california edition grade 1

Harcourt Math – GRADE 1 MODULE 13

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Institute for Learning, Department of Mathematics

Instructional Module to Enhance the Teaching of

H A R C O U R T

Math

California Edition

Grade 1

Module 13

Geometry

-WORK IN PROGRESS –

S

D

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S SAN DIEGO CITY SCHOOLS


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Grade One – Traditional Calendar – 2004-2005 Order of Units and Pacing Guide

Month Module Number of Days

September 19 instructional days

Module 1: Addition and Subtraction Concepts 19 days

October

21 instructional days Module 1: Addition an Subtraction Concepts Module 2: Addition and Subtraction Facts to

10

7days

14 days

November 18 instructional days

Module 2: Addition and Subtraction Facts to 10

Module 3: Numbers to 100

11 days

7 days

December 13 instructional days

Winter Break 12/20 – 12/31


12 days

January 20 instructional days

Module 4: Addition and Subtraction to 12 Module 5: Data and Graphing

15 days

5 days

February 17 instructional days

Module 6: Money Module 7: Time

11 days

6 days

March 18 instructional days Spring Break 3/21 – 3/25

Module 7: Time Module 8: Patterns Module 9: Addition and Subtraction to 20

5 days

4 days

9 days

April 20 instructional days

Module 9: Addition and Subtraction to 20 Module 10: Measurement

11 days

9 days

May 21 instructional days

Module 10: Measurement Module 11: Fractions Module 12: Addition and Subtraction 2-Digit

Numbers

1 day

5 days

15 days

June 13 instructional days

Module 13: Geometry

10 days


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Grade One – Year Round Calendar – 2004-2005 Order of Units and Pacing Guide

Month Module Number of Days

September 19 instructional days

Module 1: Addition and Subtraction Concepts

19 days

October

21 instructional days Module 1: Addition an Subtraction

Concepts Module 2: Addition and Subtraction Facts

to 10

7days

14 days

November 18 instructional days

Module 2: Addition and Subtraction Facts to 10


11 days

7 days

December 13 instructional days

Winter Break 12/20 – 12/31


12 days

January 10 instructional days

Module 4: Addition and Subtraction to 12

10 days

February 17 instructional days

Module 4: Addition and Subtraction to 12 Module 5: Data and Graphing Module 6: Money

5 days

4 days

8 days

March 11 instructional days Spring Break 3/16 – 4/8

Module 6: Money Module 7: Time

3 days

8 days

April 15 instructional days

Module 7: Time Module 8: Patterns Module 9: Addition and Subtraction to 20

3 days

4 days

8 days

May 21 instructional days

Module 9: Addition and Subtraction to 20 Module 10: Measurement

12 days

9 days

June 22 instructional days

Module 10: Measurement Module 11: Fractions Module 12: Addition and Subtraction 2-

Digit Numbers

1 day

5 days

15 days

July 14 instructional days

Module 13: Geometry 10 days

San Diego City Schools

Instruction and Curriculum Division MATHEMATICS CURRICULUM MAP – GRADE 1

MODULE 13 –GEOMETRY

Modules represent individual units of study that lead to essential learnings

THREADS THROUGHOUT THE YEAR- FIRST GRADE This represents what students should do throughout all modules (units of study). These items should not be isolated to a particular unit of study. Students will:

Develop understanding of numbers and the number system and use their understanding to solve problems and recognize reasonable results. Use mathematical reasoning to solve problems. Develop understanding of and fluency in basic computation and procedural skills. Use equations and to express generalizations of patterns and relationships. Communicate their mathematical thinking by using words, numbers, symbols, graphs and charts., and describe different representations Express generalizations of patterns and relationships. Make connections among mathematical ideas and between other disciplines. Develop and use strategies, skills, and concepts to solve problems. Use appropriate tools, as vehicles to learn mathematical concepts.

Essential learnings that represent bigger ideas/concepts •Students identify, describe and classify familiar plane and solid geometric shapes (e.g. circle, triangle, square, rectangle, sphere, pyramid, cube, rectangular prism) by common attributes, such as color, position, shape, size, roundness, or number of corners and explain which attributes are being used to classify. •Students match solid figures to real-life objects. •Students give and follow directions about locations (e.g., put the picture of the ball above the picture of the house). •Students arrange and describe objects in space by proximity, position and direction (e.g., near, far, above, below, up, down, behind, in front of , next to, left or right of).

Essential questions that will lead to the essential learnings: How can I identify and describe solid figures by describing their attributes? In what ways can I match solid geometric figures to real-life objects? How can I sort and classify solid figures by common attributes? How can I give and follow directions to locate objects and describe their positions? Resources: Van de Walle, Chapter 20, pp.,345–350, 352


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Harcourt Math – Grade 1

Module 13: Geometry

10 Days

Key Mathematical Concepts: • Identify, compare, sort, and classify solid figures by their properties such

as number of surfaces, edges, and corners; and relate them to real-life objects

• Identify and sort plane shapes by their properties such as size and number of sides and corners, and relate them to real-life objects

• Identify symmetrical shapes and their lines of symmetry • Identify and use terms of orientation • Solve problems by using an appropriate strategy

Chapter 20: Solid Figures and Plane Shapes DAY 1 20.1 Solid Figures 2 20.2 Sort Solid Figures 3 20.3 Flat Surfaces on Solids 4 20.4 Plane Shapes on Solid Figures 5 20.5 Sort and Identify Shapes

Chapter 21: Spatial Sense DAY 6 21.1 Same Size and Shape 7 21.2 Symmetry 8 21.3 Give and Follow Directions 9 21.4 Locate Objects

10 21.5 Problem Solving: Draw a Picture

Note: When exploring solid figures and plane shapes with students, it is always best to use real objects rather than pictures. Ideally, each classroom would have sets of geometric solids and this is not the reality in many classrooms. Therefore, the following ordinary shapes might prove helpful when teaching this unit: Cylinders Tin cans Pringles potato chip cans

Spheres Tennis balls Rubber balls

Cubes Dice Wood blocks

Rectangular prisms Cereal boxes Tissue boxes

Cone Birthday party hats

Pyramid


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Harcourt Math: Grade 1

Module 13: Geometry

10 Days

Day 1 Lesson 20.1

Day 2 Lesson 20.2

Day 3 Lesson 20.3

Day 4 Lesson 20.4

Day 5 Lesson 20.5

Day 6 Lesson 21.1

Day 7 Lesson 21.2

Day 8 Lesson 21.3

Day 9 Lesson 21.4

Day 10 Lesson 21.5


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MODULE 13: Geometry Chapter 20: Solid Figures and Plane Shapes

DAY 1: LESSON 20.1 TE p.287A

LESSON FOCUS: Solid Figures CALIFORNIA STANDARD:

Measurement and Geometry 2.2 Classify familiar plane and solid objects by common attributes, such as color, position, shape, size, roundness, or number of corners, and explain which attributes are being used for classification.

Purpose of Lesson: To identify spheres, cones, cubes, cylinders, rectangular prisms, and pyramids and to relate them to everyday objects; to use spatial sense to identify solids from different views

ROUTINE TE p. 285 For the teacher: chart paper. For each student: pencil, marker, crayon box.

Suggestion: Introducing the Chapter: TE p. 285 Or Problem of the Day: • What shape will you draw if you trace the end of a marker?

(Circle) Take out a marker and try it. • Now look at the end of the marker. Do you see the shape

you drew? Show me. • Can you find a circle somewhere else on your marker? (The

other end) • When you have a shape that has the same-sized circle at

each end, that shape is called a cylinder. Draw a picture of a cylinder on the board or chart paper and label it “cylinder.”

• Can you think of another object that is a cylinder?” (soda can, trash can, crayon)

• What shape will you draw if you trace the bottom of your

crayon box? (rectangle) First take a guess. Why do you think so? Try it. What shape did you draw? Show me where it is on the box. Can you find a rectangle anywhere else on this shape? (Every side has a rectangle)

• When you have a shape with 6 sides and each side is a rectangle, that shape is called a rectangular prism. Draw it on the chart and label it “rectangular prism.” Can you think of any other objects that are rectangular prisms? (box of tissue, suitcase, pencil, box)

• Imagine you are holding an ice cream cone. You’ve eaten

all the ice cream and only the cone is left. If you looked down at your empty cone, what shape would you see? (circle)

• What other shape has a circle on the end? (cylinder) How is a cone different from a cylinder? (a cylinder has the same-sized circles at both ends, a cone has a circle at one end and a point at the other) The point or tip of a cone is called the apex. Draw a cone on the chart and label it.


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LAUNCH TE and Workbook p.287

Introduce Activity: Workbook p.287 • Ask students to find the three 3-dimensional shapes you

talked about during routines. (cylinder, rectangular prism, and cone)

• Ask students to circle them at the top of the page. Review attributes of each.

• Ask students to find the objects on the page that represent these three shapes and color them accordingly.

• As students finish, ask, What objects are left? (spheres, pyramids, and cubes)

• Have a discussion about the attributes of these shapes and add them to your chart.

• Ask students to finish coloring. EXPLORE Students work independently identifying objects as 3-D shapes PRACTICE 6 pieces of blank paper with a shape and its name on the top

Shape Race: • Divide students into 6 groups. Give each group a blank

piece of paper with one of the 3-D shapes and its name on top.

• Ask each group to find as many things in the classroom as they can that have the same attributes as their shape.

• Ask students to either write down the name of the object or draw a picture of it.

• After a set period of time (3-4 minutes), ask students to stop and share their work.

• Students check other groups’ work by referring to the chart and the attributes of each shape.

SUMMARIZE Revisit with students the lesson’s objective by connecting the following discussion to the purpose of the lesson. Discuss: Place one example of each shape at the front of the room. • Ask students to look for similarities and differences between

the shapes and describe them. For example: Both a cube and a rectangular prism have 6 sides, but a cubes sides are all square and the rectangular prism has rectangle sides.

Homework Suggestion: Family Involvement Activities p. FA89


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LESSON FOCUS: Sort Solid Figures CALIFORNIA STANDARD:


Purpose of Lesson: To sort and classify solid figures by properties (stacking, sliding, rolling)

ROUTINE TE p.289 TE p.290 TE p.289A, sphere, cone, cube, cylinder, rectangular prism, pyramid, name card of each shape

Suggestion: Quick Review: TE p. 289 Or Mixed Review and Test Prep: TE p. 290 Or Shape Race: (see “Practice” Day 1) Change groups Or Stacking, Rolling, and Sliding: TE p. 289A

LAUNCH TE and Workbook p.289

Introduce Activity: Workbook p. 289

EXPLORE Students work together as a class discussing properties of shapes and completing workbook p. 289.

PRACTICE For each student: blank piece of paper

• Ask students to choose two different 3-D shapes that share a common attribute. For example, a cone and a pyramid both have a square bottom (base). A sphere and a cone both roll.

• Ask students to fold a piece of blank paper lengthwise in half. Write the names of their 2 shapes at the top of each column and write down the names of as many objects they can think of that are the shape.

SUMMARIZE Revisit with students the lesson’s objective by connecting the following discussion to the purpose of the lesson. Discuss: How are the two shapes you choose alike? How are they different?



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MODULE 13: Geometry

Chapter 20: Solid Figures and Plane Shapes


LESSON FOCUS: Flat Surfaces on Solids CALIFORNIA STANDARD:


Purpose of Lesson: To sort and classify solid figures by the number of flat surfaces ROUTINE TE p. 291 TE p.292

Suggestion: Quick Review: TE p. 291 Or Mixed Review and Test Prep: TE p. 292 Or Shape Race:(see “Practice” Day 1) Change groups Or Stacking, Rolling, and Sliding: TE p. 289A

LAUNCH TE p. 291A For each group, a cube, sphere, cone For each student, Workbook pp. 291-292

Introduce Activity: Count the Flat Surfaces, TE p. 291A, and Workbook pp. 291-292

EXPLORE Students work in groups exploring and discussing the surfaces of 3-D shapes, then complete workbook pages.

PRACTICE

• As time allows, Ask students to create a riddle like the one in “Problem Solving – Reasoning” on Workbook p. 292.

• Trade riddles with a partner to solve. SUMMARIZE Revisit with students the lesson’s objective by connecting the

following discussion to the purpose of the lesson. Discuss and Write: TE p. 292

Homework Suggestion: Reteach 20.3 or Challenge 20.3 (see bottom margin TE p. 291)


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MODULE 13: Geometry

Chapter 20: Solid Figures and Plane Shapes


LESSON FOCUS: Plane Shapes on Solid Figures CALIFORNIA STANDARD:

Measurement and Geometry 2.1 Identify, describe and compare triangles, rectangles, squares, and circles, including the faces of three-dimensional objects.

Purpose of Lesson: To identify plane figures as flat surfaces of solid figures ROUTINE TE p. 293A TE p. 293 TE p. 294

Suggestion: Problem of the Day: TE p. 293A Or Quick Review: TE p. 293 Or Mixed Review and Test Prep: TE p.294 Continue to keep the Number Line and Hundred Chart visible to students to use as a tool for solving problems. Continue questioning each day: • How did you think about the problem to come up with that

answer? • Did anyone think about it another way? • Do you agree or disagree with this response? • What was your strategy? • Explain how you got your answer.

LAUNCH TE p. 293A For the class, cube, rectangular prism, cylinder, cone, pyramid, sphere, paper, pencil

Introduce Activity: From Flat Surfaces to Planes • Explain that “planes” are flat shapes (circle, triangle, square,

rectangle, diamond, etc.) When you trace a “flat surface,” you draw a plane shape on your paper.

• Challenge groups to draw all of the plane shapes from the flat surfaces of their 3-D shape.

EXPLORE Students work in small groups tracing 3-D shapes and discussing the flat surfaces or planes on each.

PRACTICE TE and Workbook pp. 293-294

As time allows, TE and Workbook pp.293-294

SUMMARIZE Blank paper with one drawing each of circle, triangle, square, rectangle

Revisit with students the lesson’s objective by connecting the following discussion to the purpose of the lesson. Discuss: • Tell students that you traced some 3-D shapes before class

but forgot to record which shape you were tracing. • Ask them to help you first identify the plane shapes you drew

then determine which 3-D shape you might have traced. Homework Suggestion: Family Involvement Activities p. FA91


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LESSON FOCUS: Sort and Identify Shapes CALIFORNIA STANDARD:


Purpose of Lesson: To sort and identify plane shapes by the number of sides and corners

ROUTINE TE p. 395A For each pair, geoboard and rubber bands TE p. 295 TE p. 296

Suggestion: Problem of the Day: TE p. 295 A Or Quick Review: TE p. 295 Or Mixed Review and Test Prep: TE p. 296 Continue to keep the Number Line and Hundred Chart visible to students to use as a tool for solving problems. Continue questioning each day: • How did you think about the problem to come up with that


LAUNCH TE p. 295A For each child, attribute links, paper, pencil

Introduce Activity: Finding Corners and Sides TE p. 295A • Ask students to draw and label the corners and sides for

each attribute link. • Instruct students to name each plane shape they draw.

EXPLORE Students work independently drawing and labeling corners and sides of attribute link shapes.



SUMMARIZE Cube, rectangular prism, sphere, cylinder, pyramid, cone

Revisit with students the lesson’s objective by connecting the following discussion to the purpose of the lesson. Discuss: Display each of the 3-D shapes one at a time. Ask: • What is the name of this shape? • How do you know? (Look for children to answer with a

specific attribute such as, ‘It is a cylinder because it has two flat surfaces that are circles.’)

• Where are the flat surfaces? • What are the plane shapes of the flat surfaces?


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• Where are the sides of the plane shape, the corners? Homework Suggestion: Family Involvement Activities p. FA92


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MODULE 13: Geometry Chapter 21: Spatial Sense


LESSON FOCUS: Same Size and Shape CALIFORNIA STANDARD:


Purpose of Lesson: To identify and construct congruent shapes ROUTINE TE p. 299 TE p.301A TE p. 301A TE p.302

Suggestion: Introducing the Chapter: TE p. 299 Or Problem of the Day: TE p.301A Or Vocabulary Development: TE p.301A Or Mixed Review and Test Prep: TE p.302 Continue to keep the Number Line and Hundred Chart visible to students to use as a tool for solving problems. Continue questioning each day: • How did you think about the problem to come up with that


LAUNCH TE p. 301A For each group, attribute links

Introduce Activity: Congruent Attribute Links TE p. 301A

EXPLORE Students work in pairs identifying congruent shapes by sorting attribute links.

PRACTICE TE and Workbook pp. 301-302 Geoboards, if available

As time allows, TE and Workbook pp.301-302 If available, ask students to recreate shapes on the workbook pages using geoboards and rubber bands.

SUMMARIZE TE p.302, Dot paper (p. TR84)

Revisit with students the lesson’s objective by connecting the following discussion to the purpose of the lesson. Discuss and Write: TE p. 302 (Assess)



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LESSON FOCUS: Symmetry CALIFORNIA STANDARD:


Purpose of Lesson: To make symmetrical shapes and identify lines of symmetry ROUTINE TE p.303A TE p.303 TE p.302A For partners, pattern blocks

Suggestion: Daily Routine: TE p. 303A Or Quick Review: TE p.303 Or Advanced Learners TE p.302A Or Mixed Review and Test Prep: TE p.304 Continue to keep the Number Line and Hundred Chart visible to students to use as a tool for solving problems. Continue questioning each day: • How did you think about the problem to come up with that


LAUNCH TE p. 303 For each student, workbook p.303, construction paper, scissors, marker For partners, pattern blocks, marker

Introduce Activity: Creating a Symmetrical Shape Workbook pp.303 and Early Finishers TE p. 304A

EXPLORE Students work independently creating a symmetrical shape, then with a partner building symmetrical shapes with pattern blocks.



SUMMARIZE Revisit with students the lesson’s objective by connecting the following discussion to the purpose of the lesson. Discuss: Show me some of the symmetrical shapes you created with pattern blocks. • Where is the line of symmetry? • How do you know it is symmetrical? • Can you prove it?



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LESSON FOCUS: Give and Follow Directions CALIFORNIA STANDARD:

Measurement and Geometry 2.3 Give and Follow directions about location.

Purpose of Lesson: To use position words left, right, up, and down to give and follow directions

ROUTINE TE p. 305A TE p.305 TE p.306 TE p. 306A For each child a ball or beanbag

Suggestion: Problem of the Day: TE p. 305A Or Quick Review: TE p.305 Or Mixed Review and Test Prep: TE p.304 Continue to keep the Number Line and Hundred Chart visible to students to use as a tool for solving problems. Continue questioning each day: • How did you think about the problem to come up with that

answer? • Did anyone think about it another way? • Do you agree or disagree with this response? • What was your strategy? • Explain how you got your answer. Or Alternative Teaching Strategy: TE p.306A

LAUNCH TE and Workbook p.305 For small groups, butcher paper, markers

Introduce Activity: TE and Workbook p. 305 And Treasure Maps Divide class into 4 groups. Give each group a beanbag (or any such small object) to hide in the room. The group is to work together to create a map starting at the classroom door and ending at the hiding spot. Discuss the meaning of “paces” when giving directions. Ask students to create maps similar to the ones in their workbooks and include how many paces to walk in each direction. When finished, groups trade papers and search for treasure.

EXPLORE Students work as a whole group completing exercises on Workbook p. 305 and with small groups making and using maps.

PRACTICE TE and Workbook p. 306

As time allows, Workbook p. 306

SUMMARIZE Create an overhead transparency map

Revisit with students the lesson’s objective by connecting the following discussion to the purpose of the lesson. Discuss: • Tell students there is one more treasure hidden in the room


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(see directions under “Discuss”)

and you have made a map to help them find it. • Place an overhead transparency of your map on the board.

(Your map should be complicated, going forward and backward, retracing steps, etc.)

• When children finally get to the treasure hiding spot, ask them to compare the different maps they used today.

• “Which map helped you to find the treasure quickly and easily?

• Which map was hard to follow? Why? • When might you need a map in your life?”



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LESSON FOCUS: Locate Objects CALIFORNIA STANDARD:

Measurement and Geometry 2.4 Arrange and describe objects in space by proximity, position, and direction.

Purpose of Lesson: To use the terms above, below, behind, and in front of to locate objects and describe their positions

ROUTINE TE p. 307A TE p. 307 TE p.308

Suggestion: Problem of the Day: TE p. 307A Or Quick Review: TE p.307 Or Mixed Review and Test Prep: TE p.308 Continue to keep the Number Line and Hundred Chart visible to students to use as a tool for solving problems. Continue questioning each day: • How did you think about the problem to come up with that


LAUNCH TE p. 307A For each group, old magazines and newspapers, scissors, glue, construction paper TE p. 308A For each group, building blocks or diorama materials (shoe box, clay for making figures, paper, crayons, scissors, glue)

Introduce Activity: Choose one of the following Model Using Position Terms TE p.307A Or Art Connection TE p. 308A

EXPLORE Students work in small groups creating and describing artwork using position terms.



SUMMARIZE Revisit with students the lesson’s objective by connecting the following discussion to the purpose of the lesson. Discuss: Ask students to use position terms to describe certain items in their artwork.



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LESSON FOCUS: Problem Solving: Draw a Picture CALIFORNIA STANDARD:

Measurement and Geometry 2.4 Arrange and describe objects in space by proximity, position, and direction.

Purpose of Lesson: To use position terms to describe location and solve problems ROUTINE TE p. 309A TE p.309A

Suggestion: Calendar TE p. 309A Or Problem of the Day: TE p. 309A Continue to keep the Number Line and Hundred Chart visible to students to use as a tool for solving problems. Continue questioning each day: • How did you think about the problem to come up with that


LAUNCH Manipulatives

Introduce Activities: Problem Solving “My family went to see “The Lizzy MacGuire Movie.” The theatre was very crowded. My Mom sat on my left. My 2 brothers sat on my right. My dad sat in the row below us with my 3 cousins. How many people from my family went to see the movie?” • Ask students to solve the problem in a way that makes

sense to them. • Make manipulatives available. • Ask students to share their methods for solving the problem,

first with a partner, then with the whole class. • Record what they did on a class chart. • Discuss how to represent the problem in an equation. • Record the equation horizontally. Next, ask students to write their own story problems. They must use two of the four direction words, left right, above or below.

EXPLORE Students work independently or with a partner solving and writing story problems.



SUMMARIZE Revisit with students the lesson’s objective by connecting the following discussion to the purpose of the lesson.


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Discuss: • Students give their stories to a partner to solve. • Ask students to share the problems they worked on and their

strategies for solving them. Homework Suggestion: Take home the story problem that you wrote.

Show someone at home. Ask them to write a similar problem for you to solve. Remember to ask them to include at least two of the direction words, right, left, above, or below.


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MODULE 13: Geometry

Chapters 20 and 21

Assessment

Assessment options to choose from:

In small groups, display each of the 3-D shapes one at a time. Ask:

• What is the name of this shape? • How do you know? (Look for children to answer with a

specific attribute such as, ‘It is a cylinder because it has two flat surfaces that are circles.’)

• Where are the flat surfaces? • What are the plane shapes of the flat surfaces? • Where are the sides of the plane shape, the corners?

(See “Summarize” Day 5)

• Ask students to sort attribute links into congruent links (same size, same shape). (See Day 6)

• Ask students to use pattern blocks to create symmetrical shapes. (See Day 7)

• In small groups, ask students to describe objects in their artwork using position terms. (See Day 9)

• Create and Solve a Story Problem using position terms. (See Day 10)

california edition grade 1

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