clarify any misunderstandings or difficulties some students may have.

Independent Practice

o Explain to the students that they will have to continue filling in the rest of the boxes on the

task sheet with addition sentences that use fractions that equal one. They must not repeat the

same addition sentence, but in a different order. Every box must be filled in with a new

sentence. If they want to find more, they can write other equations on the back of the paper.

o Remind students that they can mix and match strips. For example, they can use a 12

strip, a 14

strip, and two 18

strips to make a one.

o Allow students to use their fraction strips to represent the problems they are solving. Explain

that they have to represent what they physically do with the manipulatives by writing the

equivalent numeric sentence in the box.

o As students work, walk around and assist any students that have questions or difficulties. Use

the observational checklist to judge that each student is meeting the criteria for problem

solving, number sense, mathematical connections, and representation. Check off the category

that the children are completing when it is seen.

o When students are finished, invite some students to share their number sentences on the board

and explain the reasoning behind their answers to the class.

Closure:

Dostaler 34

“Now that you have finished your task sheets, I want to review what we accomplished today. In

the lesson, we learned that there are a variety of ways to represent a whole and, in this case, it

was the number one. We looked at fractions that were equivalent to one and made addition

sentences. Who can tell me what a fraction is? What does equivalent mean? What way did we

know that our fraction strips were equivalent to one? It is important to recognize that each part

of our equation was a portion of the whole and that the different parts, whether it was one-eighth

or one-fourth, stayed the same size no matter what. Those sizes are always equal. It always will

take four of the one-fourths to make one. It will always take eight of the one-eighths to make

one. If I broke a candy bar into eight equal pieces, it would take all eight to make a whole candy

bar again. This is important in giving each person a fair share of it if we were sharing the candy.

Keep these ideas in mind, since we will continue to be working with fractions during this unit

while we explore the relationships of numbers in greater depth.”

Have the students clean up and put their fraction strips in their envelopes for safe keeping.


Tyler




Differentiation Strategy: There are several approaches that I could take with Tyler. I could have

Tyler attempt with his current strips to “make a two”. I could provide him with another strip and

have him create 1

32 out of it. He could then list an entire new and much longer list of possible

addition sentences to “make a one.” I could provide him with some other paper strips and he

could try to make create 13

, 15

, 16

, 17

, 19

, 1

12, and so forth with them and then write addition

sentences. I could also attempt to have him practice with mixed fractions.

Dostaler 35

Michelle



seems to demonstrate the ability to meet grade level expectations with more focused instruction,

especially with fraction fluency and vocabulary. Differentiation should help improve her skills.

Michelle will have hearing support by the use of a microphone that I will wear, so that she can

hear me at a higher level in her hearing aids. She also sits near the front of the classroom. The

visual demonstration of the lesson on the board (equations, pictorial representations, etc.) will

assist Michelle in understanding the concept being taught. The presented fractions and

manipulatives will be written/drawn on the board or on an individualized task sheet for her to see,

in order to ensure that she knows what the class is working on. She will have written instruction

on how to make the fraction strips as well. She can also ask her math partner for support and

explanation during class instruction. She will be pulled into a small work group with other

students that need to improve fractional math concepts. For this lesson, she will place a sticker

on one of their “fourths” fraction strips as she says aloud “one-fourth”. Then, she will put a

sticker on the second “fourths” as she says “two-fourths”. She will continue to place stickers and

count aloud until the end of the strip. She will repeat with other strips as needed to build fluency

with fraction vocabulary and familiarity with fraction models.

References:




_Mar10.pdf>.




Dostaler 36

Make a One Observational Checklist Date: _______

Objective: The fourth grade students will be able add fractions and write corresponding number sentences

using fraction strips to the 1

16.

Problem SolvingStudent had a correct plan to solve the problem that utilized fraction and addition

concepts, which could lead to an accurate answer.

Number SenseStudent shows insightful and/or creative use of fraction, whole number, and addition

understanding. There may be some minor flaws in application.

ConnectionsStudent shows some accurate evidence of numerical computation and integrates the

connection in their symbolic representation.

RepresentationStudent utilizes fraction strips to assist in representation of the fraction and addition

concepts. Student may have had needed some assistance.

Name Problem Solving Number Sense Connections Representation

Assessment:

Dostaler 37

Name: _________________________________________ Date: _____________________________

“Make a One” Recording Sheet

Write an addition sentence using fractions that equals one (1). Write each sentence in

the boxes below. Use the fraction strips to help you.

Example: 12 + 1

2 = 1 = 1

= 1 = 1

= 1 = 1

= 1 = 1

= 1 = 1

= 1 = 1

Dostaler 38

Example of completed task sheet:

Name: ___Madison________________________________ Date:

___11/9/10______________________

“Make a One” Recording Sheet

Write an addition sentence using fractions that equals one (1). Write each sentence in

the boxes below. Use the fraction strips to help you.

Example: 12 + 1

2 = 1 1/8 + 1/8 + 1/8 + 1/8 + 1/2

= 1

1/4 + 1/4 + 1/2 = 11/16 + 1/16 + 1/16 + 1/16 + 1/16 +

1/16 + 1/16 + 1/16 + 1/2 = 1

1/4 + 1/4 + 1/4 + 1/4 = 11/8 + 1/8 + 1/8 + 1/8 + 1/8 +1/8 + 1/8 +

1/8 = 1

1/16 + 1/16 + 1/16 + 1/16 + 1/16 + 1/16 + 1/16 + 1/16 + 1/16 + 1/16 + 1/16 + 1/16 + 1/16 + 1/16 +

1/16 + 1/16 = 1

1/16 + 1/16 + 1/16 + 1/16 + 1/16 +

1/16 + 1/16 + 1/16 + 1/4 + 1/4

= 1

1/16 + 1/16 + 1/16 + 1/16 + 1/16 + 1/16 + 1/16 + 1/16 + 1/8 + 1/8 + 1/8

+ 1/8 = 1

1/2 + 1/4 + 1/8 + 1/8 =

1

1/4 + 1/4 + 1/8 + 1/8 + 1/8

+1/8 = 1

1/2 + 1/4 + 1/8 + 1/16 +

1/16 = 1

Dostaler 39


PATTERN BLOCK FRACTIONS


Content Standards:











o GLE7. Construct and use number lines, pictures and models to determine and identify

equivalent ratios and fractions.

o GLE8. Locate, label and estimate (round) fractions with like and unlike denominators of

two, three, four, five, six, eight and ten by constructing and using models, pictures and

number lines.

o GLE9. Construct and use models, pictures and number lines to compare fractional parts

of a whole with like and unlike denominators of two, three, four, five, six, eight and ten.


parts of a whole, including a part of a group or groups, as simple fractions.

Dostaler 40

Learner Background:


o Understand the vocabulary terms: “numerator”, “denominator”, “equivalent”,

“rhombus”, “trapezoid”, “hexagon”, and “triangle”.

o Have experience using mathematics manipulatives, such as pattern blocks, but largely

not for fraction concepts.

o Have experience working with various fraction models from previous unit lessons,

including linear and pie.

o Have experience working with symbolic forms of fractions, but several need more

practice with this concept and will receive it in the lesson.

o Have experience representing quantities that have the same value with an equal sign.

o Have previous experience working with fractions to the 1

16.

o Have previous experience tallying results and will receive practice during this lesson.

o Have limited previous experience relating one whole to various fraction models and will

receive practice during this lesson.

Student Learning Objectives(s): The fourth grade students will be recognize and generate

equivalent fractions using pattern blocks, while understanding different models can show one whole.

Assessment: The teacher will evaluate the students using a 3-point rubric once they hand in their “A

Different Whole” Recording Game Sheet. The teacher will score the students as a 3 – Meets or

Exceeds Expectations, a 2 – Partially Meets Expectations, or a 1 – Does Not Meet Expectations. To

receive a 3, the students on the recording sheet must have tally marks present that represent game play

of ten rounds, drawings are present and correctly represent the pattern blocks utilized in this task, the

shapes are circled within the “One Whole” shape and demonstrate an understanding of 16

and 2

12 with

both fractions circled correctly, and their explanation must demonstrate an understanding about the

Dostaler 41

idea that the amounts are the same or equivalent, but created with different shapes/fraction amounts

within the “One Whole”. To receive a 2, the students on the recording sheet must have tally marks

present that represent ten rounds of game play, their drawing is present and demonstrates some

misunderstandings or difficulties representing blocks utilized in this task, shapes are circled within the

“One Whole” shape, but may demonstrate difficulties understanding 16

and 2

12, and their explanation

are general, unspecific, or demonstrate some misunderstandings about the idea that the amounts are

the same or equivalent, but created with different shapes/fraction amounts. To receive a 1, the

students on the recording sheet must have not have tally marks present that represent ten rounds of

game play, the drawing is not present or does not properly represent the blocks utilized in this task, no

shapes are circled within the “One Whole” shape or the wrong fractional amounts are circled, and

their explanation is unclear and/or does not include the idea that the amounts are the same or

equivalent, but created with different shapes/fraction amounts within the “One Whole”. In doing this

recording sheet, the students would be able to see the numerical and visual connection between

pattern blocks and that the shapes are equivalent because their sizes are the same/take up the same

amount of the whole. The teacher will score each student on the rubric from 1 to 3, with a score of 2

or higher as passing for this lesson. (See the assessment section at the end of the lesson plan.)


Pattern Blocks (Do not include the tan rhombuses or orange squares.)

Fraction Cube labeled 12

, 13

, 16

, 16

, 1

12, and

112

(One per partnered group.)

“A Different Whole” Recording Game Sheet (One for each student.)

“Pattern Block Fractions” 3-Point Rubric


Crayons

Dostaler 42

If pattern blocks are not available or for extra support, students can visit

http://www.mathplayground.com/patternblocks.html for virtual pattern blocks.



o “Today, we’re going to start our lesson by taking a survey! I want you all to think about your

answer to the options that are written on the board. You will each come up and make a tally

under the column that fits your answer. Which one of these colors is your favorite?”

o Draw this chart on the board:

Red YellowYellow Blue Green

o Have the students come up and mark one tally in their preferred column. Review how to

correctly cross off the group of five tallies.

o Total the results. Discuss the results with the students. Write the numeral amounts under

each box. Have the students find the fraction for each color of student preference. “Which

has the most tallies/greatest fraction? Which has the least tallies/smallest fraction?”

o Have the students stand up to visually represent their portion of the whole they make up.

o “Today, we are going be working with fractions using pattern blocks that are these colors!

Everyone will get a group of pattern blocks to work with. We are going to be covering up

blocks with other shapes and looking at the relationships between the whole shapes and

fraction portions. We will also try to make the same fractions over again using different

types of shapes. At the end, we will play a fraction game that uses the pattern blocks with our

math partners! First, we’re going to have some fun exploring and learning how to work with

our pattern blocks.”

Lesson Development:

Model Whole class instructional grouping

Dostaler 43

o Provide each student with a set of pattern blocks and allow them to free explore the blocks for

two minutes.


the pattern blocks for finding fractions. Like I said previously, today we are going to find

what fraction each shape is in relation to one whole. To do this, I am going to take my

yellow hexagon shape. This one shape represents one whole. We will place other shapes on

top of this shape to see what combinations we can use to fill it up and what fraction each

shape is.”

o Use the think aloud strategy to explain thoughts on how to find one way to fill the shape up

using the red trapezoid. Have the students lay one yellow hexagon on their desk and to take a

red trapezoid, while you model. Show them how this shape covers 12

of hexagon.

o “If you lay another red trapezoid on it, the two shapes completely cover the whole hexagon.

If this is the case, the red trapezoid must be 12

of the hexagon. The red trapezoid is one of

two equal parts of the hexagon. I know that 12

and 12

make one whole, because my yellow

hexagon is completely covered evenly. There are no parts of the trapezoids over hanging it.”

o Model using the manipulatives. Move them around and project them onto an overhead if

possible so that all the students can see.

o Draw a chart on the board that looks as follows:

The covers __________ of a



o Fill in the fractional amount of 12

in the blank for the red trapezoid.

Dostaler 44

o Repeat this activity with the blue rhombus. Cover up the yellow hexagon with the blue

rhombus, modeling on an overhead so that all students can see. Have them do this as well.

o “How many rhombuses did it take to cover the hexagon? (“Three.”) The rhombus is what

fractional part of the hexagon? (“One-third.”) How do you know that a rhombus is one-

third?” (“Because the three rhombuses are identical, so each one is an equal part and together

they make a whole hexagon.”)

o Fill in the fractional amount of 13

in the blank for the blue rhombus on the board.

o Repeat this activity with the green triangle and ask similar questions. Fill in the chart.

o “Can any of you think of other ways to cover the hexagon with these shapes? What about

combining more than one type of shape?” (“You can do one green triangle, one blue

rhombus, and one red trapezoid…. Two blue rhombus and two green triangles…etc.”) Ask

the students what fraction of each shape covers their whole yellow hexagon and write

amounts on the board in words and numbers. (“1 whole is the same as: 2 thirds and 2 sixths.”)

o “Which pattern blocks can you use to make 23

of ahexagon?56

of ahexagon? Make each

fraction again using different shapes.” Write the student responses on the board again.

2 thirds (23)is the same as: 5 sixths ( 5

6 )is the same as:

4 sixths(46) 1 half ( 1

2 )and 1 third (13)

1 half ( 12 )and 1 sixth (

16) 1 half ( 1

2 )and 2 sixths (26)

1 third ( 13 )and 2 sixths (

26) 2 thirds ( 2

3 )and 1 sixth (16)

Guided Practice

o Hold up a blue rhombus. “Any shape can be called one whole. We’ve been working with the

yellow hexagon as our one whole. Now I am holding up a blue rhombus. If this is now our

Dostaler 45

whole, which blocks can you cover it with to show equal parts? (“Green triangles.”) Which

block is one-half of the whole?” (“One green triangle.”)

o Have the students use their pattern blocks to figure out the answers to these questions.

o Hold up a red trapezoid. “Which block would be one-third if the trapezoid is the new

whole?” (“One green triangle.”) Allow them to use their pattern blocks again to solve.

o Ask the students to explain why a green triangle is 13

of a red trapezoid, but 12

of a blue

rhombus.


Independent Practice Partnered Instructional Grouping

o Pass around an “A Different Whole” Recording Game Sheet to each student.

o Pair off the students and provide each pair with a labeled fraction cube.

o Discuss the fractional parts of the “new” whole on the recording sheet, which is made up of

two yellow hexagons.

o “How many red trapezoids does it take to cover the whole? (“Four.”) How many to cover half

of it? (“Two.”) So two trapezoids are 12

of the whole.”

o Continue this same discussion for the green triangles and blue rhombuses.

o “What is another way to cover 12

of this whole?” (“One trapezoid, rhombus and triangle… six

triangles…three rhombuses.”

o Explain to the students that they will be playing a game with their partners. Read the

directions to the students: “Take turns with a partner using pattern blocks to cover the ‘One

Whole’ shape on the page. Use only the red trapezoid, blue rhombus, and green triangles.

When player one begins, they roll the fraction cube to find out their fraction of the “One

Whole” they need to cover and puts that shape on it. The other player then takes their turn.

The first one to EXACTLY cover the ‘one whole’ wins that round. Mark a tally in your

Dostaler 46

section when you win. Play 10 rounds. After 10 rounds, draw in the shapes covering your

‘One Whole’.”

o Go step by step playing the first round as a whole class so that the students understand what

they are doing to play the game.

o Allow the students to then continue playing with their partners until they finish the ten

rounds.

o As students play, walk around and assist any students that have questions or difficulties.

o When the students are done with 10 rounds and have drawn in their shapes, explain that they

have to circle the shape(s) that makes up 16

of their “One Whole” and the ones that make up

212

of their “One Whole.” They should write what they notice on the back of their paper.

o When students are finished, invite some students to share their responses to the final question,

including the shapes they circled, and explain the reasoning behind their answers to the class.

Closure:

“Now that you all are finished with your task sheets, let’s review what we accomplished

today. In the lesson, we learned that there are a variety of ways to represent a whole. A

whole can be any shape of our pattern blocks that we consider to be ‘one whole’. We looked

at how different smaller pattern blocks can be different fractions depending on the size of our

‘one whole’. What fraction was the green triangle when the yellow hexagon was our one

whole? (“16

What was fraction was the green triangle when the blue rhombus was our one

whole? (“12

”) How can the same shape be a different fraction? We also looked at shapes that

were equivalent to one another. What shape was one-half of the yellow hexagon? (“One red

trapezoid.”) What other shapes were one-half of the yellow hexagon? (“One blue rhombus

and a green triangle…Three green triangles.”) In this case, we learned that 13

and 16

are the

Dostaler 47

same as or equivalent to 12

and that 36

is the same as or equivalent to 12

. It is important to

remember that we always need to look at the whole shape first. Then we can determine how

much each portion of the shape another object takes up. We also need to keep in mind that

there may be different ways of making fractions by finding other numbers that are equivalent.

Keep these ideas in mind, since we will continue to be working with fractions during this unit

while we explore the relationships of numbers in greater depth.”

Have the students clean up, hand in their recording sheets, and put their pattern blocks away.


Tyler




Differentiation Strategy: In this lesson, there are several options that I can take to accommodate

Tyler’s need for more advanced explorations.

o Tyler may utilize and incorporate the tan rhombuses and orange squares to find new

fraction amounts.

o Tyler could create a picture out of the fraction blocks, trace around their edges and then

find the fractional amount of each of those shapes in relation to the one whole. He

could then find an alternative way to create the same picture using different pattern

blocks.

o Tyler could play a similar game as “A Different Whole”, but instead use his fraction

strips from the previous lesson. On his turn, he can use a counter to cover a section of

the fraction strip that matches his toss. Alternatively, he could place counters on other

strips to make equivalent fractions. For example, if Tyler tossed a 13

, he could cover 13

or two 16

units. On each turn, Tyler would record the fraction he tossed and any

Dostaler 48

equivalent fractions he made. Once again, when covering all of his strips, he would be

the winner of that round.

Michelle






sits near the front of the classroom. The visual demonstration of the lesson on the board and

overhead (moving the pattern blocks, tables with fraction amounts, etc.) will assist Michelle in

understanding the concept being taught. The presented fractions and manipulatives will be

written/drawn on the board or on an individualized task sheet for her to see, in order to ensure

that she knows what the class is working on. She can also ask her math partner for support and

explanation during class instruction. She will be pulled into a small work group with other

students that need to improve fractional math concepts. For this lesson, she may use flashcards

to match fractions with its picture and read the fraction out loud. She may then create those

fractions with the pattern blocks.

References:




_Mar10.pdf>.

McGraw-Hill Education, Co. (2004). Using Pattern Blocks as Fractions. Growing with Mathematics.

New York City, NY: Wright Group/McGraw-Hill Companies, Inc.




Dostaler 49

Pattern Block Fractions 3-Point Rubric Date: _______

Objective: The fourth grade students will be recognize and generate equivalent fractions using pattern blocks, while understanding different models can show one whole.

3Meets or Exceeds the objectives of the task.

Demonstrates a high level of understanding.

Tally marks are present representing game play and 10 rounds.

Drawing is present and correctly represents blocks utilized in this task.

There are shapes circled within the “One Whole” shape and demonstrate

and understanding of 16

and 2

12. Both fractions are circled correctly.

Explanation may demonstrate an understanding about the idea that the amounts are the same or equivalent, but created with different shapes/fraction amounts within the “One Whole”.

2Partially meets the

objectives of the task.

Demonstrates some understanding.

Tally marks are present representing game play and 10 rounds.

Drawing is present, but may demonstrate some misunderstandings or difficulties representing blocks utilized in this task.

There are shapes circled within the “One Whole” shape, but may

demonstrate difficulties understanding 16

and 2

12. One fraction amount

may be circled correctly.

Explanation may be general, unspecific, or demonstrate some misunderstandings about the idea that the amounts are the same or equivalent, but created with different shapes/fraction amounts.

1Does not meet the objectives

of the task.

Demonstrates poor or incorrect understanding.

There are no tally marks representing game play and 10 rounds.

Drawing is not present or does not properly represent the blocks utilized in this task.

There are no shapes circled within the “One Whole” shape or the wrong fractional amounts are circled.

Explanation is unclear and/or does not include the idea that the amounts are the same or equivalent, but created with different shapes/fraction amounts within the “One Whole”.

Name Score Name Score

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Assessment:

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Name: _________________________________________ Date: _____________________________

A Different Whole Recording Sheet

Take turns with a partner using pattern locks to cover your “One Whole” below. Use only these pattern blocks.

Roll a fraction cube to find out your fraction of the “One Whole” you need to cover.

The first one to exactly cover “One Whole” wins this round.

Use tally marks to record in the chart. Play 10 rounds.

Draw in the shapes covering your “One Whole” in the last round.

Player 1: _________________________________

Player 2: _________________________________

Player Name Tally Marks

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After drawing the shapes, circle the shape that makes up 16

of the “One Whole.” Circle the shape(s)

that make up 2

12 of the “One Whole.” Write about what you notice on the back of this paper.

Example of completed task sheet:Name: ___Madison_____________________________ Date:

____11/10/10__________________

A Different Whole Recording Sheet

Take turns with a partner using pattern locks to cover your “One Whole” below.

Use only these pattern blocks.

Roll a fraction cube to find out your fraction of the “One Whole” you need to cover.

The first one to exactly cover “One Whole” wins this round.

Use tally marks to record in the chart. Play 10 rounds.

Draw and color in the shapes covering your “One Whole” in the last round.

Player 1: ____ Madison__________________

Player 2: _____ Jacob ___________________

Player Name Tally Marks

Madison IIII I

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Jacob IIII

After drawing the shapes, circle the shape that makes up 16

of the “One Whole.” Circle the shape(s)

that make up 2

12 of the “One Whole.” Write about what you notice on the back of this paper. Flip

over

The parts I circled show the same amunt of the

shape. Two of the green squares are the same

size as the blue rombus. The green squares are

each a twelfth and the rombus is a sixth. So two

of the green are the same as one of the blue.

They are the same amunt.

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VISUALIZING HALVES AND FOURTHS


Content Standards:










relationships. (CT Department of Education, 2010, p. 33)



numbers.

Learner Background:


o Understand the vocabulary terms: “square”, “halves”, and “fourths”.

o Have experience using mathematics manipulatives, such as geoboards, but only for

geometry concepts in the past.



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o Have experience working with symbolic forms of fractions.

o Have some previous experience working with fractions to the 1

16, but have difficulties

visualizing them in more abstract ways and will receive practice doing so for halves and

fourths in this lesson.

o Have some previous experience relating one whole to various fraction models, but

several need more practice with this concept and will receive it during this lesson.

Student Learning Objectives(s): The fourth grade students will construct different regions to

demonstrate 12

or 14

and construct the whole unit when given a region representing 12

or 14

with the

use of geoboards.

Assessment: The students will evaluate themselves with a self-assessment sheet after completing the

“Quilt Fractions” Recording Packet. This assessment task will be answered by the students at the end

of the lesson so that they can self-evaluate their class work, as well as their participation and

cooperation. This sheet allows the teacher to determine which student partnerships had difficulties by

what is reported, as well as compare the students’ views of their participation to those observed by the

teacher. The teacher will grade the students using the same sheet. The students will evaluate

themselves on 10-point scale on a variety of areas, including working with the manipulatives,

drawing, shading, and creating ½ and ¼ fraction quilt squares, discussing ideas and results with the

class, working well with classmates, and using time well. The students have space at the bottom of

the self-evaluation to state what they liked most or did well during the lesson, as well as what they

liked least or had difficulties with during the lesson. Teachers may not recognize what students

struggle with through observations and this explanation by the students can provide insight into any

difficulties they faced when working with the fractions or manipulatives. As students work on the

recording packet, they will experiment with finding different ways to show halves and fourths of

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shapes, allowing them to think visually and explore the idea that different shapes can cover the same

area. (See the assessment section at the end of the lesson plan.)


The Quilt Story by Tony Johnston and Tomie dePaola

Geoboards (One for each pair of students.)

Geobands (5-8 for each pair of students.)

“Quilt Fractions” Recording Packet (One for each student.)

Dot Grid Paper

“Quilt Fractions” Self-Assessment (One for each student.)


Scissors (One pair for each student.)

Crayons

Quilt and/or an image of a quilt



o Show the class a quilt, either by providing them with an actual quilt or by displaying an

image of one on the overhead for them to see.

o “Who can tell me what this is? (“A quilt!”) Does anyone know how they make quilts?

(“They take pieces of fabric to make squares and then sew all of the squares together.”) What

shapes do you see inside of one of the quilt squares?” (Answers will vary.)

o “I’m going to read you a story today about a special quilt, like those we’ve seen here, that

was loved by a family for many years. The book is called The Quilt Story by Tony Johnston

and Tomie dePaola.” Read the story to the students.

o “Today, we are going to look at fractions as we make a class quilt! Everyone will get one

geoboard, several geobands, and dot grid paper to work with. I will show you how to

properly use these materials. We are going to be creating halves, fourths and whole shapes

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on the geoboards. What does half mean? (“It means we cut something down the middle

equally…etc.”) How many pieces do we have then and what does the fraction look like?

(“We will have two pieces and the fraction looks like12

.”) What does fourths mean? (“We cut

something in half and then in half again….etc.”) How many pieces do we have of an item in

this case and what does the fraction look like? (“We will have four pieces and the fraction

looks like14

.”) What is one whole? (“A whole is when we have the entire thing with no pieces

missing.”) As we explore these portions, we will be working towards making our own class

quilt that will have each of us contributing quilt squares to be displayed in our room.”

Lesson Development:

Model Whole class instructional grouping

o Provide each student with a geoboard and 5-8 geobands. Allow them to free explore the

geoboards for two minutes and to create their own images on it, such as a house. Remind

students that if the boards are used inappropriately that they will lose the privilege to utilize

them and can instead work with dot grid paper for the lesson instead.


the geoboard for finding fractions. Like I said previously, today we are going to make a shape

and then break it up into halves and fourths. To do this, I am going to make a big square on

my board. This one shape represents one whole. I am going to stretch my band across four of

the pegs and down four of them. I know it is big enough when I count nine pegs inside the

square. We will place geobands on top of this shape to see what fractions it can be divided

into. I would like you all to take one geoband and make this square like mine.”

o Use an overhead projector to demonstrate what you are doing on the geoboard to the students

or use grid dot paper to demonstrate what it should look like by drawing the square on it.

o “I am now going to use another geoband to divide the square into two equal parts.” Use the

think aloud strategy to explain thoughts on how to you would do so. Have the students find

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their solution for this by using their own geobands, while you model. Show them how this

divides the shape into 12

. “How do I know that this square is divided in half?” (“There are

two equal pieces of it…The line goes right down the middle of it.”)

o “I am now going to use another geoband to divide the square into fourths.” Use the think

aloud strategy to explain thoughts on how to you would do so. Have the students find their

solution for this by using their own geobands, while you model. Show them how this shape

divides the square into 14

. “How do I know that this square is divided into fourths?” (“There

are four equal pieces of it.”)

o Pass out the “Quilt Fractions” Recording Packet to each student. Have them record what they

did on their geoboard into question #1 on the sheet. They should draw one line down to

represent how they divided it in half. The students should then divide the same square the

other way to divide it into fourths.

o “I’m now going to divide the square on my geoboard into as many squares as I can so that

there are no more empty pegs in it.” Use the think aloud strategy to explain thoughts on how

to you would do so. Have the students find their solution for this by using their own

geobands, while you model. “How many smaller squares can be seen in this big square?

(“There are sixteen little squares inside the bigger square.”) So if there are 16 squares inside

this one, how many squares would make up half of the large one? (“Eight!”) How many

make up one-fourth? (“Four!”) I would like you to draw in the lines on question #2 so that

you have all sixteen small squares drawn.” Model this on the overhead for students to see

and copy on their paper.

Guided Practice Partnered Instructional Grouping

o “Let’s take a look at question #3 together. It says, ‘Jon, Shana, Alex and Jolene tried to find

ways of designing 12

of a quilt square. Is each piece shaded 12

of the whole? How can you

tell?’ We can see their quilt square designs below. How can we show and know their quilt

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squares are divided into equal shares? How many small squares are needed to be shaded in to

show one-half?” (“You need to have eight shaded in to show that half is colored.”)

o “We can start by looking at Jon’s quilt square. I notice that some of the small squares are not

all the way shaded in. How can we count the small squares on his if a full one isn’t shaded?

(“Well I can see that some of the squares are half-shaded, so we can count two of those as one

whole square.”) Alright, so let’s count the number of squares in Jon’s quilt square that are

shaded in to see if he has enough to make two equal shares. Remember, we need to count

two half-squares as one whole.” Count along with the students to find the number of squares

in Jon’s quilt square. “How many did we find? (“Eight! He does have half shaded in!”)

o Continue with the same line of questioning with the students to determine whether or not

Shana, Alex, and Jolene in the packet have shaded in half of their whole quilt square, as well.

o Have the students recreate the quilt square designs of Jon, Shana, Alex, and Jolene on their

geoboards for support.

o “Is each piece shaded 12

of the whole? How can you tell? (“Yes!! They all have eight squares

shaded in, which means half!”) Write your responses on the lines for question #3.”


o “I would like you all to read question #4: ‘Use your geoboards to find 4 more ways to shade

in 12

of the quilt square. Draw and shade it below.’ You can work with your math partner to

answer this question. Each design for the four quilt squares should be different.” Allow the

students some time to work on this using their geoboards. Have several share their designs at

the board or on the overhead and discuss the results when they are finished.

o “I’d like you to look at questions #5. For this question, it asks: ‘Only 12

of the whole quilt

shape is drawn. Use the geoboard to create the whole and draw it below.’ Below this

question, we can see a triangle. This shape is only half of the shape that is going to be put on

a quilt square. We need to make this shape a whole. Let’s make this shape on our geoboard.

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What do we need to do to make this shape one whole, if this triangle is only half of it? This

reminds me of when we worked with the pattern blocks.” (“We need to make another

triangle because two equal shapes/shares make one whole.”) Model this for the students by

creating the other triangle on your geoboard to be seen on the overhead and draw it in on the

grid dot paper.

o Have the students try the next two shapes on their own or with a partner. They must first

create it on their geoboard and then recreate it by drawing it in on their dot grid paper.

Remind students two equal pieces create one whole when they are only one-half.

o “I’d like you to look at questions #6. For this question, it asks: ‘Only 14

of the whole quilt

shape is drawn. Use the geoboard to create the whole and draw it below.’ Below this

question, we can see a rectangular-like shape. This shape is only one-fourth of the shape that

is going to be put on a quilt square. We need to make this shape a whole. Let’s make this

shape on our geoboard. What do we need to do to make this shape one whole, if what we see

is only one-fourth of it? This reminds me of when we worked with the pattern blocks.” (“We

need to make another three shapes like it because four equal shapes/shares make one whole

when we are using fourths.”) Model this for the students by creating the other three similar

shapes on your geoboard to be seen on the overhead and draw it in on the grid dot paper.

o Have the students try the next square shapes on their own or with a partner. They must first

create it on their geoboard and then recreate it by drawing it in on their dot grid paper.

Remind students four equal pieces create one whole when they are using fourths.


Independent Practice Individual Instructional Grouping

o “I would not like you all to take a look at question #7. Here you will be creating your own

two quilt squares that will be displayed for everyone who visits our classroom! There are

some directions for creating these squares, however. I want you to be creative!”

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o “In the directions it says: ‘Design two quilt squares to be placed on the class quilt. Color and

cut out the squares. One quilt square must be 12

yellow and 12

purple. One quilt square must

be divided into 14

of pink, yellow, purple, and blue. What fraction does the quilt square

represent? How do you know? Write your answer on the back.’”

o “You will be creating two squares: one is dealing with halves and the other with fourths.

Once you design your quilt squares and color them in the appropriate colors, you will cut

them out. On the back of the quilt squares, you will write your name and answer the

questions.”

o Pass around scissors for students to use.

o “Once you have finished your two quilt squares, I will come around and pass out a Quilt

Squares Self-Evaluation Sheet for each of you to fill out. Follow the directions on the

assessment sheet and use your Quilt Fractions Recording Packet to fill in the blanks.”

o As students work on their quilt squares in question #7, walk around and assist any students

that have questions or difficulties. Remind students that when they are done designing,

coloring, and cutting out their quilt squares should write the answers to the questions on the

back of their paper.

o When students are finished, invite some students to share their responses to the final

questions and explain the reasoning behind their answers to the class.

o Have the students complete the Quilt Fractions Self-Evaluation in order for them to evaluate

their progress, understanding, and participation during the lesson. Collect them when they

are finished filling them out.

o Collect the two quilt squares and materials (geoboards, etc.) from the students.

Closure:

“Now that you all have finished your recording packet and quilt squares, I want to review what

we accomplished today. In the lesson, we explored constructing wholes and dividing them by ½

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or ¼. A whole can be any shape that we make on the geoboard consider to be ‘one whole’ and in

our case, it was mainly the quilt square shapes. We looked at how we could divide the quilt

squares into halves or fourths in a variety of ways, yet they were all equal shares.”

“In our quilt square made on the geoboards during the investigation, how many smaller squares

made one-half of our square? (“Eight!”) How many smaller squares were there in total of our

square? (“Sixteen.”) I have a challenge question: If I were writing a fraction using these

numbers, what number is the numerator and what is the denominator? Let’s write the fraction on

the board. (“8

16”) What fraction is this equal to? (“

12

”) How do you know?” (“Eight is half of

sixteen. If you take sixteen things and get rid of half, you’d have eight left over.”)

“How many smaller squares made one-fourth of our square? (“Four!”) If I were writing a

fraction using four and sixteen, what would our fraction look like? (“4

16”) What fraction is this

equal to? (“14

”) How do you know? (“If you have sixteen things and put them into four groups,

there would be four in each group.”) As you can see, there are ways to write the same fraction

and these numbers are equivalent.”

“We also said that certain shapes were halves or fourths and constructed whole units out of them.

This can be done with any shape, as long as we know what fraction it represents. We need to

know the denominator, so we know how many shapes we need to create our whole. If one square

represents 14

, how many squares create one whole? (“Four!”) We will need to keep these ideas in

mind so that we can use them during our final investigation of fractions and wholes tomorrow.”


Tyler




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Differentiation Strategy: In this lesson, there are several options that I can take to accommodate

Tyler’s need for more advanced explorations.

o I may challenge Tyler to see how many different ways he can divide a geoboard into

fourths by recording his designs on dot grid paper. He must not repeat designs and

should be reminded that equal parts may not always look the same.

o Tyler may create his own quilt square image on the geoboard with the geobands, record

this image on dot grid paper, and then find the fractional portion of each section of his

image in relationship to the whole (including equivalent fractions).

Michelle






sits near the front of the classroom. The visual demonstration of the lesson on the board and

overhead (creating the shapes on the geoboards, drawing representations, etc.) will assist

Michelle in understanding the concept being taught. The presented fractions and manipulatives

will be written/drawn on the board or on an individualized task sheet for her to see, in order to

ensure that she knows what the class is working on. She can also ask her math partner for

support and explanation during class instruction. She will be pulled into a small work group with

other students that need to improve fractional math concepts. For this lesson, she may practice

creating halves and wholes with other students who need similar support. She will be provided

with a blank sheet of dot paper where she will take turns with a partner to make “half-shapes” on

the dot grid paper. The pair will exchange papers and make each shape into a whole. I may also

allow them to cut out the shapes so they can maneuver and manipulate them.

References:

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_Mar10.pdf>.

McGraw-Hill Education, Co. (2004). Visualizing Halves and Fourths. Growing with Mathematics.

New York City, NY: Wright Group/McGraw-Hill Companies, Inc.




Dostaler 65

Assessment:

Name: ____________________________________________ Date: _________________________

Quilt Fractions Self-EvaluationObjective: The fourth grade students will construct different regions to demonstrate

12

or 14

and construct the whole unit when given a

region representing 12

or 14

with the use of geoboards and dot grid paper.

Circle your response from 1 (Lowest) to 10 (Highest) on how you believe you accomplished the task.

Worked with the manipulativesInappropriately Always careful

1 2 3 4 5 6 7 8 9 10

Drew and shaded 12

and 14

of the quilt squares (Questions #1-4)

Drew a little Drew it all1 2 3 4 5 6 7 8 9 10

Drew the whole shapes on the dot grid paper (Questions #5-6)Drew a little Drew it all

1 2 3 4 5 6 7 8 9 10

Recorded responses to all questionsWrote a little Wrote a lot

1 2 3 4 5 6 7 8 9 10

Created my two quilt squares for the class quilt (Question #7)Completed no portions of the squares Completed all portions of the squares

1 2 3 4 5 6 7 8 9 10

Discussed ideas and results with the classSome of the time All of the time

1 2 3 4 5 6 7 8 9 10

Worked well with my partnerSome of the time All of the time

1 2 3 4 5 6 7 8 9 10

Used time wellWasted time Worked hard

1 2 3 4 5 6 7 8 9 10

Learned from this lessonLearned a little Learned a lot

1 2 3 4 5 6 7 8 9 10

Things I liked or did well: ________________________________________________________________________________________________________________________________________________________________________________________________________________________________

65

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Things I did not like or had difficulties with: ______________________________________________ ____________________________________________________________________________________________________________________________________________________________________

66

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Name: ________________________________________ Date: _____________________________

Quilt FractionsRecording Sheet

1. . . . . . . 2. . . . . . .. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

3. Jon, Shana, Alex and Jolene tried to find ways of designing 12

of a quilt square. Is each piece shaded

12

of the whole? How can you tell? ________________________________________________________________________

______________________________________________________________________________________________________________________________________________________________________________________________________________________________

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

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. . . . . . . . . . . . . .

4. Use your geoboards to find 4 more ways to shade in 12

of the quilt square. Draw and shade it below.

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

5. Only 12

of the whole quilt shape is drawn. Use the geoboard to create the whole and draw it below.

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

6. Only 14


. . . . . . . . . . . . . .

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. . . . . . . . . . . . . .

. . . . . . . . . . . . . .7. Design two quilt squares to be placed on the class quilt. Color and cut out the squares

One quilt square must be 12

yellow and 12

purple.

One quilt square must be divided into 14

of pink, yellow, purple, and blue.

What fraction does the quilt square represent? How do you know? Write your answer on the back.

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

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. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

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Example of completed task sheet:Name: ___Madison____________________________ Date:

____11/11/10____________________

Quilt FractionsRecording Sheet

1. . . . . . . 2. . . . . . .. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

3. Jon, Shana, Alex and Jolene tried to find ways of designing 12

of a quilt square. Is each piece shaded

12

of the whole? How can you tell? Y e s, each pi e ce is one-half b e caus e e ach whol e

square has 16 and half of that is 8. T hey e ach hav e 8 colored in.__________________________

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

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. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

4. Use your geoboards to find 4 more ways to design 12

of the quilt square. Draw and shade it below.

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

5. Only 12


. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

6. Only 14


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. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .7. Design two quilt squares to be placed on the class quilt. Color and cut out the squares

One quilt square must be 12

yellow and 12

purple.

One quilt square must be divided into 14

of pink, yellow, purple, and blue.

What fraction does the quilt square represent? How do you know? Write your answer on the back.

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

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. . . . . . . . . . . . . .

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. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

The fraction in thisquilt square is ½

because each colorcovers 32 squares andthere are 64 total, so

half of that is 32.

The fraction in thisquilt square is ¼

because each colorcovers 16 squares andthere are 64 total. 64 broken into 4 groupshas 16 in each group.

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SUMMING UP FRACTIONS


Content Standards:











o GLE7. Construct and use pictures and models to determine and identify equivalent

ratios and fractions.

o GLE8. Locate, label and estimate (round) fractions with like and unlike denominators of

two, three, four, five, six, eight and ten by constructing and using models, pictures and

number lines.

o GLE9. Construct and use models, pictures and number lines to compare and order

fractional parts of a whole and mixed numbers with like and unlike denominators of

two, three, four, five, six, eight and ten.

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numbers.



o GLE23. Estimate a reasonable answer to simple problems involving fractions, mixed

numbers and/or decimals (tenths).

Learner Background:


o Understand the vocabulary terms: “numerator”, “denominator”, “whole”, “equivalent”,

“halves”, and “fourths”.

o Have experience using a variety of mathematics manipulatives, such as geoboards,

pattern blocks, fraction strips, etc.



o Have experience working with symbolic forms of fractions.

o Have experience working with fractions to the 1

16, but need some minor experience

visualizing these fractions abstractly and will receive practice during this lesson.

o Have experience relating one whole to various fraction models and will demonstrate

their understanding of this concept and will receive it during this lesson.

Student Learning Objectives(s): The fourth grade students will—

recognize fractions and construct unit wholes using various manipulatives, including

geoboards, pattern blocks and fraction strips.

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16) using various

manipulatives, including geoboards, pattern blocks and fraction strips.

Assessment: The teacher will evaluate the students using informal observations as they are working

on the centers. This Student Participation Observation Rubric allows the teacher to evaluate the

students’ participation throughout all aspects of the learning process using mainly observations.

Rating on a scale from 1-5 for categories including Communication, Openness to learn, Respect,

Accepts and provides Constructive Criticism, Material Preparedness, Academic Preparedness and

Class Presence, the teacher can evaluate the students’ involvement (on a 35-point scale) in whole

class, group, and individual exploration of learning activities. During the performance task, the

students will work in a variety of centers that utilize geoboard, fraction strip, and pattern block

manipulatives as they complete a “Summing Up Fractions” Recording Packet. Students will explore

and apply their knowledge of the units’ concepts by constructing them out of the manipulatives and

recording their findings and explanations in the packet. Their packets will be graded using a scoring

tool of a corrected “Summing Up Fractions” Recording Packet. This scoring tool is a copy of the

original packet, but provides the correct potential answers for the teacher to use as a reference to

evaluate the students’ responses. They will receive a score out of 45 points. They should receive a

score above 34 to be considered as meeting the goals for the unit, which is approximately 75% of the

packet correct. Students can receive 11 points in Center A with pattern blocks, 6 points in Center B

utilizing geoboards, 10 points in Center C as they explore fractional notation, and 18 points in Center

D using fraction strips. (See the assessment section at the end of the lesson plan.)


Post-it notes

Pattern Blocks (For Centers A and C)

Geoboards (For Center B)

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Geobands (For Center B)

Dot Grid Paper (For Center B)

Fraction Strips (For Center D)

“Summing Up Fractions” Recording Packet (One for each student.)

“Summing Up Fractions” Corrected Recording Packet

Student Participation Observation Rubric

Scrap Paper


Crayons



o “Today, we are going to be wrapping up our current unit on fractions. We have been

exploring different ways to create whole units, portion these wholes into regions, write

fraction amounts, and compare fraction amounts to their equivalents. Right now, we’re going

to do an activity to review what we have been learning the past week. I’m going to separate

you all into groups and you will go around the room with a pad of Post-it notes and you will

write down any words or phrases that you remember about the topic. Our topics are

“Whole”, “Fraction”, and “Equivalent”. You can post the note on the wall. When I let you

know, you will move around to your left to the next topic. Once every group has visited

them, we will go over your responses as a class.”

o Group the students into groups of three or four and send them to their designated work areas

in the classroom to perform the experiment. Allow the students to have time to go off into

their sections around the room and begin to brainstorm ideas about each topic. Walk around

and observe the students with the Student Participation Observation Rubric for cooperation

and collaboration of ideas. After 3-5 minutes at each station, allow the students to rotate to

the next topic. This continues until students have visited every topic.

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o “Now that you all have each had a chance to visit all of the topics. I would like one volunteer

from each area to read me what all of us have written on the wall for that word. Let’s start

with ‘Whole’.” (“Whole… objects can be any shape… can be divided up… is equal to 1… is

equal to 11

… can be made up of smaller fractions… can be made up of a number of shapes,

but still considered a whole… all of the fractions inside add up to 1…“)

o “Those responses provide a great summary of what a whole is. Can I have a member from

‘Fractions’ to read the responses?” (“Fractions… are objects divided up… is when

something is shared evenly… is part of a whole item… has a numerator and denominator…

has a numerator that shows what portion of the whole… has a denominator that shows how

many parts the whole is divided into...”)

o “A member from the “Equivalent” group can now share those Post-its…” (“Equivalent…

means that the parts are equal… shows that the parts are the same… is 12

= 24

… means that

the fractions cover the same amount…”)

o Have the students collect the Post-it notes and the paper topics off the wall and return to their

seats in the classroom.

o “You all did a wonderful job participating in that review. Today to finish our unit, we are

going to be participating in a series of Fraction Centers to explore our understanding of these

concepts. You all will be in groups to investigate, but you will have recording sheets that you

will be working on individually as you complete the exploration. You must follow my

directions carefully today as we are going through the centers because the sheet needs to be

completed in a certain way.”

Lesson Development: Small Group/Individual Instructional Grouping

o Provide each student with their own copy of the “Summing Up Fractions” Recording Sheet.

Divide the students into four groups, which will be working at each center and then rotating

throughout the room.

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o “First, I’d like you all to take a look at your packets that you each have in front of you. I am

going to take you on a walk throughout the room, so that you can see what you need to do

when working in each center and how to answer the questions.”

o Have the students get up and walk to Center A, so that they can see the demonstration. They

can bring over their packets, but must leave any pencils or writing utensils at their desks.

o “In Center A, you will be working with pattern blocks to answer questions #1-3. Question #1

states: ‘If the value of the yellow hexagon is one whole, what fraction is each of the

following? Write the fraction on the line.’ You need to take the yellow hexagon and figure out

the fraction that a red trapezoid, blue rhombus, and green triangle would be of that hexagon.

You will write the fraction on the line. Underneath that, you will draw a picture to show each

of those shapes made into one whole hexagon. Question #2 states: ‘Which two pattern blocks

show the same amount shaded? What is the fraction shaded?’ You need to look at all the

shapes in the multiple choice question and circle your answer. Question #3 states: ‘What

fraction of the pattern block is shaded? What fraction is not shaded?’ You need to write the

answers on the lines provided. You can use the pattern blocks to answer any of these

questions and construct the shapes.”

o Have the students get up and walk to Center B, so that they can see the demonstration. They

can take a look at that portion on the packet sheet.

o “In Center B, you will be working with geoboards to answer questions #4-6. Question #4

states: ‘Use your geoboards to create and find a way to shade in 14

of shape A and 12

of shape

B.’ You need to make the shapes one at a time using your geoboard and geobands. Then you

need to divide up the shape accordingly. The first shape you will break it into fourths and the

second shape you will break into half. You will shade in the correct fraction on your paper.

Question #5 states: ‘Only 14

of the whole shape is drawn. Use the geoboard to create the

whole and draw it below.’ There is a portion of the whole shape drawn. You will create the

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whole shape on your geoboard and draw it on the dot grid paper. Question #6 states: ‘Only 12

of the whole shape is drawn. Use the geoboard to create the whole and draw it below.’ You

will do the same thing for this question as you did the last question, but this one uses a

different fraction.”

o Have the students get up and walk to Center C, so that they can see the demonstration. They


o “In Center C, you will be working with pattern blocks again to answer questions #7-12. For

Questions #7-10, there are directions that state: ‘Draw in the shape that represents the fraction.

Use pattern blocks to help you.’ There is an example on this section to demonstrate what you

need to do. As you can see, the orange shape represents 14

of a whole shape. If I want to

make 34

of the whole shape, it would look like this. (Build this for the students with the

pattern blocks.) I would need three orange blocks because the numerator tells me that there

are three-fourths and only one orange block represents one-fourth. I would then draw this

shape of three orange blocks on the paper. You will do the same thing for the rest of the

questions and draw the shapes that you built on the paper. Question #11 states: ‘What is the

numerator for the fraction you built in question #7? What does this number represent?’ You

need to look back to the fraction that you built in question #7, find the numerator and write it

down. Then, you will write about what that number represents in a fraction. Question #12

states: ‘What is the denominator in the fraction you built in question #8? What does this

number represent?’ You need to look back to the fraction that you built in question #8, find

the denominator and write it down. Then, you will write about what that number represents in

a fraction.”

o Have the students get up and walk to Center D, so that they can see the demonstration. They


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o “In Center D, you will be working with fraction strips to answer questions #13-16. Question

#13 states: ‘Shade four equal parts in each container. Write the fraction you shaded.’ There

are three water containers on your paper divided into sections. You need to shade four equal

parts for each container, take a look at what you shaded and write the fraction for what you

shaded on the line. You will then look at these sections, create them with the fraction strips,

and answer question #14 that states, ‘Order the fractions you found above from greatest to

least.’ You need to write these fractions on the line in that correct order according to their

size. Question #15 states: ‘There are 8 candy bars and 6 people. Which picture shows how

each person can get an equal share?’ You can use the appropriate fraction strips to solve this

problem. Take a look at the three multiple choice answers and circle the one that

demonstrates what one person’s share of the candy bar would look like. Question #16 states:

‘Using the fraction strips, draw the lines and shade an equivalent fraction to what is provided.

Write the fraction in the boxes provided.’ There are three questions that you need to answer.

There is an example to demonstrate what you need to do for this one. We can see that in the

example there is one-third shaded the first picture. There are three blocks and one is shaded

in. To answer that, we drew in six blocks in the fraction strip and colored in two of them

because two-sixths is equivalent or the same as one-third. We then wrote the number fraction

next to it. You will do the same for the rest of the exploration using the fraction strips.”

o “Now that you all know what to do at each station, I would like your group to go to the

assigned station you will begin at with a pencil. You will get approximately ten minutes to

work at each station and then I will signal when you can rotate to the next station to the right.

You will need to work quietly and independently on your packet. Do your best work. I will

be walking around to observe you all fairly working on your fraction explorations.”

o Hold a discussion to clarify any misunderstandings or difficulties some students may have

before they begin the explorations.

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o As students work in their centers, walk around and assist any students that have questions or

difficulties. Record observations on the students’ participation on the Student Participation

Observation Rubric. Remind students that they are to work their hardest and try their best on

their packets individually.

o Collect the packets when the students are finished completing them, which will be evaluated

after the end of the lesson according to the Completed “Summing Up Fractions” Recording

Packet.

o Have the students clean up the final center they are working at before returning to their seats

for closing discussion.

Closure:

“Now that you all are finished with your center explorations and your recording packet, I want to

review what we have been learning during this unit. We have been looking at “wholes” and the

fractions that make up these wholes. A whole can be any shape that we state. (Hold up a

hexagon pattern block.) I can say that this is our whole shape. If this is our whole, what fraction

would a red trapezoid block be out of this hexagon? (“½!”) How do you know that it makes up

one-half? (“Because two of them fit inside and make two equal shares of the hexagon!”) If this

red trapezoid block was now our whole, what fraction would a green triangle block be out of this

new whole? (“13

!”) How do you know that it makes up one-third?” (“Because three of them fit

inside and make three equal shares of the trapezoid!”)

“Now that we have said that three triangles fit inside of the trapezoid, I’m going to call up two

students. (Have the students come up to the front of the class.) I’m going to give you two of the

triangles and the other the last triangle. What fraction of the trapezoid does ___ have? (The

student with two triangles.) (“They have two-thirds!”) What fraction of the trapezoid does ___

have? (The student with one triangle.) (“They have one-third!”) How would I write two-thirds

on the board? (“You put a two on the top, draw a line, and then write a three on the bottom.”)

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(Write 23

on the board.) What does the two on top represent and what is that called? (“It’s called

the numerator! It tells us what part of the whole they have.”) What does the three on the bottom

represent and what is its name?” (“It’s called the denominator and lets us know how many parts

are total in the whole.”) (Do the same line of questioning for 13

.) We can see that 23

and 13

makes one whole. So we can write a number sentence to represent this. What would this look

like?” (“23+ 1

3=3

3 or 1”) Have the students sit back in their place that were holding the triangles.

“Let’s go back to our hexagon as the whole. How could I MAKE one whole using the triangles?

How many would I need? (“You need six triangles to build a hexagon!”) (Draw a hexagon on

the board and draw in the triangles. Demonstrate with pattern blocks on the overhead.) Great,

we have made our own whole shape now. If I wanted to make one whole hexagon using the blue

rhombus, how many would I need? Would it be the same number as the triangles? (“No, you

need only three because they’re bigger and a different shape than the triangles.”) (Draw a

hexagon on the board and draw in the rhombuses. Demonstrate with pattern blocks on the

overhead.) So here we have two hexagons. One is divided into three equal shares or thirds and

another is divided into six equal shares or sixths. I’m going to remove one trapezoid from our

triangle. If I remove one-third or one rhombus, how many triangles do I need to remove from the

other hexagon to make the same portion empty? (“You need to take out two!”) If I take away

two-sixths of the hexagon by removing two triangles, that means that two-sixths is the same size

or portion as one-third of the hexagon. What is the word when two portions are equal amounts?

(“Equivalent!”) We know now that 26

is equivalent to 13

! I can see that by taking two triangles

and putting them on top of one of the rhombuses. Two triangles equal one rhombus.”

“Over the course of this week, we have been doing a lot of hands-on work with our fractions.

We solved story problems, we have created and broken apart wholes, we have found equivalent

fractions, and much more we have just discussed together. You all have been very successful

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using the wide range of manipulatives to help you explore and understand fractions also,

including using the fraction strips, geoboards, and pattern blocks. We will revisit fractions again

in the future in other ways, but for now I am very proud that you all have worked your hardest to

grasp the concept of wholes and fractions. The observation and exploration skills that you all

have practiced will be very helpful in many ways throughout our math units.”


Tyler




Differentiation Strategy: In this lesson, I would like Tyler to complete the included “Summing

Up Fractions” Recording Packet, in order for his understanding of the concepts to be fairly

weighed against the other students in the class. I would like to differentiate with an additional

activity for him to create story problems at each center to accommodate Tyler’s need for more

advanced explorations. The focus of the story problem in each center is as follows:

o Center A: Identifying the fraction within a given whole

o Center B: Creating a whole from a given part/fraction

o Center C: Finding an equivalent fraction

o Center D: Sharing an object or objects equally

o The students in the class could then solve the problems that he creates as a review of

these concepts during Morning Work or other class time throughout the year.

Michelle




She has shown progress over the course of this unit with the small teacher-directed group support

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she has received to improve her skills with fractional concepts. Michelle will have hearing

support by the use of a microphone that I will wear, so that she can hear me at a higher level in

her hearing aids. She also sits near the front of the classroom and will be in the front of the

groups as students observe the modeling of the centers. The visual demonstration of how to

answer the “Summing Up Fractions” Recording Packet questions for each individual center

should help assist Michelle in understanding what is required of her to complete the assessment

lesson. She will be using a variety of manipulatives that she has previous experience with to

assist and provide her with concrete hands-on opportunities. Each center will have directions

written on an individualized task sheet for her to see, in order to ensure that she knows how the

class is to perform in each center in accordance with the packet. She will be allowed to ask for

my specific support during the center exploration time, since she has to complete the

assignment/assessment alone and cannot reference her usual math partner.

References:




_Mar10.pdf>.




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Assessment:

Student Participation Observation Rubric

Name: ___________________________ Participation Observation Rubric (____/35 pts) Date: _____________Objective: The fourth grade students will—

recognize fractions and construct unit wholes using various manipulatives, including geoboards, pattern blocks and fraction strips.


16) using various manipulatives, including geoboards, pattern blocks and fraction strips.

Fails to meet expectations (1 pt) Meets Expectations (3 pts) Exceeds Expectations (5 pts)

Communication

Provides no oral or written evidence of understanding the centers activity or group discussion

Never or rarely raises relevant questions Never or rarely provides oral or written

communication

Occasionally participates in group discussion, but rarely initiates or accepts leadership role in group

Does not elaborate on his or her understanding Often does not complete expression of his or her

thoughts and ideas

Raises relevant questions and shares ideas with peers Offers clear and concise oral and written presentation

of personal ideas and understanding, indicating that time has been devoted to thinking about the math topics/concepts

Openness to learn Rejects or dismisses centers as meaningless or boring Cannot make connections between lesson

assignments and lesson objective Reluctantly accepts participation in centers

Accepts centers participation with a positive attitude Actively seeks (by asking questions or speculating)

connections between lesson assignment and lesson objective

Respect

Dismisses the thoughts and ideas of others; possibly uses rude or abusive language to ridicule

Offers ideas that are limited to his or her personal opinions

Is tolerant of others but often dominates group activity or discussion

Listens to the ideas of others but generally maintains personal views and ideas

Listens to others; encourages others to contribute ideas; accepts alternative perspectives; is tolerant of the shortcomings of others; and helps others to succeed in the class

Accepts & provides constructive criticism

Often or always rejects constructive criticism Offers no viable alternatives to others’ suggestions

Accepts constructive criticism but does not incorporate it for improving targeted behaviors

Positively accepts constructive criticism and incorporates it into his or her approach to learning

Offers constructive criticism and critiques, including viable suggestions for improvement to peers

Academic preparedness

Is unable to respond correctly to questions regarding centers participation and packet completion

Offers responses that are consistently wrong or meaningless

Expresses surprise or confusion when probed for his or her understanding

Refers to concepts or topics related to the centers activity or discussion topic but provides incomplete written or oral responses

Expresses opinions that may have merit but is unable to support them with evidence from their recording packet

Refers to their centers experiences to present their ideas during discussions

Demonstrates awareness of the lesson objectives and teacher expectations

Material preparedness

Consistently is unprepared for class Does not properly utilize materials and manipulatives

Regularly forgets some materials or does not prepare fully; or prepares for class but is unable to retrieve his or her materials without disruption

Has some difficulties properly utilizing materials and manipulatives

Makes class materials readily available and accessible without causing interruption of activities or discussions

Properly utilizes materials and manipulatives

Derived from: Craven, J. A. III, and Hogan, T. (2001). Assessing student participation in the classroom. Science Scope, 25(1), 36-40.

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Class Presence

Sits passively in class Does not participate in group discussions Does not pay attention to classroom centers activities

Occasionally participates in group discussions Provides ideas or comments that are largely

restricted to reiterations of others’ ideas or comments

Frequently volunteers to participate in classroom activities

Demonstrates his or her focus on classroom activities by appropriate eye contact and alert posture

Derived from: Craven, J. A. III, and Hogan, T. (2001). Assessing student participation in the classroom. Science Scope, 25(1), 36-40.

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Name: ________________________________________ Date: _____________________________

Summing Up FractionsSummative Assessment - Recording Sheet

Center A1. If the value of is one whole, what fraction is each of the following? Write the fraction

on the line.

_______________ _______________ _______________

Build one whole using Build one whole using

2. Which two pattern blocks show the same amount shaded? What is the fraction shaded? _______A. B. C.

3. What fraction of the pattern block is shaded? _______ What fraction is not shaded? _______

Center B

4. Use your geoboards to create and find a way to shade in 14

of shape A and 12

of shape B.

. . A . . . . . . B . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

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. . . . . . . . . . . . . .

5. Only 14

of the whole shape is drawn. Use the geoboard to create the whole and draw it below.

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

6. Only 12

of the whole shape is drawn. Use the geoboard to create the whole and draw it below.

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .Center C

Draw in the shape that represents the fraction. Use pattern blocks to help you.

Example: If is 14

, this shape is 34

7. If is 18

, build 78

________________________________________________________________________

8. If is 13

, build 23

________________________________________________________________________

9. If is 26

, build 46

________________________________________________________________________

10. If is 12

, build 2

________________________________________________________________________

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11. What is the numerator for the fraction you built in question #7? What does this number represent?_____________________________________________________________________________ ______________ ____________ __________ ______________ ____________ __________ ___

12. What is the denominator in the fraction you built in question #8? What does this number represent?

________________________________________________________________________________________________________________________________________________________

Center D13. Shade four equal parts in each container. Write the fraction you shaded.

________________ ________________ ________________

14. Order the fractions you found above from greatest to least.

______________________________________________________________________________

15. There are 8 candy bars and 6 people. Which picture shows how each person can get an equal share?

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A.

B.

C.

16. Using the fraction strips, draw the lines and shade an equivalent fraction to what is provided. Write the fraction in the boxes provided.

Example: is the same as 13

is equivalent to 26

is the same as 36

is equivalent to

____________________________________________________________________________

is the same as 34

is equivalent to

____________________________________________________________________________

is the same as 18

is equivalent to

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Name: ___Madison______________________________ Date:

_____11/12/10________________

Summing Up FractionsSummative Assessment Corrected Recording Sheet Score: (_45_/45 pts)

Center A (11 points total)1. If the value of is one whole, what fraction is each of the following? Write the fraction

on the line. (1 point each)

_______½ ______ _______1/3________ ______1/6_______

(2 points) Build one whole using (2 points) Build one whole using

(2 points)

2. Which two pattern blocks show the same amount shaded? What is the fraction shaded? ___½ __A. B. C.

(2 points)

3. What fraction of the pattern block is shaded? __4/6_ What fraction is not shaded? __2/6__

Center B (6 points total)

4. Use your geoboards to create and find a way to shade in 14

of shape A and 12

of shape B. (2 points)

. . A . . . . . . B . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

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. . . . . . . . . . . . . .

5. Only 14

of the whole shape is drawn. Use the geoboard to create the whole and draw below. (2

points)

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

6. Only 12

of the whole shape is drawn. Use the geoboard to create the whole and draw below. (2

points)

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .Center C (10 points total)

Draw in the shape that represents the fraction. Use pattern blocks to help you. (1 point each)

Example: If is 14

, this shape is 34

7. If is 18

, build 78

________________________________________________________________________

8. If is 13

, build 23

________________________________________________________________________

9. If is 26

, build 46

________________________________________________________________________

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10. If is 12

, build 2

________________________________________________________________________

11. What is the numerator for the fraction you built in question #7? What does this number represent?______The numerator for my fraction is 7. This number shows that there are 7 pattern blocks out of the 8 total to be drawn._______________________________(3 points)

12. What is the denominator in the fraction you built in question #8? What does this number represent?______The denominator for my fraction is 3. This number shows that there are 3 total parts in the whole fraction._________________________________________________ (3 points)

Center D (18 points total)13. Shade four equal parts in each container. Write the fraction you shaded. (2 points each)

____4/4 or 1_____ ________4/5 ______ ____4/6 or 2/3____

14. Order the fractions you found above from greatest to least. (2 points)

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____________4/6, 4/5, 4/4 ________________________________________________________

15. There are 8 candy bars and 6 people. Which picture shows how each person can get an equal share? (1 point)

A.

B.

C.

16. Using the fraction strips, draw the lines and shade an equivalent fraction to what is provided. Write the fraction in the boxes provided. (3 points each)

Example: is the same as 13

is equivalent to 26

is the same as 36

is equivalent to ½

____________________________________________________________________________

is the same as 34

is equivalent to 6/8

____________________________________________________________________________

is the same as 18

is equivalent to 2/16

Documents

Nicole Dostaler - Fourth Grade - Fractions Unit