hands on • find shapes in shapes · hands on • find shapes in shapes lesson 12.6 701a chapter...

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LESSON AT A GLANCE

Hands On • Find Shapes in Shapes

LESSON 12.6

701A Chapter 12

Using Pattern BlocksThe interrelationships of the shapes in pattern blocks allow children to explore both composing and decomposing of shapes. In this lesson, children build their visualization skills as they work with composite shapes to find the shapes that compose them. To do this, children must identify which shapes were put together to create the composite shape.

Pattern blocks are excellent tools children can use as they analyze composite shapes. Children can place a pattern block directly on a composite shape and turn it, flip it, or slide it to fit part of the composite shape. At first, children may try to fit each pattern block to the composite shape. Then, as they become familiar with the relationships among pattern blocks and learn to identify shapes in composite shapes, children can choose specific pattern blocks and orient the blocks on the page to confirm their answers.

Learning ObjectiveDecompose combined shapes into shapes.

Language ObjectiveChildren write in their Math Journals how they can find shapes in other shapes.

MaterialsMathBoard, pattern blocks

F C R Focus:Common Core State Standards

1.G.A.2 Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.

MATHEMATICAL PRACTICES (See Mathematical Practices in GO Math! in the Planning Guide for full text.)MP4 Model with mathematics. MP5 Use appropriate tools strategically.

F C R Coherence:Standards Across the GradesBeforeK.G.B.6

Grade 11.G.A.2

After2.G.A.1

F C R Rigor:Level 1: Understand Concepts....................Share and Show ( Checked Items)Level 2: Procedural Skills and Fluency.......On Your Own, Practice and HomeworkLevel 3: Applications..................................Think Smarter and Go Deeper

FOCUS COHERENCE RIGOR

F C R For more about how GO Math! fosters Coherence within the Content Standards and Mathematical Progressions for this chapter, see page 667J.

ENGAGE1Daily Routines

Common Core

1 23 4 Pages 50–51 in Strategies and Practice for Skills and Facts Fluency provide additional fluency support for this lesson.

Lesson 12.6 701B

How can you f ind shapes in other

shapes?

Problem of the Day 12.6Basic Facts Add or subtract. Circle the fact that is not related. 8 + 5

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5 + 8

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13 − 8

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To build fluency, have children name the related fact that is not shown.

VocabularyInteractive Student EditionMultimedia Glossary e

with the Interactive Student Edition

Essential QuestionHow can you find shapes in other shapes?

Making ConnectionsHave children tell what they know about shapes they see in other shapes.

Point to something in the classroom, such as a window or a desk with drawers. Have children talk about shapes they see in each object.

Learning ActivityWhat is the problem the children are trying to solve? Connect the story to the problem. Ask the following questions.

• If you look at a box, what shape might you see? Possible answers: rectangle, square

• If you look at a can, what shape might you see? Possible answer: circle

Literacy and MathematicsChoose one or more of the following activities.

• Have children make a list of shapes they see in various objects in the classroom.

• Have children combine 2 or 3 pattern blocks and trace the outline of the new shape. Have partners exchange tracings and tell what shapes were used.

1 23 4 Fluency BuilderNumber RiddlesProvide children with clues about a number. Then have children guess the number. For example:

• I am thinking of a number. If you add 6 to this number you will get 14. What is the number? 8

Have children make up their own riddles to share with the class. Encourage children to write them down and solve them before sharing.

Common Core Fluency Standard 1.OA.C.6

Listen and DrawListen and Draw

MATHEMATICAL PRACTICES 5MathTalk

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Find Shapes in Shapes Essential Question How can you find shapes in other shapes?

Chapter 12 seven hundred one 701

Use pattern blocks. What shape can you make with 1 and 2 ?Draw to show your shape.

HandsOn

Lesson 12.6HANDS ON

Geometry—1.G.A.2

MATHEMATICAL PRACTICESMP4, MP5

Use Tools Can you use the same pattern blocks to make a different shape?

FOR THE TEACHER • Have children explore making new shapes with the given pattern blocks. Discuss different shapes that can be made using the same pattern blocks.

Math Talk: Possible answer: Yes, I could move one triangle to a different place. That will make a different shape.

Possible answer:

EXPLORE2

1

2

3

Name

Find Shapes in Shapes

Which two pattern blocks make this shape?

Use two pattern blocks to make the shape. Circle the blocks you use.

1. 2.

3. 4.

Lesson 12.6Reteach

12-15 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company

Name Lesson 12.6Enrich

Writing and Reasoning On a separate sheet of paper, draw a different shape using 3 of the shapes above.

1. 2.

3. 4.

Build a ShapePut three pattern blocks togetherto make each shape.Draw to show your model.

Possible answers are shown.

Check children’s work.12-16 EnrichChapter Resources

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3 DifferentiatedInstruction

701 Chapter 12

LESSON 12.61.G.A.2 Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.

Listen and DrawMaterials pattern blocks Present the following problem to the class.

Make a new shape with 1 hexagon and 2 triangles. What does your shape look like?

Have children arrange the three pattern blocks to make a new shape, and then trace the blocks on the page. If necessary, show children how to hold the pattern blocks so they can be traced. Have volunteers share their drawings and compare solutions. • Did everyone make the same shape?

Explain. Possible answer: No. Some shapes look different because the blocks are arranged in different ways.

• Does everyone’s shape have the same number of vertices and sides? Explain. Possible answer: No. Some shapes have more vertices and more sides. The numbers depend on how the blocks are arranged.

• Suppose you had 1 more triangle. What shape could you make? Possible answer: a big triangle

MathTalk

MP5 Use appropriate tools strategically. Use Math Talk to focus on children’s understanding of how to combine two-dimensional shapes to make new two-dimensional shapes.

ELL Strategy: Illustrate Understanding

Have children trace pattern blocks to illustrate their understanding of which two shapes make another shape.Place the hexagon and two triangles together to form a shape. Trace around the shape. Show the children what you traced.

• What three pattern blocks make this shape?Once children have solved this problem, have them choose three pattern blocks, create a shape, and trace around the shape. Then have them trade tracings and identify the blocks that made the shape.

HandsOn

Enrich 12.6Reteach 12.6

Model and DrawModel and Draw

Share and ShowShare and ShowShare and ShowShare and ShowShare and ShowShare and ShowShare and ShowShare and ShowMATHBOARDMATHBOARDMATHBOARDMATHBOARDMATHMATHMATHMATHBOARDBOARDBOARDBOARD

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Which two pattern blocks make this shape?

1. 2.

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Use two pattern blocks to make the shape.Draw a line to show your model. Color the shapes.Circle the blocks you use.

DO NOT EDIT--Changes must be made through “File info”CorrectionKey=B


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COMMON ERRORS COMMON ERRORS

EXPLAIN3

Quick Check

If

Rt I RR1

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Then

Advanced LearnersAdvanced Learners

Lesson 12.6 702

Error Children may use more than two pattern blocks to make the new shape.

Example In Exercise 2, children use two trapezoids and a rhombus to make the shape. Springboard to Learning Reread the directions with children, calling attention to where it says how many pattern blocks to use. Guide children to cover the shapes with only two pattern blocks.

Model and Draw MATHEMATICAL PRACTICES

MP4 Model with mathematics. As you work through the model together, have children use pattern blocks to build the pictured shape. Have children trace the line to show the two blocks and trace the circles around the triangle and hexagon. • Describe how the two blocks are put

together. A side of the triangle touches one side of the hexagon. The triangle points to the right.

• What do you notice about the sides of the hexagon and the triangle? They match; they are the same length.

• Suppose you could use three blocks. Which three blocks could make this shape? two trapezoids and one triangle

Share and Show MATHBOARDMATHBOARDMBOARDMMMMBOARDBOARDBOARDBOARDMATHATHABOARDMMMMAAAATHATHATHTHTHATHATHATHAATHAAAATHAAATHATHTHTHATHATHAAATHATHATHAAATHABOARDBOARDBOARDBOARD

Encourage children to explain their thinking.• How did you know which blocks to circle?

Possible answer: I used pattern blocks to make the shape. Then I circled the shapes I used.

• How did you know which color to use? Possible answer: I used the same color as the pattern blocks below the shape.

Use the checked exercises for Quick Check.

a child misses the checked exercises

Differentiate Instruction with • Reteach 12.6

• Personal Math Trainer 1.G.A.2

• RtI Tier 1 Activity (online)

Materials pattern blocks

• Give children a hexagon pattern block, and have them trace the outline of the hexagon onto paper.

• Have children fi t different combinations of pattern blocks into the outline to identify as many ways as they can to make the shape.

• Have children record the combinations they used on their paper. Possible answers: 2 trapezoids; 6 triangles; 3 rhombuses; 2 rhombuses and 2 triangles; 1 trapezoid and 3 triangles; 1 rhombus, 1 triangle, and 1 trapezoid

Logical / MathematicalIndividual / Partners

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On Your OwnOn Your Own

MATHEMATICALPRACTICE 5 Use a Concrete Model

Use two pattern blocks to make the shape.Draw a line to show your model. Color the shapes. Circle the blocks you use.

Chapter 12 • Lesson 6 seven hundred three 703

3. 4.

5. 6.

7. SMARTER Use three pattern blocks to make the shape. Draw lines to show your model. Color the shapes. Circle the blocks you use.

Possible answers shown.

Possible answers: 3 trapezoids or 1 hexagon, 1 triangle, and 1 rhombus


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Math on the Spot videos are in the Interactive Student Edition and at www.thinkcentral.com.

703 Chapter 12

On Your OwnMP5 Use appropriate tools strategically. If children answered Exercises 1 and 2 correctly, assign Exercises 3–7.

SMARTER

Exercise 7 requires children to use higher order thinking skills as they analyze the pattern blocks to determine which three will cover the shape. Point out that there is more than one possible solution. Make sure children understand that if they use the same block more than once to make the shape, they only need to circle that block once in the answer choices. Emphasize that the lines children draw in their model, and the colors, will show all the shapes they used. Have volunteers share their answers.

DEEPER

MP4 Model with mathematics. To extend learning, challenge children to use more than three pattern blocks to fi nd other combinations that make the shape in Exercise 7. For example, children could use 1 trapezoid, 2 rhombuses, and 2 triangles. Suggest that children communicate these combinations by tracing and coloring their shapes to refl ect the blocks that were used.• How can you make the shape with all

different blocks? Possible answer: I can use 1 hexagon, 1 rhombus, and 1 triangle.

• How can you make the shape with the most blocks? I can use 9 triangles.

MP7 Look for and make use of structure.• Which way uses the most blocks? Why?

Possible answer. All triangles because they are the smallest.

• Why can you make this shape so many different ways? There are lots of ways to make the hexagon. So I can keep trading out shapes.

4 ELABORATE

Math on the Spot Video TutorUse this video to help children model and solve this type of Think Smarter problem.


Differentiated Centers Kit

DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIES

Math Problem Solving • ApplicationsProblem Solving • Applications

MATHEMATICAL PRACTICES MODEL • REASON • MAKE SENSE

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8. Use 3 blocks.

0 — 1 —

2 — 0 —

10. Use 7 blocks.

6 — 1 —

0 — 0 —

9. Use 5 blocks.

3 — 1 —

1 — 0 —

11. Use 8 blocks.

8 — 0 —

0 — 0 —

12. SMARTER Use 4 pattern blocks to make the shape. Draw and color to show the blocks you used.

TAKE HOME ACTIVITY • Have your child use this page to explain how to find shapes within the given shape.

SMARTER Make this shape. Use the number of pattern blocks listed in the exercise. Write how many of each block you use.

Possible answers: 3 rhombuses and 1 trapezoid; 1 hexagon and 3 triangles; 2 trapezoids, 1 triangle, and 1 rhombus


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Games

EVALUATE5 Formative Assessment

Differentiated Centers Kit

DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIESDIFFERENTIATED INSTRUCTION

MATHEMATICAL PRACTICES

Lesson 12.6 704

Children practice describing the attributes of two-dimensional shapes to win the game.

GamesOn the Water

Children read the book and identify the shapes of signs.

LiteratureSigns Shape Up

Children complete purple Activity Card 10 by combining two-dimensional shapes to create new shapes.

ActivitiesBuilding Blocks

Have children follow along as you read the directions at top of the page.

SMARTER

MP1 Make sense of problems and persevere in solving them. Encourage children to use pattern blocks and their MathBoard to help them complete Exercises 8–11.

SMARTER

Exercise 12 requires children to look for structure and fi nd shapes in the composite fi gure. Children who answer incorrectly may struggle to combine more than two shapes. Have them use pattern blocks to explore ways to make parts of the composite fi gure, a hexagon and a trapezoid. Then ask them to combine shapes to fi nd an arrangement of four pattern blocks. Remind children to use the colors of the pattern blocks to show which shapes they used.

Essential QuestionRefl ect Using the Language Objective Have children write in their Math Journal to answer the Essential Question.How can you fi nd shapes in other shapes? Possible answer: I can put different pattern blocks together to make the shape.

Math Journal Math

Use pictures or words to explain what shapes can be put together to make a hexagon shape.


Problem Solving • Applications

Problem SolvingProblem Solving

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Find Shapes in Shapes

Use two pattern blocks to make the shape. Draw a line to show your model. Circle the blocks you use.

Chapter 12 seven hundred fi ve 705

Make the shape to the right. Use the number of pattern blocks listed in the exercise. Write how many of each block you use.

3. Use 3 blocks.

2 — 1 — 0 — 0 —

1. 2.

COMMON CORE STANDARD—1.G.A.2 Reason with shapes and their attributes.

Lesson 12.6Practice and Homework

4. Math Use pictures or words to explain what shapes can be put together to make a hexagon shape.

Possible answer shown.

Lines drawn may vary.

Check children’s work.

Practice and HomeworkUse the Practice and Homework pages to provide children with more practice of the concepts and skills presented in this lesson. Children master their understanding as they complete practice items and then challenge their critical thinking skills with Problem Solving. Use the Write Math section to determine children’s understanding of content for this lesson. Encourage children to use their Math Journals to record their answers.

COMMON CORECOMMCOMMCOMMCOMMON CON CON CON COREOREOREORE

PROFESSIONALDEVELOPMENT Math Talk in Action

After children complete Exercise 2, discuss how to analyze new shapes.

Teacher: What kind of shape is the new shape in Exercise 2?

Darnell: It is a trapezoid.

Teacher: Could you use a triangle pattern block to make the shape?

Shawna: Yes, the triangle pattern block can make the left side of the new shape.

Teacher: Yes, Shawna, the triangle is one of the shapes! How can you find the other shape?

Tobie: I put the triangle pattern block on the left side of the new shape. I can put the other shapes on the right side of the new shape to see which one fits.

Teacher: That is one way, Tobie. What is another way?

Judith: I put the triangle pattern block on the left side of the shape, too. But I can look at the rest of the outline and see which shape will work.

Teacher: Very good, Judith! You can also start with the second shape. You can look at the shape of the outline. What would that shape be?

Stu: A rhombus!

Teacher: Excellent work, children!

705 Chapter 12

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Personal Math Trainer

FOR MORE PRACTICE GO TO THE

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2. Write the time.

2:30

Spiral Review (1.MD.B.3, 1.MD.C.4, 1.G.A.1)

Lesson Check (1.G.A.2)

3. Write tally marks to show the number 8.

4. How many vertices does a have?

4 _ vertices

1. Circle the pair of pattern blocks that can make this shape. Continue concepts and skills practice with

Lesson Check. Use Spiral Review to engage children in previously taught concepts and to promote content retention. Common Core standards are correlated to each section.

Lesson 12.6 706

hands on • find shapes in shapes · hands on • find shapes in shapes lesson 12.6 701a chapter...

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