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T1 © The Math Learning Center | mathlearningcenter.org Bridges in Mathematics Grade 2 Teacher Masters Session 1 class set, plus 1 copy for display Unit 6 Work Place Log 6A Last Shape In Wins 6B Find the Area 6C Make the Area 1 2 3 6D Fill for Less 6E Halves & Half-Nots Personal Practice Computer Activity Work with the Teacher Unit 6 Module 1

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T1 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

Session 1 class set, plus 1 copy for display

Unit 6 Work Place Log

6A Last Shape In Wins 6B Find the Area 6C Make the Area

1

2

3

6D Fill for Less 6E Halves & Half-Nots

Personal Practice Computer Activity Work with the Teacher

Unit 6 Module 1

T2 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

Session 1 1 copy kept in a clear plastic sleeve and stored in the Work Place bin

Work Place Guide 6A Last Shape In Wins

SummaryPlayers take turns placing pattern blocks on a large hexagon, using lines drawn on the board to help position the blocks accurately. On each turn, players place one shape—a triangle, a trapezoid, a blue rhombus, or a hexagon—on the board. The player who is able to place the last block and complete the entire hexagon wins.

Skills & Concepts• Create a composite shape by composing two-dimensional shapes (1.G.2)• Recognize shapes having specified attributes (2.G.1)• Identify triangles, quadrilaterals (trapezoids and rhombuses), and hexagons (2.G.1)• Make sense of problems and persevere in solving them (2.MP.1)

Materials

Copies Kit Materials Classroom Materials

TM T2 Work Place Guide 6A Last Shape In WinsTM T3 Work Place Instructions 6A Last Shape In Wins

• 3 Last Shape In Wins Game Boards • 3 containers of pattern blocks (each container needs about 10 hexagons, and 20 each of the following: triangles, trapezoids, and blue rhombuses)

Assessment & Differentiation

If you see that… Differentiate Example

One or more students are having difficulty getting the pieces to stay in place.

SUPPORT Use craft sticks to create a small border around the perimeter of the large hexagon on the game board.

Each side of the large hexagon on the game board is 3” long, and craft sticks are 4.5” long. If you break or cut 3/4” off each end of 6 craft sticks and then tape or glue them flat around the perimeter, this very narrow lip will help students line up the pattern blocks more accurately along the lines on the board, and will help prevent slippage.

One or more students are very comfortable with the game but continue to argue that going first or second is more advantageous.

CHALLENGE Have students take turns going first for four or six games. Record the name of the person that goes first and the name of the person that wins each round.

Students can extend this record keeping into Work Places over the coming weeks to look for evidence that going first or second is advantageous. Place a piece of paper with a two column table (one for First Player, one for Second Player) with this Work Place. Ask students to keep a record of the winner of each game by placing a tally mark in the appropriate column.

Students are comfortable with the game and could benefit from a challenge.

CHALLENGE Have students devise and test various strategies for winning. Keep a running list on a piece of chart paper somewhere in the classroom during the weeks this Work Place is out, and invite students to add (and remove) strategies as they generate and test them.

Here are examples of student-generated theories:

• Always place your block next to another.

• Never place your block next to another unless you have to.

• Use hexagons for as long as possible.

• Create isolated small areas around the board.

• As you get close to the end of the game, try to think ahead.

English-Language Learners Use the following adaptations to support the ELL students in your classroom.

Consider using the game to reinforce color and shape vocabulary. You might meet with small groups of students, some of whom are fluent in English, to play a 2-team version of the game. As you play, model shape names and colors, but also model the use of language to describe shape attributes, such as number of sides, number of angles, side lengths relative to one another (e.g., this rhombus has 4 sides of equal length, but the trapezoid only has 2 sides of equal length).

Unit 6 Module 1

T3 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

Session 1 1 copy kept in a clear plastic sleeve and stored in the Work Place bin

Work Place Instructions 6A Last Shape In Wins1 Players share a game board and a set of pattern blocks.

2 Players decide in a fair way who will go first.

3 Players take turns placing blocks on the game board following these guidelines:• On a given turn, a player can place one block anywhere that hasn’t already been covered on the game board.

Shapes do not have to be placed next to each other.• Shapes have to be placed in such a way that they line up with the spaces and lines on the board.

• A player can use any one of the four shapes on any given turn, as long as that shape will fit into the space available.• Players have to take their turns every time, down to the very end.

4 Players continue taking turns placing pieces on the board until it is completely filled.

5 The player who puts the last piece on the board wins.

Unit 6 Module 1

T4 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

Session 1 class set, plus 1 copy for display

Unit 6 Pre-Assessment page 1 of 4

1 Fill in the bubble to show the name of each shape below. Then tell how you know.

a N square How do you know? Give at least one reason.

N rectangle

N trapezoid

N rhombus

b N square How do you know? Give at least one reason.

N hexagon

N triangle

N pentagon

c N triangle How do you know? Give at least one reason.

N rectangle

N trapezoid

N pentagon

d N hexagon How do you know? Give at least one reason.

N rhombus

N pentagon

N octagon

2 Which of these shapes is a cube? Fill in the bubble to show.

N N N N

Unit 6 Module 1

NAME | DATENAME | DATE

(continued on next page)

T5 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

3 Follow the instructions to make each shape on your geoboard. Then copy the shape you built on this sheet and write its name on the line below. Use a ruler to help make the sides of the shapes straight when you draw them.a Make a shape with 3 sides and 3

corners or vertices. Shape name: _________________

b Make a shape with 4 sides that are all the same length. Shape name: _________________

4 Find all the quadrilaterals in the box below. Color them green. Do not color any of the other shapes.

Session 1 class set, plus 1 copy for display

Unit 6 Pre-Assessment page 2 of 4

Unit 6 Module 1

NAME | DATENAME | DATE

(continued on next page)

T6 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

5 Use tiles to cover this entire rectangle. Do not leave any holes or gaps. Then answer the questions below.

a How many tiles did it take to cover the entire rectangle? _________________

b Write an addition equation to show how many tiles it took to cover the rectangle.

6 Here are three different shapes. Use them to answer the questions below.

a Divide each shape into two equal parts. Use a ruler to help draw straight lines.

b When you divide a shape into two equal parts, what is each part called? Fill in the bubble to show.

N one-fourth N one second N one-third N one-half

c Eric says that two halves is the same as one whole. Do you agree with Eric? Why or why not?

Session 1 class set, plus 1 copy for display

Unit 6 Pre-Assessment page 3 of 4

Unit 6 Module 1

NAME | DATENAME | DATE

(continued on next page)

T7 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

7 Use these shapes to answer the questions below.

a Find the trapezoid. Draw a line to cut it in half. Color in one-half red.

b Find the rectangle. Color one-half of the rectangle blue. Color the other half yellow.

c Find the circle that is divided into two equal parts. Color in two halves of that circle green.

8 Dad made sandwiches exactly the same size for Sam and Sarah. Then he cut each sandwich in half like this. Sam said, “That’s not fair! Sarah got bigger halves than me!” Is Sam right? Why or why not? Use labeled sketches, words, and/or numbers to explain.

Sarah's Sandwich Sam's Sandwich

Session 1 class set, plus 1 copy for display

Unit 6 Pre-Assessment page 4 of 4

Unit 6 Module 1

NAME | DATE

T8 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

Session 2 class set, plus 1 copy for display

Triangle DrawMake four different triangles on your geoboard. Draw each one below, using a ruler to help you make the lines very straight. Then cut out the little geoboards and put your name on the back of each.

Unit 6 Module 1

NAME | DATE

T9 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

Session 3 class set, plus 1 copy for display

Quadrilateral DrawMake four different quadrilateral on your geoboard. Draw each one below, using a ruler to help you make the lines very straight. Then cut out the little geoboards and put your name on the back of each.

Unit 6 Module 1

NAME | DATE

T10 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

Session 5 class set, plus 1 copy cut apart before the session

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Unit 6 Module 1

T11 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

Session 5 class set, plus 1 copy cut apart before the session

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Unit 6 Module 1

T12 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

Session 5 1 copy for display

Guess My Shape Riddles page 1 of 2

Guess My Shape, Riddle 1

1 My shape does not have 3 sides.

2 My shape has 4 corners or vertices.

3 The sides on my shape are not all the same length.

4 Only 2 of the sides on my shape are parallel.

These 2 lines are parallel. They run side by side like train tracks and will never cross, no matter how long they get.

These 2 lines are not parallel. If I make them longer, they will cross eventually.

5 My shape has exactly 1 line of symmetry. Answer My shape is the trapezoid.

Guess My Shape, Riddle 2

1 My shape has 3 straight sides.

2 My shape has exactly 1 line of symmetry.

3 Only 2 of the sides on my shape are equal in length.

4 Two of the sides on my shape meet to form a square corner (a right angle). Answer My shape is the right triangle.

Unit 6 Module 1

(continued on next page)

T13 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

Guess My Shape, Riddle 3

1 My shape is not a quadrilateral.

2 All the sides on my shape are equal in length.

3 If you cut my shape in half from one vertex to the vertex opposite that one, you will get 2 trapezoids.

4 My shape has 6 sides. Answer My shape is the hexagon. (“Hex” means 6 in Latin.)

Guess My Shape, Riddle 4

1 If you cut my shape in half you could get 2 triangles.

2 My shape is a quadrilateral.

3 My shape has exactly 2 lines of symmetry.

4 My shape has 2 pairs of parallel lines.

5 All the sides on my shape are equal in length. Answer My shape is the rhombus.

Session 5 1 copy for display

Guess My Shape Riddles page 2 of 2

Unit 6 Module 1

T1 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

Session 1 optional, run as needed

If a Triangle Is Worth One Challenge page 1 of 2

If the area of a triangle is worth 1 unit, what is the area of each of the shapes below? Be sure to prove your answers.

area = _______ units

area = _______ units

area = _______ units

Unit 6 Module 2

(continued on next page)

T2 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

Session 1 optional, run as needed

If a Triangle Is Worth One Challenge page 2 of 2

If the area of a triangle is worth 1 unit, what is the area of each of the shapes below? Be sure to prove your answers.

area = _______ units

area = _______ units

Unit 6 Module 2

T3 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

Session 2 1 copy for display

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Unit 6 Module 2

T4 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

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Session 2 half-class set, plus 1 copy for displayUnit 6 Module 2

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T5 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

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Session 2 half-class set, plus 1 copy for displayUnit 6 Module 2

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T6 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

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T7 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

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Session 2 half-class set, plus 1 copy for displayUnit 6 Module 2

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T8 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

Session 3 half-class set, plus 1 copy for display

Geoboard Square Measuring Sheet

Unit 6 Module 2

T9 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

Session 4 1 copy kept in a clear plastic sleeve and stored in the Work Place bin

Work Place Guide 6B Find the Area

SummaryStudents work individually to find the areas of different figures on four different activity sheets. The sheets, which increase in difficulty, each contain sketches of figures on geoboards. Students must not only find the area of each figure, but provide enough information through sketching and equations to demonstrate how they found their answers.

Skills & Concepts• Find the total number of objects in an array with up to 5 rows and 5 columns, using addition (2.OA.4)• Write an equation to represent the total number of objects in an array with up to 5 rows and 5 columns as the sum

of equal addends (2.OA.4)• Draw shapes having specified attributes (2.G.1)• Partition a rectangle into rows and columns of same-size squares (2.G.2)• Count the total number of squares in a rectangle that has been partitioned into rows and columns of same-size

squares (2.G.2)

Materials

Copies Kit Materials Classroom Materials

TM T9–10 Work Place Guide 6B Find the AreaTM T11 Work Place Instructions 6B Find the AreaTM T12–15 6B Find the Area Record SheetsTM T8 Geoboard Square Measuring Sheet

• 6 geoboards with geobands • beans or buttons or some other small markers (optional)

Note There are 4 different record sheets for this Work Place. You may wish to place copies of each in a folder, and then place the folders in the Work Place bin. Make 6 copies of the Geoboard Square Measuring Sheet Teacher Master, place each in a clear plastic sleeve, and store them in the Work Place bin.

Assessment & Differentiation

If you see that… Differentiate Example

Students are struggling with more advanced sheets.

SUPPORT Encourage students to work in order from Sheet 1 to Sheet 4. Give students a reasonable goal for the number of exercises and sheets to finish in each visit.

Students aren’t sure how to get started or how to interpret what they are doing.

SUPPORT Model using geoboards, measuring sheets, and counting tools such as beans or buttons to find the area.

For the figure toward the bottom left of sheet 1, work with students to create the “H” shape on a geoboard using three different geobands—one for each “leg” and one for the middle square. Set the geoboard on top of one of the measuring sheets to guide students in partitioning the shape into square units. Model how to draw line segments on the record sheet to show these units, and number each one. Then have students continue this process for the other figures on the record sheet.

A student can complete the tasks that involve whole squares, but struggles with triangular parts or the student is counting triangles as 1.

SUPPORT Remind students that the square equals one unit. You might help them understand that one of the small triangles is half a square unit by inviting them to form a small square on a geoboard and then using another rubber band to divide the square into two triangles.

Unit 6 Module 2

(continued on next page)

T10 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

If you see that… Differentiate Example

One or more students are working quickly and successfully to complete all of the sheets in the set.

CHALLENGE Ask students to find and discuss the greatest and smallest areas possible on the geoboard. Also, for very advanced students, you can shift the unit of measure from the smallest square on the board to the square that bounds 8 pegs, and ask them to find the areas of the some of the shapes on the first couple of record sheets based on the new unit.

1

Teacher What if we define the unit of area like this, instead of as the smallest square on the board?

Some students may be quick to note that the smallest area is 1 and the largest is 16. Push students beyond these answers by asking them to form the smallest triangle possible on the board and determine its area (1/2 or even 1/4 of a unit).

1/2

Student A I don’t think 1 is the smallest. Look at the triangle I made. The area of that one is 1/2 a square. Student B I split up a square to make 4 triangles. Each one of those is worth 1/4 a square. I think that’s the smallest.

Shifting the unit of measure to a larger square poses some significant challenges in that it requires fractional thinking.

1

1 11/2

Student C Okay, if that big square has an area of 1, it’s kind of like saying that 1 is worth 4 of the little squares. Student D So, on this H shape, there are 4 little squares over here, that’s worth 1, and 4 little squares over there, that’s worth another 1, but what about the part in the middle?Student C That’s 2 little squares, and 2 is half of 4, so the area of the H is 2 and a half of the big units.

Session 4 1 copy kept in a clear plastic sleeve and stored in the Work Place bin

Work Place Guide 6B Find the Area

Unit 6 Module 2

T11 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

Session 4 1 copy kept in a clear plastic sleeve and stored in the Work Place bin

Work Place Instructions 6B Find the Area1 Students bring a pencil, choose a record sheet from the folder, and write their name at the top.

The sheets are numbered in order, according to their challenge level. • Students might also need a geoboard, some geobands, and a Geoboard Square Measuring Sheet.

2 Students find the area of each shape on the sheet, using the smallest square bounded by four pegs as the unit of measure.

= 1 unitof area

Students can:• create each shape on a geoboard and use a Geoboard Square Measuring Sheet to help find its area.• draw in and count the squares and triangles on the sheet.

3 Students record the area of each shape on the record sheet and write at least one equation to show how they found the answer.

Mark

8

1 2 3 45 6 7 8

2+2+2+2=84+4=8

Unit 6 Module 2

T12 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

Session 4 1 copy of page 1 for display, plus a class set, stored in the Work Place bin

6B Find the Area Record Sheet page 1 of 4Find the area of each shape below. Write at least one equation to show how you found your answer.

= 1 unitof area

area = _____ units area = _____ units

area = _____ units area = _____ units

area = _____ units area = _____ units

area = _____ units area = _____ units

Unit 6 Module 2

NAME | DATENAME | DATE

(continued on next page)

T13 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

Session 4 1 copy of page 1 for display, plus a class set, stored in the Work Place bin

6B Find the Area Record Sheet page 2 of 4

Find the area of each shape below. Write at least one equation to show how you found your answer.

= 1 unitof area

area = _____ units area = _____ units

area = _____ units area = _____ units

area = _____ units area = _____ units

area = _____ units area = _____ units

Unit 6 Module 2

NAME | DATENAME | DATE

(continued on next page)

T14 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

Session 4 1 copy of page 1 for display, plus a class set, stored in the Work Place bin

6B Find the Area Record Sheet page 3 of 4

Find the area of each shape below. Write at least one equation to show how you found your answer.

= 1 unitof area

area = _____ units area = _____ units

area = _____ units area = _____ units

area = _____ units area = _____ units

area = _____ units area = _____ units

Unit 6 Module 2

NAME | DATENAME | DATE

(continued on next page)

T15 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

Session 4 1 copy of page 1 for display, plus a class set, stored in the Work Place bin

6B Find the Area Record Sheet page 4 of 4

Find the area of each shape below. Write at least one equation to show how you found your answer.

= 1 unitof area

area = _____ units area = _____ units

area = _____ units area = _____ units

area = _____ units area = _____ units

area = _____ units area = _____ units

Unit 6 Module 2

NAME | DATE

T16 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

Session 4 1 copy kept in a clear plastic sleeve and stored in the Work Place bin

Work Place Guide 6C Make the Area

SummaryStudents work individually to create figures with a given area. The four activity sheets challenge students to create four figures for each of the following areas—6, 7, 8, and 9 square units. Students must not only create each figure, but provide enough information through labeled sketches and equations to demonstrate how they know their figure has the designated area.

Skills & Concepts• Find the total number of objects in an array with up to 5 rows and 5 columns, using addition (2.OA.4)• Write an equation to represent the total number of objects in an array with up to 5 rows and 5 columns as the sum

of equal addends (2.OA.4)• Draw shapes having specified attributes (2.G.1)• Partition a rectangle into rows and columns of same-size squares (2.G.2)• Count the total number of squares in a rectangle that has been partitioned into rows and columns of same-size

squares (2.G.2)

Materials

Copies Kit Materials Classroom Materials

TM T16 Work Place Guide 6C Make the AreaTM T17 Work Place Instructions 6C Make the AreaTM T18–21 6C Make the Area Record SheetsTM T8 Geoboard Square Measuring Sheet

• 6 geoboards with geobands • 6 rulers

Note There are 4 different record sheets for this Work Place. You may wish to place copies of each in a folder, and then place the folders in the Work Place bin. Make 6 copies of the Geoboard Square Measuring Sheet Teacher Master, place each in a clear plastic sleeve, and store them in the Work Place bin.

Assessment & DifferentiationHere are some quick observational assessments you can make as students begin to play this game on their own. Use the results to differentiate as needed.

If you see that… Differentiate Example

Students don’t know how to get started.

SUPPORT Encourage students to put the geoboard over the Geoboard Square Measuring Sheet before forming the shape.

Students can mark off six connected squares with six individual geobands to represent an area of 6. Then students can form a figure around these squares using one geoband of a different color.

One or more students are working quickly and successfully to complete all of the sheets in the set.

CHALLENGE Introduce the idea of perimeter. Challenge students to measure and record the perimeter of each shape on one of their record sheets. Have them use a ruler and measure the perimeter of each shape to the nearest centimeter.

Unit 6 Module 2

T17 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

Session 4 1 copy kept in a clear plastic sleeve and stored in the Work Place bin

Work Place Instructions 6C Make the Area1 Students choose a record sheet from the folder and write their name at the top. Each sheet

states the number of square inches to make—6, 7, 8, or 9. Students also need a geoboard, some geobands, a pencil, a ruler, and a Geoboard Square Measuring Sheet.

2 Students use geobands on their geoboard to create a shape with the area stated at the top of the record sheet, and use a Geoboard Square Measuring Sheet to check for accuracy.

3 Students then copy their shape onto one of the geoboards on the record sheet, label it, and write an equation to show that the area is accurate.

1

2

3

1+2+3=6

Unit 6 Module 2

T18 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

Session 4 1 copy for display, plus a class set, stored in the Work Place bin

6C Make the Area Record Sheet: 6 Square Units page 1 of 4Make 4 different shapes on your geoboard. Each one should have an area of 6 square units. Use a ruler to copy your shapes below. Label each shape and write an equation on the line below your drawing to show that it is really 6 square units.

______________________________________________ ______________________________________________

______________________________________________ ______________________________________________

Unit 6 Module 2

NAME | DATENAME | DATE

(continued on next page)

T19 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

Session 4 1 copy for display, plus a class set, stored in the Work Place bin

6C Make the Area Record Sheet: 7 Square Units page 2 of 4

Make 4 different shapes on your geoboard. Each one should have an area of 7 square units. Use a ruler to copy your shapes below. Label each shape and write an equation on the line below your drawing to show that it is really 7 square units.

______________________________________________ ______________________________________________

______________________________________________ ______________________________________________

Unit 6 Module 2

NAME | DATENAME | DATE

(continued on next page)

T20 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

Session 4 1 copy for display, plus a class set, stored in the Work Place bin

6C Make the Area Record Sheet: 8 Square Units page 3 of 4

Make 4 different shapes on your geoboard. Each one should have an area of 8 square units. Use a ruler to copy your shapes below. Label each shape and write an equation on the line below your drawing to show that it is really 8 square units.

______________________________________________ ______________________________________________

______________________________________________ ______________________________________________

Unit 6 Module 2

NAME | DATENAME | DATE

(continued on next page)

T21 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

Session 4 1 copy for display, plus a class set, stored in the Work Place bin

6C Make the Area Record Sheet: 9 Square Units page 4 of 4

Make 4 different shapes on your geoboard. Each one should have an area of 9 square units. Use a ruler to copy your shapes below. Label each shape and write an equation on the line below your drawing to show that it is really 9 square units.

______________________________________________ ______________________________________________

______________________________________________ ______________________________________________

Unit 6 Module 2

NAME | DATE

T22 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

Session 5 half-class set, plus a few extra on 3 or 4 different colors of copy paper

Rectangles

BA

C

D

Unit 6 Module 2

T23 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

Session 5 1 copy for display

Rectangle ZHow many units this size do you think it will take to cover Rectangle Z without leaving any holes or gaps?

Z

Estimates Equations

Actual Measure: _______ square units

Unit 6 Module 2

T1 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

Session 1 1 copy kept in a clear plastic sleeve and stored in the Work Place bin

Work Place Guide 6D Fill for Less

SummaryStudents work individually to fill different figures using as few pattern blocks as possible. Once students have found a solution, they color in the figure using colors that match the pattern blocks. This Work Place features six different record sheets, sequenced by challenge level.

Skills & Concepts• Recognize and create shapes having specified attributes (2.G.1)• Identify triangles, rhombuses, trapezoids, and hexagons (2.G.2)• Make sense of problems and persevere in solving them (2.MP.1)

Materials

Copies Kit Materials Classroom Materials

TM T1 Work Place Guide 6D Fill for LessTM T2 Work Place Instructions 6D Fill for LessTM T3–8 6D Fill for Less Record Sheets

• pattern blocks (hexagons, trapezoids, triangles, and blue rhombuses only)

• red, green, yellow, and blue crayons

Note There are 6 different record sheets for this Work Place. You may wish to place copies of each in a folder, and then place the folders in the Work Place bin.

Assessment & Differentiation

If you see that… Differentiate Example

Students are struggling with more advanced sheets.

SUPPORT Vary the required number of sheets based on the needs of the students.

Decide how many sheets you want students to complete with each visit. Some of the sheets are fairly challenging, and each requires a fair amount of work in terms of building and rebuilding, and then coloring to show a solution. It is not necessary for all students to complete all sheets.

Students are not finding the minimum number of pattern blocks needed to complete one or more of the sheets, but they think they are done.

SUPPORT Post a chart near the location for this Work Place that gives the minimum number of blocks for each shape without giving any information about the types of blocks or their arrangement.

Some students are able to find the solutions more easily if they know how many total blocks a figure requires, without knowing exactly how many triangles, hexagons, trapezoids, and/or rhombuses are needed for that figure. For your reference the solutions are:

Page 1 The Trapezoid: 4 blocks (4 trapezoids)The Star: 6 blocks (6 rhombuses or 3 trapezoids and 3 triangles)Page 2 The Large Rhombus: 5 blocks (4 trapezoids and 1 hexagon)Page 3 The Dog: 9 blocks (5 rhombuses, 2 hexagons, 1 trapezoid, and 1 triangle)Page 4 The Large Trapezoid: 7 blocks (2 hexagons and 5 trapezoids)Page 5 The Large Hexagon: 12 blocks (6 hexagons and 6 trapezoids)Page 6 The Large Star: 13 blocks (7 hexagons and 6 triangles)

One or more students are working quickly and successfully to complete all of the sheets in the set.

CHALLENGE Pair students working at roughly the same level and invite them to try game variation A.

English-Language Learners Use the following adaptations to support the ELL students in your classroom.

• Have pairs of ELL students observe another student working on the task.• Model replacing a set of smaller blocks, such as two trapezoids, with a larger block, such as the hexagon, to illustrate the idea of building the

same shape with fewer blocks.

Unit 6 Module 3

T2 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

Session 1 1 copy kept in a clear plastic sleeve and stored in the Work Place bin

Work Place Instructions 6D Fill for Less1 Students need some pattern blocks, crayons, and a copy of one of the Fill for Less Record Sheets.

Note Students can work on the Fill for Less Record Sheets in any order they choose, and may reasonably be expected to complete one or two of the sheets each time they visit this Work Place.

2 Students work with the pattern blocks to find a way to fill the figure on the sheet with the smallest number of blocks possible. • Students can place their blocks directly on the sheet as they’re working or build the figure off to the side.

3 When students believe they have found a way to make the shape with the fewest blocks, they record the solution by coloring in the picture on the record sheet. Note If students have built directly on the sheet, they may remove the blocks one at a time, coloring as they go. They might also slide the blocks to the side and rearrange them so they can copy from the blocks to the sheet.

4 Students can take another Fill for Less Record Sheet and repeat steps 1–3, or leave and come back to this Work Place another time.

Game Variation

A Some students may enjoy working with a partner to create a game of this Work Place. Have pairs fill a figure with as many pattern blocks as possible. Then have each player take turns replacing a group of smaller pattern blocks with a larger one that fills the same space. Players should take turns until no more blocks can be replaced. The winner is the last person to replace blocks.

Unit 6 Module 3

T3 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

Session 1 1 copy for display, plus a half-class set, stored in the Work Place bin

6D Fill for Less Record Sheet page 1 of 6Build the pictures below with the fewest possible blocks. Show your solutions by coloring in the pattern blocks you used.

NAME | DATE

Unit 6 Module 3

NAME | DATE

(continued on next page)

T4 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

Session 1 1 copy for display, plus a half-class set, stored in the Work Place bin

6D Fill for Less Record Sheet page 2 of 6

Build the picture below with the fewest possible blocks. Show your solution by coloring in the pattern blocks you used.

Unit 6 Module 3

NAME | DATENAME | DATE

(continued on next page)

T5 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

Session 1 1 copy for display, plus a half-class set, stored in the Work Place bin

6D Fill for Less Record Sheet page 3 of 6

Build the picture below with the fewest possible blocks. Show your solution by coloring in the pattern blocks you used.

Unit 6 Module 3

NAME | DATENAME | DATE

(continued on next page)

T6 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

Session 1 1 copy for display, plus a half-class set, stored in the Work Place bin

6D Fill for Less Record Sheet page 4 of 6

Build the picture below with the fewest possible blocks. Show your solution by coloring in the pattern blocks you used.

Unit 6 Module 3

NAME | DATENAME | DATE

(continued on next page)

T7 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

Session 1 1 copy for display, plus a half-class set, stored in the Work Place bin

6D Fill for Less Record Sheet page 5 of 6

Build the picture below with the fewest possible blocks. Show your solution by coloring in the pattern blocks you used.

Unit 6 Module 3

NAME | DATENAME | DATE

(continued on next page)

T8 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

Session 1 1 copy for display, plus a half-class set, stored in the Work Place bin

6D Fill for Less Record Sheet page 6 of 6

Build the picture below with the fewest possible blocks. Show your solution by coloring in the pattern blocks you used.

Unit 6 Module 3

NAME | DATE

T9 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

Session 2 class set, plus 1 copy for display

Churn Dash Quilt Block

Unit 6 Module 3

NAME | DATE

T10 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

Session 3 class set, plus a few extra

Centimeter Square Grid Paper

Unit 6 Module 3

NAME | DATE

T11 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

Exp

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Session 5 1 copy for displayUnit 6 Module 3

T12 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

Session 5 1 copy kept in a clear plastic sleeve and stored in the Work Place bin

Work Place Guide 6E Halves & Half-Nots

SummaryStudents do at least one of four worksheets in which they find the area of the gray and the white regions on two different quilt blocks. They determine whether each block is exactly half gray and half white, or more than half of one color or the other.

Skills & Concepts• Find the total number of objects in an array with up to 5 rows and 5 columns, using addition (2.OA.4)• Write an equation to represent the total number of objects in an array with up to 5 rows and 5 columns as the sum

of equal addends (2.OA.4)• Partition a rectangle into rows and columns of same-size squares (2.G.2)• Count the total number of squares in a rectangle that has been partitioned into rows and columns of same-size

squares (2.G.2)• Partition a rectangle into 2 equal parts and use the terms halves and half of to talk about the 2 equal parts (2.G.3)• Describe a whole rectangle as 2 of two equal parts (2.G.3)

Materials

Copies Kit Materials Classroom Materials

TM T12 Work Place Guide 6E Halves & Half-NotsTM T13 Work Place Instructions 6E Halves & Half-NotsTM T14–17 6E Halves & Half-Not Record Sheets

• 1” construction paper squares (about 100 in each of two different colors)

Note There are 4 different record sheets for this Work Place. You may wish to place copies of each in a folder, and then place the folders in the Work Place bin.

Assessment & DifferentiationHere are some quick observational assessments you can make as students begin to play this game on their own. Use the results to differentiate as needed.

If you see that… Differentiate

Students are struggling with more advanced sheets.

SUPPORT Encourage students to work in order from Page 1 to Page 4. Give students a reasonable goal for the number of exercises and sheets to finish in each visit.

Students aren’t sure how to get started. SUPPORT Model using the paper squares to cover all the patches of one color on a quilt block. Explain that the number of paper squares will equal the area of that colored region. Encourage students to cut the paper squares in half when necessary, and work with them to see that two halves combine to make one whole square unit.

One or more students are working quickly and successfully to complete all of the record sheets in the set.

CHALLENGE Invite students to create their own gray and white quilt blocks—one where exactly half of the area is gray, one where gray makes up a little less than half, and one where gray makes up a little more than half of the total area. Students can share their blocks with classmates.

Unit 6 Module 3

T13 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

Session 5 1 copy kept in a clear plastic sleeve and stored in the Work Place bin

Work Place Instructions 6E Halves & Half-Nots1 Students need one of the Halves & Half-Not Record Sheets and some paper squares.

2 Students find the area of the white and the gray region on the first quilt block. • They can use the paper squares or any other counting method they choose to determine the area of each region.

3 Students use numbers, equations, and/or labeled sketches to show how they determined the area of each region on the quilt block. • The answer alone is not enough.

4 Students record the area of each region in the box below the quilt block and mark the sentence that best describes the portion of the block allotted to each color.

Jensen

22 2

22

222

8 8

5 Students repeat steps 2–4 with the second quilt block on the record sheet.

6 Students share their record sheet with someone in class to make sure they understand the work and agree with the results.

Unit 6 Module 3

T14 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

6E

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Session 5 half-class set, plus more as needed, stored in the Work Place binUnit 6 Module 3

NA

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T15 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

6E H

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Session 5 half-class set, plus more as needed, stored in the Work Place binUnit 6 Module 3

NA

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T16 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

6E H

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Session 5 half-class set, plus more as needed, stored in the Work Place binUnit 6 Module 3

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T17 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

6E H

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Session 5 half-class set, plus more as needed, stored in the Work Place binUnit 6 Module 3

NA

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T18 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

Session 6 class set, plus 1 copy for display

Unit 6 Post-Assessment page 1 of 4

1 Fill in the bubble to show the name of each shape below. Then tell how you know. a N square How do you know? Give at least one reason.

N rectangle

N trapezoid

N rhombusb N square How do you know? Give at least one reason.

N hexagon

N triangle

N pentagonc N triangle How do you know? Give at least one reason.

N rectangle

N trapezoid

N pentagond N hexagon How do you know? Give at least one reason.

N rhombus

N pentagon

N octagon

2 Which of these shapes is a cube? Fill in the bubble to show.

N N N N

Unit 6 Module 3

NAME | DATENAME | DATE

(continued on next page)

T19 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

3 Follow the instructions to make each shape on your geoboard. Then copy the shape you built on this sheet and write its name on the line below. Use a ruler to help make the sides of the shapes straight when you draw them.a Make a shape with 3 sides and 3

corners or vertices. Shape name: _________________

b Make a shape with 4 sides that are all the same length. Shape name: _________________

4 Find all the quadrilaterals in the box below. Color them green. Do not color any of the other shapes.

Session 6 class set, plus 1 copy for display

Unit 6 Post-Assessment page 2 of 4

Unit 6 Module 3

NAME | DATENAME | DATE

(continued on next page)

T20 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

5 Use tiles to cover this entire rectangle. Do not leave any holes or gaps. Then answer the questions below.

a How many tiles did it take to cover the entire rectangle? _________________

b Write an addition problem to show how many tiles it took to cover the rectangle. __________________________________________________________

6 Here are three different shapes. Use them to answer the questions below.

a Divide each shape into two equal parts. Use a ruler to help draw straight lines.

b When you divide a shape into two equal parts, what is each part called? Fill in the bubble to show.

N one-fourth N one second N one-third N one-half

c Eric says that two halves is the same as one whole. Do you agree with Eric? Why or why not?

Session 6 class set, plus 1 copy for display

Unit 6 Post-Assessment page 3 of 4

Unit 6 Module 3

NAME | DATENAME | DATE

(continued on next page)

T21 © The Math Learning Center | mathlearningcenter.orgBridges in Mathematics Grade 2 Teacher Masters

7 Use these shapes to answer the questions below.

a Find the trapezoid. Draw a line to cut it in half. Color in one-half red.

b Find the rectangle. Color one-half of the rectangle blue. Color the other half yellow.

c Find the circle that is divided into two equal parts. Color in two halves of that circle green.

8 Dad made sandwiches exactly the same size for Sam and Sarah. Then he cut each sandwich in half like this. Sam said, “That’s not fair! Sarah got bigger halves than me!” Is Sam right? Why or why not? Use labeled sketches, words, and/or numbers to explain.

Sarah's Sandwich Sam's Sandwich

Session 6 class set, plus 1 copy for display

Unit 6 Post-Assessment page 4 of 4

Unit 6 Module 3

NAME | DATE