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4◆7 Building Trapezoids Work Mat

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LESSON

Open Response

and Reengagement

2-DAY LESSON

► Focus: Solving the Open Response Problem 25–35 min | Math Masters, pp. 60–63

WHOLE GROUP SMALL GROUP PARTNERS CENTER

K.G.1, K.G.2, K.G.6

Core Activities

Daily Routines

10–15 min | Children practice mathematics as they perform the daily routines.

Before You Begin Decide how you will pair children, and prepare to photograph their work.

Terms to Use above • below • beside • hexagon • next to • rhombus • solution • square• trapezoid • triangle

Materials Day 1: Math Masters, pp. 60 and 62 (per partnership) and pp. 61 and 63 (per child); pattern blocks; crayons or markers; camera Getting Ready for Day 2: Math Masters, page 125; photographs of children’s work mats; completed recording sheets Day 2: Activity Card 33, Math Masters, pp. 62–63; selected children’s work (photographs and recording sheets); pattern blocks

Day 1: Open Response

Common CoreState StandardsFocus Clusters• Identify and describe shapes

(squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).

• Analyze, compare, create, and compose shapes.

4-7Building HexagonsOVERVIEW Day 1: Children combine pattern blocks in different ways to make a hexagon. Day 2: Children reengage with their work to consider many ways to cover a hexagon.

Math Masters, p. 60

K.G.1, K.G.2, K.G.6, SMP1, SMP6

1Lesson 4-7

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4◆7 Building Hexagons Work Mat


Standards and Goals for Mathematical PracticeSMP1 Make sense of problems and

persevere in solving them.GMP1.5 Solve problems in more than one way.

GMP1.6 Compare the strategies you and others use.

SMP2 Attend to precision.GMP6.1 Explain your mathematical thinking clearly and precisely.

Warm Up Briefly review the names of the pattern-block shapes: hexagon, rhombus, square, trapezoid, and triangle. Explain to children that today they will use pattern blocks to build other shapes. Show them a trapezoid outline on the Building Trapezoids Work Mat (Math Masters, page 60), and ask: What is one way we could build a trapezoid using pattern blocks? Sample Answer: We could build it with one red trapezoid. GMP6.1

Model the solution by placing the corresponding pattern block(s) on the outline. Then ask: What is a different way we could build this shape using pattern blocks? Sample Answer: We could use a blue rhombus and a green triangle. Model this solution with pattern block(s) on the second outline, and invite a child to use pattern blocks to show a third way to build the trapezoid. GMP1.5

Display a copy of the Building Trapezoids Recording Sheet (Math Masters, page 61) alongside the Building Trapezoids Work Mat. The recording sheet has dashed guiding lines dividing the trapezoid into three triangles to make recording easier. Demonstrate how to represent a solution by using crayons or markers to color the first trapezoid outline on the recording sheet to match the first trapezoid on the work mat. Have children help you color the recording-sheet trapezoids to match the remaining work-mat solutions. (Expect that some children may be confused by the recording sheet initially. With experience during the task, most children will figure out how to record their solutions accurately.)

Building Hexagons Tell children that you have a new challenge for them. Display the Building Hexagons Work Mat (Math Masters, page 62) and tell children that they will work with a partner to find several different ways to build a hexagon with pattern blocks. Explain that once they find six ways to build the hexagon on their work mats, you will give them their own Building Hexagons Recording Sheets (Math Masters, page 63) to record their solutions. The dashed guiding lines on the recording sheet hexagons divide the shapes into six triangles.

Give each pair of children a Building Hexagons Work Mat and plenty of pattern blocks. (Later, if children are interested in finding more than six solutions, give them additional work mats.)

This task provides a good opportunity for children to experience solving problems in more than one way and for you to reinforce the value of this mathematical practice across a wide range of problem-solving situations. GMP1.5 It also provides

opportunities for children to use clear and precise language to compare their various strategies and solutions. GMP1.6 , GMP6.1

Professional Development

Math Masters, p. 62

K.G.1, K.G.2, K.G.6, SMP1, SMP6

2Lesson 4-7

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While children are working to find different ways to build the hexagon, circulate and ask questions such as:

• How did you cover this hexagon?

• What shapes did you use? How many of each kind did you use?

• How is this way similar to another way you covered the hexagon? How is it different?

• What is another way you could cover the hexagon? GMP1.5 GMP1.6 GMP6.1

Listen to children’s strategies and approaches. Are they motivated to find multiple solutions? Do they keep any part of one solution to use in another? Do they make connections among their solutions? In your discussions with children, reinforce the value of solving problems in more than one way and comparing various strategies and solutions. Model and encourage the use of positional language, such as above, below, beside, and next to, when explaining shape locations on the hexagons. GMP1.5 GMP1.6 GMP6.1

Hand out a Building Hexagons Recording Sheet to each child as partners are ready to record their solutions (once they have found six ways to build hexagons on their work mats).

As you hand out the sheets, ask: How can you record your hexagons on the sheet? What might you do first? How can the triangles on the sheet help you record your solutions? Sample answers: I can use the same colors as the pattern-block shapes to color in the hexagon. I could use colors to outline the shapes first. The triangles can help me know the right amount of space to color for each shape. Give multiple recording sheets to children who have found more than six solutions.

To conclude this part of the lesson, have children count the number of different solutions they found. Photograph children’s work mats alongside their recording sheets for use in the Reengagement discussion. Explain that children will have a chance to look at each other’s ideas and solutions in a few days. Children may not always record their solutions accurately. Note

that only the first and fourth solutions above are recorded correctly on the right. Consider photographing children’s recording sheets alongside their work mats to use in the Reengagement discussion on Day 2.

3Lesson 4-7



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Children may repeat some solutions. This is something you may wish to discuss during Reengagement on Day 2.

A pair of children finds six different ways to cover the hexagon (center). Partner 1 (left) records only two of the solutions accurately, but Partner 2 (right) records all six solutions accurately.

4Lesson 4-7

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Reengagement Planning Form

Planning the Reengagement Discussion

Common Core State Standard (CCSS):

Focus Mathematical Practice (MP):

Students’ strengths and understandings

Students’ weaknesses and misconceptions

Issue to addressWork samples that illustrate this issue

Questions to ask about the sample student work

Both Partner 1 and Partner 2 show six different ways to build a hexagon on their recording sheets. The two hexagons circled above contain the same shapes, but they are in different positions.

Getting Ready for Day 2

Planning a Follow-Up DiscussionReview the photographs of children’s work mats alongside their recording sheets. Use the Reengagement Planning Form (Math Masters, page 125) and the rubric on page 6 to assist you in evaluating the work and planning a discussion of the task. Look for trends in children’s work and analyze their errors. What mathematical understandings and misconceptions do they appear to have? You may organize the discussion of children’s work in one of the ways listed below or in another way you choose. Highlight the practices of solving the problem in more than one way and of comparing solutions.

Display a child’s recording sheet that shows six different ways to cover the hexagon. (See Partner 1’s sheet below.) Choose one solution to recreate with the class by placing pattern blocks on an empty work mat. (See circled solution.) Ask:

• Which shapes did this child use to cover the hexagon? Sample answer: Two triangles and two blue rhombuses• Where is each shape? Sample answers: The two triangles are on the top (left). One rhombus is below the triangles and

the other is next to them. GMP6.1

Then display another child’s recording sheet (below right) that also has six different solutions, one of which is similar to Partner 1’s solution discussed above. Draw attention to Partner 2’s solution (circled below). Ask:

• How is this solution similar to Partner 1’s solution? Sample answer: They both use two triangles and two blue rhombuses. GMP1.6 GMP6.1

• How is this solution different from Partner 1’s solution? Sample answers: The shapes are in different places. In Partner 2’s solution, the triangles are on the top and the bottom and rhombuses are on the sides. GMP1.6 GMP6.1

Math Masters, p. 125

Partner 1 Partner 2

5Lesson 4-7

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Display the recording sheet of a child who used two trapezoids to build a hexagon and have the child describe the solution and model it with pattern blocks on an empty work mat as shown in the first hexagon below. (The child may position the trapezoids differently than those shown.) Place one trapezoid on the next hexagon in the same position as one of the trapezoids in the first hexagon. Ask: Did anyone use one trapezoid and fill the remaining space a different way? Sample answers: I did it with three triangles. I used a triangle and a blue rhombus. GMP1.5 Encourage children to model their ideas on a work mat, placing one trapezoid in the same position in all of their solutions (on the right). Once finished, ask:

• Why do you think it takes more triangles than trapezoids to cover a hexagon? Sample answers: The triangles are smaller than the trapezoids. Three triangles make one trapezoid. GMP1.6 GMP6.1

• What did you learn about shapes by solving this problem in more than one way? Sample answer: You can make a trapezoid with three triangles or with a rhombus and a triangle. GMP1.5 GMP6.1

Children model four different solutions that all use one trapezoid in the same position.

Goals for Mathematical Practice

GMP1.5

Solve problems in more than one way.

Not Meeting Expectations

Partially Meeting Expectations

Meeting Expectations

Exceeding Expectations

Finds no solutions or 1 solution.

Finds 2–4 different solutions.

Finds 5–6 different solutions.

Finds more than 6 different solutions.

6Lesson 4-7

NOTE These Day 2 activities will ideally take place within a few days of Day 1. Prior to beginning the Day 2 activities, see page 5.

Core Activities

► Reengaging with the Task K.G.1, K.G.2, K.G.6, SMP1, SMP6

20–30 min WHOLE CLASS SMALL GROUP PARTNERS CENTER

Review the Problem Review the Building Hexagons problem from pages 1–4. Tell the class that they will look at solutions from different partnerships and compare the strategies. GMP1.6 If many children tried to use incorrect shapes (the square and tan rhombus, for example), you may wish to display a photograph or re-create a work mat (Math Masters, page 62) of children’s attempts and ask:

• Do these shapes fit together to make a hexagon? How can you tell? Sample answer: No. The tan rhombuses are too tall and do not fit into the hexagon outline. GMP6.1

• Can we use these shapes to build a hexagon? How do you know? Sample answer: No. They don’t fit the hexagon and there aren’t any shapes to fit in the empty spaces. GMP6.1

Before You Begin Use the Reengagement Planning Form (Math Masters, page 125) and plan the discussion. (See lesson 3-7.) Decide how you will display selected children’s work.

Terms to Use above • below • beside • hexagon • next to • rhombus • solution • square• trapezoid • triangle

Materials Day 2: Activity Card 33, Math Masters, pp. 62–63; selected children’s work (photographs and recording sheets); pattern blocks

Day 2: Reengagement

Building HexagonsOVERVIEW Day 2: Children reengage with their work from Day 1 to consider many ways to cover a hexagon.

7Lesson 4-7

Guidelines for DiscussionsDuring our class discussions, we will . . .

✔ Listen closely to our classmates’ ideas.

✔ Ask questions. ✔ Share different ideas. ✔ Agree and disagree respectfully.

✔ Make and learn from mistakes.

Revisit Guidelines To promote a cooperative environment, revisit the class Guidelines for Discussion. Review the guidelines and have children reflect on those they are following well and those they need to follow more closely. You may wish to focus on one or two behaviors for children to practice throughout the discussion. Continue modeling and role-playing situations to support constructive behavior during class discussions about mathematics and other topics.

Reengage with the Task This is an opportunity for children to reengage with the problem by analyzing and critiquing their own and other children’s work in a whole-class discussion. Organize and facilitate this discussion based on the decisions you made in Getting Ready for Day 2. See sample discussion questions on pages 5–6. You may wish to have children “turn and talk” with a partner about the questions you pose before they discuss them with the whole class.

Conclude by congratulating children for working hard to find many ways to build hexagons. Mention that they will have other opportunities to build hexagons in the Math Center. See Activity Card 33.

Assessment Check-In K.G.1, K.G.2, K.G.6

Expect most children to compose a hexagon from other shapes correctly and to identify and name triangles, squares, rhombuses, trapezoids, and hexagons. Many children will be able to use positional language to describe the location of shapes. You can also use this task to gather information about whether and how children seek, find, and compare multiple solutions to a problem. You may use the rubric on page 6 to evaluate children’s work with respect to Goal for Mathematical Practice 1.5, the focus of this lesson. GMP1.5

33

K.G.1, K.G.2, K.G.6, SMP1, SMP6

Use with Lesson 4-7 or after.

What To Do1 Usepatternblockstobuildthehexagonmanydifferentways.

2 Recordyouranswers.

3 Tellapartnerhowyouranswersarethesameanddifferent.

What You Need

BuildingHexagonsWorkMat

BuildingHexagonsRecordingSheet

patternblocks

Building Hexagons

Activity Card 33

8Lesson 4-7

33

K.G.1, K.G.2, K.G.6, SMP1, SMP6

Use with Lesson 4-7 or after.

What To Do1 Usepatternblockstobuildthehexagonmanydifferentways.

2 Recordyouranswers.

3 Tellapartnerhowyouranswersarethesameanddifferent.

What You Need

BuildingHexagonsWorkMat

BuildingHexagonsRecordingSheet

patternblocks

Building Hexagons

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Name Date

Reengagement Planning Form

Planning the Reengagement Discussion

Common Core State Standard (CCSS):

Focus Mathematical Practice (MP):

Students’ strengths and understandings

Students’ weaknesses and misconceptions

Issue to addressWork samples that illustrate this issue

Questions to ask about the sample student work

open responseand reengagement building hexagons 2-day ... · em4_tlg1_gk_s04_l07_011a.tif...

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