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COMPUTATIONS WITH FRACTIONS

Grade 5 Unit Plan: Developing Strategies for Computations with Fractions

By Johanna Neumann, Angela Brown, SophieAnne Lalonde Leblanc, & Sarah Lyons

COMPUTATIONS WITH FRACTIONS 1

Table of Contents Developing Fraction Concepts …………………………………………………………....p. 2

Developing Strategies for Fraction Computations ………………………………………..p. 3

NCTM & NB Fraction Expectations for Grade 5…………………………………………p. 4

NB Curriculum Strategies…………………………………………………………………p. 5

Fraction Concept Review……....………………………………………………………….p. 7

Introduction to Computation...……………………………………………...…..……...….p. 11

Adding Fractions to Make a Flag………………………………………………………….p. 15

Subtraction Computation Activities….…………………………………………………....p. 21

Fraction Computation Review…………………………………………………………….p. 26

Fraction Computation Summative Assessment…………………………………………...p. 33

References………………………………………………………………………………...p. 36


Developing Strategies for Computations with Fractions

Our unit is full of lessons to teach fractional computations for Grade 5. In New Brunswick, Fractional Computations are not taught until middle school. Therefore, this unit should be used as an enrichment resource to prepare students for higher level learning. We will begin by reviewing fractional concepts and using the knowledge, activities, and handouts gained to preassess students before entering into the conceptual learning of addition and subtraction concepts in fractional computations.

Fractional Concepts

A fraction is a representation of parts of a whole. Fractions can be modeled as an area, a length, or a set. It is important to help ease students’ anxiety with fractions when you begin teaching it to them. To do so, real life examples and use of manipulates will help. When fractions are first introduced, it is beneficial to teach fractional parts of a whole as a sharing activity for students to connect the ideas of fair shares and fractional parts. Terminology can also be used in real life examples. If you had 4 shoes; 3 blue and 1 pink, 1/4 represents 1 different pink shoe out of a total of 4 shoes. The denominator is the bottom number emphasizing all of the parts of the whole. The top, called a numerator, is what either is being taken, focused on, left, or different.

Fractions are a part of daily life and giving the students reason to understand the concepts is important. Some students may assume that all equivalent fractions are the same. If one whole is smaller than the one with the same fraction, the fractional proportion will be different. Therefore, fraction size is relative. Half of a small pizza is not the same as a third of a party sized pizza. If you had to choose one and wanted the largest amount, half a small pizza will not offer you as much as a third of a larger one. Whether fractional concepts have been covered in the past, or not at all, it is a good idea to refresh the concepts of fractions and ensure understanding before diving into computations.

Big Ideas

There are 5 main aspects about teaching fractions that should be kept in mind:

1. Students need to experience fractions in different ways to understand them. As part of a whole, ratios, division.

2. When working with fractions, there are three categories you can model fractions in: area, length, and set or quantity.

3. Partitioning and iterating helps students understand the meaning of fractions. 4. Students will need lots of experiences in estimating fractions. 5. Most importantly, students need to understand equivalent fractions (Van De Walle, 2015, p.

284).


Fraction Computations

It is important for students to flexibly and accurately compute with fractions because it is closely related to algebra. If students enter algebra with a low understanding of fractions and only know the formulas or procedures they will continue to struggle throughout their schooling because it has such a huge foundation to everything else. Therefore, it is important for students to understand fraction number sense before moving on. When students are following a specific procedure they are not actually understanding what they are doing and it doesn’t cause them to think about it. They do not have the means to assess their results to see if they make sense. The same goes for addition and subtraction of fractions because if they are just using a procedure they are not really understanding what they are adding or subtracting. Our goal in this lesson is for students to use manipulatives and different contexts where they can apply adding and subtracting fractions and get use to fraction number sense.

Big Ideas

Estimation is an important factor in computation development as it keeps students’ attention on the meanings of the operations and the expected sizes of the results. Operations with fractions should begin by applying these same meanings to fractional parts:

1. When adding and subtracting, the numerator tells the number of parts and the denominator tells the unit. These parts are what is added or subtracted.

2. Partition and measurement models lead to two different thought processes for division of fractions (Van De Walle, 2015, p. 310).


National Council of Teachers of Mathematics Standards: Grades 35 Number and Operations

For learning fractions, all students should:

Understand numbers, ways of representing numbers, relationships among numbers, and number systems 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; Recognize and generate equivalent forms of commonly used fractions, decimals, and percents;

Compute fluently and make reasonable estimates

Develop and use strategies to estimate computations involving fractions and decimals in situations relevant to students’ experience;

Use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals;

NB Curriculum Outcomes: Student Expectations

GCO: Number (N): Develop number sense SCO: N7: Demonstrate an understanding of fractions by using concrete and pictorial representations to:

create sets of equivalent fractions

compare fractions with like and unlike denominators. [C, CN, PS, R, V]


NB Curriculum: Strategies for Lessons

Achievement Indicators Guiding Questions:

What evidence will I look for to know that learning has occurred? What should students demonstrate to show their understanding of the mathematical concepts and

skills? Use the following set of indicators as a guide to determine whether students have met the corresponding specific outcome.

Create a set of equivalent fractions and explain why there are many equivalent fractions for any given fraction using concrete materials.

Model and explain that equivalent fractions represent the same quantity. Determine if two given fractions are equivalent using concrete materials or pictorial representations. Formulate and verify a personal strategy for developing a set of equivalent fractions. Identify equivalent fractions for a given fraction. Compare two given fractions with unlike denominators and explain the strategy. Position a given set of fractions with like and unlike denominators on a number line and explain

strategies used to determine the order. Planning for Instruction

Before introducing new material, consider ways to assess and build on students' knowledge and skills. Guiding Questions:

What learning opportunities and experiences should I provide to promote learning of the outcomes and permit students to demonstrate their learning?

What teaching strategies and resources should I use? How will I meet the diverse learning needs of my students?

Choosing Instructional Strategies

Consider the following strategies when planning lessons: Provide the students with a variety of activities that include the three interpretations of

fractions: 1) part of a whole (e.g., part a chocolate bar); 2) part of a set (e.g., part of 30 marbles); and 3) part of a linear measurement (e.g., part of a 4 m piece of rope).

Provide many opportunities for students to model fractions both concretely and pictorially, using a variety of models such as, pattern blocks, grid paper, fraction pieces, fraction towers, counters, Cuisenaire rods, egg cartons, number lines, etc.

Point out to the student that to rename 8 6 as 4 3 , you can "clump" the 8 sections of the whole into twos. There are then four groups of 2 sections; three of the four groups are shaded.

Use number lines and other models to compare fractions and explore equivalencies.


Use children’s literature, such as Fraction Action by Loreen Leedy, to review basic fraction concepts.

Possible Models:

grid paper, number lines, double number lines, fraction pieces, Cuisenaire rods, counters, egg cartons, pattern blocks, geoboards, colour tiles, fraction circles, dominoes

Assessment Strategies

Look back at what you determined as acceptable evidence. Guiding Questions

What are the most appropriate methods and activities for assessing student learning? How will I align my assessment strategies with my teaching strategies? Assessment can and should

happen every day as a part of instruction. A variety of approaches and contexts should be used for assessing all students: as a class, in groups, and individual students.

Followup Assessment

Guiding Questions What conclusions can be made from assessment information? How effective have instructional approaches been? What are the next steps in instruction?


Angela Brown Lesson: Fraction Concept Review Grade: 5 Time: 6070 minutes Lesson Description: Students will review fraction concepts through handson and discussion based learning. They will use fraction tiles, walk and create a 3D fractional number line in groups, create equivalent pizza slices, and … The teacher will use this class as a preassessment tool by observing students at work and conferring with individuals at their tables to see if more needs to be taught before diving into fractional computation enrichment. The following classes should challenge and prepare students for middle school, thus these concepts must be learnt first and foremost. NCTM: GCO: Grades 3–5 Expectations: In grades 3–5 all students should:

Understand numbers, ways of representing numbers, relationships among numbers, and number systems 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; Recognize and generate equivalent forms of commonly used fractions, decimals, and percents;

Compute fluently and make reasonable estimates

Develop and use strategies to estimate computations involving fractions and decimals in situations relevant to students’ experience;

Use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals;

NB Curriculum Outcomes: SCO: Students will be expected to:

Review previous knowledge of fraction concepts Show understanding of equivalent fractions through handson activities and discussion Use different representations of fractions appropriately Work together to share ideas and prior knowledge

Objective:


Students will review fraction concepts and further their understanding Students will work together and individually to review fraction concepts Students will use correct terminology when describing fractions Students will ask questions and discuss possible answers with one another

Materials:

Painter’s tape to create a number line on the floor. Be sure to tape down a large sheet that reads “0” and a “1” in the correct spot of the number line, with enough room for the fraction cards to be placed along it.

Fraction cards (these are best made by writing fractions in marker on card stock to ensure the fraction line is horizontal instead of diagonal. Be sure to use fractions up to 12, and enough cards for an equal amount per team. You can also add in decimals and percentages for a challenge)

Fraction Strips Sheet http://timvandevall.com/wpcontent/uploads/blankfractionstrips.png (coloured and black and white fraction strips are available at this site)

Fraction Rods (optional, but a great addition to understanding the fraction strip sheet) Whiteboard marker & whiteboard (or Smart board if already turned on/preferred) Pizza Worksheets with equivalent fractions worksheet, pizza problem solving and pizza fraction cut

outs, free download at: “Pizza Fraction fun” www.lauracandler.com Engagement (10 minutes):

Students will be intrigued by the painters tape on the floor. The teacher will mention that we will test our knowledge with it at the end of the class. Have materials placed on student tables to generate interest.

Begin with the fraction strips sheet. Activate prior knowledge from last class by asking questions. “Can the first rod at the top represent 1 whole or is it fractioned?” Draw it on the board and colour in part of it (1/2). Ask the students to tell you what fraction it now represents. Ask if the rod below it also shows this, and go through the sheet together, moving on to see if students can shade in 2/3, and explain how 3/3 is one whole.

Instruct students to label the rest of their sheet. This will come in handy for the next day. Students will have fraction rods at their table that they will be instructed to use if they wish. They can be placed and manipulated on top of the blank fraction sheet for better understanding.

After a couple minutes of labeling, the teacher will tell students to turn to the “Pizza Problem” sheet from the baggie (be sure to give a lined sheet of paper for them as well).

The teacher will ask the question to the class, and let students give their answer on loose leaf. The answers will be collected to find out about their prior knowledge of fraction concepts.

Exploration (20 minutes):

The teacher will give each team a set of pizzas in all fraction sizes. Instruct students to place the handout labeled, “pizza fraction placement” in the middle of their teams

table.


Students will place the Pizza Fraction Placemat (the whole divided into twelfths) in the middle of the team.

Ask each student to choose a pizza and share with their group what pizza they have. The teacher will remind students to carefully cut apart their pizzas on the lines. The teacher will instruct all students to write the fraction labeled on their handout on the back of each

piece. Ex. “fourth,” “halve,” “third.” The teacher will go over the terms, “numerator” and “denominator” by asking the students if they

remember what it may be, and drawing a visual (fraction) on the whiteboard to help them remember. As they do so, ask the class, “if your pizza slices were not labeled, how might you know what fraction it

represents?” Do not give the answer, allow students to hypothesize. The teacher will then have them find the 5 equivalent fractions worksheets in their teams baggy if not

already out and each student will take one and begin working together to answer the sheet. Students create the problem on the Pizza Placemat. Whoever has the fraction needed will help with the

question by placing it on the mat and comparing. Each student will record the answer on their own worksheet.

Explanation (510 minutes):

The teacher will instruct students to look at their pizza problem question sheet. A discussion in table groups about the pizza problem from the engagement stage will take place to allow students to reflect and help each other come to a conclusion.

The teacher will ask each group what they think the answer is, and the whole class will find out together what the true answer is.

The teacher can also draw the same problem or similar problem on the board as a chocolate bar, and see if students can answer it with a different representation.

Expansion and Elaboration (20 minutes):

Near the end of the day, the teacher will direct the students’ attention back to the long line of tape on the floor. The teacher will have students stay with their partner, or be placed in larger groups to make the game quicker, and give each group an even amount of fraction cards.

The teacher will ensure that students understand not to walk on or over the fraction cards on the number line. They are to walk around the number line to allow other teams to move around.

The teacher will tell them that on the count of 3, they will work with their teams to place each fraction they have on the correct spot along the number line. Students may designate one person to persuade another team to move their fraction piece if they believe theirs is suppose to go there.

When all fraction tiles are placed, the teacher will ask students to step back into a circle around the number line and look to see if they think anything needs to be changed. Students will lead this discussion. The teacher will make sure they are using the correct fractional language when describing fractions.


Evaluation and Clean up (510 minutes):

The teacher will observe students at work and help where needed throughout the lesson. This will also help the teacher keep track of the learning and how each individual student is doing.

The teacher will pass out an exit slip at the end of the day for students to complete in class. The teacher will ask that it be handed in when done. This should take no more than 5 minutes to complete. The exit slip is on the next page.

The teacher will also collect the equivalent fractions worksheets, fraction strip sheet, and pizza problem answer sheet, ensuring a name is written on all, to track understanding and participation.

Students will put everything back the way it was found at the start of class. Accommodations

For early finishers, or those needing a challenge, the teacher can instruct that they add other equivalent fractions to the equivalent fractions worksheet.

Students will work together to further their understanding and memory of fraction concepts through hands on activities, movement, discussion, independent work and teamwork.

Exit Slip Name: _______________________ I already knew how to…

use a number line

label fraction strips

place fractions on a number line

the difference between a fraction

and a whole

explain what a numerator and

denominator is

make equivalent fractions up to /8

Today I learned… ____________________________________

____________________________________

____________________________________

____________________________________

____________________________________

____________________________________

____________________________________

____________________________________

____________________________________


make equivalent fractions up to /12

Angela Brown Lesson: Review and Introduction to Computation Grade: 5 Time: 60 minutes Lesson Description: Students will review fraction concepts and terminology used last class with lego manipulates to ensure they understand the concept in different ways. This lesson will enhance understanding and slowly introduce students, in groups, to fraction computations by adding fraction tiles to a whole. NCTM: GCO: Grades 3–5 Expectations: In grades 3–5 all 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; Use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions

and decimals; NB Curriculum Outcomes: SCO: Students will be expected to:

Review and show understanding of fraction concepts and terms with legos Express their thoughts and ideas of fraction parts and wholes Use different manipulates to show and enhance knowledge of fractions Work together to help each other learn fractional computations

Objective:

Students will have enough knowledge of fraction concepts to advance on to computations. Students will understand how fractions can be used in different ways. Students will be able to use their problem solving skills to answer questions.

Materials: Equivalent Fractions with Legos worksheets (available free to print:

https://www.scholastic.com/teachers/sites/default/files/posts/u24/images/lego_exploring_equivalent_fractions_with_legos.pdf)

Legos (a bucket of regular sized legos per table to use)


whiteboard markers Fraction strip manipulates Fraction tiles / fraction strips (for each student to use) Fraction strip sheet from previous lesson

Engagement (1520 minutes):

The teacher will give students time to play with the legos at their table. The teacher will instruct that they make lego towers during this play time! After a couple minutes, or until all students have stuck a few lego pieces together, the teacher will tell students to place their lego creation in front of them and place their hands on their lap/anywhere off the table!

Students will be instructed to trade creations with the person in front of them and with a whiteboard marker, write on the table how many fractions of each colour they see in the lego creation. The teacher can also instruct students to create decimals and percentages with each fraction!

The teacher will ask students to give back the lego creation to the creator. They will check each others answers by explaining to their partner how they got each fraction/decimal/percentage and their partner will provide verbal assessment and help after they explain.

The teacher will circulate and check to see how students are doing with their fraction concepts throughout.

Students will then fill out their equivalent fractions worksheet and they will be allowed to use the legos to help them complete it.

Exploration (510 minutes):

The teacher will model how to play “Roll a Whole.” He/she will roll the fraction die and say what fraction it landed on (ex. ⅚). Then the teacher will take out the whole tile from the fraction tiles, and inquire from the students to find out how to show ⅚ of a whole with the other tiles available. 5 of the ⅙ tiles will be chosen, and then the teacher will ask a student to try!

Students will be able to practice with the tiles and the die for practice. Each student gets a turn rolling the die and placing the tiles out. Students will help each other make 1 whole in different ways.

The teacher will circulate and help when other students at the table cannot. The teacher will also ask students at various times while they practice, how they can show the number on the die in another way? This makes them use their knowledge of equivalent fractions.

Explanation (1020 minutes):

After 5 minutes of practice, the teacher will tell the students that it is time to play “Roll a Whole!” The objective is to roll the dice, make the fraction, and keep rolling and adding fractions to the whole strip until it is full! We want to find out if all tables can roll and make a whole fraction in just 10 minutes! (The teacher does not have to designate the game to 10min. exactly, the idea is to have all tables achieve the goal of rolling to a whole).

The teacher will model the game to the class and answer any questions about the game.


Students will work with their tables, with each individual having a turn to roll and add to the whole when possible.

Elaboration (510 minutes):

The teacher will elaborate on any questions that may come up during or after game play to ensure understanding

The teacher will ask that students put away their fraction tiles and take out some legos. Students will work with their table to create an addition problem with legos. When they create one, one

student will raise their hand and the teacher will come over to check it and/help. Evaluation (5 minutes):

The teacher will circulate around the room and check for understanding The teacher will listen to student discussion and ask questions when needed to ensure they are using the

right terminology, to challenge, or for understanding An exit slip will be passed out at the end of class for students to complete. This will help the teacher

tailor future lessons to the students needs. Accommodations:

Students will work together with manipulatives to further knowledge of fractions and advance into the realm of computations.

Students will be encouraged to help each other during the lesson and learn from one another. The teacher will ask probing questions, join in where needed, or alter the task at hand throughout the

learning if he/she believes a challenge is needed or steps need to be broken down for someone struggling.


Exit Slip Name: ________________________

Today I learned… ______________________________________________________________________________________________

______________________________________________________________________________________________

______________________________________________________________________________________________

Questions I have… ______________________________________________________________________________________________

______________________________________________________________________________________________

______________________________________________________________________________________________

I now feel like… A fraction wiz I understand I may need more help I am really confused


SophieAnne Lalonde Leblanc Lesson title: Adding fractions to make a flag Brief lesson description: This lesson will be used to introduce computing fractions by allowing students to be creative while still manipulating fractions in a challenging way. The teacher will begin the lesson by modelling how adding fractions looks in a visual manner by drawing a few squares on the board and telling a story on how they had to give away a certain amount of their pizzas to others. Students will then be given a small booklet where they will be able to practice and apply the concept. This booklet will also be used as a formative method of evaluation to ensure students understand what they need to do. Provincial content/standards outcomes: GCO: Number (N): Develop number sense

SCO: N7: Demonstrate an understanding of fractions by using concrete and pictorial representations to: create sets of equivalent fractions compare fractions with like and unlike denominators.

Materials:

White board & dryerase marker Activity booklet Smart Board

Procedure: Before the lesson:

Ensure that you have enough copies of the booklet for all students. Warm up (~ 5 minutes):

Ask students to shadein the appropriate amount of different shapes on the Smart Board. Minilesson (~ 15 minutes):

Explain to students a story: “Last night I had some people over for supper. We cooked 3 different kinds of pizzas and I cut

them so they would all have 8 pieces. I gave one slice to each of the 10 kids, then 8 more to each adult. How much of all pizzas did I give away?”

Show them, on the board, what it looks like (by taking pieces from different pizzas) and shade in each of the pieces you mention.


When you reach the 18/24 conclusion, ask students if there is a simpler way to write the fraction (3/4) Ensure that you show them how it looks as the 3/4

Activity booklet (~ 20 minutes): Explain to students what they are expected to do in the booklet – they are to use the appropriate colours

and shade in the appropriate amount of the flag mentioned. Remind students that fractions don't all have to look the same and remind them to count the squares to

know how to calculate the fractions. Allow students to work on their booklet and walk around the room to confer with some students. Help any student who may be confused or blocked.

Cleanup (~ 5 minutes):

Ask students to put away all their materials and cleanup their tables.


Name: ____________________________

Make your own flag

Colour 2/6 of the flag Blue and 2/3 Red.

Colour 1/3 of the flag Red, 4/9 Blue and 2/9 Pink


Colour 1/2 of the flag in Yellow, 2/5 in Orange and 1/10 in Blue

Colour 1/2 of the flag Red, 1/4 Blue, and 1/4 Green


Colour 1/8 of the flag Yellow, 1/2 Orange, 1/5 Green, 1/8 Blue, and 1/20 Pink

Colour 1/7 of the flag Red, 1/2 Pink, 1/8 Blue, 2/14 Green, 1/14 Black, and 1/56 Yellow


How much white is there in the flag? Write your answer as a fraction: __

How much Yellow is there in the flag? Write your answer as a fraction: __ How much Orange is there in the flag? Write your answer as a fraction: __

What fraction does the Yellow and Orange, altogether, represent of the flag? Write your answer as a fraction: __


Teacher: Ms. Lyons Elementary Math: Developing Strategies for Computation with Fractions SUBTRACTION Grade: 5 Time: 45 minutes

Materials: ∙ Masking Tape ∙ White Board

∙ Skittles ∙ Pencil and Paper

NB Essential Standards and Clarifying Objectives GCO: Number (N) Develop number sense SCO: N9: Describe and represent decimals (tenths and hundredths) concretely, pictorially and symbolically. [C, CN, R, V] NCTM Standards: Grades 3–5 Expectations: In grades 3–5 all students should– ∙ use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals;

Lesson Objectives: By isolating or removing portions of a group of people or objects students will develop their skills in subtracting fractions with like denominators.

Differentiation Strategies: The exploration phases of the learning process will be done as a whole group and then in small groups, providing group support as students become familiar with the material.

Activity 1: Exile Island – 15 mins

Procedure: Teacher ∙ Teacher creates two large circles on the floor using masking tape, and designates one circle as “Home Base”, and the second as “Exile Island”. ∙ Teacher calls 5 students to come stand in Home Base.

Students ∙ Student answers 5/5. 100% 1.0, 1.


∙ Teacher asks, since there are five people in the group, what fraction represents the whole group? Records answer on white board. Teacher asks how to represent the number as a percent, decimal and whole number. ∙ Because the gods of the island despise the colour orange, the teacher exiles from the group everyone ∙ wearing an orange shirt. ∙ Teacher asks what percentage of the whole group have been exiled, and records answer. ∙ Teacher asks what percentage of the whole group remain, and records answer. ∙ Teacher reiterates, while adding equation marks to the notes taken: “So, if you subtract 1/5, from 5/5, you get 4/5?” ∙ “So if the rules of math are consistent, then 4/5 + 1/5 = 5/5?” ∙ Teacher demonstrates the equation pictorially, drawing five squares in a line and filling them in to represent 5/5. Teacher has a volunteer depict the addition equation using this pictoral representation, and another volunteer to depict the subtraction equation (using the whiteboard eraser. *Activity continues for several rounds, with the teacher collecting small groups and exiling members as per student suggestions (everyone with brown hair/all of the boys/people who dislike broccoli). * When common fractions arise (¼, ½, ¾) teacher asks students to identify the decimal and percent equivalents and records them below the fractions. *Teacher regularly asks students whether there are more students in Home Base or Exile Island, and what approximate percentage of the group each cluster represents.

∙ Students wearing orange shirts defect to Exile ∙ Island. ∙ Student answers 1/5. ∙ Student answers 4/5. ∙ Students reflect on how the equation on the board represents the scenario that just played out. ∙ Students agree that this formula makes sense and is true. ∙ Student 1 depicts addition equation pictorally student 2 considers how to depict subtraction pictorially and decides on using the eraser.

Activity 2: Now Let’s Digest What We Learned – 20 mins


Exploration Teacher ∙ Teacher divides students into groups of five and places a paper plate in the middle of each group. ∙ Teacher writes 5 colours on the board and asks the groups to assign each member a colour. Each member must record their name and the list of member colours at the top of a piece of loose leaf. ∙ Teacher introduces the activity, listing the steps on the board as they are given: Each group will be given one bag of skittles. Empty the Skittles into your plate. As a group perform each operation from 110. Each member must record the answers on their own piece of paper. 1. What fraction represents the whole number of Skittles in your plate? 2. Have Purple Player remove all purple Skittles, count them, and then eat them. Write the subtraction equation that represents this action. 3. Determine the NEW whole number of skittles in the plate. 4. Have Red Player remove, count, and eat the red Skittles. Write the subtraction equation that this action represents. 5. Determine the NEW whole number of skittles in the plate. 6. Have Green Player remove, count, and eat the green Skittles. Write the subtraction equation that this action represents. 7. Determine the NEW whole number of skittles in the plate. 8. Have Orange Player remove, count, and eat the orange Skittles. Write the subtraction equation that this action represents. 9. Determine the NEW whole number of skittles in the plate.

Students ∙ Students list their names and colour choices on paper. ∙ Purple player counts and eats purple skittles/students record fractions. ∙ Red player counts and eats red skittles/students record fractions. ∙ Green player counts and eats green skittles/students record fractions. ∙ Orange player counts and eats orange skittles/students record fractions.


10. Have Yellow Player remove, count, and eat the yellow Skittles. Write the subtraction equation that this action represents.

∙ Yellow player counts and eats yellow skittles/students record fractions.

Activity 3: Who Ate the Most Skittles? – 10 mins

Evaluation: Teacher ∙ Teacher has students return to their desks to complete the 11th question before discussing/ handing in their results. Question 11: Who in your group ate the most Skittles? Explain your answer. ∙ Teacher leads a discussion about who ate the most Skittles in each group. Was it the person who ate the largest numerator, or the person who ate the largest percentage? Teacher converts one group’s list of fractions to percentages to demonstrate how the changing denominator skews the results. Why are the different fractions you recorded not representative of each person’s portion of the bag of skittles? Why does the denominator have to stay the same in this case? ∙ Teacher asks students to cross out the fractions on their sheets with a single slash and write the appropriate fraction that represents each person’s portion, then answer a 12th question. Question 12: What subtraction equation (using fractions) would best represent the number of skittles eaten by the yellow player on your team?

Students ∙ Students return to their desks to complete 11th question. ∙ Students offer up ideas and suggestions as the class works through the material together. While the teacher guides the discussion, the students pose their own questions and make their own hypotheses. ∙ Students complete 12th questions and hand in result sheets so that teacher can verify understanding.

Reference Van de Walle, J.A., Folk, S., Karp, K.S., & Bay Williams, J.M. (2013). (4th Canadian ed.). Elementary and Middle School Mathematics: Teaching Developmentally. Toronto, ON: Pearson.


Mathematics Grade 5 Curriculum NB: http://www.gnb.ca/0000/publications/curric/Mathematics_NB_Curriculum_Grade_5.pdf


Title of Lesson: Review of Fractions

Teacher: Miss Neumann

Subject: Mathematics

Grade: 5

Date: February 20th 2015

Curriculum Outcome: GCO: Number (N): Develop number sense SCO: N7: Demonstrate an understanding of fractions by using concrete and pictorial representations to: • Create sets of equivalent fractions • Compare fractions with like and unlike denominators. [C, CN, PS, R, V] NCTM Standards: Grades 35 Expectations: In Grades 35 all students should:

Use visual models, benchmarks and equivalent forms to add and subtract commonly used fractions and decimals;

Class Objective: The objective for this lesson is for students to understand that fractions are equivalent that have a different denominator and for students to understand the value of fractions by placing them on a number line. Time Required for this lesson: It will take about 10 minutes to go over the smart board activity and then another 10 minutes for the students to put the fraction pieces together and then the last activity where they have to order fractions on the number lines will take 25 minutes, which will be a total of about 45 minutes.

Materials/Resources:

- Number line - Fraction Pieces - Smart board


- Blank fraction piece worksheet to fill in and cut out

Methods /Structures: - Small Groups - Whole class Discussion

Instructional Strategies/Procedure for the Class: Engagement: I will introduce this lesson by going over their prior knowledge of fractions by starting with a smart board lesson about fractions, decimals and percentages. Much of this lesson will be a review for the students before the summative assessment of the unit. The only main focus of new material that this lesson will focus on will be comparing fractions with like and unlike fractions using a number line and fraction pieces. Teacher will ask students if a fraction can be equal when it has a different denominator? If the denominator is a higher number does it mean it’s a bigger or smaller part then a number with a lower number as a denominator? The Middle: Students will be given fraction pieces and then instructed to put the pieces together like the picture below so that they fit together. I will remind students how fractions are all part of a whole and that each piece is one part of a whole.


The End: Students will end by making a huge number line with everybody’s fraction to see how many fractions are equivalent. First the students will pick what color they want the number line to be, then they will use masking tape to make the number line and glue on the referents, 0, ½ and 1. Next each group will have a sheet of fractions to cut out and figure out where they go on the number line once and then glue it on their. There should be many fractions that are equal.


Appendix A. Smart Board Lesson




Title of Lesson: Summative Assessment Fractions Unit

Teacher: Miss Neumann

Subject: Mathematics

Grade: 5

Date: February 20th 2015

Curriculum Outcome: GCO: Number (N): Develop number sense SCO: N7: Demonstrate an understanding of fractions by using concrete and pictorial representations to: • Create sets of equivalent fractions • Compare fractions with like and unlike denominators. [C, CN, PS, R, V] NCTM Standards: Grades 35 Expectations: In Grades 35 all students should:

Use visual models, benchmarks and equivalent forms to add and subtract commonly used fractions and decimals;

Class Objective: The objective for this lesson is for students to apply everything they learnt in this unit about fractions. Including fractions are equivalent that have a different denominator and for students to understand the value of fractions by placing them on a number line. As well as adding fractions. Time Required for this lesson: It will take about five minutes for each student to finish the assessment individually with the teacher and while each student takes a turn to apply their knowledge of fractions. Math centers will be set up around the room and each group will stay at each station for ten minutes for a total of fifty minutes and five different groups.

Materials/Resources: - Math center games -

Methods /Structures:


- Small Groups - Whole class Discussion - Teacher conferencing - Summative assessment

Instructional Strategies/Procedure for the Class:

1. Students will be in math centers while the teacher is testing each child individually for a few minutes each.

2. There will be five math centers that the students will be rotating through. 3. The first math center is called capture the fraction. 4. The second math center is called greater than or less than. Students will use a dice to roll two

numbers and fill them in the spot and then write whether the fraction is greater, less than or equal to the other fraction.

5. The third center will be called no prep differentiated fraction game. Each group of partners are given counters in a small cup and dump them out. Then they are instructed to sort them into red and yellow. Have students make as many equivalent fractions as possible using the counters. The largest denominator possible is 12.

6. The fourth center will be organizing fractions and decimals on a number line. 7. The fifth math center will be Making subtraction fraction sentences with playing cards.


Appendix A.

1. Order the fractions in order from least to greatest on the number line.

21

84

31

43

51

2. How much white is there in the flag? Write the answer as a fraction____ How much blue and red is there in the flag? write the answer as an addition fraction sentence_________________


3. What fraction represents the whole number of skittles?___ You got really hungry and ate all the red skittles. Write the subtraction equation that represents this action. _________________________________________

4. How many fraction pieces are made with mushrooms? ______ How many fraction pieces are made with pepperoni? _______ How many fraction pieces are made with green pepper? ______


References

Candler, L (2012). Pizza fraction fun. Teaching Resources Mathdrills (2013). Unlabeled fractions worksheets. Mathematics Grade 5 Curriculum NB: http://www.gnb.ca/0000/publications/curric/Mathematics_NB_

Curriculum_Grade_5.pdf

Misskprimary (2007, May 8). Fractions display. Flickr. Tripp, K. (2013, April 24). Roll a whole: Fractions math game. Teach Beside Me. Van De Walle, J.A., Folk, S., Karp, K.S., & BayWilliams, J.M. (2011). Elementary and middle school mathematics: Teaching developmentally (3rd ed.). Toronto Zimmerman, A. (2012). Exploring equivalent fractions with legos. Scholastic. No prep differentiated fraction game (2013, May 13). Retrieved March 14, 2015.

Documents

COMPUTATIONS WITH FRACTIONSmsangelabrown.weebly.com/.../mathunit-fractions.pdf · Identify equivalent fractions for a given fraction. Compare two given fractions with unlike denominators