Common Core Unit 2 INVESTIGATION 1 Features of 2-Dimensional and 3-Dimensional Shapes Day Session Common Core Adaptation Common Core Standards 1 1.1A Subtraction Facts See p. CC9. MP1, MP6, MP7 2.OA.2 2 1.1 Geoblock Faces MP5, MP7 2.OA.1, 2.OA.2, 2.G.1 ACTIVITY Introducing Quick Images: Shapes Teaching Note Additional Shapes Display the pentagon (Shape U), the hexagon (Shape V), and the octagon (Shape X) before going on to Activity 2. Discuss the number of sides, and ask students whether or not they know the name of each shape. Use Student Math Handbook p. 117, Naming Polygons, as a reference. SESSION FOLLOW-UP Daily Practice and Homework Family Letter: Make and send home copies of C9–C10, Family Letter, as a replacement for M5–M6, Family Letter. 3 1.2 Working with Geoblocks MP5 2.OA.1, 2.OA.2, 2.OA.4, 2.G.1 4 1.3 Sorting Geoblocks MP3, MP5 2.OA.4, 2.NBT.2, 2.G.1 5 1.4 Addition Combinations and Ways to Fill MP5 2.OA.2, 2.MD.7, 2.G.1 6 1.5 Combining Shapes MP5 2.G.1 CLASSROOM ROUTINES Quick Images: Drawing Shapes In addition, when students compare and contrast the three Shape Cards, focus specifically on the number of sides of each shape, pointing out that while irregular, these shapes (quadrilateral, pentagon, and hexagon) are still named by the number of sides. SESSION FOLLOW-UP Daily Practice Family Letter Make and send home copies of C11–C12, Family Letter, as a replacement for M17–M18, Family Letter. Mathematical Practices (MP) Domains • Operations and Algebraic Thinking (OA) • Number and Operations in Base Ten (NBT) • Measurement and Data (MD) • Geometry (G) Shapes, Blocks, and Symmetry Instructional Plan CC5
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(MP) Shapes, Blocks, and Symmetry...Images: Shapes Teaching Note Additional Shapes Display the pentagon (Shape U), the hexagon (Shape V), and the octagon (Shape X) before going on
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Common CoreUnit 2
I N V E S T I G AT I O N 1
Features of 2-Dimensional and 3-Dimensional Shapes
Day Session Common Core Adaptation Common Core Standards
1 1.1A Subtraction Facts See p. CC9. MP1, MP6, MP72.OA.2
Teaching NoteAdditional Shapes Display the pentagon (Shape U), the hexagon (Shape V), and the octagon (Shape X) before going on to Activity 2. Discuss the number of sides, and ask students whether or not they know the name of each shape. Use Student Math Handbook p. 117, Naming Polygons, as a reference.
SESSION FOLLOW-UPDaily Practice and Homework
Family Letter: Make and send home copies of C9–C10, Family Letter, as a replacement for M5–M6, Family Letter.
3 1.2 Working with Geoblocks MP52.OA.1, 2.OA.2, 2.OA.4, 2.G.1
In addition, when students compare and contrast the three Shape Cards, focus specifically on the number of sides of each shape, pointing out that while irregular, these shapes (quadrilateral, pentagon, and hexagon) are still named by the number of sides.
SESSION FOLLOW-UPDaily Practice
Family Letter Make and send home copies of C11–C12, Family Letter, as a replacement for M17–M18, Family Letter.
mathematical Practices (MP)
Domains• Operations and Algebraic Thinking (OA)• Number and Operations in Base Ten (NBT)• Measurement and Data (MD)• Geometry (G)
Shapes, Blocks, and Symmetry
Instructional Plan CC5
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I N V E S T I G AT I O N 2
What Is a Rectangle?Day Session Common Core Adaptation Common Core Standards
7 2.1 Assessment: Sorting Shapes by Number of Sides
MP32.OA.1, 2.OA.2, 2.G.1
ACTIVITYSorting Shape Cards
Math NoteSorting and Naming Polygons Polygons are named for the number of sides they have. Students are likely to be familiar with the regular pentagon (Shape U) but be surprised that Shape T is also a pentagon because it has 5 sides. Similarly, they will be surprised by the hexagons Shape V (regular) and Shape I and the octagons Shape X (regular) and Shape W. Look for opportunities throughout Sessions 2.1 and 2.2 to point out and discuss pentagons and hexagons.
Teaching NoteShapes with More Than 4 Sides As students are sorting Shape Cards by the number of sides, spend a short amount of time looking at the set of shapes with “more than 4 sides.” Have students further sort this set into shapes with 5, 6, and 8 sides. Discuss the name of each shape and the number of sides and angles.
What’s a Rectangle?Teaching NotePentagons, Hexagons, Octagons When discussing the set of shapes with more than four sides, discuss the name of each shape, the number of sides, and angles.
Use Shape U instead of Shape P. Have students compare and contrast the three shape cards, focusing specifically on the number of sides and the number of angles. Use Student Math Handbook p. 117, Naming Polygons, as a reference.
CC6 UNIT 2 Shapes, Blocks, and Symmetry
INV12_TE02_U02.indd 6 6/8/11 7:37 PM
I N V E S T I G AT I O N 2
What Is a Rectangle? continued
Day Session Common Core Adaptation Common Core Standards
10 2.4 Building Rectangles MP3, MP52.OA.1, 2.OA.2, 2.OA.4, 2.G.2
MATH WORKSHOPDouble It
Include Double It in Math Workshop. Student Activity Book page 21A or C13 (Double It Recording Sheet) Make copies. (1 per pair)
Teaching NoteDouble It This game, introduced in Counting, Coins, and Combinations (Unit 1) is added to this session and subsequent sessions and provides additional practice with the doubles combinations. Students practice the doubles combinations by drawing a number card, doubling the result, and recording the sum on the recording sheet.
Include Double It in Math Workshop. C13 (Double It Recording Sheet) Make copies. (1 per pair)
12 2.6 How Many Rectangles MP5, MP62.OA.2, 2.OA.4, 2.G.2MATH WORKSHOP
Double ItInclude Double It in Math Workshop. C13 (Double It Recording Sheet) Make copies. (1 per pair)
13 2.7 Assessment: Is It a Rectangle?
MP6, MP72.OA.1, 2.OA.2, 2.G.1
SESSION FOLLOW-UPDaily Practice
Homework: Students play Double Arrays and Double It at home. Have students complete Student Activity Book pages 28B–28C or C14–C15 (Double Arrays and Double It)
14 2.8 Making Boxes from Rectangles
MP12.NBT.2, 2.G.1, 2.G.2
15 2.9 Assessment: Faces of a Geoblock
MP32.MD.7, 2.G.1
16 2.10A End-of-Unit Assessment See p. CC14. MP1, MP22.OA.2, 2.OA.4, 2.G.2
3E
2F
2F
Instructional Plan CC7
INV12_TE02_U02.indd 7 6/8/11 7:36 PM
I N V E S T I G AT I O N 3
Symmetry Skip this Investigation.
Day Session Common Core Adaptation Common Core Standards
3.1 Mirror Symmetry
3.2 Copy Tiles
3.3 Paper Folding and Cutting
3.4 Is It Symmetrical?
3.5 End-of-Unit Assessment This End-of-Unit Assessment is now Session 2.10A.
CC8 UNIT 2 Shapes, Blocks, and Symmetry
INV12_TE02_U02.indd 8 5/25/11 5:05 PM
s e s s i o n 1 . 1 A
Activity
Addition Combinations and Related Subtraction Facts 20 Min clAss PAirs
Developing fluency with the subtraction facts related to the Plus 1, Plus 2, and Make 10 addition combinations
Classroom RoutinesQuick Images: Double Arrays Using the transparent double arrays from Rectangular Arrays (T24), display the 2 × 4 array. Follow the basic Quick Images activity. Students determine the total number of squares and share how they determined the amount. Record an equation using addition (e.g., 4 + 4 = 8) that represents the array. Repeat with 2 × 7 and 2 × 9.
Addition Combinations and Related Subtraction Facts
ClAss pAIrs20 MIn
Begin this session by referring to the sets of addition combinations that students worked on and were assessed on in the previous unit.
You each have sets of cards for the Plus 1, Plus 2, and the Make 10 combinations. Today, we are going to look at some subtraction problems that are related to these addition combinations.
Write the following on the board, and have students record them on a piece of paper.
7∙ 1∙ _____8∙ 1∙ _____8∙ 7∙ _____
Here are three problems that are related to one another. Solve each of the problems, and then talk with a partner about how you think these problems are related.
Most students will quickly solve these problems, and many will recognize that they can use what they know about one problem (7 + 1 = 8) to solve the related subtraction problems (8 – 1 = 7 and 8 – 7 = 1).
Show students the tower of 8 cubes (7 yellow and 1 red) that you have prepared. Ask volunteers to explain how the problems in this set are related using the cubes to demonstrate their ideas. As students explain their thinking, model it for the class.
Here are two other sets of problems. Solve each problem, and build a cube model of each set. Then talk with a partner about how the problems are related.
When students are finished, briefly discuss their thinking about how these sets of problems are related. 1
A C T I V I T Y
Which Subtraction Facts Do I Know?
IndIVIdUAlS pAIrS30 MIn
In the previous unit you were working on three sets of addition combinations, the Plus 1, Plus 2, and Make 10 combinations. Just as it is important to quickly know addition combinations with small numbers, it is also important to be able to quickly solve subtraction problems with small numbers. Today, you are going to get sets of subtraction fact cards that are related to the addition facts you already know.
Refer to the sets of problems that students just worked on as examples of each set. 2
Related to Related to Related to +1 combinations +2 combinations combinations of 10
Facts Students build on their growing understanding of the inverse relationship between addition and subtraction, as well as their fluency with addition combinations, to learn the related subtraction facts. Students will work on sets of subtraction facts in Units 2, 4, 5, and 9, following the assessment of a set of related addition facts (i.e., in Unit 1 students are assessed on the Plus 1, Plus 2, and Make 10 addition combinations. In Unit 2 they work on the related sets of subtraction facts). You can use this session as a model for introducing new sets of facts as indicated in subsequent units.
2 SubtractionFactsRelatedtoAdditionCombos Point out to students that one set has Subtraction Facts related to the +1 addition combinations, one set has Subtraction Facts related to the +2 combinations, and one set has Subtraction Facts related to the combinations of 10.
Distribute the three sets of Subtraction Cards (C2–C6) to each student. Explain to students that they should write their initials on the back of each card. Tell them that they should not write the answers to the problems on the cards, and for now, they should leave the Clue: blank.
Once students have initialed their cards, give each student two envelopes. Have students write their name on both envelopes and label one with “Subtraction Facts I Know” and the other with “Subtractions Facts I Am Still Working On.”
The Subtraction Cards are going to work just like your Addition Cards. Look through the cards and sort them into two groups. If you look at a card and you know the answer without having to stop and solve the problem, put that card in the “Subtraction Facts I Know” envelope. Put the cards that you aren’t sure about or have to stop and figure out the answer to in the “Subtraction Facts I Am Still Working On” envelope.
As you circulate, take subtraction cards from each student’s “Subtraction Facts I Know” envelope and see whether you agree that the student knows these facts. Re-file cards as needed.
Have pairs of students work together to practice with the cards. They should mix up the sets of cards so that related cards (i.e., Subtraction Cards related to +1 combinations) are not together.
Facts Throughout this unit and in subsequent units, students should continue to practice the subtraction facts in their “working on” piles. This practice can be assigned as additional homework, a Math Workshop activity, or something students work on when they have a few minutes after completing another activity. C7 allows you to individualize this practice according to student needs.
▲ resource masters, C2–C6
CC12 inveStigAtiOn 1 Features of 2-dimensional and 3-dimensional Shapes
Practicing with Subtraction CardsChoose 6 Subtraction Card problems from your “working on” pile, and write these on the blank cards below. Practice these at home with a friend or family member.
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Addition Clue:
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Addition Clue:
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Addition Clue:
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Addition Clue:
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Addition Clue:
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Addition Clue:
note Students practice subtraction facts and use related addition facts to help.
After most students have sorted and practiced their sets of Subtraction Cards, call the group together to discuss how to use the Clue on each Subtraction Card.
Write following problems on the board.
9∙ 2 10∙ 4
Clue:____________ Clue:____________
Suppose you were stuck on these two subtraction facts. Talk with the person next to you about what addition problem you could use as a clue to solve the subtraction problem.
Ask volunteers to explain their thinking about which addition problem they would record. Use cubes to model their ideas.
Explain to students that they should work with a partner to write addition clues for any of the cards that are in the “Subtraction Facts I Am Still Working On” envelope. Each student should work on his or her own set of cards but can consult with a partner if they need a suggestion about the related addition clue. 4
Have students choose 6 problems from their “Working On” envelopes that they want to practice at home. They record those subtraction facts on Student Activity Book page 1A or C7.
S e S S i o n F o l l o w - U p
Daily Practice and Homework DailyPractice: For ongoing review, have students complete
Student Activity Book page 1B or C8.
Homework: Students work on the subtraction facts they recorded on Student Activity Book page 1A or C7 at home with a friend or family member.
teaching notes4 AssessingSubtractionFacts Most
students should be comfortable with most of these first sets of Subtraction Facts. Students will be assessed on these three sets of facts in Session 2.10A as a part of the End-of-Unit Assessment.
▲ Student Activity Book, Unit 2, p. 1A;Resource Masters, c7
▲ Student Activity Book, Unit 2, p. 1B;Resource Masters, c8
Session 1.1A Subtraction Facts cc13
INV12_TE02_U02_S1.1A.indd 13 6/8/11 6:39 PM
s e s s i o n 2 . 1 0 A
Classroom RoutinesToday’s Number: 29 Students individually generate numerical expressions for the number 29 using addition and/or subtraction. They record these expressions on blank paper which they have labeled with the date and heading Today’s Number: 29. This work will give you some information on how students are understanding and working with Today’s Number. Additionally, this is the second in a series of work samples for Today’s Number that will be collected throughout the year.
AssessMenT ACTiViTY
End-of-Unit Assessment Problems 60 Min indiViduAls
• C16–C19, end-of-unit Assessment Make copies. (1 per student)
• M15, inch Grid Paper Make copies. (1 per student; plus extras as needed)
• M29, Centimeter Grid Paper Make copies. (optional)
• C20, Assessment Checklist: doubles Combinations Make copies. (2 or 3 sheets)
• C21, Assessment Checklist: subtraction Facts Make copies. (7 or 8 sheets)
• M19, Addition Cards set 2: doubles Combinations (from Session 1.4; optional) ; color tiles; tape\
session Follow-uP
Daily Practice • Student Activity Book, p. 30B or C22, Fly Away! Make copies. (as needed)
• Student Math Handbook, pp. 47, 126
Today’s Plan Materials
End-of-Unit AssessmentMath Focus Points
Constructing and describing rectangular arrays of tiles
Achieving fluency with the doubles combinations
Developing fluency with subtraction facts related to the Plus 1, Plus 2, and Make 10 addition combinations
1. Make a rectangle using 18 color tiles. Draw it on grid paper.
Cut out your rectangle and tape it in this space.
2. Describe your rectangle. Include how many rows and how many tiles are in each row.
INV12_BLM02_U2.indd 16 4/21/11 5:47 PM
Professional Development 1 TeacherNote:End-of-Unit Assessment,
pp. 166–167, 171
1 Assessment Activity 2 Session Follow-Up
A S S E S S M E N T A C T I V I T Y
End-of-Unit AssessmentINDIVIDUAlS60 MIN
This End-of-Unit Assessment focuses on two of the unit’s benchmarks. 1
There are three parts to the End-of-Unit Assessment. Each student works independently to solve the problem Make a Rectangle (C16) that assesses Benchmark 2: Identify the number of rows and the number of squares in each row in an array. Students also complete Doubles Combinations (C17) that assesses Benchmark 6: Demonstrate fluency with addition combinations: doubles combinations to 10 + 10.
They are also assessed on their fluency with the subtraction facts related to +1 and +2 combinations and combinations of 10 as they complete Subtraction Facts (C18–C19).
As students are working on the assessment, have individuals or small groups of students cycle through a station with you to complete the assessments for Doubles Combinations and Subtraction Facts.
Part 1: Make a RectangleOn End-of-Unit Assessment: Make a Rectangle (C16), students make a rectangle using 18 color tiles, draw it on Inch Grid Paper (M15), cut it out, and attach it to the assessment sheet. Then students describe the rectangle.
Students may need to tape together two sheets of inch grid paper to make their rectangle, or students may choose to draw their rectangle on Centimeter Grid Paper (M29).
ONgOINg ASSESSMENT: Obser ving Student s at Work
Students make a rectangular array and describe it.
Part 2: Doubles CombinationsThe Doubles Combinations assessment can be done in one of two ways. Both involve observation. If you choose to use End-of-Unit Assessment: Doubles Combinations (C17), observe students as they complete the sheet to see how fluent they are in their responses.
Alternately, you can interview students, using a blank set of the Addition Cards Set 2: Doubles Combination (M19), and they can respond orally. Keep track of student responses on the Assessment Checklist: Doubles Combinations (C20). 2
OngOing Assessment: Obser ving student s at Work
Students solve doubles combination problems.
• Do students accurately and efficiently solve all the problems in a reasonable amount of time?
Part 3: Subtraction Facts Students solve a selection of subtraction facts related to +1 and +2 combinations and combinations of 10. The subtraction facts assessment can be done in one of two ways and involves observation. If you choose to use End-of-Unit Assessment: Subtraction Facts (C18–C19), observe 5–6 students at a time as they complete the sheet to see how fluent they are in their responses. Record information on the Assessment Checklist: Subtraction Facts by circling the facts that the student is not yet fluent with (C21).
Alternately, you can interview students using their sets of subtraction fact cards and record your observations on C21 as well.
OngOing Assessment: Obser ving student s at Work
Students solve subtraction problems related to +1 and +2 combinations, and combinations of 10.
• Do students accurately and efficiently solve all the problems in a reasonable amount of time?
s e s s i O n F O l l O W - U p
Daily Practice Daily Practice: For enrichment, have students complete
Student Activity Book page 30B or C22.
Student Math Handbook: Students and families may use Student Math Handbook pages 47 and 126 for reference and review. See pages 178–182 in the back of this unit.
1 Assessment Activity 2 session Follow-Up
▲ Resource masters, C21
▲ student Activity Book, Unit 2, p. 30B; Resource masters, C22
teaching note 2 Subtraction Facts Related to the
Doubles Combinations (Set 4) This set of facts will be introduced at the beginning of Session 1.2 in Unit 3. In preparation, make copies and cut apart C25, Subtraction Cards Set 4 (1 per student).
note Students practice subtraction facts and use related addition facts to help.
Practicing with Subtraction CardsChoose 6 Subtraction Card problems from your “working on” pile, and write these on the blank cards below. Practice these at home with a friend or family member.
Practicar con tarjetas de resta Escoge 6 problemas de tarjetas de resta de la pila con la cual estás trabajando y escríbelos en las tarjetas en blanco de abajo. Practícalos en casa con un amigo o un miembro de tu familia.
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Pista para la suma:
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Pista para la suma:
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Pista para la suma:
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Pista para la suma:
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Unidad 2 Sesión 1.1A
notA Los niños practican operaciones de resta y usan operaciones relacionadas de suma como ayuda.