Beaverton Rural Schools 2013: Grade 2 CCSS-M Everyday Mathematics Instructional Guide v4.0 Key: CCSS-M = Common Core State Standards for Mathematics; EDM = Everyday Mathematics; TLG = Teacher’s Lesson Guide; MM = Math Masters; MRB = My Reference Book; AH = Assessment Handbook; Grade 2 RSA = Recognizing Student Achievement; R = Readiness; E = Enrichment; EP = Extra Practice; SMJ = Student Math Journal; TRM = Teacher Reference Manual; Page 1 Unit 1A: Numbers and Routines – Part 1 Pacing: 3 weeks, almost thru the end of September (week 4). CCSS-M Critical Ideas for this Unit Before counting and comparing numbers in the 100s students need to understand place value, 2.NBT.1. Several lessons in the EDM Unit 1 depend on students having covered most of these Grade 2 standards in Grade 1. This is no longer the case since CCSS-M asks that teachers focus on mastery of their own grade level standards. For this reason Unit 1 has been split into two parts in order to expand and provide ample time to cover the missing content. Unit 1A will now focus on representing place value in the 100s, 2.NBT.1; comparing numbers, 2.NBT.4; and continuing basic counts, 2.NBT.3. Money, 2.MD.8, in unit 1A, is simply used as a tool to support place value concepts. Basic “add to” and “take from” word problems within Grade 1 number ranges should be reviewed. Do these lessons in the order in which they are listed. Learning Target EDM Edits Comments Vocabulary Games Advanced Prep 1♦2 Use dimes and pennies to review place value with 10s and 1s. 1.NBT.2 & 2.MD.8 To support vocabulary point out the ruler portion of their template or say that “the template includes both an inch ruler and a centimeter ruler.” slate, tool kit, Lost-and- Found Box, Pattern- Block Template, ruler, total Prepare and label Toolkits. Provide ‘Lost-and- Found’ box for misplaced Toolkit items. See TLG p23. Part 3 (EP) uses the book. Arctic Fives Arrive. 1♦3 Use clocks to tell & show time to the nearest half-hour. 1.MD.3 MOVE to Unit 3? Time will be addressed in Unit 3. You can either review hour & ½ hour here or move this lesson to Unit 3. calendar, ordinal numbers Post name of the months in classroom. 1♦A Use a system of bundles to determine a count for large numbers of objects. 2.NBT.1 Supplemental Activities to support Place Value Concepts: 1 Day Spend a day in class having students count large quantities (>200) of objects using bundles of 10 to keep track. Each table can count a different set of objects (beans, unifix cubes, pattern blocks, etc). After an initial attempt discuss strategies for keeping track of counts. Lead the discussion to bundling 10 ones to make a ten and bundling 10 tens to make a hundred. After they are finished have students go see the work of other tables and determine each count based on the bundles they see. 2.NBT.1 Gr1 8♦2 Use dollars bills and coins to represent amounts written in dollars-and-cents notation. 1.NBT.2; 2.NBT.1 Supplemental Lesson to support place value Grade 1 Lesson 8♦2: Dollars In this lesson students look at dollars- and-cents notation and represent money using dollar bills and coins. Note the deliberate absence of quarters and nickels in the One-Dollar Exchange game. This game is designed to support students’ understanding of the base-10 number system by relating it to money and supports the concepts covered in the next lesson 8♦3. decimal point P1 One-Dollar Exchange: MRB p144, MM p224 For Part 1, students cut out MM p331 & 332, 5 bills per student, leftovers go into class bank. The book, “Follow the Money” relates to lesson content. Gr1 8♦3 Write 3-digit whole numbers modeled with base-10 blocks. 1.NBT.2; 2.NBT.3 Supplemental Lesson to support place value Grade 1 Lesson 8♦3: Hundreds, Tens, and Ones During “Naming Numbers Shown with Base-10 Blocks” model expanded form (2.NBT.3) with student participation. For example, 1 flat, 4 longs, and 6 cubes is written as 100+40+6= 146. Next, have the students read the 3-digit numbers aloud (also 2.NBT.3). Add these practices to your daily routines. hundreds, tens, ones, hundreds place, tens place, ones place P2 Tric-Trac: MRB p156, MM p360;; P3R Beat the Calculator: SMJ p116 In Part 1, students use Base-10 blocks. For Part 1, teaching master or poster of MM p324 might be helpful. 1♦5 Use bills to make exchanges on a place value mat. 2.NBT.1 This is a great opportunity to talk about the meaning of the 100s, 10s & 1s digits (2.NBT.4). After completing SMJ p6, have students identify place value digits (i.e. “Which digit in $325 tells me how many ten dollar bills I have?”; “What is the value of that digit?”) For additional practice use Gr2 Singapore Extra Practice Book p74 problems 1-5. This skill will later be used to compare 3 digit numbers (also 2.NBT.4) digit, value P1, 2 Money Exchange Game: MRB p128, MM p448-461; P2 Addition Top-It: MM p449; P3R Penny-Nickel Exchange Game: MRB p128 Prepare money for toolkits. See TLG p38. Teaching Master of MM p458. 3♦1 Use base-10 blocks, drawings and digit cards to represent 2- and 3-digit numbers. 2.NBT.1 & 2.NBT.4 Revised Matching Numbers and Playing Digit Game to better support 2.NBT.1 New Activity Using Place Value to compare Number to better support 2.NBT. 4 MOVED: Modification: 2-Days Extend this lesson using the readiness activity from Lesson 3♦2, Penny-Dime-Dollar Exchange and provide an have students write equations to support expanded form 2.NBT.3 (i.e. if you have one dollar, five dimes and 3 pennies, students can write 100+50+3=153 pennies or $1.53) This is the only time this game is referenced in second grade. Play it at least three more times during the year. base-10 system, cube, long, flat, digit P2 Digit Game: MRB p132-3 Prepare sets of Base-10 blocks for partners. Prepare teaching Master of Place-Value Mat. See TLG p184. Planning Ahead: For 3♦2, prepare poster or Teaching Master of MM p58. See Number Talk and Word Problem instructional notes on bottom of following page. UNIT 1A COMMON ASSESSMENT
Key: CCSS-M = Common Core State Standards for Mathematics; EDM = Everyday Mathematics; TLG = Teacher’s Lesson Guide; MM = Math Masters; MRB = My Reference Book; AH = Assessment Handbook; Grade 2 RSA = Recognizing Student Achievement; R = Readiness; E = Enrichment; EP = Extra Practice; SMJ = Student Math Journal; TRM = Teacher Reference Manual; Page 1
Unit 1A: Numbers and Routines – Part 1 Pacing: 3 weeks, almost thru the end of September (week 4).
CCSS-M Critical Ideas for this Unit
Before counting and comparing numbers in the 100s students need to understand place value, 2.NBT.1. Several lessons in the EDM Unit 1 depend on students having covered most of these Grade 2 standards in Grade 1. This is no longer the case since CCSS-M asks that teachers focus on mastery of their own grade level standards. For this reason Unit 1 has been split into two parts in order to expand and provide ample time to cover the missing content. Unit 1A will now focus on representing place value in the 100s, 2.NBT.1; comparing numbers, 2.NBT.4; and continuing basic counts, 2.NBT.3. Money, 2.MD.8, in unit 1A, is simply used as a tool to support place value concepts. Basic “add to” and “take from” word problems within Grade 1 number ranges should be reviewed. Do these lessons in the order in which they are listed.
Learning Target EDM Edits Comments Vocabulary Games Advanced Prep
1♦2 Use dimes and pennies to
review place value with 10s and 1s. 1.NBT.2 & 2.MD.8
To support vocabulary point out the ruler portion of their template or say that “the template includes both an inch ruler and a centimeter ruler.”
slate, tool kit, Lost-and-Found Box, Pattern-Block Template, ruler, total
Prepare and label Toolkits. Provide ‘Lost-and-Found’ box for misplaced Toolkit items. See TLG p23. Part 3 (EP) uses the book. Arctic Fives Arrive.
1♦3 Use clocks to tell & show time to
the nearest half-hour. 1.MD.3 MOVE to Unit 3? Time will be addressed in Unit 3. You can either review hour & ½ hour here or move this lesson to Unit 3.
calendar, ordinal numbers Post name of the months in classroom.
1♦A Use a system of bundles to
determine a count for large numbers of objects. 2.NBT.1
Supplemental Activities to support Place Value Concepts: 1 Day Spend a day in class having students count large quantities (>200) of objects using bundles of 10 to keep track. Each table can count a different set of objects (beans, unifix cubes, pattern blocks, etc). After an initial attempt discuss strategies for keeping track of counts. Lead the discussion to bundling 10 ones to make a ten and bundling 10 tens to make a hundred. After they are finished have students go see the work of other tables and determine each count based on the bundles they see. 2.NBT.1
Gr1 8
♦2 Use dollars bills and coins to
represent amounts written in dollars-and-cents notation. 1.NBT.2; 2.NBT.1
Supplemental Lesson to support place value Grade 1 Lesson 8♦2: Dollars In this lesson students look at dollars- and-cents notation and represent money using dollar bills and coins. Note the deliberate absence of quarters and nickels in the One-Dollar Exchange game. This game is designed to support students’ understanding of the base-10 number system by relating it to money and supports the concepts covered in the next lesson 8♦3.
decimal point P1 One-Dollar Exchange: MRB p144, MM p224
For Part 1, students cut out MM p331 & 332, 5 bills per student, leftovers go into class bank. The book, “Follow the Money” relates to lesson content.
Gr1 8
♦3
Write 3-digit whole numbers modeled with base-10 blocks. 1.NBT.2; 2.NBT.3
Supplemental Lesson to support place value Grade 1 Lesson 8♦3: Hundreds, Tens, and Ones During “Naming Numbers Shown with Base-10 Blocks” model expanded form (2.NBT.3) with student participation. For example, 1 flat, 4 longs, and 6 cubes is written as 100+40+6= 146. Next, have the students read the 3-digit numbers aloud (also 2.NBT.3). Add these practices to your daily routines.
hundreds, tens, ones, hundreds place, tens place, ones place
P2 Tric-Trac: MRB p156, MM p360;; P3R Beat the Calculator: SMJ p116
In Part 1, students use Base-10 blocks. For Part 1, teaching master or poster of MM p324 might be helpful.
1♦5 Use bills to make exchanges on
a place value mat. 2.NBT.1
This is a great opportunity to talk about the meaning of the 100s, 10s & 1s digits (2.NBT.4). After completing SMJ p6, have students identify place value digits (i.e. “Which digit in $325tells me how many ten dollar bills I have?”; “What is the value of that digit?”) For additionalpractice use Gr2 Singapore Extra Practice Book p74 problems 1-5. This skill will later be used to compare 3 digit numbers (also 2.NBT.4)
digit, value
P1, 2 Money Exchange Game: MRB p128, MM p448-461; P2 Addition Top-It: MM p449; P3R Penny-Nickel Exchange Game: MRB p128
Prepare money for toolkits. See TLG p38. Teaching Master of MM p458.
3♦1
Use base-10 blocks, drawings and digit cards to represent 2- and 3-digit numbers. 2.NBT.1 & 2.NBT.4
Revised Matching Numbers and Playing Digit Game to better support 2.NBT.1 New Activity Using Place Value to compare Number to better support 2.NBT. 4
MOVED: Modification: 2-Days Extend this lesson using the readiness activity from Lesson 3♦2, Penny-Dime-Dollar Exchange and provide an have students write equations to support expanded form 2.NBT.3 (i.e. if you have one dollar, five dimes and 3 pennies, students can write 100+50+3=153 pennies or $1.53) This is the only time this game is referenced in second grade. Play it at least three more times during the year.
Prepare sets of Base-10 blocks for partners. Prepare teaching Master of Place-Value Mat. See TLG p184. Planning Ahead: For 3♦2, prepare poster or Teaching Master of MM p58.
See Number Talk and Word Problem instructional notes on bottom of following page.
Key: CCSS-M = Common Core State Standards for Mathematics; EDM = Everyday Mathematics; TLG = Teacher’s Lesson Guide; MM = Math Masters; MRB = My Reference Book; AH = Assessment Handbook; Grade 2 RSA = Recognizing Student Achievement; R = Readiness; E = Enrichment; EP = Extra Practice; SMJ = Student Math Journal; TRM = Teacher Reference Manual; Page 2
1♦1
Use a number line to sequence numbers to 1,000 and count by 1s and 100s. 2.NBT.2 & 2.NBT.3
MOVED: This lesson was moved in order to have time to cover place value before doing counts and sequences within 1,000. Also have student count by 100s to 1000 2.NBT.2
Math Message, number line, order
P3R Number Line Squeeze: MM p464
Start collecting for your “Mathematics All Around” Bulletin Board. See TLG p18 for details. Planning Ahead: For 1♦2, prepare coins for student toolkits (4 Q, 10 D, 5N, 20P) Collect socks for slate activities (white boards).
1♦12
Count numbers in the 100s using base-10 blocks (Exploration B). 2.NBT.1
New Writing/Reasoning Prompt on TLG p74 to explain how you know numbers are odd and even.
MOVED: Measuring temperature is no longer a standard. Skip Exploration A (temperature) and focus on place value. Instead, use Lesson 3♦4 Exploration A, Building and Renaming Numbers. Exploration B is OK since it builds on fact practice
EXPLORATIONS: Plan for group work in Explorations. Consider creating a poster like the one on TLG p73. Cover Celsius side of Class Outdoor Thermometer with masking tape.
Instructional Note: Number talks were developed for classroom teachers to engage students in "mental math" through grappling with interesting mathematics problems. Educators can use number talks regularly as introductions to the day’s mathematical practice, as “warm ups” for other lessons, or as stand-alone extended engagements with mathematical concepts. Teachers should use Number Talks in practice often. See instructional video at: Number Talk Video
The main addition and subtraction situations students work with are listed in Table 1
Key: CCSS-M = Common Core State Standards for Mathematics; EDM = Everyday Mathematics; TLG = Teacher’s Lesson Guide; MM = Math Masters; MRB = My Reference Book; AH = Assessment Handbook; I Grade 2 RSA = Recognizing Student Achievement; R = Readiness; E = Enrichment; EP = Extra Practice; SMJ = Student Math Journal; TRM = Teacher Reference Manual; Page 3
Unit 1B: Numbers and Routines – Part 2 Pacing: 2 weeks, thru mid October (week 7).
CCSS-M Critical Ideas for this Unit
This unit continues the place value work, 2.NBT.1, begun in 1A and extends it to comparing 3-digit numbers with symbols, 2.NBT.4, counting by 10s from any 3-digit number, 2.NBT.2, and expanded form, 2.NBT.3. Like with all units, dedicate some time to work with word problems (see "additional word problems" link for resources). Review “change unknown” and “put together/take apart” word problems. Additional Word Problems.
Learning Target EDM Edits Comments Vocabulary Games Advanced Prep
1♦B Write 3-digit numbers in
expanded form. 2.NBT.3 Supplemental Activity to support Expanded Form: To address expanded form in 2.NBT.3, use Supplement 1♦B: Expanded Notation. In addition begin to look for opportunities in Math Boxes where students can write numbers in expanded form in addition to what is required. For example, problem #3 in SMJ p84, #3 in SMJ p104, and #1&3 in SMJ p112.
1♦4 Compare 2- and 3- digit
numbers. 2.NBT.4
MOVED: Addition Top-it is a good game to introduce the Top-it games and it begins work on +,- facts 2.OA.2. Spend part of the lesson also playing 2- and 3- digit Top-it to support 2.NBT.4. Have students draw 2 or 3 cards, make the largest or smallest number possible and compare. Winner takes the cards. The Number Grid Patterns in Part 2 are important to support counting by 10 from any number 2.NBT.2
total, value P1, 3R Addition Top-It: MRB p122, SMJ p5, MM p449; P3E Coin Top-It: MM p452-3
Post ‘Working With a Partner’ poster. Display Number-Grid Poster (yearlong). Copy MM p416 or p418 on cardstock and laminate or use sheet protectors for students to always have available.
1♦6
Find equivalences for 10- Complements of 10 (Penny Plate). K.OA.4 & 1.OA.6
Modification: Penny Plate has mostly been used for complement of 10 (K.OA.4). Although this is a Kinder standard, it is perhaps one of the most useful fact sets to master. If any of your students do not have fluency with complements of 10, this is the time to address it. You can also extend this game for complement of 100 with multiples of 10 (100 pennies, 40 are on top & 60 inside). Otherwise use Penny Plate to decompose numbers to 20 (1.OA.6).
My Reference Book, Table of Content, Math Boxes, problem
Part 2, Penny-Plate game requires containers such as paper or plastic plates.
1♦7 Use a number grid poster to find
patterns in the base-10 number system. 2.NBT.2
Use the number grids to work on counting by 10s from any number (2.NBT.2). Have them apply the pattern to fill out their number scrolls vertically to help with the number grid puzzles in lesson 1♦7. Counting by 5s is also important (2.NBT.2). Allow time to work on that if necessary since it will be needed later for telling time in Unit 3. Odds and evens numbers (2.OA.3) is now a Gr. 2 standard but it will be better addressed in Unit 7.
number scroll, even number, odd number, number pattern
P2 Addition Top-It: MRB p122-3, MM p449
Prepare poster for Group Work. Classroom Management Tip: See margin of TLG p48 for red cup / green cup group agreement system, when help from teacher is needed. Prepare adequate copies of MM p9 & p10 for number scrolls.
1♦8
Use patterns in the base-10 number system to complete number grid puzzles. PE 1.1.B & 2.1.A
P2 Number Grid Game: MRB p142-3, MM p418
Part 3 R, MM p12, cut out and laminate or use cardstock.
1♦9 Use a calculator to show
equivalent expressions. 1.OA.7 & 1.OA.8
Focus on broken calculator to work on composing and decomposing numbers. The TI-15 calculators have a “quiz button” (see right) that asks for the unknown in a variety of positions (1.OA.8) (i.e. 6 + ? = 14). Also practice T & F equivalencies to review the meaning of the equal sign 1.OA.7.
equivalent name, program
Before lesson, practice with student calculators, especially the ‘repeat’ key. Disregard all the Thermometer Prep from TLG p60.
1♦10
Identify patterns when counting by different numbers. 3.OA.9
SKIP Lesson: Although EDM has made revision to address odd and even numbers in this lesson (2.OA.3), CCSS relates even number to those that are a sum of 2 equal addends. This will be better addressed in Unit 7.
1♦11
Use symbols to compare number values. 2.NBT.4
is equal to, is less than, is greater than, represent, symbol
P2 Addition Top-It: MRB p122-3, MM p449; P3E Number Top-It (5-digit numbers): MM p465-6
Key: CCSS-M = Common Core State Standards for Mathematics; EDM = Everyday Mathematics; TLG = Teacher’s Lesson Guide; MM = Math Masters; MRB = My Reference Book; AH = Assessment Handbook; I Grade 2 RSA = Recognizing Student Achievement; R = Readiness; E = Enrichment; EP = Extra Practice; SMJ = Student Math Journal; TRM = Teacher Reference Manual; Page 4
Unit 2: Addition and Subtraction Facts Pacing: 4 weeks, thru mid November (week 11).
CCSS-M Critical Ideas for this Unit
Fluency with facts to 20 in CCSS (2.OA.2) is addressed very differently than what EDM tries to do with this unit. Fluency is not established through timed drills to memorize facts. It is slowly develops through the use of flexible mental strategies using derived facts (1.OA.6) and gradually and progressively building this bank of memorized facts until all facts are mastered. These flexible strategies should not be explicitly taught but should be shared by students through frequent classroom discussions. A daily 10-15 minute Number Talk would provide ample opportunity to develop and share these strategies. Use this unit to establish norms for classroom discussions and to expose some of the most commonly used mental strategies. Work with fluency within 10 if needed, review important grade 1 standards for multi-digit addition/subtraction, 1.NBT.4 & 1.NBT.6, including word problems within these number ranges, 2.OA.1, and then move on to Unit 3 while continuing daily discussions to develop fluency throughout the year.
Learning Target EDM Edits Comments Vocabulary Games Advanced Prep
Notes on mental strategies: Proper naming of the strategy is not a standard. Use friendlier, more descriptive names for strategies such as “make 10”, “turn-around”, “doubles plus 1”, etc. Here are some commonly used strategies: Making 10: break one number in order to make a complement of 10 for the other number (7 + 6 = 7 + 3 + 3 = 10 + 3); Decomposing to 10: same as making 10 but for subtraction (14 – 7 = 14 – 4 – 3 = 10 – 3); Doubles plus/minus 1: (6 + 5 = 1 + 5 + 5 = 1 + 10); Undo subtraction: 15 – 7 = ? is the same as 7 + ? = 15; Counting on with complements of 10: 7 + ? = 15, from 7, need 3 to get to 10 and then 5 to get to 15, 3 + 5 = 8. Compensation: 14 – 9 = 14 – 10 + 1, subtracted 10 instead of 9 (too much) so had to put 1 back. 7 + 9 = 7 + 10 – 1, added 10 instead of 9 (too much) so had to give 1 back.
2♦1
Create, write equations (number models) for and solve addition word problems (number stories). 2.OA.1
New notes on TLG p95 to address problem types. Also revised Adjust the Activity and RSA
Model number stories multiple times for students. Have students write the word “equation” above the words “number model” on SMJ p21. Note: Expressions are what is at either side of the “=” symbol. Basically, an equation states that one expression is equivalent to another.
addition number story, story, word problem, unit box, number model, difference, equation, expression, equivalent, solve, symbol
2♦2 Use properties of +0 and +1
facts to develop automaticity. 1.OA.6
New step added to Beat the Calculator to track facts mastered. New notes on TLG p101 & 102
COMBINE: 3-4 Days All of these strategies should come from students during classroom discussions. Do not teach these as a procedure. Over the next 3-4 days, work on solving problems that will give students opportunity to share a variety of strategies and on establishing norms for discussions.
Doubles facts may or may not be part of students’ bank of derived facts. This strategy is only useful for those who know their double facts.
Introduce vocabulary of even by comparing 2 equal towers of unifix cubes and referring to its doubles fact. (I.e. if these two towers are even I can call the total an even number and write it as a doubles fact). 2.OA.3
Spend some time working with 10-frames to help students develop this strategy on their own. Work with +10 facts first then move onto +9 facts.
Prepare a large Facts Table from SMJ p27 and see TLG p105 for options. Prepare “Unit Box” on board and use accordingly.
2♦4 Use patterns in an addition facts
table to develop automaticity with +10 & +9 facts. 1.OA.6
turn-around facts, +9 facts, +9 shortcut, even
P2 Beat the Calculator: MRB p124-5, SMJ p24
Prepare “Unit Box” on board and use accordingly.
2♦5 Develop strategies for addition
that uses doubles facts. 1.OA.6 Revised MM Follow-Up and Readiness to address even numbers. 2.OA.3
doubles-plus-1 facts, doubles-plus 2 facts, even
P2 Domino Top-It: MRB p122-3 Prepare “Unit Box” on board and useaccordingly.
2♦6 Use dominoes and word
problems to develop an understanding of how turn-around facts and undoing subtraction work. 1.OA.3 & 1.OA.4
Revised MM Follow-Up to include number lines. 2.MD.6
Modification: Writing facts families on its own, does not support the inverse relationship between addition and subtraction. Instead pose word problems in which an action is being undone. Subtraction undoes addition and addition undoes subtraction. 1.OA.4
Working with turn-around fact through well posed word problems does support the understanding of the commutative property of addition (1.OA.3). Many students who just work with fact families try to apply it subtraction too, where it does not work.
Key: CCSS-M = Common Core State Standards for Mathematics; EDM = Everyday Mathematics; TLG = Teacher’s Lesson Guide; MM = Math Masters; MRB = My Reference Book;SMJ = Student Math Journal; Grade 2 RSA = Recognizing Student Achievement; R = Readiness; E = Enrichment; EP = Extra Practice; TRM = Teacher Reference Manual; word = A non-appropriate EDM vocabulary word; word = Additional MSP vocabulary word Page 5
2♦8
Use repeated addition strategies to solve “equal groups” problems (Exploration C). 2.OA.4
Revised Exploration A and New Exploration B (Note: neither are appropriate changes to address CCSS)
SKIP Explorations A & B: The new Exploration B: Rules for Adding Odd and Even Numbers does not address the related CCSS standard, 2.OA.3. Exploration C is a good intro for repeated addition in equal groups, 2.OA.4; this will be better addressed in Unit 7. Preview it now or save it for Unit 7
ounce, pound, pan balance, heavier, lighter, in balance (balanced), spring scale
P2 Beat the Calculator: MRB p124-5, SMJ p24
EXPLORATIONS: Exploration A: collect objects found in classroom between ½ ounce and 8 ounces such as student tape measure, 2-in binder clip, calculator, card deck, scissors, mug, pad of paper, small books, etc.
Modification: Name Collection boxes are a good opportunity to cover strategies like “Make 10” or “Decomposing to 10”. Instead of a number, use an expression in the “tag” and have students come up with equivalent expressions. Discuss how to manipulate the numbers to get from the “tag” to the new expression. Use Supplement 2♦9: Balanced Equations to support 1.OA.7 & 1.OA.8.
name-collection box, equation, expression
P1 Name That Number: MRB p138, MM p462; P3R Two-Fisted Penny Addition
Prepare ‘Unit Box” on board and useaccordingly.
2♦10
Solve repeated addition or subtraction problems based on a rule (Frames-and-Arrows). 1.OA.4
OPTIONAL: Frames and Arrows and Function Machines help understanding of the inverse relationship between addition and subtraction by undoing these operations, 1.OA.4. Review if needed.
Frames-and-Arrows diagrams, frame, arrow, arrow rule, number pattern
P2 Name That Number: MRB p138, MM p462
Prepare ‘Unit Box” on board and use accordingly. For Part 1, prepare Teaching Master of MM p43.
2♦11
Develop strategies to solve for missing numbers in function machine problems. 1.OA.4
“What’s My Rule?”, function machine
For Part 1, “What’s My Rule?” prepare Teaching Masters of MM 425 & 426 (optional).
2♦12
Use counting-up strategy to solve subtraction problems. 1.OA.5
The Counting-Up Activity in Part 1 is extremely important to support operating with number lines latter on. 2.MD.5 difference
Before 2♦13, Part 2, have students prepare the Fact Triangles on Activity Sheets 3 & 4.
2♦13
Use models to develop compensation strategies for -9 & -8 facts. 1.OA.6
This lesson is where the compensation strategy comes up. Use the readiness activity and counters to model how this works. Have students make sense of it rather than using a trick on the number grid.
-9 facts, -9 shortcut, -8facts, -8 shortcut
For 3♦1, organize base-ten blocks for partners. See TLG p165.
2♦A
Use strategies from single digit addition to solve 2-digit addition & subtraction. 1.NBT.4 & 1.NBT.6
Supplemental Activity to support review Grade 1 standards critical to 2-digit operations in Unit 4: This would be a good place to review some important grade 1 skill as an extension of the work begun in this Unit. For example: Ask students what strategies they use for 6 + 7 and can they do the same to solve 26 + 7 or 56 + 7? Students should be able to use the same strategy used for single digit addition (1.NBT.4). Similarly with subtraction, if 8 – 6 = 2, what is 80 – 60? (1.NBT.6). Also have student work on adding any multiple of 10 to a 2-digit number. How is adding 26 + 7 different than adding 26 + 70? (1.NBT.4)
Exit SlipAdding & Subtracting Tens Worksheet Supplement to 2ASee below for additional resources
OPTIONAL LESSON 2-B: If formative assessments indicate that students continue to lack important grade 1 skills, this lesson can be included in your instructional progression: Lesson 2-B (optional)
Break Apart Trees (decomposing practice)
These materials may be used as extensions to Lesson 2A: Exit Slip - Open Number Line Make a Double or TenExit Slip - Make a Double or TenDecomposing to Subtract
Decomposing Numbers to Add Tens Decomposing Numbers RegroupingMissing Number Subtraction
Exit Slip - Decomposing Numbers to Tens and Ones Exit Slip - Decomposing Numbers Exit Slip - RegroupingMissing Addend
Key: CCSS-M = Common Core State Standards for Mathematics; EDM = Everyday Mathematics; TLG = Teacher’s Lesson Guide; MM = Math Masters; MRB = My Reference Book; AH = Assessment Handbook; Grade 2 RSA = Recognizing Student Achievement; R = Readiness; E = Enrichment; EP = Extra Practice; SMJ = Student Math Journal; TRM = Teacher Reference Manual; Page 6
Unit 3: Place Value, Money, and Time Pacing: 3 weeks, thru first week of December (week 14).
CCSS-M Critical Ideas for this Unit
This unit’s focus is on telling time to the nearest 5 minutes, 2.MD.7, and computing coin combinations in the context of story problems, 2.MD.8. Place value was covered in units 1A and 1B so only review if needed. Be sure students can write 3-digit numbers in words, 2.NBT.3. Address time telling slowly by developing counts by 5s and working with the minute hand and then moving onto the hour hand. Also take some time to review some key Grade 1 standards like “sums of three addends” and “True or False equations”, 1.OA.3 & 7.
Learning Target EDM Edits Comments Vocabulary Games Advanced Prep
3♦1
Use base-10 blocks, drawings and digit cards to represent 2- and 3-digit numbers. 2.NBT.1 & 2.NBT.4
Revised Matching Numbers and Playing Digit Game to better support 2.NBT.1 New Activity Using Place Value to compare Number to better support 2.NBT.4
MOVED: This lesson was moved to Unit 1 where place value was covered. If needed use the time to review and reassess any place value standards that were not met.
2-Day Lesson Prepare sets of Base-10 blocks for partners. Prepare teaching Master of Place-Value Mat. See TLG p184. Planning Ahead: For 3♦2, prepare poster or Teaching Master of MM p58.
3♦2
Draw coins to show coin combinations for priced market items. 2.MD.8
P2 Spinning for Money: SMJ p55, MM p472; P3R Penny-Nickel Exchange: MRB p128-9, MM p428; P3R Penny-Dime-Dollar Exchange: MRB p144-5, MM p428
For Part 1, prepare Teaching Master of MM p58, “Fruit and Vegetable Stand”. Planning Ahead: Lesson 3♦2 requires a demonstration clock with hour hand only. Use MM p60 & a paper fastener or draw a clock face on the board. Prepare student clocks for tool-kits.
1♦3 Use clocks to tell & show time to
the nearest half-hour. 1.MD.3 MOVED from Unit 1? You may have decided to skip this lesson in Unit 1. If so, this is where you can teach this lesson.
calendar, ordinal numbers Post name of the months in classroom.
Gr1 4
♦8
Show and tell time to the nearest quarter hour. 2.MD.7
Supplemental Lesson to support Telling Time, 2.MD.7 Grade 1 Lesson 4♦8: Telling Time on the Quarter Hour This lesson was skipped from grade 1. Connect the fractional language, 1.G.3, half and quarter, to minutes on a clock. If 1 hr is 60 min, what is half? What is a quarter? What is halfway between 30 and 60? Include analog notation with time phrases (i.e. quarter past 7 o’clock = 7:15). Do all of Part 1
3♦3 Show and tell time to the nearest
5-minute mark. 2.MD.7
Extension to 3 Days: This is the last lesson that actively teaches time. 2.MD.7 Day 1: work only with the minute hand and counting by 5s. Day 2: work only with the hour hand with “Estimating Time with an Hour Hand” but using the same vocabulary as Lesson 3♦A. Day 3: work on telling time with both hands to the nearest 5 minutes and about the different activities done in the a.m. and p.m. hours. Have student make a timeline of everything they do in a 24 hr period. Begin having students write the time and date on each of their papers. Having an analog clock in your classroom, rather than a digital clock, is crucial. Also, provide practice during Daily Routines.
minute hand, hour hand, clock face, analog clock, digital clock
2-day Lesson Math Message uses student clocks. Use MM p61 to prepare take-home clocks for 3♦3 Home-Link.
Key: CCSS-M = Common Core State Standards for Mathematics; EDM = Everyday Mathematics; TLG = Teacher’s Lesson Guide; MM = Math Masters; MRB = My Reference Book; AH = Assessment Handbook; Grade 2 RSA = Recognizing Student Achievement; R = Readiness; E = Enrichment; EP = Extra Practice; SMJ = Student Math Journal; TRM = Teacher Reference Manual; Page 7
3♦5
Answer questions about pocket data represented on a tally chart and bar graph. 2.MD.9 & 2.MD.10
New Note about pacing on TLG p208. Revised Activity to do picture graphs instead of Bar Graph on TLG p210 to address 2.MD.10 Delete Dollar Rummy from Part 2
2 Day Lesson MOVE to Unit 6. Data will be better addressed in Unit 6A
predict, middle number, bar graph, range, chart, most, least, greatest, survey, table, title
P2 Dollar Rummy (Complements of 10): SMJ p65, MM p454-5
For Math Message, MM p71, 1 per 2 students. Teaching Masters of MM p72 & 72.
3♦6 Solve Frames-and-Arrows
problems with 2 rules. 3.OA.9 New Dollar Rummy in Part 2 moved from Lesson 3♦5. SKIP Lesson: These concepts will be addressed in 3rd grade. number pattern
For Math Message, MM p75, 1 per 2 students. Prepare Teaching Master of MM p75 – 77 and 431, or draw a 2-rule Frames-and-Arrows diagram.
3♦7
Use the counting-up method of subtraction to find differences between money amounts (make change). 2.MD.8
Revised MMR to include counting by 100s 2.NBT.2. Revised Digit Game to include 3-digit numbers, 2.NBT.1
This is a challenging lesson for students. Start small (differences <10; i.e. costs 24¢ paid with 3 dimes; difference is 6¢ so need 1 nickel and 1 penny) and model frequently. Consider adding “making change” problems to your Daily Routines.
make change by counting up
P2 Digit Game: MRB p132-3; P3R High Roller
3♦8
Share and justify strategies to determine coin combinations for money amounts. PE 2.2.I & 2.2.H
Model for students putting in exact change vs. not exact change so students can experience the difference first hand. “Share and justify” strategies are mentioned in several Learning Targets. At times, the TLG mentions sharing opportunities but there may not be a detailed description of a possible discussion. As part of High Leverage Moves, have more than one student not only share, but to also explain why or how they determined their responses.
exact change light For Math Message Follow-Up, use document camera to display Master of MM p84.
These materials can be used with Unit 3: Making Change with Pictures of Dollars and Cents
Key: CCSS-M = Common Core State Standards for Mathematics; EDM = Everyday Mathematics; TLG = Teacher’s Lesson Guide; MM = Math Masters; MRB = My Reference Book;SMJ = Student Math Journal; Grade 2 RSA = Recognizing Student Achievement; R = Readiness; E = Enrichment; EP = Extra Practice; TRM = Teacher Reference Manual; word = A non-appropriate EDM vocabulary word; word = Additional MSP vocabulary word Page 8
Unit 4A: All New Measuring Length Unit Pacing: 2 weeks, thru end of December (week 16).
CCSS-M Critical Ideas for this Unit
Before students can use number lines and open number lines (see below) for multi-digit addition and subtraction, 2.MD.6, they first need to understand how number lines relate to concepts of distance. Much of this work is found in the Grade 1 EDM even though these are 2nd grade standards. For this reason, Supplemental Unit 4A has been created to address measuring and comparing measurement between cm. and in. 2.MD.1 & 2MD.2, estimating lengths, 2.MD.3 and beginning to operate with lengths, both in simple contexts, 2.MD.4 as well as in real world problems, 2.MD.5. All of this work will support a variety of strategies covered in the revised CCSS EDM grade 2 Unit 4 (now 4B). Teach and assess this unit before moving on to unit 4B.
Learning Target EDM Edits Comments Vocabulary Games Advanced Prep
4A♦A
Use paper clip rulers to determine the need for a tool with standard units. 2.MD.1
Supplemental Activity to support measuring with standard units. 2-days Day 1: Group student into 3 tables and have them make rulers out of paper clips taped to cardboard (see image below). Have a group make the ruler out of jumbo paper clips, another out of medium paper clips and one out of small paper clips. Refer to all clips as just “paper clips” and do not make reference to their different sizes. Give each group the same set of objects to measure using their rulers and have them record it on a chart. Be sure to select objects that will yield different measures with the 3 different sized clips. Day 2: Measuring should be complete by now so, jigsaw the groups so that students from different tables can compare their measures around one object. Have the new groups discuss and try to agree to a measure for the object (i.e. the bottle is 9 paper clips long). Afterwards, have a group discussion about how difficult it was to agree when we all had different sized paper clips. Pose examples where this would cause problems (i.e. if some asks you to bring a string that is 7 paper clips long, how do you know exactly how long it should be?). As students contribute solutions to this problem lead the discussion to the need for standard units. A unit that is the same for everyone everywhere in the world. Introduce the terms for the most common units of measurements we use.
Vocabulary: standard unit, inch, centimeter, foot, meter, mile, kilometer, ruler.
Advanced Prep: boxes of different sized paper clips, cardboard, tape. Gather objects to measure: you will need at least 3 identical objects of each kind. Select objects long enough that they will yield different measures with the 3 different sized clips.
Gr1 4
♦4
Use a ruler to measure objects to the nearest inch. 1.MD.1; 2.MD.1; 2.MD.3
Revised MM p313 to include cm ruler. Added discussion to Measuring with Cut out Ruler to address transitive property, 1.MD.1 Supplement Lessons to support measuring to the nearest unit.
Grade 1 Lesson 4♦4: The Inch; Lesson 4♦5: The 6-Inch Ruler; Lesson 4♦6: Measuring with a Tape Measure; & Lesson 6♦6: The Centimeter
These lessons were most likely only touched upon in Grade 1 since measurement using standard units is a 2nd grade standard. The important skills to get out of these lessons are getting the basics on how to use a ruler properly and telling the difference between inches and centimeters on a ruler.
Also be sure to include comparing length of objects. Have student measure 2 objects with a ruler using the same unit and determine how much longer one object is than the other. 2.MD.4
inch; in. P2 Time Match: MM p354-9 One inch cubes. MM p354-355, one set per partner, cut apart – save for 4♦10. For Part 3 (R), cut 10”& 11” strips
Gr1 4
♦5
Estimate lengths, and then measure to the nearest inch. 2.MD.1; 2.MD.3
estimate P2 Domino Top-It
Gr1 4
♦6
Measure around and across objects with a tape measure. 2.MD.1; 2.MD.3
tape measure Tape measures placed in Tool Kits, labeled. For Part 3 (R), prepare 8 objects, 8 strings. See TLG p302.
Gr1 6
♦6
Use ruler to measure to the nearest centimeter. 1.MD.1; 2.MD.1; 2.MD.3;
New Notes on TLG 565 & 566. New Activity Comparing Lengths of Objects to address transitive property, 1.MD.1
cm, centimeter, metric system
For Math Message have base-10 longs available. Part 2; prepare spinners ahead of time, MM p328. See TLG p563 and p 566.
4A♦B
Share and develop strategies for accurately drawing and navigating open number lines. 2.MD.6
Supplemental Activities to Support Number Line Concepts, 2.MD.6 2 days. Discuss how a ruler is like a number line. Have student freely make their own number lines 0-10 on a blank sheet. Discuss difficulties they may have had, especially around spacing. Have student share strategies to use to keep evenly spaced marks. Have them try again. Then have them do one that counts by 5s 0-50 and one that counts by 10s to 100. Have students find some missing numbers. “If I start at 35 and go 1 less on the number line, what number I’m I on?” (It should be 34 not 30 because 1 less than 35 is 34; 1 less does not mean jump 1 span back). Have students practice navigating an open number line. For example on the number line by 10s: “Start on the number 40 go back 3, then go forward 20. What number are you on?” (3 back from 40 is 37 [which we can’t see] then forward 20 can be counted by 10s so from 37 I go 47 and 57.
number line; open number line
Click here for open number line resources: Open Number Line Helps
Click here for measuring boxes & number line slides: Powerpoint SlidesClick here for 2 worksheets with objects to measure: Measurement Objects
Lesson 6.6 Home LinkLesson 6.6 pg. 144Lesson 6.6 Math BoxesLesson 4.4 Home LinkLesson 4.4 pg. 75Lesson 4.4 Math Boxes
Click here for worksheets with paperclip, pencil, etc.: Paperclip ...Worksheets
Click here for worksheets with pen, thumbtackl, etc.: Pen ...Worksheets
Key: CCSS-M = Common Core State Standards for Mathematics; EDM = Everyday Mathematics; TLG = Teacher’s Lesson Guide; MM = Math Masters; MRB = My Reference Book;SMJ = Student Math Journal; Grade 2 RSA = Recognizing Student Achievement; R = Readiness; E = Enrichment; EP = Extra Practice; TRM = Teacher Reference Manual; word = A non-appropriate EDM vocabulary word; word = Additional MSP vocabulary word Page 9
4♦7
Compare lengths when measured with different units (Pre-Explorations). 2.MD.1 & 2.MD.2
Revised SMJ p99 to include cm. Replace Fact Triangle with Beat the Calculator. Revised enrichment activity.
A critical discussion in this lesson occurs while examining the two scales before the exploration begins (top of TLG p284). During discussion, lead students to make a generalization about the inverse relationship between size of the unit and measure: “If you measure a length with a smaller unit (cm) you will get a larger measurement number than with a larger unit (in)”. The importance of this activity ties into estimation of length (2.MD.3). Getting a better sense of unit sizes leads to better estimates.
inch (in), centimeter (cm), tiling, attribute/ property, blocks, ruler
EXPLORATIONS: Spend your time on Explorations D. EXPL. E will be compled in Unit 7. EXPL. F, MM p107-8.
4A♦C
Determine the length of objects when not starting with 0 on the ruler. 2.MD.5 & 2.MD.1
Supplemental activity to support relating addition and subtraction to length, 2.MD.5 Tape 2 rows of five 1 in squares pattern block on the board and tape a ruler under each. Have 1 ruler start at 0 on the left and the other start at 1. Ask which row is longer? Discuss length as being the same regardless of the position on the ruler. “Length is the difference between 2 numbers on a number line (ruler)”. The difference between 0 and 5 is the same as the difference between 1 and 6. Broken Rulers: Copy Gr1 MM p313 used in Lesson 4♦4 and cut out the 12 inch paper rulers. Tear out the first few inches of each in different way so that each is missing anywhere between 1-5 inches. Have students pair up to measure objects around the class using different broken rulers. Students should be able to determine the length of an object regardless of the ruler they have. Repeat the activity on another day using a 30 cm broken paper ruler.
Measuring with a paper clip ruler made with medium sized clips
Key: CCSS-M = Common Core State Standards for Mathematics; EDM = Everyday Mathematics; TLG = Teacher’s Lesson Guide; MM = Math Masters; MRB = My Reference Book;SMJ = Student Math Journal; Grade 2 RSA = Recognizing Student Achievement; R = Readiness; E = Enrichment; EP = Extra Practice; TRM = Teacher Reference Manual; word = A non-appropriate EDM vocabulary word; word = Additional MSP vocabulary word Page 10
Unit 4B: Addition and Subtraction Pacing: 3 weeks, almost thru the end of January (week 19).
CCSS-M Critical Ideas for this Unit
Several edits that EDM has made to better fit with CCSS include the use of open number lines as a model, 2.MD.6, to solve addition and subtraction problems within 100, 2.NBT.5. Use these as a way to model students thinking during classroom discussions or Number Talks. Just as you did with facts to 20, have students be the ones to come up with a variety of mental strategies, 2.NBT.8 and guide discussions so that students are trying to make sense of and explaining each other’s strategies, 2.NBT.9. Bring other models when necessary. Now that students have covered measurement, include contexts that involve lengths within 100 units, 2.MD.5, and other word problems within 100, 2.OA.1.
Notes on Strategies: Opposite Change (+): Take from one addend and give it to the other (48 + 26 = 50 + 24); Same Change/Constant Difference (–): Do the same to both numbers (52 – 38 = 54 – 40); Place Value: 37 + 45 = (30 + 40) + (7 + 5) = 70 + 12 or 83 – 28 = (80 – 20) + 3 – 8 = 60 – 5, think of 3 – 8 as either -5 or a difference of 5 but going back; Counting up (–): 83 – 28, 28 + 2 → 30 + 50 → 80 + 3, or 28 + 55 = 83; Compensation: Round a number, solve, then adjust (37 + 45 = 40 + 45 – 3, added too much so had to take it back; or 83 – 28 = 83 – 30 + 2, took away too much so had to put it back); Decomposing Numbers/Chunks: 37 + 45 = 37 + 3 + 40 + 2 or 83 – 28 = 83 – 3 – 20 – 5; Proper naming of the strategy is not a standard. Use friendlier, more descriptive names for strategies.
4♦1 Use change-to-more diagrams
to solve addition word problems. 2.OA.1
New Note about problem types. Revised content to include using “?” as the unknown. Revised MJ p82 to include 2-step problems. 2.OA.1
The fish weights context provides is a good opportunity to work on some of the more challenging word problem types like “change unknown” and “start unknown”, 2.OA.1. Note: Change-to-more ≠ change unknown, it just means “add to”.
change-to-more number story, word problem, change diagram, mental arithmetic
Display a change diagram. See TLG p248 for options.
4♦2 Use parts-and-total diagrams to
solve addition word problems. 2.OA.1
Added text to MM Follow-Up to address open number lines 2.MD.6
Parts-and-Total problems are referred to as Put together/Take Apart in CCSS-M. Note the difference in these types from the “add to” and “take from” word problems in that there is no change in quantity. Nothing is added or removed. There are simply 2 quantities that can be thought as independently or as a total, 2.OA.1.
parts-and-total diagram, parts-and-total number story
P2 Addition Spin: MRB p120-1, MM p447-8
Display a parts-and-total diagram. See TLG p248 for options. For Part 3 (R) prepare paper plates for parts-and-total diagrams. Planning Ahead: Save extra MM copies for future lessons. Prepare Class Thermometer Poster. See TLG p 259.
4♦3
Use Coin Stamp Booklets to create addition and subtraction word problems involving money. 2.OA.1 & 2.MD.8
Replace Addition Spin with Fact Triangles to address 2.OA.2
Focus on Exploration B since it supports 2.MD.8. Skip Explorations A & C since temperature is no longer a standard and sorting block is a Kindergarten standard.
degrees Fahrenheit, degrees Celsius, thermometer, degree marks
P2 Addition Spin: MRB p120-1, MM p447-8
4♦4
Solve addition and subtraction problems involving lengths (instead of temperatures). 2.MD.5
Revised MM Follow-Up to be slightly condensed. Revised How Much Warmer (Cooler) to include open number line, 2.MD.6. Revised SMJ p89 #3 includes 2-step problems.
Temperature could provide a context for number line problems but getting kids comfortable with reading a thermometer and the degree units of F° & C° may take up too much of your lesson. It may be best to drop the temperature context and do the same problems within a context of lengths to address 2.MD.5. This would affect the use of all SMJ and MM pages dealing with temperature.
Prepare for display of change diagrams. For Part 3 (R), paper copy and transparency of MM p101 for each child, MM p102, several copies, cut apart. Part 3 (E), 1 glass of ice water.
4♦5
Share and justify strategies for adding 2-digit numbers. 2.NBT.5 & 2.NBT.9
These are the first lessons in grade 2 where student are working within 100 with regrouping. Control any desire to explicitly teach particular strategies or algorithms and allow students to share their own invented strategies. Use models and open number line to show student’s thinking and making it accessible to other students. Money, here, is simply providing the context and does not necessarily support 2.MD.8.
Estimate, less than (<), greater than (>), equal to (=)
P2 Name That Number: MRB p138-9, MM p462
Teaching copy of 4♦4 Home Link, MM p99-100. Part 3 (R), prepare pictures or index cards to match items on SMJ2, p 104.
4♦6 Revised MM Follow-Up to include
open number line, 2.MD.6 P2 Addition Spin: MRB p120-1, MM p447-8 For Part 1, extra bills are on MM p459-461.
4♦8
Share and justify invented strategies for finding the sum of 2-digit numbers. 2.NBT.5 & 2.NBT.7
Revised Solving Addition Problems to include multi-digit fact families. New note about goals for algorithms, 3.NBT.2.
Invented Strategies: 2-day Lesson. Provide base-10 blocks and open number lines to your students. A focus for the discussion is to identify similarities and differences between strategies. Encourage students to try a different strategy as they solve more problems both using trades with blocks and with jumps on the number line. Focus on having student develop ways to record their thinking so others can understand their strategy. Note that EDM’s goal is to develop algorithms in grade 2 but algorithms are really a 3rd grade standard. Skip Ballpark Estimates.
Key: CCSS-M = Common Core State Standards for Mathematics; EDM = Everyday Mathematics; TLG = Teacher’s Lesson Guide; MM = Math Masters; MRB = My Reference Book;SMJ = Student Math Journal; Grade 2 RSA = Recognizing Student Achievement; R = Readiness; E = Enrichment; EP = Extra Practice; TRM = Teacher Reference Manual; word = A non-appropriate EDM vocabulary word; word = Additional MSP vocabulary word Page 11
4♦9
Use base-10 blocks to model Partial-Sums for addition of 2-digit numbers. 2.NBT.1, 2.NBT.5 & 2.NBT.7
Revised Partial-Sums Algorithms to include 3-digit numbers, 3.NBT.2.
Skip most of this Lesson. Build in Modeling as part of classroom discussions. Partial-sums is a place value strategy that students often come up with on their own. It is important that this strategy is left informal at this time. Do not try to formalize partial-sums into a procedure or algorithm like EDM does in this lesson. Instead wait until a student shares this strategy, model it with blocks if necessary and record the students reasoning. Find new ways to record the strategy.
algorithm P2 Fact Extension Game: MRB p134-5
3-day Lesson Plan ahead for how to demonstrate partial-sums addition with base-10 blocks.
Key: CCSS-M = Common Core State Standards for Mathematics; EDM = Everyday Mathematics; TLG = Teacher’s Lesson Guide; MM = Math Masters; MRB = My Reference Book;SMJ = Student Math Journal; Grade 2 RSA = Recognizing Student Achievement; R = Readiness; E = Enrichment; EP = Extra Practice; TRM = Teacher Reference Manual; word = A non-appropriate EDM vocabulary word; word = Additional MSP vocabulary word Page 12
Unit 5 & 8: 3-D and 2-D Shapes and Fractions Pacing: 4 weeks, almost thru the end of February (week 23).
CCSS-M Critical Ideas for this Unit
Early fraction concepts in 1st and 2nd grades are introduced through geometry. These concepts evolve from composing 2-D shapes with a variety of shapes (1.G.1) to decomposing or partitioning a 2-D shape into equal shares and using fractional language (thirds, fourths, etc) (2.G.3) to describe them and understand that these shares are named after the number of parts in the whole. For this reason this unit combines the lessons from unit 5 focusing on shapes (their defining attributes and on vocabulary including all quadrilaterals) (2.G.1) and lessons from unit 8 to address fractional parts. There are two very important shifts in the way that fractions are approached in CCSS-M: (1) Halves, thirds and fourths are described and compared in terms of their geometric size (1.G.3), without using numerical symbols (½, ⅓, ¼) or by measuring. (2) Equivalence is introduced through the concept that equal shares of identical wholes are the same size even if they are not the same shape (2.G.3). This is very different that saying a fourth is the same as 2 eighths, which will come later in grade 3.
Learning Target EDM Edits Comments Vocabulary Games Advanced Prep
5♦1
Sort shapes based on defining attributes (Exploration A). 1.G.1
Cut circles and rectangles into equal shares (Exploration B). 1.G.3 & 2.G.3
Expand to 2-Day with critical Modifications: Day 1: Exploration A focuses on non-defining attributes like size and color. Instead use cards made from Shape Sheets 1 & 2 to have student sort the different cards by shape. Spend the day having students justify their sorts using the shapes defining attributes, 1.G.1. This will help with discussions about why a square is also a rectangle and a rhombus and why some shapes are not polygons. Use Exploration C as day 1’s Part 2. Day 2: Exploration B: Equal shares using counters begins to address division, which is a 3rd grade standard. In place of this activity, geometrically explore equal shares. Have pictures of food items that look like circles and rectangles (i.e. pizzas, cookies, chocolate bars, brownies, etc) and discuss how to cut them into equal shares for 2, 3, or 4 people, 1.G.3 & 2.G.3. Then do Part 2.
EXPLORATIONS: For Math Message and Part 1 prep, see TLG p 316 & 317. Plan to spend most of your time on Exploration A.
5♦2 Draw shapes based on
specific attributes. 2.G.1 New Activity Practicing with Fact Triangles to support 2.OA.2 replaced activity in Part 2.
Modification: Drawing line segments with a ruler is a 4th grade standard. Use the readiness activity Making Geoboard Designs but base it on specified attributes, 2.G.1. Give directions like “Make a shape that has 6 angles and all straight sides.” “Make a 4 sided shape where all angles are not the same size.” Then have students draw their shapes on MM p128. They can draw these by hand but can use a straightedge only if they really want to. Have students work in pairs. One partner secretly makes a shape on a Geoboard and gives instructions to his/her partner to make the same shape but without naming it.
point, straightedge, line segment, endpoint
Before 5♦6, collect objects for Shapes Museum. See TLG p326.
5♦3 Identify shapes that have
sides going in the same direction (parallel) 2.G.1
New Activity Solving Addition Problems Using Open Number Lines in Part 2 with revised MJ p118
“Parallel” is not a 2nd grade vocabulary word but it is an attribute that will support the conversation when looking at quadrilaterals. Use descriptive language like “lines going the same direction” to clarify the term. Also, use the term “quadrilateral” instead of “quadrangle”.
EXPLORATIONS: Prepare word wall. Part 3 (EP) uses the book, The Greedy Triangle. For 5♦5, prepare MM p139 & 140 ahead of time. Prepare shapes ahead of time for 5♦5. See TLG p337.
5♦5
Identify similarities and differences among attributes of quadrilaterals. 2.G.1
Use “quadrilateral” instead of “quadrangle”. “Square corner” or “square angle” is an appropriate term to use for right angles. When Exploring Similarities and Differences Among Quadrilaterals include looking at the sizes of the angles (i.e. a rhombus (when not a square) has 2 big angles and 2 small angles.)
Key: CCSS-M = Common Core State Standards for Mathematics; EDM = Everyday Mathematics; TLG = Teacher’s Lesson Guide; MM = Math Masters; MRB = My Reference Book;SMJ = Student Math Journal; Grade 2 RSA = Recognizing Student Achievement; R = Readiness; E = Enrichment; EP = Extra Practice; TRM = Teacher Reference Manual; word = A non-appropriate EDM vocabulary word; word = Additional MSP vocabulary word Page 13
8♦1
Use paper cutouts to compare equal shares of same sized wholes (halves, thirds & fourths). 1.G.3
New MMR to support 2.OA.2. Revised activity Reviewing Basic Fraction Concepts, 1.G.3. New Activity in Part 2 Bamboo Plant Number Stories with revised MJ p185 to support 2.OA.1. New Planning Ahead note on TLG p609.
MOVED: Skip Reviewing Basic Fraction Concept and Writing Fractions. Use the Readiness MM p228Activity and Folding Squares into Equal Parts to provide a solid conceptual introduction and review. Refer to these as equal shares of a whole or parts that are the same size. Use words like halves, thirds, fourths, etc and not their numerical representation (i.e. The rhombus is a third of the hexagon). Have students compare part sizes from the same whole. “The thirds of the hexagon are smaller than the halves of the hexagon” (1.G.3). Do not use the vocabulary words “fractions”, “numerator” & “denominator”.
congruent, ONE (the whole), fraction, denominator, numerator, whole number
Before Math Message, prepare three, 8” paper squares per student. Read TLG p603, Fractions Museum before distributing Home-Link 8♦1. Part 3 (EP) uses the book Ed Emberley’s Picture Pie.
8♦A Use pattern block to find
equal shares of larger shapes. 1.G.3 & 1.G.2
Supplemental Lesson to compose larger shapes from equal parts. Use Grade 2 Activity 2: Build-4-Less materials from Bridges Pattern Blocks K-2 CCSS Supplements starting on p27. In this activity students use pattern blocks to compose larger shapes using the fewest blocks possible. Modification: Use only pages 1, 2 and 4 (trapezoid, star, large rhombus & large rhombus). Have students do the activity as written, but also ask if there are any solutions using only one type or color of block. For example the large rhombus on page 2 can be filled with 6 red trapezoids or 9 blue rhombi (even if these do not use the fewest blocks). Have students name these equal shares using words like fourths, sixths, ninths, eighteenths, etc and describe the whole as the total of its parts (i.e. four fourths). Make connections between the number of blocks needed to fill in the shape and the size of the blocks then use fractional language to describe this (i.e. in the rhombus, sixths are larger than ninths). Pretend these large shapes are birthday cakes and the shares are the pieces they eat to provide a context for this conversation. 1.G.3
Print out lesson for yourself. Make 15 copies each of Sheets 1, 2 and 4.
8♦B Describe congruent parts as
equal shares of a whole. 2.G.3
Supplemental Lesson 8♦B to support equal shares. Use Supplement 8♦B: Equal Shares of Brownies. To minimize time cutting, have students pair up to share the cutting. One partner cuts Tom’s share on brownie A and the other on B. Then they use each other’s papers to compare the sizes. Keep the results of the survey at the end to later connect to Lesson 8♦C.
Copies of p2-5 should be done on tag paper to make them more durable while cutting. One per pair. Save a copy for yourself and pre-color it according to instructions.
8♦2
Use pattern blocks to compare fractional parts with varied representations of ONE (Exploration A). 2.G.3
New Activity Beat the Calculator in part 2 to support 2.OA.2. New Note on TLG p613 about estimating in arrays.
MOVED: Use “ONE” and “The Whole” interchangeably and often. Whenever the book asks “What fraction…?” you ask “What word can I use to describe this part?” Have students write the words “a third” or “a fourth” on MJ p187 & 188. Guide the discussion to the importance of saying “the whole” when using these words. A third has no meaning (size) unless you say a third of what.
cubic centimeter, volume, ONE (the whole)
EXPLORATIONS: Prepare area for Fractions Museum in classroom.
8♦C Describe congruent parts as
equal shares of a whole. 2.G.3
Supplemental Lesson 8♦C to support equal shares. Use Supplement 8♦C: Rectangular Pizzas. Encourage students to be as precise as possible with their cutting. Students could draw in lines where they intend to cut a piece in order to guide their cutting. Once students fit a piece into another have them glue it on. These can be used as a display.
Copies of p3-4 should be done on tag paper to make them more durable while cutting. One per pair.
5♦6 Identify basic 3-D shapes
by the description of their attributes. 2.G.1
Pyramids are not included in the 2nd grade list of 3-D shapes. However, pyramids would support the conversation about edges, corners and faces.
Prepare poster of 3-D shapes with labels. Prepare labels for Shapes Museum. See TLG p326 & p343. Before 5♦7 prepare straws. See TLG p348.
5♦7
Use straws and twist-ties to make and describe the difference between rectangular prisms and cubes. 2.G.1
Modification: Pyramids are not a required shape for grade 2, so instead make cubes and rectangular prisms with straws. Use small clay balls for the corners. The long thin coffee straws would provide best results. Construction paper can be used to make a surface for the faces. Focus the discussion on the number of corners, edges and faces and finding equal (congruent) faces. Skip the different types of pyramids.
Key: CCSS-M = Common Core State Standards for Mathematics; EDM = Everyday Mathematics; TLG = Teacher’s Lesson Guide; MM = Math Masters; MRB = My Reference Book;SMJ = Student Math Journal; Grade 2 RSA = Recognizing Student Achievement; R = Readiness; E = Enrichment; EP = Extra Practice; TRM = Teacher Reference Manual; word = A non-appropriate EDM vocabulary word; word = Additional MSP vocabulary word Page 14
Unit 6: Whole-Number Operations and Number Stories Pacing: 4 weeks, thru end of March (week 27).
CCSS-M Critical Ideas for this Unit
Everyday Mathematics relies on several models (diagrams) to assist with problem solving (2.OA.1). Students need opportunities to develop these models on their own and to share them with others. Students then choose to use the models because they make sense to them in the context of various problems types. By the end of this unit, students will have been exposed to all types of +/- word problems and must get enough practice with these before moving onto the more complex 2-step problems (2.OA.1). This is also the time where +/- strategies within 100, with and without regrouping and with three or more addends (2.NBT.6), must be solidified, if students are to work on fluency after unit 6 (2.NBT.5). To do so, they must have plenty of opportunities to share various strategies through classroom discussions or Number Talks (2.NBT.9). Lastly, students will review representing data with bar graphs and move onto representing the data with pictographs. These pictographs are limited to those with each picture representing a single unit (2.MD.10).
Learning Target EDM Edits Comments Vocabulary Games Advanced Prep
Notes on Unit 6 Sample Assessments: Unit 6 assessment is divided into 2 parts. Unit 6 Word Problems assessment is a collection of word problems that should be assessed over time starting after lesson 6♦4. We suggest giving one item (word problem) a day as an exit slip for eight days to assess all of these items. The other Unit 6 assessment is a regular end-of unit assessment to be given like any of the others.
6♦1
Use the Associative Property as a strategy to solve problems with three or more addends. 2.NBT.6
Expanded Adding Three Numbers in any Order and Playing Three Addends. Revised MJ p131 & 132. Revised MM p156 & 157.
Extend to 2-Days: Use tree diagrams to show strategic use of the associative property by finding complements of 10 (option 2 in TLG 380). On Day 2 include three 2-digit numbers and have a Number Talk or class discussion about the strategies. Skip Ballpark Estimates on MJ p132.
sum, total, equation, expression
P1 Three-Addends: SMJ p131, MM p473
6♦2 Develop strategies for solving
comparison word problems. 2.OA.1
New MMR & Math Message. Revised Math Message Follow up to better address comparison stories.
Extend to 2-Days: Modification: Spend this time investigating and illustrating comparison word problems. Have students develop their own representation (diagram) to show what is going on in each story and then an equation to go with each. Share these strategies during Number Talks or class discussions. Include problems where the smaller or larger quantity is unknown, in addition to those where the difference is unknown. Note that these problems can also be represented by both addition and subtraction equations.
comparison number story, difference, comparison diagram, equation, expression
P2 Addition Top-It: MRB p122-3, MM p449
See TLG p384 for suggestions on preparing a comparison diagram.
6♦4 Develop strategies for solving
different types of word problems. 2.OA.1
New Math Message & Follow up. New Selecting Diagrams and Solving Number Stories replaces old. Revised MJ p141.
Extend to 2-Days: Modification: Just as you did for lesson 6♦2, spend this time having students develop different representations for different types of word problems. Develop posters with a few representations kids come up with. For example “Here are 3 ways to represent problems where a quantity changes” (increases or decreases). Make sure to include examples of word problems where the result is unknown, the change is unknown and the start is unknown. Again, skip Ballpark Estimates in Part 2.
2-day Lesson For Part 1, prepare teaching master, transparency or poster of MM p437.
6♦5
Share and justify invented strategies for finding the difference between 2-digit numbers. 2.NBT.5 & 2.NBT.9
Revised Math Message Follow-Up to include Number Grid and number line strategies. Revised MJ p144 to include 3-digit numbers.
Modification: Just like students developed their own strategies for addition in lesson 4♦8, take the time to have students come up with their own strategies for multi-digit subtraction. Provide students with a variety of materials, including base-10 blocks, number grids, number lines, and counters. Again, make a record of the strategies they share and focus the discussion on identifying similarities and differences between strategies. Encourage students to try a different strategy as they solve more problems. A 2nd grade goal is to have students develop their own conceptual models for multi-digit addition and subtraction.
trade (a base-10 long for 10 cubes)
P2 Number-Grid Difference Game: MRB p140-1, MM p463; P3R Base-10 Trading Game: MM p427
7♦2
Use complements of 10 as a strategy for counting up on a number line. 2.NBT.8 & 2.NBT.9
Modification: Hit the Target is a great game to work on Counting Up, but the tables in SMJ p163 can be very confusing. Instead, give students blank number lines so they can set their start and target numbers and use strategic jumps to get from the start to the target. Encourage working with complements of 10 as a strategy (see image below).
P1 Hit the Target: MRB p136-7, MF p163, MM p418&457
6♦3 Answer questions about data
represented on a tally chart and bar graph. 2.MD.10
New MMR. Revised and extended Discussing the Favorite-Food Data Table to better support 2.MD.10.
MOVED: This lesson was moved to allow focus on the multi-digit addition and subtraction, before moving onto data.
basic food groups, data table, bar graph
For Part 1, prepare teaching masters or transparencies, MM p162-64.
6♦A Create and interpret data on
single unit pictographs. 2.MD.10
Supplemental Lesson to support data with pictographs (2.MD.10) Texas Project 9: Pictographs. Modification: This lesson covers single- as well as multi-unit pictographs, the later which will be addressed in grade 3 (3.MD.3). For now focus only on single unit pictographs. Do the first activity spending more time on the top of Gr3 SRB p88 and the modified SRB TX14B made for grade 2. Then have students work on the new MJ pTX10B with the Rainbow trout graph and MJ pTX12 creating a butterfly pictograph. Modify the discussions from the TLG to fit the use of single unit pictographs. Do the extension in Part 2 (1-in grid paper is MM p420).
Key: CCSS-M = Common Core State Standards for Mathematics; EDM = Everyday Mathematics; TLG = Teacher’s Lesson Guide; MM = Math Masters; MRB = My Reference Book;SMJ = Student Math Journal; Grade 2 RSA = Recognizing Student Achievement; R = Readiness; E = Enrichment; EP = Extra Practice; TRM = Teacher Reference Manual; word = A non-appropriate EDM vocabulary word; word = Additional MSP vocabulary word Page 15
Key: CCSS-M = Common Core State Standards for Mathematics; EDM = Everyday Mathematics; TLG = Teacher’s Lesson Guide; MM = Math Masters; MRB = My Reference Book;SMJ = Student Math Journal; MMR = Mental Math and Reflexes; Grade 2 RSA = Recognizing Student Achievement; R = Readiness; E = Enrichment; EP = Extra Practice; TRM = Teacher Reference Manual; word = A non-appropriate EDM vocabulary word; word = Additional MSP vocabulary word Page 16
Unit 7: Patterns and Rules Pacing: 4 weeks, thru end of April (week 29)
CCSS-M Critical Ideas for this Unit
Even numbers are defined as numbers divisible by 2. For second graders who have not yet developed division concepts, this usually means trying to pair objects or count by 2s. CCSS-M takes this concept further by having students connect even numbers to sums of two equal addends (2.OA.3). All these strategies can also be modeled with an array of 2 (rows or columns). For this reason, this unit will first define arrays by looking at how they are arranged or structured (2.OA.4). Partitioning rectangles into rows and columns of same-size squares (2.G.2) will follow since some of the language is the same as with arrays, but will focus more on counting the number of squares inside the rectangle rather than determining an area using square units. Both of these models will then support the conversations about odd and even numbers. The common thread that links these new concepts and connects them to previous understanding is “sums of equal addends”. All of this is planting the seeds for multiplication, but this new operation is not introduced until grade 3. Multiple measurements expressed as line plots will also connect to repeated addition (2.MD.9) since line plots show frequency data. Be sure to provide opportunities for student to begin working with 2-step word problems (2.OA.1). Begin with simple problems where the actions (add-to & take-from) are very clear and keep them within single digit addends. Also continue to provide practice for +/- fluency within 100 and facts to 20 (2.OA.2).
Learning Target EDM Edits Comments Vocabulary Games Advanced Prep
7♦1
Identify patterns on a number grid when skip counting by different numbers. 2.NBT.2
Focus on counting by 2s, 5s and 10s only. Counting by 2’s will help with even numbers, 2.OA.3. multiple of 10 For Part 1, make extra copies of MM p195 plus teaching master or transparency.
7♦2
Use complements of 10 as a strategy for counting up on a number line. 2.NBT.8 & 2.NBT.9
MOVED: This lesson was previously taught in unit 6. Continue using open number lines to have students share strategies for +/- within 100.
P1 Hit the Target: MRB p136-7, MF p163, MM p418&457
7♦3 Share and justify
strategies for adding four 2-digit numbers. 2.NBT.6
Added number line model to examples on TLG p556.
Provide ample time for students to share addition strategies (see #4 TLG p556). For Basketball Addition have each student be a team and the “players” on the recording sheet MM p200 are just 4 individual rolls. Also use 4 dice instead of 3 so the numbers are a bit larger.
P1 Basketball Addition: SMJ p166-7, MM p200, 418&451
For Basketball Addition, prepare class chart of scoreboard MM p200 or SMJ p167, or transparency.
7♦A Identify groups of
arranged objects as arrays or non-arrays. 2.OA.4
Supplemental activity to introduce array concepts, 2.OA.4 Begin having students carefully study the examples and non-examples of arrays from the Arrays document and share their thoughts with a partner. Lead a discussion in which students use their own language to define an array. As students talk about lines or objects in a line, introduce the vocabulary of rows and columns to support the discussion. Ask questions like “Why is this one not an array?” as you point to a non-example. After students complete the bottom part of the sheet, place loose counters on the table along with the Array Cards and have students draw a card and try to build an array with that number of counters. Have student share their arrangements and have the class decide whether it is an array or not an array.
Have sets of the Array Cards precut and available in baskets. 1 set per table. Vocabulary: array, row, column
6♦6 Use geoboards to model
arrays (Exploration A). 2.OA.4
New Activity Making a Picture Graph replaces Playing Three Addends.
MOVED: Modification: Focus on Exploration A, but do not use rubber bands on the geoboards. Instead call out an array (i.e. 2 rows of 5) and have students use pennies to represent the array in the geoboard (see image below). Then ask students “How would I show this array’s total as a sum?” Have students write an equation as a sum of equal addends (i.e. 5+5=10 or 2+2+2+2+2=10). Call out other arrays and have students write the sums. Do Exploration B. Skip Exploration C.
P2 Three-Addends: SMJ p131,MM p473
EXPLORATIONS: MM p172, 175, & 176 give directions for the Explorations. Have pennies and Geoboards available.
6♦8 Solve array word problems
using sums of equal addends. 2.OA.4
New Title: Array Number Stories. Small Revisions throughout to include repeated addition as a number model. Revised SMJ p150 & 151 and MM p182.
MOVED: Modification: Skip all the reference to multiplication. If someone brings it up, mention that that is another way to represent arrays that they will be studying in 3rd grade. Focus on sums of equal addends. Try to generate two equations per array to show that both columns and rows can serve as the addends while still getting the same total.
multiplication diagram, x-by-y array
P2 Fact Extension Game: MRB p134-5; P3R Simon Says
For Part 1, MM p438, use transparency or create wall chart for multiplication models.
7♦4 Find and record patterns
for doubling and halving. 3.OA.9
Skip Part 1 of this lesson. Do Hit the Target in Part 2 with open number lines like in the previous unit. half, double P2 Hit the Target: MRB p136-7, MM p418&457
For 7♦5, collect books of varying weights and analog bath scale. See TLG p564 for details.
7♦5
Use pattern blocks to create and record visual patterns- tessellations (Exploration C). 4.OA.4
Skip this Lesson P2 Hit the Target: MRB p136-7, MM p418&457
EXPLORATIONS: For Math Message, have a 1 pound and a 3 pound book available.
Key: CCSS-M = Common Core State Standards for Mathematics; EDM = Everyday Mathematics; TLG = Teacher’s Lesson Guide; MM = Math Masters; MRB = My Reference Book;SMJ = Student Math Journal; MMR = Mental Math and Reflexes; Grade 2 RSA = Recognizing Student Achievement; R = Readiness; E = Enrichment; EP = Extra Practice; TRM = Teacher Reference Manual; word = A non-appropriate EDM vocabulary word; word = Additional MSP vocabulary word Page 17
7♦B Use square tiles to
partition rectangles into rows and columns. 2.G.2
Supplemental Activity to introduce partitioned rectangles, 2.G.2 Make a 3 by 4 array using 1-in square tiles and another using pattern block hexagons (see image below). Ask a student to come up and join the hexagons together so that there are no gaps or overlaps (tiling). Have another student do the same with the squares. Ask “What do you notice?” or “What was interesting about tiling with the squares?” Lead the discussion to help students to realize that tiling an array with squares makes a rectangle. Try other pattern block shapes. Bring out the 6x8 blue rectangle. Explain that area of the rectangle is the amount of space it covers. “What type of block can I use to completely cover the entire area of this rectangle so that no blue parts are showing?” Have students come up and try different types (hexagons, triangles, etc) to show how parts are left uncovered. Have a student use squares. Ask how many squares were able to fit inside the rectangle? (48) Use the Tiling Rectangles document to have student practice tiling using 1-in squares and drawing in the tiles inside the rectangles. Spend some time modeling and sharing strategies for drawing the tiles since this may be a bit challenging for some 2nd graders. Ask how many tiles fit in each rectangle? How are they organized? Discuss rows and columns as it was done with arrays.
Cut out a 6 by 8 inch rectangle out of blue construction paper. Have enough 1-in tiles available (25 per pair). Vocabulary: tiling, area, rows, columns
9♦7 Partition rectangle into
equal-sized squares. 2.G.2
All of Part 1 was revised to better support 2.OA.4. Revisions for the first two activities. Three new activities replace the rest of Part 1. New SMJ p 222A and 222B. Revised Home Link MM p283
MOVED: Modifications: There are significant changes to this lesson made by EDM, but not all of them are appropriate for 2nd grade. Focus the lesson on partitioning rectangles into equal-sized squares. Disregard the standard units (sq cm or sq in) and skip the discussion on perimeter. Begin with the readiness activity and count squares without using the pennies. Do Part 1 using the new SMJ p222A and 222B which can be found in Unit 9 Editing Kit. Note that these pages and MM p283 have been revised further as well. For each rectangle discuss rows and columns of equal squares and representing their total with sums of equal addends.
Use pennies to determine if numbers are odd or even. 2.OA.3
Supplemental Lesson to support odd and even number concepts, 2.OA.3 Grade 1 Lesson 3♦2: Even and Odd Number Patterns. Start with the readiness activity and use this concept (2 equal groups) to define even. Encourage kids to make arrays of 2 rows or columns with their pennies. For additional practice have student use the Balancing Dominoes document.
even number; odd number P2 Penny-Nickel Exchange 40 pennies per partner.
7♦C Represent even numbers
as sums of equal addends. 2.OA.3
Supplemental Activity to support understanding of odd and even numbers, 2.OA.3. Grab a handful of counters and ask students “How can I find out if I have and odd or even number of counters?” Some students may suggest counting them or may know the pattern (numbers ending in 2, 4, 6, 8 or 0), but ask “How can we be sure?” Lead the discussion to pairing counters into 2 rows. Ask student to tell you a sum for the rows you built. Repeat a couple of times with other even numbers. Ask “What do you notice about all of these sums?” (They are doubles facts). Reverse the process and ask “If I give you an even number would you be able to tell me what array of 2 rows I can make?” Try that with a few even numbers. Then say an odd number “How would my rows look like if I had an odd number?” Continue to ask students to give you equations for each. Students should start to generalize that even numbers can make sums of equal addends (doubles) and odd numbers make sums where the addends differ by 1 (near doubles). Pass out copies of the Odd and Even Equations document. Have students think, pair, share part 1 and discuss as a class. Have students use equations to justify their claims. Then pair up students to work on part 2 using the Array Cards from Lesson 7♦A.
Make additional sets of the Array Cards from Lesson 7♦A. 1 per pair.
7♦6
Develop routines and procedures for consistent and accurate use of measuring tools. 2.MD.1 & 2.MD.2
Revised Collecting and Recording Standing Long Jump Data and Arm Span Data to include both inches and centimeters (2.MD.2).
3-5 days of Lessons Modifications: This is really the first time students are introduced to frequency data. The collection of long jump and arm span data alone may take up to two days. A simpler measuring activity like measuring all the pencils in the class may be more appropriate to introduce line plots. Spend a day collecting pencil length data, have students organize this data in a table with numbers and tally marks and make a line plot as a class using post-its like in Lesson 7♦8. Repeat this process of collecting data, organizing it in a table and representing it with a line plot with both the long jump and arm span data. Provide a Line Plot Template so students can represent their data. Skip all discussion of the median or middle number like in Part 1 of Lesson 7♦7. Focus the discussion on the process of making a line plot. Starting with the smallest measurement and ending with the largest and including all numbers in between (not skipping any numbers even if there is no data for it). Keeping the X same sized and stacked evenly. Appropriate data analysis questions include things like: the difference between the largest and smallest measure; the sum of 2 or 3 measures; the total number of measures (i.e. how many pencils did we measure?)
arm span P2 Array Bingo: SMJ p154-5, MM p450
For Math Message, prepare stick figure diagram from TLG p571. Part 1, mark several “starting” lines on floor with masking tape for long jump activity, or go outside.
7♦7 Use a concrete model to
find the median of a set of data. 6.SP.5c
New MMR and revised Math Message and Follow-Up (2.MD.4 & 2.MD.5). Revised SMJ p173, 177 to include both inches and centimeters (2.MD.2).
median, middle value, sort (the data)
For Math Message, prepare half-sheets of paper for recording. Prepare 20-foot baseline on floor. See TLG p576 & 578.
7♦8
Use collected data to create frequency tables, line plots and bar graphs. 2.MD.10
Revised Math Message Follow-Up to find measured differences using length (2.MD.4 & 2.MD.5).
line plot, title P2 Soccer Spin: SMJ p179, MM p470-1
Math Message requires sticky notes for recording arm-span. For Part 1, prepare Teaching Masters charts of MM p219 & 220.
Penny array in Geoboard for Lesson 6♦6
Tiling arrays for Lesson 7♦B
Use EXPL E from Lesson 4-7. Revised Exploration E to limit only to square tiling, 2.G.2. For EXPL. E, provide cardstock for tiling: can also use 3x5 cards.
Key: CCSS-M = Common Core State Standards for Mathematics; EDM = Everyday Mathematics; TLG = Teacher’s Lesson Guide; MM = Math Masters; MRB = My Reference Book;SMJ = Student Math Journal; MMR = Mental Math and Reflexes; Grade 2 RSA = Recognizing Student Achievement; R = Readiness; E = Enrichment; EP = Extra Practice; TRM = Teacher Reference Manual; word = A non-appropriate EDM vocabulary word; word = Additional MSP vocabulary word Page 18
Unit 8: Fractions
CCSS-M Critical Ideas for this Unit
Numerical representations for fractions will be covered in Grade 3. For this reason, most of this unit is not grade level appropriate. The few lessons that were rescued were moved to unit 5 to support looking at equal shares of a whole geometrically, rather than numerically. If needed use this time as review of these standards and/or practicing word problems and operating within 100.
Learning Target EDM Edits Comments Vocabulary Games Advanced Prep
8♦1
Use paper cutouts to compare equal shares of same sized wholes (halves, thirds & fourths). 1.G.3
New MMR to support 2.OA.2. Revised activity Reviewing Basic Fraction Concepts, 1.G.3. New Activity in Part 2 Bamboo Plant Number Stories with revised SMJ p185 to support 2.OA.1. New Planning Ahead note on TLG p609.
MOVED to unit 5
congruent, ONE (the whole), fraction, denominator, numerator, whole number
Before Math Message, prepare three, 8” paper squares per student. Read TLG p603, Fractions Museum before distributing Home-Link 8♦1. Part 3 (EP) uses the book Ed Emberley’s Picture Pie.
8♦2
Use pattern blocks to compare fractional parts with varied representations of ONE (Exploration A). 2.G.3
New Activity Beat the Calculator in part 2 to support 2.OA.2. New Note on TLG p613 about estimating in arrays.
MOVED to unit 5 cubic centimeter, volume, ONE (the whole)
EXPLORATIONS: Prepare area for Fractions Museum in classroom.
8♦3 Use manipulatives to find and
name fractional parts of a set. 5.NF.4a
New Activity in Part 2 Counting Equal Parts & revised SMJ p193, 2.G.3.
Skip Lessons 8♦3 thru 8♦7 Fractions of a set, equivalent fractions and comparing fractions are all above grade level.
If needed spend some time reviewing the major understandings for fractional parts from grade 1 and grade 2. 1.G.3 & 2.G.3
Equal shares are only the same size if they are from identical wholes. The more equal shares you have from identical wholes, the smaller the shares get. Equal shares from identical wholes are still the same size even if they are different shapes.
8♦4 Use manipulatives to find and
name equivalent fractions. 3.NF.3a,b,c
Revised directions and discussion for Making Display of Equivalent Fractions 3.NF.3a,b.
equivalent, equivalent fractions
P2 Name That Number: MRB p138-9, MM p462
Math Message uses MM p239, one per student plus extras. Part 1 uses fraction circles (commercial) or cut from MM p239 for teacher modeling.
8♦5
Use fraction cards to share and justify strategies for determining fractional equivalencies. 3.NF.3a,b,c
P1 Equivalent Fractions Game: SMJ p198-9
Use SMJ, Activity Sheets 5 & 6 (with storage bag or paper clips) or matching Everyday Math Deck cards.
8♦6
Use fraction cards to share and justify strategies for comparing fractions. 3.NF.3d
Before Part 1, SMJ p206, create and pose additional fraction word problems as needed. Use similar problems in future Mental Math and Reflexes sessions.
Key: CCSS-M = Common Core State Standards for Mathematics; EDM = Everyday Mathematics; TLG = Teacher’s Lesson Guide; MM = Math Masters; MRB = My Reference Book;SMJ = Student Math Journal; MMR = Mental Math and Reflexes; Grade 2 RSA = Recognizing Student Achievement; R = Readiness; E = Enrichment; EP = Extra Practice; TRM = Teacher Reference Manual; word = A non-appropriate EDM vocabulary word; word = Additional MSP vocabulary word Page 19
Units 9 thru 12: Place Value, Measurement & Line Plots Pacing: 4 weeks, thru end of May (week 34).
CCSS-M Critical Ideas for this Unit
Before students can estimate lengths (2.MD.3), they need extensive experience measuring (2.MD.1) with the unit they are estimating. Estimating using a personal reference like a thumb length for an inch is helpful. Common references also make estimation easier. For example, thinking about the size of standard sheet of paper may help you estimate the dimensions of your computer monitor. Estimates of longer lengths should be done with larger units. For example, it might be easier to estimate the width of your desk in feet than in centimeters (2.MD.2). Keep estimates to numbers less than 15. For addition and subtraction within 1,000, provide lots of experiences with models and drawing and gradually work your way up to written strategies (2.NBT.7). Begin by working with just multiples of 10 and 100, then doing 100 more or less and 10 more or less (2.NBT.8), then problems with only one 3-digit number without regrouping, then with regrouping and finally problems with two 3-digit numbers. Continue to facilitate Number Talks or discussions where students share and justify their strategies (2.NBT.9). For telling time, the focus should be on using a.m. and p.m. (2.MD.7).
Learning Target EDM Edits Comments Vocabulary Games Advanced Prep
Notes on the organization of this MIG Unit: Units 9 thru 12 in EDM contain many lessons that are not aligned to grade 2 standards. For this reason a selection of lesson have been combined to form a single unit to address base-10 operations in the hundreds, measurement and line plots. Please follow the lessons in the order they appear in the MIG. Lessons not shown should be skipped, at this time.
9♦1 Measure and estimate
length using meters. 2.MD.1, 2.MD.3 & 2.MD.4
Revised Checking Estimates activity to use metersticks instead of yardsticks to support 2.MD.3. New Comparing Measurements activity in Part 2 to support 2.MD.4
Extend to 2 days. Day 1: To develop a personal reference for the meter, mark a spot on the doorway that is exactly 1m from the floor. Have students stand next to the spot and notice where on their body the spot hits. For the average 44 inch tall 2nd grader it should be around eye level. Before doing estimates, have students measure the classroom dimension with a meterstick. Skip the yard. Day 2: Do Part 2, Comparing Measurements, and collect all SMJ p210 as data to be used for line plots in later lessons, 2.MD.9. Have students estimate their shoe length before measuring it, 2.MD.3.
standard unit, yard, meter
Part 1 requires a meter stick. For Part 3 (E), create masking tape paths. See TLG p660. Planning Ahead: For 9♦2, gather materials for Measures All Around Museum.
9♦2
Use rulers to measure objects to the nearest inch, foot, centimeter. 2.MD.2, 2MD.3
New MMR. Revised Measuring in Feet and Inches to include estimate, 2.MD.3. Revised Extra Practice to include comparison questions, 2.MD.4.
Extend to 2 Days. Day 1 Modification: Skip anything on the decimeter and yard. Have students find a personal reference for a standard foot. Repeat the activity on SMJ p209 from Lesson 9♦1 but with feet instead of meters. Have students measure the same objects. Have students compare their measurement in feet to their measurement in meters. Ask students why the results are different, 2.MD.2. Day 2: Do the activity on SMJ p212 but cross out decimeters. Again, ask students to compare their result with the different units and explain how the size of the unit affects the measure.
inch, centimeter, foot, decimeter
P2 Name That Number: MRB p138-9, MM p462
Set up Museum. For Part 3 (ELL), collect materials and create posters. Planning Ahead: Organize boxes students brought for 9♦4. See TLG p671.
9♦3 Compare measurement in
inches and centimeters. 2.MD.4
Revised measuring activity to stay within nearest whole unit, 2.MD.2. New Fact Triangle activity in Part 2. New Writing/Reasoning prompt.
Modification: Skip Introducing Fractional Units of Length. Instead, have students use unifix cubes to build a tower based on the number of letters in their name. Then have students pair up to measure each other’s towers (to the nearest unit) and determine how much longer one is than the other in inches and then in centimeters. Switch pairs and repeat the activity.
For Part 1, MM p260 & 261 will be helpful for teacher demo. For Part 3 (R) and (E) activities see prep TLG p672.
10♦8
Use base-10 blocks to represent 10 and 100 more or less. 2.NBT.8
Revised activity Representing 3- and 4-Digit Numbers to support expanded form, 2.NBT.3. New Extra Practice activity to support 2.NBT.1 & 2.NBT.4.
Modification: Briefly review modeling 3-digit (not 4-digit) numbers with base-10 blocks and writing them in expanded form, 2.NBT.8. Do the Extra Practice activity with the new MM p 322A & 322B (from Unit 10 editing kit). Then ask students, “How much would it be if I added (or removed) a 100s block (a flat)? How much would it be if you added (or removed) a 10s block (a long)? What digit would change?” Have students practice some of these types of problems with their blocks. Be sure to include problems like “10 less than 402”. Then use 100 and 10 More & Less documents for practice. Model the same concept with the expanded form (see example below).
flat, long, cube, place value, big cube
P1 Money Exchange Game: SMJ p253-4, MM p321
For Math Message, display 1 each of base-10 blocks. For Part 1, teaching master of MM p320 & 321.
10♦9
Use Place-Value Book to display 10 and 100 more or less. 2.NBT.8
Modification: Have students make the Place-Value Book for only 3-digit numbers. Use the full page 12 of the book as the back cover (with thousands & ten-thousands), but for pages 1-11 have them cut only three boxes of digits. Do some of the routines from Part 2, but spend the bulk of your time on the fifth routine, 10 more (less), 100 more (less). Try some tricky ones like 10 less than 308. Skip any discussions that go beyond 1,000.
ones, tens, hundreds, thousands, ten-thousands
To prepare demo model of place-value tools, use MM p330-336. Paper Card Holder uses 5 copies of MM p327 for repeated digits.
Key: CCSS-M = Common Core State Standards for Mathematics; EDM = Everyday Mathematics; TLG = Teacher’s Lesson Guide; MM = Math Masters; MRB = My Reference Book;SMJ = Student Math Journal; MMR = Mental Math and Reflexes; Grade 2 RSA = Recognizing Student Achievement; R = Readiness; E = Enrichment; EP = Extra Practice; TRM = Teacher Reference Manual; word = A non-appropriate EDM vocabulary word; word = Additional MSP vocabulary word Page 20
10♦A
Use base-10 blocks to represent 3-digit addition and subtraction. 2.NBT.7
2-Day Supplemental activity to support 2.NBT.7 Students need to have time to model 3-digit addition and subtraction problems with base-10 blocks. Spend one day on addition and one on subtraction. Start with problems that do not require trading. Then do problems that add/subt. a 2-digit number to/from a 3-digit number that requires a trade. Then move on to problems with two 3-digit numbers requiring one or two trades. At first, provide base-10 blocks then work on representing these problems with drawings of the blocks. If time allows, you can have them represent sums in expanded form problems. (See example below)
11♦3
Develop written strategies for 3-digit addition and subtraction. 2.NBT.7
Make line plots with class personal measurement data. 1.MD.9
New MMR & RSA. New activity in Part 2 Displaying Head Size Data on a Line Plot.
2- Day Extension & Modification: Day 1: DO NOT TEACH TRADE FIRST AS AN ALGORITHM. Spend this time having students transfer their strategies from the concrete model or drawing to a written method. Ask students, “How can I just use numbers to show what I’m doing with the blocks? What other strategies do you use that you can show as a written method?” Trading first is a strategy that may naturally develop from students representing subtraction with base-10 blocks. However, we want students to develop their own ways to record their thinking rather than teaching a written procedure to be followed by everyone (an algorithm). Day 2: Spend day two making line plots with the measurement data gathered in Lesson 9♦1 when you collected SMJ p210 from students. Do the Part 2 activity from Lesson 10♦5, Displaying Shoe Length Data then do Part 2 for this lesson, Displaying Head Size Data.
algorithm, trade-first (subtraction)
12♦3
Use a timeline to display daily events in sequential order. 2.MD.7
Modification: Instead of making a timeline in years for the last two centuries, have students make their own “Typical School Day” timeline. Introduce the concept of A.M. and P.M. by explaining why we needed these for telling the difference between the two sets of 12 hours in the 24 hour day. Start and end the time line at 12:00a.m. with ½ hour intervals. Have students represent and sequence at least ten events on the time line. Students should draw a line from each of their events to an exact point on the timeline and write the time for each event. Also use revised SMJ p295 Sequencing Events to have student locate events in a daily timeline.
communicate, timeline, decade, century
For Part 1, prepare a timeline from 1830 to 2010, showing 10-year intervals.
12♦1
Use a calendar and clock to describe relationships among units of time.
Touch and go time unit conversions in part 1. Focus on telling time to the nearest 5 minutes and on telling the difference between A.M and P.M. For each clock on SMJ p289 ask, “What would you be doing if this time was in the A.M.? P.M.?”
For Math Message, MM p377, 1 per 4 students, cut apart. For Part 3 (EP) you will need the dates for the 1st day of summer vacation and the 1st day of next school year.
12♦2
Use and recognize alternate phrases to tell time. 2.MD.7
New Beat the Calculator activity in Part 2. Touch and go. Continue to ask A.M and P.M questions about each time shown on clocks.
375 + 249 = 300 + 70 + 5 + 200 + 40 + 9
300 + 70 + 5 + 200 + 40 + 9 500 + 110 + 14
600 + 20 + 4 = 624
100 less 500 = 538
638 = 600 + 30 + 8
100 more 700 = 738
10 less 20 = 628
638 = 600 + 30 + 8
10 more 40 = 648
Modeling 100 and 10 more or less with Expanded Form for Lesson 10♦8
Representing sums in Expanded Form for Lesson 10♦A
