M3G1 Students will further develop their understanding …southsidethird.pbworks.com/f/3rd+Grade_Unit3.pdf · also state and explain their properties ... elapsed time, unit Harcourt

Instructional Tools: Unit Essential Question(s):

Unit 3 Geometry

& Measurement (9 Weeks)

Standards: M3G1 Students will further develop their understanding of geometric figures by drawing them. They will also state and explain their properties M3M1 Students will further develop their understanding of the concept of time by determining elapsed time of a full, half, and quarter hour. M3M2 Students will measure length choosing appropriate tools and units. M3M3 Students will understand and measure the perimeter of simple geometric figures (squares and rectangles.) M3M4 Students will understand and measure the area of simple geometric figures (squares and rectangles).

Concept Concept Concept Concept Geometry: Understanding Plane Figures

Geometry: Understanding Solid Figures

Linear Measurement: Perimeter and Area

Measurement: Elapsed Time

Lesson Essential Questions: Lesson Essential Questions: Lesson Essential Questions: Lesson Essential Questions:

What are the attributes of a shape? How are plane and solid shapes related? How can a shape be divided into parts? How can angles be classified?

How can solid figures be combined to make different solid objects? How are plane and solid figures related?

Why do we need to measure accurately? How do we choose a measurement unit? How do we choose a measurement tool? What estimation strategies are used in measurement? How are perimeter and area related? When is measurement if perimeter used? When is measurement of area used?

How can I determine the amount of time that passes between two events?

Vocabulary: Vocabulary: Vocabulary: Vocabulary: acute angle, angle, circle, classify, congruent, diameter, edge, equilateral, hexagon, isosceles, obtuse, parallelogram, plane figure, polygon, quadrilateral, radius, rectangle, rhombus, right angle, scalene triangle, side, square, sort, triangle, trapezoid, vertex

face, solid figure area, centimeter, foot, inch, kilometer. meter, millimeter, perimeter, yard

time, elapsed time, unit

Harcourt Math: Chapters 7, 8, 9, 10 3rd Grade - Revised June 2010 Literature Links: The Greedy Triangle, Sea Squares

GADOE frameworks, square unit pieces, inch and centimeter rulers, string, or yarn, markers, yard stick, meter stick, trundle wheel, Think Math Kit

Geometric figures can be classified according to their properties. Acute, right, and obtuse angles can be identified based upon appearance and comparison of their angles. Geometric figures can be combined or separated to form different geometric figures. Objects can be measured using standard units. The duration of time is called elapsed time and it can be measured.

How are plane and solid figures related? How can we see geometry in the real world? How do we choose appropriate measurement tools?

Enduring Understanding:

Richmond County School System Page 1

Unit 3 “Home Sweet Home” Culminating Task Student Page Standards: M3G1 Students will further develop their understanding of geometric figures by drawing them. They will also state and explain their properties. M3M1 Students will further develop their understanding of the concept of time by determining elapsed time of a full, half, and quarter hour. M3M2 Students will measure length choosing appropriate units and tools. M3M3 Students will understand and measure the perimeter of simple geometric figures. M3M4 Students will understand and measure the area of simple geometric figures.

Task: You have been hired as a Junior Architect at Kid Houses Inc. Your job is to create a fantasy home that will be shown on a TV show later this year. There are some rules though to make sure the house has all the parts you need. You will keep an architect’s journal to show your new boss what you did.

House Plan Rules: 1. Your house must be built entirely of polygons. 2. Make sure you use

at least one of each of these shapes: rhombus, trapezoid, scalene triangle, isosceles triangle, equilateral triangle, square, rectangle, and quadrilateral. 3. You must trace or draw the shapes using a ruler first then cut from construction paper. 4. Label each shape with its correct mathematical name. 5. On ten of the shapes, record the length of the shape to the nearest quarter inch. 6. Find the perimeter of your house by measuring and record it on the back of your project. 7. Find the area of your project by tiling and record it on the back of your project.

· Introduction page: Write at least 5 sentences to describe the type of house you will build and what you will need to do to build it. · Daily pages: For each page after the introduction, record the date, how much time you spend designing and building your home that day and a picture illustration of your work and a written description of what you accomplished. · Data page: Make a table showing time data that tells how long you spent each day working to the nearest quarter hour. Calculate the total amount of time you spent working. · Conclusion page: Write at least 5 sentences to describe the inside and outside of your house.

Journal:


Unit 3 “Home Sweet Home” Culminating Task Teacher Page

Standards: M3G1 Students will further develop their understanding of geometric figures by drawing them. They will also state and explain their properties. M3M1 Students will further develop their understanding of the concept of time by determining elapsed time of a full, half, and quarter hour. M3M2 Students will measure length choosing appropriate units and tools. M3M3 Students will understand and measure the perimeter of simple geometric figures. M3M4 Students will understand and measure the area of simple geometric figures.

**Complete project by the end of the 18th week of school. **

Helpful Websites: http://www.math-kitecture.com/ http://www.archkidecture.org/ Suggestions: · Create a sample to share with students. · Review unit standards and elements; post a list on chart paper for reference. · Read a book such as How a House is Built by Gail Gibbons or Building a House· You may want to bring in actual or sample blueprints to illustrate how architects draw buildings using shapes.

by Byron Barton

· You may want to break the project into parts so students have enough time to complete it by the deadline. Materials: · Construction paper, glue, scissors, student journals, rulers, markers, pencils, square tiles Evidence of Learning: By the conclusion of this unit, students should be able to demonstrate the following competencies: • Draw common polygons and circles • Sort triangles by the length of their sides • Classify angles and identify acute, right, and obtuse angles within polygons • Draw a circle and identify its center, a radius and a diameter • Choose between millimeter, centimeter, meter and kilometer the appropriate metric unit of measure for length • Choose between inch, foot, yard and mile the appropriate unit of customary measure for length • Measure accurately to the nearest 1/4 inch • Find the area and perimeter of a rectangle • Describe and extend patterns

http://www.math-kitecture.com/�

http://www.archkidecture.org/�


Unit 3 “Home Sweet Home” Culminating Task Rubric Standards: M3G1 Students will further develop their understanding of geometric figures by drawing them. They will also state and explain their properties. M3M1 Students will further develop their understanding of the concept of time by determining elapsed time of a full, half, and quarter hour. M3M2 Students will measure length choosing appropriate units and tools. M3M3 Students will understand and measure the perimeter of simple geometric figures. M3M4 Students will understand and measure the area of simple geometric figures. Exceeds Meets Partially Meets Does Not Meet M3G1 >8 polygons

used will detailed explanation

8 polygons used with explanation

5-7 polygons used with some explanation

<5 polygons used with little to no explanation

M3M1 Explains time to the nearest 5 minute or 1 minute interval

Explains time to the full, half, and quarter hour

Explains time with 2 of the 3 requirements

Explains time with 1 or fewer time intervals

M3M2 Measures to the nearest 1/8 in or 1/16

Measures to the nearest ¼ in

Measures to the nearest ½ inch

Measures to the nearest inch

M3M3 Measures perimeter accurately with a detailed explanation

Measures perimeter accurately with sufficient explanation

Measures part of the perimeter accurately with some explanation (? 50%)

Does not measure perimeter accurately; little to no explanation

M3M4 Same as perimeter, but change to area

Same as perimeter, but change to area



Name: _____________________________________________Task: ____________________________________

Richmond County School System Adapted from Exemplars

0 – 9 points = Did Not Meet Standard 10 – 14 = Emerging Toward Standard 15 – 17 = Proficient with Standard 18 - 20 = Exceeding Standard

Mathematics Problem Solving Rubric Does Not Meet

Standard (1 point) Progressing Toward Standard (2 points)

Meets Standard (3 points)

Exceeds Standard (4 points)

Problem Solving M3P1. Students will solve problems (using appropriate technology).

No strategy is chosen, or a strategy is chosen that will not lead to a solution. Little or no evidence of engagement in the task is present.

A partially correct strategy is chosen, or a correct strategy for only solving part of the task is chosen. Evidence of drawing on some relevant previous knowledge is present, showing some relevant engagement in the task.

A correct strategy is chosen based on the mathematical situation in the task. Planning or monitoring of strategy is evident. Evidence is solidifying prior knowledge and applying it to the problem solving situation is present.

An efficient strategy is chosen and progress toward a solution is evaluated. Adjustments in strategy, if necessary, are made along the way, and/or alternative strategies are considered. Evidence of analyzing the situation in mathematical terms, and extending prior knowledge is present.

Reasoning and Proof M3P2. Students will reason and evaluate mathematical arguments.

Arguments are made with no mathematical basis. No correct reasoning or justification for reasoning is present.

Arguments are made with some mathematical basis. Some correct reasoning or justification for reasoning is present.

Arguments are constructed with adequate mathematical basis. A systematic approach and/or justification of correct reasoning is present. This may lead to: -clarification of the task -exploration of mathematical phenomenon -noting patterns, structures and regularities.

Deductive arguments are used to justify decisions and may result in more formal proofs. Evidence is used to justify and support decisions made and conclusions reached. This may lead to: -testing and accepting or rejecting of a hypothesis or conjecture. -explanation of phenomenon -generalizing and extending the solution to other cases.

Communication M3P3. Students will communicate mathematically.

No awareness of audience or purpose is communicated.

Or Little or no communication of an approach is evident

Or Everyday, familiar language is used to communicate ideas.

Some awareness of audience or purpose is communicated, and may take place in the form of paraphrasing of the task.

Some communication of an approach is evident through verbal/written accounts and explanations, use of diagrams or objects, writing and using mathematical symbols.

Or

Some formal math language is used, and examples are provided to communicate ideas.

Or

A sense of audience or purpose is communicated.

and/or Communication of an approach is evident through a methodical, organized, coherent, sequenced and labeled response. Formal math language is used through the solution to share and clarify ideas.

A sense of audience and purpose is communicated.

And/or Communication at the meets standard level is achieved and communication of arguments is supported by mathematical properties used. Precise math language and symbolic notation are used to consolidate math thinking and to communicate ideas.

Connections M3P4. Students will make connections among mathematical ideas and to other disciplines.

No connections are made.

Some attempt to relate the task to other subjects or to own interests and experiences is made.

Mathematical connections or observations are recognized.

Mathematical connections or observations are used to extend the solution.

Representation M3P5. Students will represent mathematics in multiple ways.

No attempt is made to construct mathematical representations.

An attempt is made to construct mathematical representations to record and communicate problem solving.

Appropriate and accurate mathematical representations are constructed and refined to solve problems or portray solutions.

Abstract of symbolic mathematical representations are constructed to analyze relationships, extend thinking and clarify or interpret phenomenon.

Grade 3 Mathematics Frameworks

Unit 3 Geometry and Measurement

MA

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Georgia Performance Standards Framework Third Grade Mathematics • Unit 3 • 1st Edition

Georgia Department of Education Kathy Cox, State Superintendent of Schools

MATHEMTATICS GRADE 3 UNIT 3: GEOMETRY AND MEASUREMENT October 2009 Page 2 of 78

Copyright 2009 © All Rights Reserved

Unit 3 GEOMETRY AND MEASUREMENT

(9 weeks) TABLE OF CONTENTS

Overview ..............................................................................................................................3 Key Standards & Related Standards ....................................................................................4 Enduring Understandings.....................................................................................................6 Essential Questions ..............................................................................................................6 Concepts & Skills to Maintain .............................................................................................7 Selected Terms and Symbols ...............................................................................................7 Classroom Routines .............................................................................................................9 Strategies for Teaching and Learning ..................................................................................9 Literature Connections .......................................................................................................10 Evidence of Learning .........................................................................................................10 Tasks ..................................................................................................................................11

• What Makes a Shape? ............................................................................................12 • Geoboard Geometry ...............................................................................................18 • Tangram Challenge ................................................................................................22 • Measure Me ...........................................................................................................27 • Pentomino Perimeter ..............................................................................................30 • Guess Who’s Coming to Dinner? ..........................................................................37 • Rectangles Rule .....................................................................................................42 • Soaring on Air ........................................................................................................47 • How Big is a Desk?................................................................................................52 • Daily Schedule .......................................................................................................58 • Touring Georgia .....................................................................................................64 • Measuring Words ...................................................................................................70

Culminating Task

• Home Sweet Home ................................................................................................73





OVERVIEW

In this unit students will: • further develop understandings of geometric figures • identify and describe plane figures and solid figures based on geometric properties • identify the diameter, radius, and center of a circle • expand the ability to see geometry in the real world • tell time to the nearest minute • further develop their understanding of the concept of time by determining elapsed time (to

an hour, half, and quarter-hour) • continue to develop their abilities to recognize the appropriate unit of length needed to

measure a specified item • compare the relationship of one unit to another within a single system of measurement • check by measuring to determine if estimates are accurate for length • determine a tool that is appropriate for measuring length • recognize benchmarks for commonly used units of measure • measure perimeter of geometric figures • determine area of rectangles and squares

Although the units in this instructional framework emphasize key standards and big ideas at

specific times of the year, routine topics such as counting and ordering numbers, working with calendars and clocks, counting collections of coins, and patterning should be addressed continually through the use of a daily math meeting board, centers, and games. These activities allow students to gradually understand the concept of number.

To assure that this unit is taught with the appropriate emphasis, depth, and rigor, it is important that the tasks listed under “Evidence of Learning” be reviewed early in the planning process. A variety of resources should be utilized to supplement, but not completely replace, the textbook. Textbooks not only provide much needed content information, but excellent learning activities as well. The tasks in these units illustrate the types of learning activities that should be utilized from a variety of sources.





STANDARDS ADDRESSED IN THIS UNIT

Mathematical standards are interwoven and should be addressed throughout the year in as many different units and activities as possible in order to emphasize the natural connections that exist among mathematical topics. KEY STANDARDS M3G1. Students will further develop their understanding of geometric figures by drawing them. They will also state and explain their properties.

a. Draw and classify previously learned fundamental geometric figures and scalene, isosceles, and equilateral triangles.

b. Identify and compare the properties of fundamental geometric figures. c. Examine and compare angles of fundamental geometric figures. d. Identify the center, diameter, and radius of a circle.

M3M1. Students will further develop their understanding of the concept of time by determining elapsed time of a full, half, and quarter-hour. M3M2. Students will measure length choosing appropriate units and tools.

a. Use the units kilometer (km) and mile (mi.) to discuss the measure of long distances. b. Measure to the nearest ¼ inch, ½ inch and millimeter (mm) in addition to the previously

learned inch, foot, yard, centimeter, and meter. c. Estimate length and represent it using appropriate units. d. Compare one unit to another within a single system of measurement.

M3M3. Students will understand and measure the perimeter of geometric figures.

a. Understand the meaning of the linear unit and measurement in perimeter. b. Understand the concept of perimeter as being the length of the boundary of a geometric

figure. c. Determine the perimeter of a geometric figure by measuring and summing the lengths of the

sides. M3M4. Students will understand and measure the area of simple geometric figures (squares and rectangles).

a. Understand the meaning of the square unit and measurement in area. b. Model (by tiling) the area of a simple geometric figure using square units (square inch,

square foot, etc.). c. Determine the area of squares and rectangles by counting, addition, and multiplication with

models.





RELATED STANDARDS

M3N5. Students will understand the meaning of decimal fractions and common fractions in simple cases and apply them in problem-solving situations.

b. Understand that a decimal fraction (i.e. 3/10) can be written as a decimal (i.e. 0.3). c. Understand the fraction a/b represents a equal sized parts of a whole that is divided into b

equal sized parts. d. Know and use decimal fractions and common fractions to represent the size of parts created

by equal divisions of a whole. M3A1. Students will use mathematical expressions to represent relationships between quantities and interpret given expressions.

a. Describe and extend numeric and geometric patterns. b. Describe and explain a quantitative relationship represented by a formula (such as the

perimeter of a geometric figure).

M3P1. Students will solve problems (using appropriate technology). a. Build new mathematical knowledge through problem solving. b. Solve problems that arise in mathematics and in other contexts. c. Apply and adapt a variety of appropriate strategies to solve problems. d. Monitor and reflect on the process of mathematical problem solving.

M3P2. Students will reason and evaluate mathematical arguments.

a. Recognize reasoning and proof as fundamental aspects of mathematics. b. Make and investigate mathematical conjectures. c. Develop and evaluate mathematical arguments and proofs. d. Select and use various types of reasoning and methods of proof.

M3P3. Students will communicate mathematically.

a. Organize and consolidate their mathematical thinking through communication. b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and

others. c. Analyze and evaluate the mathematical thinking and strategies of others. d. Use the language of mathematics to express mathematical ideas precisely.

M3P4. Students will make connections among mathematical ideas and to other disciplines.

a. Recognize and use connections among mathematical ideas. b. Understand how mathematical ideas interconnect and build on one another to produce a

coherent whole. c. Recognize and apply mathematics in contexts outside of mathematics.

M3P5. Students will represent mathematics in multiple ways.

a. Create and use representations to organize, record, and communicate mathematical ideas. b. Select, apply, and translate among mathematical representations to solve problems. c. Use representations to model and interpret physical, social, and mathematical phenomena.





ENDURING UNDERSTANDINGS

• Geometric figures can be classified according to their properties. • Triangles can be classified according to the lengths of its sides. • Acute, right, and obtuse angles can be identified based upon appearance and comparison of

their angles. • A circle has a diameter, radius, and center. • Objects can be measured using standard units. • An inch or centimeter would be a good unit to measure small items such as the length of a

pencil. • A yard or meter would be an appropriate unit to use when measuring the length of a room. • A mile or kilometer would be appropriate to use when measuring the distance from one city

to another. • The duration of an event is called elapsed time and it can be measured. • The length around a polygon can be calculated by adding the lengths of its sides. • The space inside a rectangle or square can be measured in square units.

ESSENTIAL QUESTIONS

• How can I use attributes to compare and contrast shapes? • How can angles be classified? • How can triangles be classified according to the length of their sides? • How can shapes be combined to create new shapes? • Can a shape be represented in more than one way? How and why? • How can I compare measurements? • What determines the choice of a measurement tool? • What estimation strategies are used in measurement? • How is the appropriate unit for measurement determined? • How is the reasonableness of a measurement determined? • Why are units important in measurement? • How are the perimeter and area of a shape related? • How does combining and breaking apart shapes affect the perimeter and area? • How can rectangles have the same perimeter but have different areas? • How does estimating length change with more frequency of measurement? • How do the measures of lengths change when the unit of measure changes? • What methods can I use to determine the area of an object? • How can we determine the amount of time that passes between two events? • What part does elapsed time play in our daily living? • Where are radius, center, and diameter located on a circle and how can they be used to show

distance on a map? • How can we communicate our thinking about mathematical vocabulary? • How can I demonstrate my understanding of the attributes of two-dimensional figures and

the measurement of length, perimeter, area, and time?





CONCEPTS/SKILLS TO MAINTAIN

It is expected that students will have prior knowledge/experience related to the concepts and skills identified below. It may be necessary to pre-assess in order to determine if time needs to be spent on conceptual activities that help students develop a deeper understanding of these ideas.

• Basic geometric figures and spatial relationships • Comparison/Estimation/Ordering of measurements • Fluency with basic addition • Duration and sequence of events • Telling time • Sorting and classifying • Use straight edge and pencil to draw straight lines

SELECTED TERMS AND SYMBOLS

The following terms and symbols are often misunderstood. These concepts are not an inclusive list and should not be taught in isolation. However, due to evidence of frequent difficulty and misunderstanding associated with these concepts, instructors should pay particular attention to them and how their students are able to explain and apply them. The definitions below are for teacher reference only and are not to be memorized by the students. Teachers should present these concepts to students with models and real life examples. Students should understand the concepts involved and be able to recognize and/or demonstrate them with words, models, pictures, or numbers.

Acute Angle: An angle whose measure is greater than 0 degrees but less than 90

degrees. Angle: The region between two rays.

Area: A measurement of the region enclosed by a plane figure. Area is always

expressed in square units. Centimeter: A standard unit of length in the metric system where 1 centimeter = 1/100

of a meter. Circle: The set of all points in a plane that are the same distance (called the radius)

from a given point (the center). Diameter: A line segment passing through the center of a circle with endpoints on the

circle. Edge: The intersection of a pair of surfaces in a three-dimensional figure.

Equilateral Triangle: A triangle with three equal sides and three equal angles.





Face: A flat surface of a three-dimensional shape. Foot: A customary unit of length. 1 foot = 12 inches

Hexagon: A polygon with six sides.

Inch: A customary unit of length where 1 inch = 1/12 of a foot.

Isosceles Triangle: A triangle with at least two equal sides and two equal angles.

Kilometer: A standard unit of length in the metric system where 1 kilometer = 1000

meters. Meter: A standard unit of length in the metric system where 1 meter = 100 centimeters

= 1,000 millimeters. Millimeter: A standard unit of length in the metric system where 1 millimeter =

1/1,000 of a meter. Obtuse Angle: An angle whose measure is greater than 90 degrees but less than 180

degrees. Parallelogram: A quadrilateral with opposite sides that are parallel.

Perimeter: The sum of the lengths of the sides of a polygon.

Plane Figure: A 2-dimensional figure; all points of the figure lie in the same plane.

Polygon: A closed plane figure (no gaps or openings) made with 3 or more straight

sides. Quadrilateral: A polygon with 4 sides.

Radius: The distance from the center of a circle to any point on the circle.

Rectangle: A parallelogram with four right angles.

Rhombus: A parallelogram with four equal sides.

Right Angle: An angle that measures exactly 90 degrees.

Scalene Triangle: A triangle in which all three sides have different lengths.

Side: A straight line segment that forms part of a polygon.

Solid Figure: A three-dimensional figure having length, width, and height.





Square: A parallelogram with four equal sides and four right angles.

Triangle: A polygon with three sides.

Trapezoid: A quadrilateral with exactly one pair of parallel sides.

Vertex (of a 2-D figure): The common endpoint of two line segments that serve as two

sides of a polygon. (plural: vertices)

Vertex (of a 3-D figure): The point where three or more edges intersect. Yard: A customary unit of length where 1 yard = 3 feet.

CLASSROOM ROUTINES

The importance of continuing the established classroom routines cannot be overstated. Daily routines must include such obvious activities as taking attendance and lunch count, doing daily graphs, problem of the day, and calendar activities at a math meeting board. They should also include less obvious routines, such as how to select materials, how to use materials in a productive manner, how to put materials away, how to interact with others during small group discussions, and how to access classroom technology such as computers and calculators.

Routinely allow plenty of time for children to explore new materials before attempting any directed activity with these new materials. Make it a practice to write in math class by using a math journal, ask students to respond to lessons using prompts such as, "What I learned today," and regularly writing to justify and explain solutions to problems.

The regular use of these routines is important to the development of students’ number sense, flexibility, and fluency, which will support students’ performance on the tasks in this unit. STRATEGIES FOR TEACHING AND LEARNING:

• Students should be actively engaged by developing their own understanding. • Mathematics should be represented in as many ways as possible by using graphs, tables,

pictures, symbols, and words. • Appropriate manipulatives and technology should be used to enhance student learning. • Students should be given opportunities to revise their work based on teacher feedback, peer

feedback, and metacognition which includes self-assessment and reflection. • Students need to write in mathematics class to explain their thinking, to share how they

perceive topics, and to justify their work to others.





LITERATURE CONNECTIONS

The books below are mentioned in the following tasks. This is not an exhaustive list and is provided only as a suggestion of types of books that would be appropriate with this unit.

• The Greedy Triangle by Marilyn Burns (polygons) • Grandfather Tang’s Story by Ann Tompert (polygons) • Three Pigs, One Wolf and Seven Magic Shapes by Maccarone and Neuhaus (polygons) • The Tangram Magician by Lisa Campbell Ernst (polygons) • Measuring Penny by Loreen Leedy (measurement) • Spaghetti and Meatballs for All by Marilyn Burns (area and perimeter) • Bigger, Better, Best! (MathStart) • Racing Around (MathStart) by Stuart J. Murphy (perimeter)

by Stuart J. Murphy (area using non-standard units)

• The Long Wait by Annie Cobb (elapsed time) EVIDENCE OF LEARNING

By the conclusion of this unit, students should be able to demonstrate the following competencies:

• Draw common polygons and circles • Compare and classify geometric figures according to their properties • Sort triangles by the length of their sides • Classify angles and identify acute, right, and obtuse angles within polygons • Draw a circle and identify its center, a radius and a diameter • Tell time to the nearest minute and determine elapsed time of a full, half, and quarter-

hour • Choose between millimeter, centimeter, meter, and kilometer the appropriate metric unit

of measure for length • Choose between inch, foot, yard, and mile the appropriate unit of customary measure for

length • Measure accurately to the nearest 1/4 inch • Give reasonable estimates for measures of length • Choose the appropriate tool to measure length • Find the area of rectangles with models • Find the perimeter of geometric figures • Describe and extend geometric patterns





TASKS

The following tasks represent the level of depth, rigor, and complexity expected of all third grade students. These tasks or a task of similar depth and rigor should be used to demonstrate evidence of learning. It is important that all elements of a task be addressed throughout the learning process so that students understand what is expected of them. While some tasks are identified as a performance task, they also may be used for teaching and learning (learning task).

Task Name Task Type Grouping Strategy Skills

What Makes A Shape? Learning Task Whole Group/Partner Task Sorting and Classifying Shapes

Geoboard Geometry Learning Task Whole Group/Individual Task

Defining Triangles, Rectangles, and Squares

Tangram Challenge Performance Task Whole Group/Individual Task

Combining and Creating Geometric Figures

Measure Me Performance Task Partner Task

Selecting and Using Appropriate Measurement Tools and Units

Pentomino Perimeters Learning Task Whole Group/Partner Task

Determining Perimeter and Area, Finding Different Perimeters with Same Area

Guess Who’s Coming to Dinner?

Performance Task Small Group Task

Making Different Rectangles, Finding Different Perimeters with Same Area

Rectangles Rule Learning Task Individual Task

Finding Different Areas Keeping Perimeter the Same

Soaring on Air Learning Task Partner Task Estimating and Measuring Length

How Big Is a Desk? Learning Task Whole Group/Partner Task

Estimating and Measuring Perimeter and Area, Using Different Units of

Measurement

Daily Schedule Performance Task Whole Group/Individual Task Determining Elapsed Time

Touring Georgia Learning Task Whole Group/Partner Task

Identifying and Using Parts of a Circle, Using a Scale

Measuring Words Learning Task Small Group/Partner Task

Identifying and Classifying Measurement Terms

Culminating Task: Home Sweet Home

Performance Task Individual Task

Using Geometry and Measurement in the Real World





LEARNING TASK: What Makes a Shape? STANDARDS ADDRESSED M3G1. Students will further develop their understanding of geometric figures by drawing them. They will also state and explain their properties.


b. Identify and compare the properties of fundamental geometric figures. c. Examine and compare angles of fundamental geometric figures.

M3P1. Students will solve problems (using appropriate technology).

a. Build new mathematical knowledge through problem solving. b. Solve problems that arise in mathematics and in other contexts. c. Apply and adapt a variety of appropriate strategies to solve problems. d. Monitor and reflect on the process of mathematical problem solving.











ESSENTIAL QUESTIONS

• How can I use attributes to compare and contrast shapes?





MATERIALS

• Small bag with a set of paper polygons for each student or pair of students

• Glue • The Greedy Triangle by

Marilyn Burns or other book about shape attributes

• “What Makes a Shape? Shapes for Sorting” student sheet, copied on colored paper

• “What Makes a Shape? Venn Diagram” student recording sheet, copied on white paper

GROUPING

Whole Group/Partner Task TASK DESCRIPTION, DEVELOPMENT AND DISCUSSION

In this task, students begin the process of exploring shapes for their many attributes and use

critical vocabulary to describe and compare those shapes through higher-level thinking skills.

Comments Teachers may want to begin this task by reading a book about shape attributes such as The

Greedy Triangle. While reading, questions should be posed to the students that lead to the discovery of shape attributes – their similarities and differences. A list of attributes may be generated on the board throughout the reading or each student may be asked to keep a list of attributes.

Students may sort shapes by such attributes as number of sides, number of vertices, or shapes that contain acute angles. Responses should clearly indicate how the shapes were grouped. Exemplary responses would include the use of a graphic organizer, explanations or labels that are clear, and appropriate mathematical vocabulary.

When students are working in pairs, the teacher should monitor the questioning and discussion between the students and if necessary model a discussion prior to or during the work time.

Once students have completed their Venn diagrams, encourage students to share their work. A few students can be selected during the work time to share their work and explain their thinking. Or if students have had experience sharing their work, they can be placed in small groups and each student can share their work with their group.





Background Knowledge Students should have had experiences with common plane figures and the identification of their

sides and angles. Students should also be familiar with grouping and ways to express their findings using common graphic organizers.

Teachers might want to view the classroom video from second grade titled, “What’s In a Name?” A link to the video can be found below. Two things to notice from this video are (1) the expectations of second grade (teachers can think about how this knowledge and understanding can be further developed in third grade), and (2) how the teacher, Kayte Carlson, developed students’ understanding of key vocabulary words for geometry. http://gadoe.georgiastandards.org/mathframework.aspx?PageReq=MathName Task Directions

Students will follow the directions below from the “What Makes a Shape?” student recording sheet.

1. Cut out the shapes below. 2. Sort the shapes in different ways. (Use the list of attributes to help you think of different

ways to sort the shapes.) 3. Choose two attributes and label the Venn diagram. 4. Sort your shapes in the Venn diagram leaving any shapes that don’t fit outside of the

Venn diagram. 5. Once you have checked your work, glue the shapes on the Venn diagram. 6. Write to explain your thinking and to describe any observations you made.

Questions/Prompts for Formative Student Assessment

• How could you describe this figure in relationship to another figure? • Why did you place the figure here? (Indicate a section of the Venn diagram.) • How do you know this shape is in the correct place? • Choose one plane figure and tell me how it is used in the world and why its attributes are

important in that use. • Can you choose a shape not in the bag and tell me where it would fit on your paper and

why? Questions for Teacher Reflection

• Are students able to clearly describe attributes of the shapes? • Can students effectively compare and contrast the shapes? • Have students organized their thinking in a logical way? • Are students able to explain their thinking in written form?

http://gadoe.georgiastandards.org/mathframework.aspx?PageReq=MathName�





DIFFERENTIATION Extension

• Have students select different ways to compare/contrast the shapes, then compare their way of sorting with another student.

• Use solid figures instead of plane figures. • Incorporate a writing opportunity by having students write a compare/contrast paragraph

using 2 shapes.

Intervention • Select a smaller sample of shapes. Provide the labels and a graphic organizer for students or

do the reverse in a discovery model and set out some of the shapes in the organizer and let students determine the correct labels, then sort the remaining shapes.

• If students are having difficulty participating in productive conversations, the teacher should model using think-alouds or self-questioning strategies.

TECHNOLOGY CONNECTION

• •

http://standards.nctm.org/document/eexamples/ch0. ap4/4.2/index.htm “Making Triangles” applet and background information.

• http://standards.nctm.org/document/eexamples/chap4/4.2/part2.htm “Creating Polygons” applet and background information.

• http://nlvm.usu.edu/en/nav/frames_asid_172_g_2_t_3.html?open=activities&from=category_g_2_t_3.html Interactive geoboard from the National Library of Virtual Manipulatives http://nlvm.usu.edu/

http://standards.nctm.org/document/eexamples/chap4/4.2/index.htm�


http://standards.nctm.org/document/eexamples/chap4/4.2/part2.htm�

http://nlvm.usu.edu/en/nav/frames_asid_172_g_2_t_3.html?open=activities&from=category_g_2_t_3.html�


http://nlvm.usu.edu/�





Name __________________________________________ Date ____________________________

What Makes a Shape? Shapes for Sorting

1. Cut out the shapes below. 2. Sort the shapes in different ways. (Use the list of attributes to help you think of

different ways to sort the shapes.) 3. Choose two attributes and label the Venn diagram. 4. Sort your shapes in the Venn diagram leaving any shapes that don’t fit outside of the

Venn diagram. 5. Once you have checked your work, glue the shapes on the Venn diagram. 6. Write to explain your thinking and to describe any observations you made.

Georgia Performance Standards Framework

Third Grade Mathematics • Unit 3 • 1st Edition




Name _____________________________________________________ Date _____________________________________________

What Makes a Shape? Venn Diagram






LEARNING TASK: Geoboard Geometry STANDARDS ADDRESSED M3G1. Students will further develop their understanding of geometric figures by drawing them. They will also state and explain their properties.




















ESSENTIAL QUESTIONS

• How can I use attributes to compare and contrast shapes?

• How can angles be classified? • How can triangles be classified according to

the length of their sides? MATERIALS

• Geoboards • Rubber bands • “Geoboard Geometry” student recording sheet

(3 per student) GROUPING

Whole Group/Individual Task TASK DESCRIPTION, DEVELOPMENT AND DISCUSSION

In this task, students begin exploring how to create plane figures using straight lines and angles

and then discover common features of rectangles, squares, and triangles.

Comments Students should be given the opportunity to explore freely with the geoboard and rubber bands

before working this task. Also, teachers may want to begin this task by giving students opportunities to explore the geoboard by making a variety of shapes, lines, and angles. Throughout this task teachers should promote the key vocabulary of acute, obtuse, and right angles and equilateral, isosceles, and scalene triangles as students see them in context. Also, students should be encouraged to use these key vocabulary words.

At the completion of this task the class will have created a definition for rectangles, squares, and triangles. These can be posted in the classroom along with each shape’s attributes. Background Knowledge

Before beginning this task, students should be familiar with common plane figures and the identification of their sides and angles. Also, they should also be able to use a geoboard and transfer that information to paper. Some students may need specific instructions on how to transfer figures to the paper (e.g. counting the spaces between dots and directionality). Finally, students should be able to make multiple representations of the same shape with variance in size and orientation, and still determine it to be the same shape based on its attributes. Task Directions

Students are asked to create all of the different rectangles they can find on the geoboard and then record them on geoboard paper. Ask students to say aloud or write as many complete






sentences as they can that begin with “All (or none, or some) of the rectangles….” in order to draw general conclusions about the shapes. After general conclusions have been stated or recorded, the teacher can lead the students to create an appropriate definition for a rectangle.

Follow the same procedures to create an appropriate definition for a square and a triangle. Finally, create, discuss, and define equilateral, isosceles, and scalene triangles. Questions/Prompts for Formative Student Assessment

• What is your definition of a rectangle (or square, or triangle)? • What are the attributes of a rectangle (or square, or triangle)? • How can you change this shape and only change one attribute?

Questions for Teacher Reflection

• Were students able to construct the shapes correctly? • Were students able to find similarities and differences between shapes? • Were students able to make generalizations and draw accurate conclusions about the

shapes? • Were students able to communicate effectively about their findings?


Have students create a morph chain of a shape changing one attribute at a time and label each morphed shape with its description. (For example: small, red equilateral triangle morphs into a small, blue, equilateral triangle and then into a small, blue, isosceles triangle, etc.) Intervention

Provide the definition of the shape first and deconstruct the definition while creating each part of the shape until the shape is complete. Then have students create a congruent shape. Finally ask students to create a non-congruent shape, changing one attribute. TECHNOLOGY CONNECTION

• http://nlvm.usu.edu/en/nav/frames_asid_172_g_2_t_3.html?open=activities This site offers an easy to use virtual geoboard.

• http://nlvm.usu.edu/en/nav/frames_asid_271_g_2_t_3.html?open=instructions&from=category_g_2_t_3.html Students follow a pattern to create attribute trains based on color, shape, or the number on the shape (e.g. triangle, square pattern; red, red, blue pattern; triangle, square, square pattern; 2,3,1 pattern).

http://nlvm.usu.edu/en/nav/frames_asid_172_g_2_t_3.html?open=activities�

http://nlvm.usu.edu/en/nav/frames_asid_271_g_2_t_3.html?open=instructions&from=category_g_2_t_3.html�








Name ________________________________________ Date ___________________________

Geoboard Geometry






PERFORMANCE TASK: Tangram Challenge STANDARDS ADDRESSED M3G1. Students will further develop their understanding of geometric figures by drawing them. They will also state and explain their properties.













ESSENTIAL QUESTIONS

• How can shapes be combined to create new shapes? • Can a shape be represented in more than one way? How and why?






MATERIALS

• Grandfather Tang’s Story by Ann Tompert, or similar story that incorporates tangrams

• Tangram sets, plastic or “Tangram Challenge” student sheet

• Tangram Shape Charts (preferably on poster or butcher paper)

GROUPING


In this task, students will create shapes from other basic shapes by combining the individual shapes. Then students will compare the attributes of the created shapes. Comments

Students should be given the opportunity to explore freely tangram pieces before working this task. To introduce this task, teachers may read aloud Grandfather Tang’s Story to students or a similar book about tangrams. Similar books include Three Pigs, One Wolf and Seven Magic Shapes by Maccarone and Neuhaus and The Tangram Magician by Lisa Campbell Ernst.

While reading the story or after finishing the story, discuss the components of each animal and ask the students explore building some of the shapes with the tangrams. Teachers may need to discuss how shapes may be turned or flipped in order to create the shapes. Background Knowledge

Students should be aware of the number of sides in common plane figures and be able to identify right, acute, and obtuse angles. Also students should understand how to read a chart and identify parts of the chart using columns and rows. Task Directions

Ask students to create a square using any number of pieces, and then compare the squares with their neighbors. Record the squares by tracing them on a piece of paper challenging students to make as many different squares as they can. Ask students to define their squares using the attributes of four right angles and four equal sides. Refer to the posted definitions from the previous task.

Display the Tangram Shape Chart and demonstrate to students how to use the chart by placing some of their squares in the appropriate row on the chart. Then have students work in groups to find other shapes that can be made from tangram pieces and sketch those in the appropriate square on the chart. All students are not expected to complete the entire chart (in fact not all shapes are possible), instead encourage students to continue to work on this task throughout this unit by occasionally asking students to share one of their solutions.






Questions/Prompts for Formative Student Assessment • How do you know this is a square (rectangle, triangle, or trapezoid)? • How many pieces did you use to create this shape? Where does this shape belong on the

chart? How do you know? • How did you count the number of sides? How did you count the number of angles?


• Are students able use the tangram pieces to create given shapes in more than one way? • Can students create a definition of a given shape by using its attributes? • Have students correctly placed their shapes on the Tangram Shape Chart?


• Have students create the chart as an independent study with sketches and written explanations of how the figures were created.

• Have students add additional shapes to the chart like irregular polygons and concave polygons.

• Encourage students to explore some of the web pages below that provide additional tangram puzzles.

Intervention

• For each shape, provide only the pieces that will make that specific shape and give directions such as, “Use the smallest triangle and the four-sided figure that is not a square to make a trapezoid.”

• Give students copies of the completed shape outlines so that students can use the pieces to make the puzzle.


• http://www.linkslearning.org/Kids/1_Math/2_Illustrated_Lessons/7_Tangrams/ An animated movie that discusses the attributes of the pieces of tangrams and asks students to create different shapes while showing how to make the seven tangram pieces.

• http://pbskids.org/cyberchase/games/area/tangram.htmlVirtual tangrams with several pictures for students to build.

• http://nlvm.usu.edu/en/nav/frames_asid_289_gChallenge_2_t_3.html?open=activities Interactive tangram puzzles

• http://standards.nctm.org/document/eexamples/chap4/4.4/part2.htm Tangram challenges from the National Council of Teachers of Mathematics.

• http://standards.nctm.org/document/eexamples/chap4/4.4/index.htm Interactive tangram pieces.

http://www.linkslearning.org/Kids/1_Math/2_Illustrated_Lessons/7_Tangrams/�

http://pbskids.org/cyberchase/games/area/tangram.html�

http://nlvm.usu.edu/en/nav/frames_asid_289_gChallenge_2_t_3.html?open=activities�

http://standards.nctm.org/document/eexamples/chap4/4.4/part2.htm�







Tangram Pieces






Name ________________________________________ Date ___________________________

Tangram Challenge

Find as many ways as possible to create the shapes below using tangram pieces. You may work with a partner or a small group. Sketch how you made the shapes in the appropriate boxes below. See the examples below.

Tangram Shape Chart

# of pieces

Square

Rectangle

Triangle

Trapezoid

1

2

3

4

5

6

7






PERFORMANCE TASK: Measure Me STANDARDS ADDRESSED M3M2. Students will measure length choosing appropriate units and tools.

b. Measure to the nearest ¼ inch, ½ inch and millimeter (mm) in addition to the previously learned inch, foot, yard, centimeter, and meter.

c. Estimate length and represent it using appropriate units. d. Compare one unit to another within a single system of measurement.




by equal divisions of a whole. M3P1. Students will solve problems (using appropriate technology).















M3P5. Students will represent mathematics in multiple ways. a. Create and use representations to organize, record, and communicate mathematical ideas. b. Select, apply, and translate among mathematical representations to solve problems. c. Use representations to model and interpret physical, social, and mathematical phenomena.

ESSENTIAL QUESTIONS

• How can I compare measurements? • Why are units important in measurement? • What determines the choice of a measurement tool? • How is the appropriate unit for measurement determined?

MATERIALS

• Variety of measuring tools for length • Large piece of butcher paper per child • Measuring Penny by Loreen Leedy or similar book about measurement

GROUPING

Partner Task TASK DESCRIPTION, DEVELOPMENT AND DISCUSSION

In this task, students will measure, record, and compare length using a variety of tools and units. Comments

One way to introduce this task would be by engaging students in a discussion about when a measurement of length is needed, their experiences in making those measurements, and when accurate measurements are used in real world situations. Then read Measuring Penny, a book about a girl who measures her dog, Penny, and compares the measurements to other dogs. Involve students in a discussion about measurement based on the events in the story.

Students should be able to label lengths using different units within the same system. If a student’s leg is 26”, students should recognize that is equivalent to 2 feet, 2 inches. If a student’s height is 40”, they should be able to rewrite the measure as 1 yard, 4 inches, as well as 3 feet, 4 inches. Similarly, if a student measures a finger as 62mm, students should be able to write the equivalent measure of 6 cm and 2 mm.

Background Knowledge

Students should have had experiences measuring length to the nearest ¼” and ½” using a tape measure, ruler, and yardstick. Students should also understand units of length and how they relate to each other.






Task Directions Working in pairs, ask students to trace the outline of their bodies on butcher paper. Using

different measurement tools, students will measure parts of their bodies such as arms, hands, and legs. Have students record the measurements on their outlines. Students should use a variety of tools and units, such as yards, feet, inches, (if using inches, students can measure to the nearest ¼” or ½”), meters, centimeters, and millimeters, as well as non-standard units like paper clips or linking cubes. Be sure students include the units in their recording.

When finished measuring, ask students to use the measurements to write comparison statements for different units, different body parts, and different people. Questions/Prompts for Formative Student Assessment

• Should you use the same unit when comparing measurements? Why? • How did you measure the length of your arm? Foot? Leg? Body? • What unit of measure did you use to measure your arm? Foot? Leg? Body? • How did you select the most appropriate tool for measuring? • What units did you use most often? Why? • How can you compare your measurements?


• Were students able to accurately measure and record the measurements? • Can students select the most appropriate measurement tools? • Do students understand the importance of using like units when making measurement

comparisons? DIFFERENTIATION Extension

• Ask students to measure their arm span and then their height. Determine if their height is more than or less than their arm span. Measure other students in the same way to determine whether their height or arm span is greater. Create a graph of the data collected.

• In the book, Measuring Penny by Loreen Leedy, the girl also measures elapsed time. Ask student pairs to choose an activity and time it. Record the activity and the start and stop times and determine the elapsed time.

Intervention

• Assign specific measurement tasks and help students decide on the tool and the unit together.


http://www.innovativeclassroom.com/Files/Worksheets/AmIaSquare.pdf “Am I a Square?” measurement and graphing activity.

http://www.innovativeclassroom.com/Files/Worksheets/AmIaSquare.pdf�






LEARNING TASK: Pentomino Perimeters STANDARDS ADDRESSED M3M3. Students will understand and measure the perimeter of geometric figures.






models. M3A1. Students will use mathematical expressions to represent relationships between quantities and interpret given expressions.


perimeter of a geometric figure). M3P1. Students will solve problems (using appropriate technology).












M3P4. Students will make connections among mathematical ideas and to other disciplines. a. Recognize and use connections among mathematical ideas. b. Understand how mathematical ideas interconnect and build on one another to produce a




ESSENTIAL QUESTIONS

How are the perimeter and area of a shape related? MATERIALS

• “Pentominos Perimeters” student recording sheet (2 pages)

• Pentominos • Racing Around by Stuart J. Murphy

or similar book about finding perimeter

GROUPING


In this task, students will explore area and perimeter and their relationship. Comments

One way to introduce the concept of perimeter is to read Racing Around by Stuart J. Murphy or a similar book about finding perimeter.

Students should be given the opportunity to explore pentominos pieces freely before working this task. To further explore pentominos, ask students to sort the pentomino pieces and determine the common attributes of the set (i.e., each piece has an area of 5 square units and all sides meet to form a right angle). Also, ask students to sort the shapes by perimeter. Students should notice that all of the pieces have a perimeter of 12 linear units with the exception of one shape that has a perimeter of 10 linear units. Discuss why only one piece has a different perimeter. Be sure students determine that shapes can have the same area but have different perimeters and vice versa. Use the correct terminology of square units and linear units in discussions.






Teachers may want to discuss the questions on the “Working with Perimeters” activity on the following web site: http://nlvm.usu.edu/en/nav/frames_asid_114_g_2_t_3.html?open=activities before students complete this task.

In preparation for working with pentominos, teachers may need to discuss how to manipulate the pieces by turning or flipping them. Background Knowledge

To be successful with this task, students will need to understand how to find the perimeter and area of a figure. Also, students will need to understand the definition of a polygon so that they will be able to create a polygon using pentominos.

Task Directions

Students will follow the directions below from the “Pentomino Perimeters” student recording sheet.

1. In each box below, choose three pentominos and create a polygon. Trace your polygon in the box.

2. Find the area and perimeter of each polygon. Be sure to include the correct label for each measure.

3. Write to tell how you found the area and perimeter of your polygons. 4. Write to explain what you noticed about the areas and perimeters of your polygons. 5. CHALLENGE: Using 3 pentominos pieces, what is the longest perimeter you can make?

Sketch it below and explain how you know it is the longest possible perimeter. Questions/Prompts for Formative Student Assessment

• How does the area compare to the perimeter of this shape? • What units are used to measure each? Why? • What generalizations can you make about the relationship of perimeter and area of shapes?


• Can students determine the common attributes of the pentomino pieces? • Can students clearly explain their rationale for the groups of shapes they sorted? • Can students explain the relationship between area and perimeter of shapes? • Can students effectively and accurately explain their results in written form?








• Ask students to complete the challenge on the student recording sheet. • Challenge students to find 4 pieces that create a 4 x 5 rectangle or 5 pieces that form a 5 x 5

square. For more extension activities, see the following web site: http://people.rit.edu/mecsma/Professional/Puzzles/Pentominoes/P-A.html

Intervention

• Have students copy and draw the square units inside a pentomino piece and then label the perimeter and area for further understanding.

• Use a visual model for students to copy. TECHNOLOGY CONNECTION

• http://nlvm.usu.edu/en/nav/frames_asid_114_g_2_t_3.html?open=activities Interactive pentomino tasks

• http://people.rit.edu/mecsma/Professional/Puzzles/Pentominoes/P-A.html Provides several beginner problems with solutions for pentominos.

• http://puzzler.sourceforge.net/docs/pentominoes.html Solutions to several pentominos puzzles such as the one below.

http://people.rit.edu/mecsma/Professional/Puzzles/Pentominoes/P-A.html�


http://people.rit.edu/mecsma/Professional/Puzzles/Pentominoes/P-A.html�

http://puzzler.sourceforge.net/docs/pentominoes.html�






Pentomino Pieces






Name ________________________________________ Date ___________________________

Pentomino Pandemonium

1. In each box below, choose three pentominos and create a polygon. Trace your polygon in the box.

A. B.

C. D.

2. Find the area and perimeter of each polygon. Be sure to include the correct label for each

measure.

Polygon A Polygon B Polygon C Polygon D

Area

Perimeter






3. Write to tell how you found the area and perimeter of your polygons.

________________________________________________________________________________

________________________________________________________________________________

________________________________________________________________________________

________________________________________________________________________________

________________________________________________________________________________

4. Write to explain what you noticed about the areas and perimeters of your polygons.

________________________________________________________________________________

________________________________________________________________________________

________________________________________________________________________________

________________________________________________________________________________

________________________________________________________________________________

________________________________________________________________________________

5. CHALLENGE: Using 3 pentominos pieces, what is the longest perimeter you can make? Sketch it below and explain how you know it is the longest possible perimeter.

________________________________________________________________________________

________________________________________________________________________________

________________________________________________________________________________

________________________________________________________________________________






PERFORMANCE TASK: Guess Who’s Coming to Dinner?

STANDARDS ADDRESSED M3M3. Students will understand and measure the perimeter of geometric figures.

a. Understand the meaning of the linear unit and measurement in perimeter.

b. Understand the concept of perimeter as being the length of the boundary of a geometric figure.

c. Determine the perimeter of a geometric figure by measuring and summing the lengths of the sides.

M3M4. Students will understand and measure the area of simple geometric figures (squares and rectangles).





















ESSENTIAL QUESTIONS

• How are the perimeter and area of a shape related?

• How does combining and breaking apart shapes affect the perimeter and area?

MATERIALS

• Spaghetti and Meatballs For All by Marilyn Burns or similar book about perimeter

• “Guess Who’s Coming to Dinner?” student recording sheet

• 8 colored squares per group (about 2-inch squares)

• 1 large paper per group (about 18 x 24) GROUPING

Small Group Task TASK DESCRIPTION, DEVELOPMENT AND DISCUSSION

In this task, students will manipulate squares to alter the perimeter of given shapes in order to maximize seating potential. Comments

As an introduction to this task, read Spaghetti and Meatballs for All. In the story, relatives come to dinner and begin rearranging tables which results in losing seating places. After reading the book, have groups use the squares to model some of the events in the book. Discuss changes in area and/or perimeter caused by the moves.

Student responses to the “Guess Who’s Coming to Dinner?” task should reflect a variety of solutions. Student work should demonstrate that they paid close attention to the details of the problem. Work should be clearly labeled to show guest’s names. Written explanation should be






easily understood. Ask students to share their solutions along with highlights of their group’s discussion that occurred while finding their solutions. Background Knowledge

Students should have had experience with area and perimeter and understand the different uses for each. As students manipulate the squares, they will discover that when two separate squares (tables of four) are rearranged into a rectangle, two seating spaces are lost where the squares are joined together. Other observations about joining tables will become apparent as students manipulate the squares. Some students may recognize that as the perimeter gets smaller, the rectangle gets closer and closer to a square.

Remind students that most of the pentominos had a perimeter of 12 units, except for the one in which most of the squares shared two sides. This information may be helpful when working on this task.

Task Directions

Students will follow the directions below from the “Guess Who’s Coming to Dinner?” student recording sheet.

Pretend that four people live at your house (Your mom, dad, sister, and

you). Aunt Sue, Uncle John and their six children (Jamal, Kevin, Carl, Annie, Stephanie, and Maxine) are coming for dinner. Uncle Kenny is coming, too. He is bringing his wife (Aunt Jenny) and four kids (Earl, Charles, Jasmine and Justine).

Mom has six square folding tables she can use but you don’t have to use all of them. (Each folding table seats four, one on each side.) You can put two or more of the folding tables together to form a rectangle if you like.

Work with a partner to decide on a seating arrangement that is best for your family and guests. When finished, draw a picture of the table arrangement and label each place to show who will be sitting there. Mom has the following rules:

• There should be no empty seats. • There must be at least one grown-up at each table.

Write a few sentences to describe what happened to the perimeter as tables were pushed together. Then explain why the arrangement you chose is the best possible arrangement.


• How does the area compare to the perimeter of this shape? • How does combining or pulling apart shapes affect the perimeter and area of your pieces? • What happens when you combine squares? • What strategies are you using to make sure each guest has a seat?






Questions for Teacher Reflection • Are students able to explain why seats are lost when two squares are joined? • Can students accurately describe the area and perimeter of the shapes? • Were students able to work together to effectively solve all parts of the problem? • Did students’ writing explain their process?


• Ask students work with a total of 24 dinner guests and 8 square tables. • Challenge students to find more than one way to solve the problem. • Ask students to describe how area and perimeter are alike and/or different.

Intervention

• As students try out a possible solution have them trace the squares on a separate piece of paper and label the area and length of sides to determine the perimeter. Continue with this until the perimeter matches the number of guests. Then have students use name cards to move the guests around until a suitable solution is found.


• http://nlvm.usu.edu/en/nav/frames_asid_169_g_1_t_3.html?open=activities&from=category_g_1_t_3.html The squares from this virtual pattern blocks web site can be used. Students can use six squares from the pattern blocks and find different arrangements of the squares that meet the required conditions.

• http://www.learner.org/courses/learningmath/measurement/session9/part_a/index.html An interactive task for teachers to explore area and perimeter.



http://www.learner.org/courses/learningmath/measurement/session9/part_a/index.html�






Name ________________________________________ Date ___________________________

Guess Who’s Coming to Dinner?

Pretend that four people live at your house (Your mom, dad, sister, and you). Aunt Sue, Uncle John and their six children (Jamal, Kevin, Carl, Annie, Stephanie, and Maxine) are coming for dinner. Uncle Kenny is coming, too. He is bringing his wife (Aunt Jenny) and four kids (Earl, Charles, Jasmine and Justine).

Mom has six square folding tables she can use but you don’t have to use all of them. (Each

folding table seats four, one on each side.) You can put two or more of the folding tables together to form a rectangle if you like.

Work with a partner to decide what seating arrangement is best for your family and guests.

When finished, draw a picture of the table arrangement and label each place to show who will be sitting there. Mom has the following rules:

• There should be no empty seats. • There must be at least one grown-up at each table.

Write a few sentences to describe what happened to the perimeter as tables were pushed together. Then explain why the arrangement you chose is the best possible arrangement.

___________________________________________________________________________________________________________

___________________________________________________________________________________________________________

___________________________________________________________________________________________________________

___________________________________________________________________________________________________________

___________________________________________________________________________________________________________






LEARNING TASK: Rectangles Rule

STANDARDS ADDRESSED M3M3. Students will understand and measure the perimeter of geometric figures.

a. Understand the meaning of the linear unit and measurement in perimeter.

b. Understand the concept of perimeter as being the length of the boundary of a geometric figure.

c. Determine the perimeter of a geometric figure by measuring and summing the lengths of the sides.

M3M4. Students will understand and measure the area of simple geometric figures (squares and rectangles).

a. Understand the meaning of the square unit and measurement in area. c. Determine the area of squares and rectangles by counting, addition, and multiplication with



















ESSENTIAL QUESTIONS

• What is the relationship between perimeter and area?

• How can rectangles have the same perimeter but have different areas?

MATERIALS

• “Rectangles Rule” student recording sheet • Construction paper • Glue and scissors

GROUPING

Individual Task TASK DESCRIPTION, DEVELOPMENT, AND DISCUSSION

In this task, students will use given perimeters to draw rectangles and compare areas of various rectangles.

Comments

When drawing rectangles with a given perimeter, it might be helpful for some students to share methods of finding rectangles with the correct perimeter. Some students might use trial and error or an organized list; others might realize they need to find two numbers that add up to half of the perimeter. By sharing strategies, some students might be able to use more efficient methods. However, allow students to use a method that makes sense to them.

Once students have finished with the task, post the students’ work so that students can see several different examples of rectangles with the same perimeter arranged in order by area. Ask students to compare their work with others and then engage them in a discussion of the relationship between perimeter and area. Students should notice that the more narrow the rectangle, the smaller the area. Also, students should notice that the largest area is found in rectangles that are squares or






as close to a square as possible, given the perimeter. Students may also notice some of the properties of rectangles: four right angles, four sides, and opposite sides equal. Background Knowledge

Students should have had prior experience determining area and perimeter. Task Directions

Students will follow the directions below from the “Rectangles Rule” student recording sheet. Assign each pair of students a perimeter. Possible perimeters are 12, 18, 24, 34, and 36.

Directions: 1. On the dot paper below, draw all the rectangles you can with the same perimeter.

My perimeter is _____________.

2. Find the area and record it inside the rectangle. Show how you found the area. 3. Cut out the rectangles and order them from smallest area to largest area. 4. Glue them on construction paper in order. 5. Write a paragraph explaining what you notice about how the shape of a rectangle

and its area are related. Questions/Prompts for Formative Student Assessment

• Have you found all of the rectangles possible? How do you know? • What strategies are other students using to find rectangles with the given perimeter? • What do you notice about the shape of the rectangles? • How are shape and area related? • Other than perimeter, what do all of these rectangles have in common?


• How efficient are students at finding the area and perimeter of a rectangle? • Can students accurately explain the relationship of shape and area?


Given a rectangle with a perimeter of 36 units, what is the smallest possible area it could have? What is the largest possible area? How do you know?

Intervention

Use graph paper instead of dot paper to count the square units.







http://nlvm.usu.edu/en/nav/frames_asid_172_g_2_t_3.html?open=activities Geoboard with area/perimeter activity (Look for the activity titled, “Shapes with Perimeter 16.”) http://highered.mcgraw-hill.com/sites/0072532947/student_view0/grid_and_dot_paper.html Printable dot and graph paper


http://highered.mcgraw-hill.com/sites/0072532947/student_view0/grid_and_dot_paper.html�






Name ____________________________________________ Date _______________________

Rectangles Rule

Directions: 1. On the dot paper below, draw all the rectangles you can with

the same perimeter. My perimeter is _____________.

2. Find the area and record it inside the rectangle. Show how you

found the area. 3. Cut out the rectangles and order them from smallest area to

largest area. 4. Glue them on construction paper in order. 5. Write a paragraph explaining what you notice about how the shape of a rectangle and its

area are related.






LEARNING TASK: Soaring on Air STANDARDS ADDRESSED M3M2. Students will measure length choosing appropriate units and tools.

a. Measure to the nearest ¼ inch, ½ inch and millimeter (mm) in addition to the previously learned inch, foot, yard, centimeter, and meter.

b. Estimate length and represent it using appropriate units. c. Compare one unit to another within a single system of measurement.




by equal divisions of a whole. M3P1. Students will solve problems (using appropriate technology).
















ESSENTIAL QUESTIONS

• How does estimating length change with more frequency of measurement?

• What determines the choice of a measurement tool?

• What estimation strategies are used in measurement?

• How is the appropriate unit for measurement determined?

• How is the reasonableness of a measurement determined?

MATERIALS

• Paper • Yarn • Graph Paper • Rulers • Yardsticks • Tape • The World Record Paper Airplane Book by Ken Blackburn or similar book about paper

airplanes GROUPING

Partner Task TASK DESCRIPTION, DEVELOPMENT AND DISCUSSION

In this task, students will estimate and measure length using different units within the same system. Comments

You may want to introduce this task by reading The World Record Paper Airplane Book by Ken Blackburn, reading a similar book about paper airplanes, or use a website such as http://www.paperplane.org/ for ideas (click on “paper airplane patterns”).

Before students work on this task, they will need to create a paper airplane. It is best to do this task on a calm day (no breeze).

http://www.paperplane.org/�






When summarizing this task, be sure to discuss what students noticed when measuring using a different unit of measure. Also, ask students to comment on whether they were able to estimate more accurately after estimating and measuring their yarn one or two times.

At the end of the task, all students should have three pieces of yarn taped their paper. Yarn should be measured accurately. Graphs should accurately represent the data collected. Background Knowledge

Students should be able to measure length using a variety of tools and units. Task Directions

Students will follow the directions below from the “Soaring on Air” student recording sheet.

You and a friend will be measuring how far your paper airplanes will fly outside. You and your partner will each throw your plane, estimate, and measure three times. Read through all of the directions before going outside.

1. Use something to mark the place where you are standing when you throw your

airplane. 2. Take three practice throws. 3. Throw your airplane. Cut a piece of yarn exactly the same length as the distance

from your throwing spot to the airplane. Record your estimate for the distance your plane traveled.

4. Use a ruler to measure the number of feet your airplane flew. Record your data. 5. Once you have collected all of your data, graph your results on a separate piece of

paper.

6. Change to another unit in the same system of measurement (inches, yards) and estimate then measure each piece of yarn (use the same yarn). When finished, tape your pieces of yarn to your paper.

7. Write a paragraph to describe and explain what happened. Did your estimates get more accurate each time you measured your yarn?






Questions/Prompts for Formative Student Assessment • Why would you measure using more than one unit? • How did your estimation strategies change throughout the task? • What happened when you changed units of measurement? • What type of graph is most appropriate for this data?


• Were students able to estimate accurately? • Were students able to measure accurately? • Did students make connections between different units of measurement in the same system?


Using several airplane designs, do test flights and compare the flight distance of each. Which design won? By how much? Intervention

Allow students to verbalize their ideas before recording them. TECHNOLOGY CONNECTION

http://www.paperplane.org/ Ideas for designing paper airplanes – click on “paper airplane patterns.”

http://www.paperplane.org/�






Name ____________________________________________ Date _______________________

Soaring On Air

You and a friend will be measuring how far your paper airplanes

will fly outside. You and your partner will each throw your plane, estimate, and measure three times. Read through all of the directions before going outside.

1. Use something to mark the place where you are standing when

you throw your airplane. 2. Take three practice throws. 3. Throw your airplane. Cut a piece of yarn exactly the same length as the distance from your

throwing spot to the airplane. Record your estimate for the distance your plane traveled. 4. Use a ruler to measure the number of feet your airplane flew. Record your data. 5. Once you have collected all of your data, graph your results on a separate piece of paper.

Flight Estimate Measurement (include units)

1.

2.

3.

6. Change to another unit in the same system of measurement (inches, yards) and estimate then measure each piece of yarn (use the same yarn). When finished, tape your pieces of yarn to your paper.

Flight Estimate Measurement (include units)

1.

2.

3.

7. On the back of this paper, write a paragraph to describe and explain what happened. Did

your estimates get more accurate each time you measured your yarn?






LEARNING TASK: How Big Is a Desk? STANDARDS ADDRESSED M3M2. Students will measure length choosing appropriate units and tools.

c. Estimate length and represent it using appropriate units. d. Compare one unit to another within a single system of measurement.







models. M3P1. Students will solve problems (using appropriate technology).
















ESSENTIAL QUESTIONS

• How do the measure of lengths change when the unit of measure changes?

• How are the perimeter and area of a shape related?

• What methods can you use to determine the area of an object?

MATERIALS

• Square units (i.e. centimeter cubes, 1-inch square tiles, 1x1 foot square pieces of paper)

• Bigger, Better, Best!

by Stuart J. Murphy or a similar book about measuring area

GROUPING


In this task, students will use square units to estimate and measure the perimeter and area of a figure and compare the perimeter and area using different units.

Comments

As an introduction to this task, read Bigger, Better, Best! by Stuart J. Murphy or a similar book about measuring area

It is very likely that the multiplication involved for finding area will be larger than a 1-digit number by a 2-digit number. Since students will not be required to find the product of two 2-digit numbers until fourth grade, allow students to use calculators for this activity. The goal of this task is

. Then review perimeter and area and the units that can be used for each (linear units vs. square units). Throughout the lesson emphasize the key vocabulary used in determining perimeter and area.






to explore the relationship between the size of linear units used to measure and the resulting perimeter and area. Therefore, the use of a calculator is appropriate.

Students should recognize that as the size of the unit of measure increases the number of units required to describe perimeter and area decreases. Conversely, as the size of the unit of measure decreases the number of units required to describe perimeter and area increases. In other words, if the pieces are smaller, you will need more of them to cover the same area; and if the pieces are larger you will need fewer of them to cove the same area. Background Knowledge

Students should have had several opportunities to work with the perimeter and area of a rectangle and understand the difference between linear and square units. Task Directions

Students will follow the directions below from the “How Big Is a Desk?” student recording sheet.

How would you describe the size of your desk? You will measure your desk using one

inch tiles, a one foot ruler, and one centimeter cubes. • Before measuring, look at the one inch tiles and record an estimate for the length and

width of your desk in the table below. • Use the tiles to find the actual measurement and record it in the table below. • Find the perimeter of your desk using the tiles (or a method of your choice) and

record it below. • Find the area of your desk using the tiles (or a method of your choice) and record it

below. • Repeat steps 1 through 4 for the ruler and then for the centimeter cubes. Note: There

are probably not enough centimeter cubes to measure the area of the desks. What other method could be used?






1. Write to explain how you found the perimeter of your desk. What is a different way

to find perimeter? 2. Write to explain how you found the area of your desk. What is a different way to

find area? 3. What happened to the perimeter and area of the desk as different units of measure

were used?

Questions/Prompts for Formative Student Assessment • What unit is the most appropriate to use to measure the desk? Why? • What method would you choose to use when measuring a rectangle? Why? • Describe how you found the perimeter of your desk. • Describe how you found the area of your desk.


• Do students have a clear understanding of the difference between perimeter and area? • Are students able to determine methods for finding the perimeter and area? Can they do it in

more than one way? • Can students articulate their predictions, observations, and findings? • Can students explain how the measurement changes as the size of the unit of measure

changes? DIFFERENTIATION Extension

Have students use 3” squares and/or 6” squares (cut from paper) to use as one square unit. In a math journal, ask students to estimate the area and perimeter of their desk and explain how they determined their estimates. Then ask them to find the area of their desk by tiling or multiplying. Intervention

Have one inch and one centimeter grid paper available for those students who would like to “tile” their desks to find the area. If the grid paper is cut into 10 x 10 squares, counting to find the area will be easier. TECHNOLOGY CONNECTION

• http://www.shodor.org/interactivate/activities/ShapeExplorer/?version=1.6.0_07&browser=MSIE&vendor=Sun_Microsystems_Inc.&flash=10.0.32 Randomly generated rectangles for which the perimeter and the area can be found

• http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/perimeter_and_area/ind

ex.html Instruction on finding area and perimeter of shapes with practice. Levels 2 and 3 for area require finding the area of several rectangles and adding the areas together.

http://www.shodor.org/interactivate/activities/ShapeExplorer/?version=1.6.0_07&browser=MSIE&vendor=Sun_Microsystems_Inc.&flash=10.0.32�

http://www.shodor.org/interactivate/activities/ShapeExplorer/?version=1.6.0_07&browser=MSIE&vendor=Sun_Microsystems_Inc.&flash=10.0.32�

http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/perimeter_and_area/index.html�

http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/perimeter_and_area/index.html�






Name ________________________________________ Date ___________________________

How Big Is a Desk?

How would you describe the size of your desk? You will measure your desk using one inch tiles, a one foot ruler, and one centimeter cubes.

• Before measuring, look at the one inch tiles and record an estimate for the length and width of your desk in the table below.

• Use the tiles to find the actual measurement and record it in the table below. • Find the perimeter of your desk using the tiles (or a method of your choice) and record it

below. • Find the area of your desk using the tiles (or a method of your choice) and record it below. • Repeat steps 1 through 4 for the ruler and then for the centimeter cubes. Note: There are

probably not enough centimeter cubes to measure the area of the desks. What other method could be used?

My Desk

Length Width Estimate Actual Estimate Actual Perimeter Area

1 Inch Tiles

1 Foot Ruler

1 Centimeter

Cubes

1. Write to explain how you found the perimeter of your desk. What is a different way to find perimeter? __________________________________________________________________________

__________________________________________________________________________

__________________________________________________________________________






2. Write to explain how you found the area of your desk. What is a different way to find area? __________________________________________________________________________

__________________________________________________________________________

__________________________________________________________________________

3. What happened to the perimeter and area of the desk as different units of measure were used? __________________________________________________________________________

__________________________________________________________________________

__________________________________________________________________________

__________________________________________________________________________

__________________________________________________________________________

__________________________________________________________________________






PERFORMANCE TASK: Daily Schedule

STANDARDS ADDRESSED M3M1. Students will further develop their understanding of the concept of time by determining elapsed time of a full, half, and quarter-hour. M3P1. Students will solve problems (using appropriate technology).

















ESSENTIAL QUESTIONS

• How can we determine the amount of time that passes between two events?

• What part does elapsed time play in our daily living?

MATERIALS

• The Long Wait by Annie Cobb, or a similar

book about elapsed time • “Daily Schedule” student recording sheet • Clock (Classroom clock or individual clocks

for each student) GROUPING


In this task, students will record and draw time to the nearest minute and calculate elapsed time in 15, 30, and 60 minute intervals. Comments

Teachers may want to begin with a discussion of daily activities in students’ lives and the amount of time those activities typically take. For example, getting ready for school may begin at 7:06 AM and end at 7:36 AM, a 30 minute duration. Then engage students in a discussion of activities that typically happen during the school day and their estimates of the duration of these activities. One book that explores elapsed time, The Long Wait by Annie Cobb, discusses wait-time at an amusement park.






As the calculations are made, you may want to encourage students to explore a linear model of time as well as a traditional analog clock. The linear model can be created using an open number line. Jumps are made from the beginning time to the ending time much like movement on a number line and increments of time may be recorded above the jumps. An example is shown below:

To find the elapsed time from 2:16 pm to 4:31 pm, start with an open number line:

Add the starting time:

Then count up to the ending time using jumps that make sense to the students:

Background Knowledge

If telling time is built into daily routines, students should have had classroom experiences with telling time to the nearest minute. Daily routines can be extended to elapsed time by asking students the stopping time if they start work now and work for 15 minutes or 30 minutes. Additionally, students could be asked what time they will return to the classroom if they will be returning in one hour. Task Directions

Note: As students record daily events, be sure the elapsed time is in 15, 30, or 60 minute intervals. Alternatively, provide a daily schedule that is already filled in with start and stop times. Then have students calculate the elapsed time, or duration, of each activity and record it on the chart.

Students will follow the directions below from the “Daily Schedule” student recording sheet.

In the Daily Schedule chart below, record six of your class’ daily activities. Then calculate the elapsed time, or duration, of each activity and record it on the chart.

Choose three events. List the event and record the start time and end time for each event on the clock faces below.

Choose one of the events above and explain how you found the elapsed time.

Questions/Prompts for Formative Student Assessment • How did you determine your start and end times? • What kinds of activities can you typically complete in a quarter-hour, half-hour and hour? • How did you determine the elapsed time?

2:16






Questions for Teacher Reflection • Are students able to record beginning and ending times accurately? • Can students effectively and accurately explain how to determine elapsed time?


• Have students use a digital camera to create an interactive slide show, flipchart, or schedule chart for display of the daily school events.

• On a paper divided into fourths, have students list as many things as they can that last approximately 15 minutes/30 minutes/1 hour/more than 1 hour.

• Ask students to complete a similar chart for a typical weekend day. Intervention

• Provide beginning and ending times for activities that do not cross the hour mark. For example, show a beginning time of 11:15 and an ending time of 11:45 for a given activity. Be sure students understand the elapsed time of 30 minutes before moving to activities of a longer duration that begin and end in different hours.


• http://nlvm.usu.edu/en/nav/frames_asid_318_g_2_t_4.html Elapsed time problems using two clocks, both analog and digital

• http://www.shodor.org/interactivate/activities/ElapsedTime/?version=disabled&browser=MSIE&vendor=na&flash=10.0.32 Several activities surrounding elapsed time using analog or digital clocks.

• http://donnayoung.org/math/clock.htm Printable blank clock faces.

http://nlvm.usu.edu/en/nav/frames_asid_318_g_2_t_4.html�

http://www.shodor.org/interactivate/activities/ElapsedTime/?version=disabled&browser=MSIE&vendor=na&flash=10.0.32�

http://www.shodor.org/interactivate/activities/ElapsedTime/?version=disabled&browser=MSIE&vendor=na&flash=10.0.32�

http://donnayoung.org/math/clock.htm�






Name ________________________________________ Date ___________________________

Daily Schedule In the Daily Schedule chart below, record six of your class’ daily

activities. Then calculate the elapsed time, or duration, of each activity and record it on the chart.

Choose three events. List the event and record the start time and end time for each event on the clock faces below. 1. Event: ___________________________________________________________________ Start Time End Time

Daily Schedule

Event Start Time Stop Time Duration of Event






2. Event: ___________________________________________________________________ Start Time End Time

3. Event: ___________________________________________________________________ Start Time End Time

4. Choose one of the events above and explain how you found the elapsed time.






LEARNING TASK: Touring Georgia STANDARDS ADDRESSED M3M2. Students will measure length choosing appropriate units and tools.

a. Use the units kilometer (km) and mile (mi.) to discuss the measure of long distances.

b. Measure to the nearest ¼ inch, ½ inch and millimeter (mm) in addition to the previously learned inch, foot, yard, centimeter, and meter.

M3G1. Students will further develop their understanding of geometric figures by drawing them. They will also state and explain their properties.

d. Identify the center, diameter, and radius of a circle. M3P1. Students will solve problems (using appropriate technology).

















ESSENTIAL QUESTIONS

• Where are radius, center, and diameter located on a circle and how can they be used to show distance on a map?

MATERIALS

• Map of Georgia (with scale) • Index cards • Rulers • Compasses • Highlighters

GROUPING


In this task, students will use map scales and rulers to determine distances. Students also use a compass to draw a circle with a given radius. Comments

Teachers may want to begin this task by discussing maps and how and why they are used. Ask students to describe experiences in which they have needed directions or have drawn a map of their own.

Demonstrate to students how to create a “ruler” using the scale. By placing an index card below the scale, students can mark 50 mile intervals. Students can use this scale “ruler” to draw a100 mile radius, and later to find the distances to cities to which they would like to travel.

Be sure students draw the parts of the circle correctly and can define each part. Discuss the length of the diameter based on the knowledge that the radius is 100 miles. Also, students should be aware that points on the circle are exactly 100 miles from the center of the circle; the points inside the circle are less than 100 miles from the center of the circle, and the points outside the circle are more than 100 miles from the center of the circle. Ask students if any of the cities on the map are exactly 100 miles from the center of their circle (i.e. Are any cities on the circle?). Background Knowledge

Students should be able to use a map legend and scale to mark equal intervals and to determine distance. Also, students should know the following parts of a circle: center, diameter, and radius.






Task Directions Students will follow the directions below from the “Touring Georgia” student recording sheet.

1. Choose a city in Georgia and highlight it on the map. 2. Using the scale, determine how long 100 miles is on the map. Draw

a line segment that length north from the city you chose. 3. Use a compass to draw a circle using that line as the radius. Highlight

the circle. 4. Draw a diameter for the circle. Label the radius and the diameter. 5. On the chart below, list 6 cities that are more than 100 miles from your city and 6 cities

that are less than 100 miles from your city. 6. Choose 3 cities to which you would like to travel. Draw a line segment to each city from

your chosen city. Using a ruler and the scale, determine the approximate distance to each city.

7. Complete the chart by listing cities that are the given distance from your highlighted city.

8. List 3 Georgia cities you would like to visit and their approximate distance from your highlighted city.


• Why do we use a scale on a map? • How does a compass provide more accurate information of distance from a city than just a

ruler? • What would happen to the map if the scale were different?


• Are students able to accurately use a scale on a map? • Can students accurately compute distances using a scale and ruler? • Can students describe the radius and diameter of a circle?


On the task directions above, change step number 8 so that students are asked to connect the three cities they would like to visit in the order in which they would like to visit them on a trip. Start and finish at the center of their circle (their highlighted city). Determine the length of the trip on the given map or allow students to map the trip on a road map and determine the distance they would travel. Finally, students may use the road map to find an alternative route, one that avoids highways, one that would take more or less time, or one that would save on gasoline. Intervention

Provide students with a scale “ruler” with distances labeled or assist students in making one.







• http://www.worldatlas.com/webimage/countrys/namerica/usstates/printpage/galarge.htm A map of Georgia that can be easily printed. This is the map used on the student recording sheet.

• http://www.fhwa.dot.gov/hep10/nhs/maps/ga/ga_georgia.pdf A road map of Georgia that can be easily printed.

http://www.worldatlas.com/webimage/countrys/namerica/usstates/printpage/galarge.htm�

http://www.fhwa.dot.gov/hep10/nhs/maps/ga/ga_georgia.pdf�






Name ________________________________________ Date ___________________________

Touring Georgia

1. Choose a city in Georgia and highlight it on the map. 2. Using the scale, determine how long 100 miles is on the map. Draw a line

segment that length north from the city you chose. 3. Use a compass to draw a circle using that line as the radius. Highlight the circle. 4. Draw a diameter for the circle. Label the radius and the diameter. 5. On the chart below, list 6 cities that are more than 100 miles from your city and 6 cities that are

less than 100 miles from your city. 6. Choose 3 cities to which you would like to travel. Draw a line segment to each city from your

chosen city. Using a ruler and the scale, determine the approximate distance to each city. 7. Complete the chart by listing cities that are the given distance from your highlighted city.

8. List 3 Georgia cities you would like to visit and their approximate distance from your

highlighted city.






Name ________________________________________ Date ___________________________

Map of Georgia

http://www.worldatlas.com/webimage/countrys/namerica/usstates/printpage/galarge.htm

http://www.worldatlas.com/webimage/countrys/namerica/usstates/printpage/galarge.htm�






LEARNING TASK: Measuring Words STANDARDS ADDRESSED M3M4. Students will understand and measure the area of simple geometric figures (squares and rectangles).

a. Understand the meaning of the square unit and measurement in area.



figure. M3M2. Students will measure length choosing appropriate units and tools.

d. Use the units kilometer (km) and mile (mi.) to discuss the measure of long distances. M3P1. Students will solve problems (using appropriate technology).

e. Build new mathematical knowledge through problem solving. f. Solve problems that arise in mathematics and in other contexts. g. Apply and adapt a variety of appropriate strategies to solve problems. h. Monitor and reflect on the process of mathematical problem solving.















ESSENTIAL QUESTIONS

• How can we communicate our thinking about mathematical vocabulary? MATERIALS

• Chart paper • Vocabulary list

GROUPING

Small Group/Partner Task TASK DESCRIPTION, DEVELOPMENT AND DISCUSSION

In this task, students will use thinking skills to build upon prior knowledge of measurement vocabulary. Students will use classification skills to compare/contrast the terms.

Comments

Classification and compare/contrast activities are powerful tools to promote critical thinking about the contents and attributes of each classified group. You may want to find opportunities for students to explain what attributes are not present with a given term. These non-examples help solidify meaning and understanding. Background Knowledge

Students should have a basic understanding of common measurement terms and their connections. Task Directions

Have students brainstorm a list of words they know related to measurement. Record the words on chart paper. If necessary, use the key vocabulary list at the beginning of the unit to add to the student-generated list. In pairs or small groups, have students decide on a way to classify the words by their attributes. Then have individual students create a Venn diagram using as many words as possible. Questions/Prompts for Formative Student Assessment

• How and when have you used these types of measurement? • What guidelines did you use in your classification? • Can you explain why you did not put some of these terms in a specific group?






Questions for Teacher Reflection • Are students able to accurately explain their classification guidelines? • Do students understand a Venn diagram?


• Have students sort the vocabulary words with different categories. • Do the same activity with geometry terms. • Incorporate this task into a lesson to work on class consensus.

Intervention

• Provide the words and/or classification labels on index cards to manipulate into groups. • Provide math dictionaries or picture definitions of the words to assist in the understanding of

each term. TECHNOLOGY CONNECTION

Please Note: As with any resource, definitions will vary. Please refer to the “Selected Terms and Symbols” section of the frameworks for the definitions for the Georgia Performance Standards.

• http://www.teachers.ash.org.au/jeather/maths/dictionary.html A first dictionary for

elementary students. • http://intermath.coe.uga.edu/dictnary/homepg.asp A great resource for teachers, geared

towards middle and high school, 3-5 students can be directed to specific information and activities.

• http://mathworld.wolfram.com/ For teacher reference

http://www.teachers.ash.org.au/jeather/maths/dictionary.html�

http://intermath.coe.uga.edu/dictnary/homepg.asp�

http://mathworld.wolfram.com/�






Unit 3 Culminating Task

PERFORMANCE TASK: Home Sweet Home STANDARDS ADDRESSED M3G1. Students will further develop their understanding of geometric figures by drawing them. They will also state and explain their properties.


b. Identify and compare the properties of fundamental geometric figures. c. Examine and compare angles of fundamental geometric figures. d. Identify the center, diameter, and radius of a circle.

M3M1. Students will further develop their understanding of the concept of time by determining elapsed time of a full, half, and quarter-hour. M3M2. Students will measure length choosing appropriate units and tools.

a. Use the units kilometer (km) and mile (mi.) to discuss the measure of long distances. b. Measure to the nearest ¼ inch, ½ inch and millimeter (mm) in addition to the previously

learned inch, foot, yard, centimeter, and meter. c. Estimate length and represent it using appropriate units. d. Compare one unit to another within a single system of measurement.







models. M3P1. Students will solve problems (using appropriate technology).







M3P2. Students will reason and evaluate mathematical arguments. a. Recognize reasoning and proof as fundamental aspects of mathematics. b. Make and investigate mathematical conjectures. c. Develop and evaluate mathematical arguments and proofs. d. Select and use various types of reasoning and methods of proof.









ESSENTIAL QUESTIONS

How can I demonstrate my understanding of the attributes of two-dimensional figures and the measurement of length, perimeter, area, and time?

MATERIALS

• Construction paper • Rulers, compasses, and/or pattern block

templates GROUPING

Individual Task






TASK DESCRIPTION, DEVELOPMENT AND DISCUSSION

In this task, students will complete a summative assessment that includes multiple standards addressed in the previous tasks. Comments

This culminating task may be introduced with a discussion of homes and floor plans. If possible, bring in an example of a floor plan, either from a magazine or an actual architect’s drawing.

When students are working on this task, create in-school work time of 15 minute intervals, so that students will be able to determine each segment of time spent working as 15, 30, 45 minutes, or 1 hour (or more).

Assist students who have a curved part of their perimeter by laying string on the curved part and cut to size. Then straighten out the string and measure it with a ruler. Alternatively, students can place one inch tiles along the curved side to approximate the length.

Student work will be unique, representing the personality of the artist-mathematician. When this work is assessed, you will want to be sure students followed all directions, including in the written portion. You may want to encourage the class to develop a rubric related to this culminating task and be sure all students understand the rubric before work begins. When creating a rubric for this task, think about how students can demonstrate understanding of the standards and elements of this unit. Ask yourself, your grade-level peers, and/or your students how this understanding could be demonstrated. Background Knowledge

The work students have done on the tasks in this unit should serve as preparation for this culminating task. Students have had opportunities to classify, draw, identify, and understand geometric figures and to measure length, perimeter, area, and time. Task Directions

Students will follow the directions below from the “Home Sweet Home” student recording sheet.

You have the opportunity to create a floor plan for a fantasy home! Follow these directions:

1. The floor plan must be built using two-dimensional figures. Use at least 6 different two-dimensional figures. Be sure to use as many of the shapes that we have studied as you can.

2. Either trace the shapes or use a ruler/compass to draw them on construction paper. Then cut out the shapes.

3. Label each shape with its name and attributes. 4. For two of the polygons, you must record the length of each side of the shape to

the nearest quarter inch. 5. Determine the perimeter of the floor plan and use square tiles to determine an

approximate area.






6. Keep a record of the amount of time you spend creating your floor plan in the chart below. Be sure to make an entry in your chart each time you work on your floor plan.

Work

Session Start Time End Time Elapsed Time

#1

#2

#3

#4

#5

7. Write a paragraph to tell about your floor plan. Include data that tells how long

you spent on the design. Questions/Prompts for Formative Student Assessment

• How are you selecting shapes that will work together to complete your plan? • What is your strategy for calculating the perimeter of your five shapes? • What is your strategy for calculating the perimeter of your home? • How can you estimate total area if the square tiles don’t fit exactly?


• Are students able to accurately label the shapes they’ve used? • Can students accurately measure the perimeter of the shapes as directed? • Do students understand the relationship between area and perimeter? • Can students effectively communicate their ideas in writing?


Have students build a floor plan that meets the following restrictions: Use twice as many rectangles as triangles. Use half as many hexagons as pentagons and three times as many rhombuses as

hexagons. Half of the triangles should be equilateral triangles. There should be 21 shapes in the floor plan.






Intervention Allow students to use pre-cut shapes. Encourage students to measure and label each shape

before arranging it in the floor plan. TECHNOLOGY CONNECTION

http://www.houseplans.com/ This is one of many websites that show house plans. Viewing plans before creating their own allows students to visualize what is required in their work.

http://www.houseplans.com/�






Name ____________________________________________ Date _______________________

Home Sweet Home

You have the opportunity to create a floor plan for a fantasy home! Follow these directions:

1. The floor plan must be built using two-dimensional figures. Use at least 6 different two-dimensional figures. Be sure to use as many of the shapes that we have studied as you can.

2. Either trace the shapes or use a ruler/compass to draw them on construction paper. Then cut out the shapes.

3. Label each shape with its name and attributes. 4. For two of the polygons, you must record the length of each side of the shape to the

nearest quarter inch. 5. Determine the perimeter of the floor plan and use square tiles to determine an

approximate area. 6. Keep a record of the amount of time you spend creating your floor plan in the chart

below. Be sure to make an entry in your chart each time you work on your floor plan.

Work

Session Start Time End Time Elapsed Time

#1

#2

#3

#4

#5

7. Write a paragraph to tell about your floor plan. Include data that tells how long you

spent on the design. (Continue on the back if necessary.) __________________________________________________________________________

__________________________________________________________________________

__________________________________________________________________________

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Documents

M3G1 Students will further develop their understanding …southsidethird.pbworks.com/f/3rd+Grade_Unit3.pdf · also state and explain their properties ... elapsed time, unit Harcourt