Lesson 2.1a Addition Number Stories Common Core Focus 2.OA.1. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1 Lesson INSERT ADDITION BAR MODELING PRACTICE http://www.thinkingblocks.com/tb_addition/addition.html (tchr video on bar modeling) Practice simple word problems using counters, grids and pictorial rep of bar models Ind practice D1.2, P1.2 HW: R 1.2 Manipulatives Number Grid Counters Slate board Bar modeling flashcards (on wiki)

Change and Wholes Compa R e Bar Modeling Teaches The Importance of Language When Solving Math Problems Compa R e Change Parts Parts Parts Parts Parts Parts and Wholes

Bar Modeling- Scaffolding the Notion of Proportion Number Model: _____________+_____________=_____________ _____________=_____________+_____________

Bar Modeling Number Model: _____________+_____________=_____________ _____________=_____________+_____________

Bar Modeling Number Model: _____________+_____________=_____________ _____________=_____________+_____________

Bar Models Provide a Foundation For Algebraic Understanding Fred has 6 toys. Mary has 2 toys. How many toys do they have altogether? T 6 2 T is the same as 6+2 T=6+2 T=8 There are 8 toys altogether.

Bar Modeling- Part/Part Whole Number Model: _____________+_____________=_____________ _____________-_____________=______________

Part/Part/Whole = + 1st Part 2nd Part End There were 4 butterflies and 2 ladybugs sitting on a branch. How many insects were sitting on the branch?

Bar Modeling-Part/Part/Whole (6) 1st Part (4) 2nd Part (2) Number Model: 4+2=6 6-4=2 6-2=4

Bar Modeling: Part/Part/Whole Whole Unknown # Story There were 2 apples and 8 bananas in the fruit bowl? How many pieces of fruit were in the bowl? X=2+8 First Part Unknown Jim had 10 brothers and sisters. How many sisters did he have if head 2 brothers? 10=x+2 Second Part Unknown Jim had 10 brothers and sisters. If he had 5 brothers, how many sisters did he have? 10=5+x X 2 8 10 x 2 10 5 x

Bar Modeling: Part/Part/Whole Whole Unknown Picture First Part Unknown Second Part Unknown

Bar Modeling: Part/Part/Whole Whole Unknown Number Model First Part Unknown Second Part Unknown

Bar Modeling: Part/Part/Whole Whole Unknown Picture First Part Unknown Second Part Unknown

Bar Modeling: Part/Part/Whole Whole Unknown Number Model First Part Unknown Second Part Unknown

Bar Modeling: Part/Part/Whole Whole Unknown # Story ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ First Part Unknown Second Part Unknown

Bar Modeling: Part/Part/Whole- Whole Unknown Picture

Bar Modeling: Part/Part/Whole- Whole Unknown Number Model

Bar Modeling: Part/Part/Whole- Whole Unknown # Story ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Bar Modeling: Part/Part/Whole- First Part Unknown Picture

Bar Modeling: Part/Part/Whole- First Part Unknown Number Model

Bar Modeling: Part/Part/Whole- First Part Unknown # Story ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Bar Modeling: Part/Part/Whole—Second Part Unknown Picture

Bar Modeling: Part/Part/Whole—Second Part Unknown Number Model

Bar Modeling: Part/Part/Whole—Second Part Unknown # Story ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Part/Part/Whole Number Stories First Part Second Part Whole

Addition and Subtraction- Change You start with an amount You add or subtract an amount You end with a total amount Beginning Change End Addition Part Add (join) a Part Total Subtraction Subtract (separate) a Part

Addition Problems: Change Bar Modeling End Beginning Change Number Model: _____________+_____________=_____________

Change-Addition = + Start Change End 4 butterflies were sitting on a branch. 2 more landed on the branch. How many butterflies were on the branch now?

Addition Problems: Change Bar Modeling End (6) Beginning (4) Change (2) I136843350 Number Model: 4+2=6

Bar Modeling: Joining (Addition- Change) Samples Total Amount Unknown # Story The team had 8 runs. They scored 2 more. How many do they have in all? 8+2=x Amount Joined Unknown John has $2 in his piggy bank. He needs $10 to buy the new toy he wants. How much more does he need to save to have enough money? 2+x=10 Initial Amount Unknown Mary added 5 books to her library. Now she has 10 books in her library. How many books did she start with? X+5=10 x 8 2 10 2 x 10 x 5

Bar Modeling: Joining (Addition-change) Total Amount Unknown Picture Amount Joined Unknown Initial Amount Unknown

Bar Modeling: Joining (Addition-Change) Total Amount Unknown Number Model Amount Joined Unknown Initial Amount Unknown

Bar Modeling: Joining (Addition-Change) Total Amount Unknown # Story ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ Amount Joined Unknown Initial Amount Unknown

Bar Modeling: Joining (Addition-Change)- Total Amount Unknown Picture

Bar Modeling: Joining (Addition-Change)- Total Amount Unknown Number Model

Bar Modeling: Joining (Addition-Change)- Total Amount Unknown # Story ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Bar Modeling: Joining (Addition-Change)- Amount Joined Unknown Picture

Bar Modeling: Joining (Addition-Change)- Amount Joined Unknown Number Model

Bar Modeling: Joining (Addition-Change)- Amount Joined Unknown # Story ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Bar Modeling: Joining (Addition-Change)- Initial Amount Unknown Picture

Bar Modeling: Joining (Addition-Change)- Initial Amount Unknown Number Model

Bar Modeling: Joining (Addition-Change)- Initial Amount Unknown # Story ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Change- Addition Number Stories Initial Amount Amount Joined Total

Bar Modeling- Subtraction-Change Beginning Change End Number Model: _____________-_____________=_____________

Change-Subtraction = - Start Change End There were 4 butterflies sitting on a branch. 2 flew away. How many were left?

Bar Modeling- Subtraction-Change Beginning (5) Change (2) End (3) Number Model: 5-2=3

Bar Modeling: Separating (Subtraction-Change) Amount Remaining Unknown # Story Suzie had $10. She spent $8 on lunch. How much money does she have left over? 10-8=x Amount Separated Unknown John had to read 10 books over the summer. He only has 2 left to read. How many books did he read? 10-x=8 Initial Amount Unknown Jim ate 5 cookies out of the box. He only has 5 left. How many were in the box? X-5=5 10 8 x 10 x 8 x 5

Bar Modeling: Separating (Subtraction-Change) Amount Remaining Unknown Picture Amount Separated Unknown Initial Amount Unknown

Bar Modeling: Separating (Subtraction-Change) Amount Remaining Unknown Number Model Amount Separated Unknown Initial Amount Unknown

Bar Modeling: Separating (Subtraction-Change) Amount Remaining Unknown # Story ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ Amount Separated Unknown Initial Amount Unknown

Bar Modeling: Separating (Subtraction-Change)- Initial Amount Unknown Picture

Bar Modeling: Separating (Subtraction-Change)- Initial Amount Unknown Number Model

Bar Modeling: Separating (Subtraction-Change)- Initial Amount Unknown # Story ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Bar Modeling: Separating (Subtraction-Change) Amount Remaining Unknown Picture

Amount Remaining Unknown Bar Modeling: Separating (Subtraction-Change)- Amount Remaining Unknown Amount Remaining Unknown Number Model

Amount Remaining Unknown Bar Modeling: Separating (Subtraction-Change)- Amount Remaining Unknown Amount Remaining Unknown # Story ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Amount Separated Unknown Bar Modeling: Separating (Subtraction-Change)- Amount Separated Unknown Amount Separated Unknown # Story ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Change- Subtraction Number Stories Initial Amount Amount Separated Amount Remaining

Warning, Warning! There are 3 types of addition/subtraction problems: change, part/part/whole and comparison. Change and part/part whole problems are based on the concepts of parts building wholes. COMPARISON PROBLEMS DO NOT! COMPARISON PROBLEMS ARE BASED ON FINDING THE DIFFERENCE BETWEEN TWO PARTS

Bar Modeling- Multiplication LARGER AMOUNT SMALLER AMOUNT DIFFERENCE Number Model: _________-__________=_________ (more or less)

Bar Modeling- Comparison Larger Smaller Amount Amount - = Jim has 5 butterflies. Mary has 2. How many more butterflies does Jim have than Mary?

Comparison Number Model: 5-2=3 Larger Amount (5) Smaller Amount (2) Difference 3 More Number Model: 5-2=3

Bar Modeling Number Model: __________________________=_____________

Bar Modeling: Comparison- All Amount More (or Less) Unknown x # Story Ted has 10 crayons. Neil has 4 crayons. How many more crayons does Ted have than Neil? How many fewer crayons does Neil have than Ted? 10-4=x Smaller Amount Unknown 6 Ted had 10 crayons. Neil has 6 less than Ted. How many crayons does Neil have? 10-6=x Larger Part Unknown 5 Ted Has 5 crayons. Neil has 5 more than Ted. How many crayons does Neil have? 5+5=x 10 4 10 x x 5

Bar Modeling: Comparison- Smaller Amount Unknown Picture

Bar Modeling: Comparison- Smaller Amount Unknown Number Model

Bar Modeling: Comparison- Smaller Amount Unknown # Story ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Bar Modeling: Comparison- Amount More (or less) Unknown Picture

Bar Modeling: Comparison- Amount More (or less) Unknown Number Model

Bar Modeling: Comparison- Amount More (or less) Unknown # Story ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Bar Modeling: Comparison- Larger Unknown Picture

Bar Modeling: Comparison- Larger Unknown Number Model

Bar Modeling: Comparison- Larger Part Unknown # Story ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Comparison Number Stories- How Many More? Smaller Amount Larger Amount How Many More?

Comparison Number Stories- How Many Less? Larger Amount Smaller Amount How Many More?

Lesson 2.1b Addition Number Stories Continued Common Core Focus 2.OA.1. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1 Lesson Mental Math and Reflexes: use # grid- discuss strategies (Part 1) All: (no p/p/t or change to more…use bar modeling) -Have students write own stories - students should use counters and bar models to show problem (Part 3) All: Do after pt 1…more practice writing/modeling word problems (Part 2) All: number grid- ask “How can our 100 number grid help us with the bottom of page 22?” *Substitute bar modeling diagrams for part-part-whole. Manipulatives Number Grid Counters Slates

Number Grids Start Number Count On (+) End Number

Lesson 2.2a Review Easy Addition Facts Common Core Focus 2.OA.2. Fluently add and subtract within 20 using mental strategies.2 By end of Grade 2, know from memory all sums of two one-digit numbers Lesson Mental Math and Reflexes: use bar model diagrams/counters/number line: show different ways to find answer (w/o an algorithm) Part 1–No Beat the Calculator, Do just +1, +0, Part 2- J pg 25…use number line to answer +0, +1, Students can make bar model flash cards for these facts (see wiki) -Math Boxes (no calculator) Use a number line to solve problems; find a “floor” number line or table number line. Facts should be acquired in this order: +0, +1, doubles, +9, doubles +1, doubles +2 Manipulatives Number Lines

Complete The Number Line Learning Goal- use your knowledge of place value to correctly order numbers along a number line Look at the beginning numbers. Use your knowledge of place value to fill in the rest of the numbers along the number line.

Number Grids Start Number Count On (+) End Number

Part/Part/Whole Flashcards

Commutative Property (Turn Around Rule) Fact Turn Around Fact

Getting Ready- Fact Shortcuts Example Notice, ,Think, Wonder Turn- Around Facts (Commutative Property) +1 +0 Doubles +9 Doubles +1 Doubles +2

Lesson 2.2b Common Core Focus 2.OA.2. Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers Lesson (Part 3) from 2.2 All Use bar modeling to solve each other’s story problems. Practice facts: +1, +2….practice with flash cards and number line. Play Do Manipulatives Number llines Flash cards

Domino Top-It Player 1 Player 2 4 < 6 5 = >

Domino Top It- Comparison Bar Modeling 6 4 Difference=2 6 is 2 more than 4 5 No difference: 5=5

Balanced Equations (Turn Around Equations) < = >

Bar Model Number Model _____+_____=_____l

Lesson 2.3a Doubles Facts Common Core Focus 2.OA.2. Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers Lesson Mental Math and Reflexes: discuss different strategies…have students tell how the got the answer…NOT “I did it in my head” Show on # line, # grid, drawing proofs (draw longs/cubes on boards, put together to find sum) Part 3- Readiness Activity/Enrichment…can do all together or small groups, can also have students find all doubles dominoes- write down fact- (Part1) All: Do not teach Doubles or Nothing…play a top it game instead (Part 2) All (No game- play Domino Top-It instead) Math Boxes- no calc for #2 Materials Dominoes

Double Fact Bar Models Sum

Lesson 2.3c Odd and Even Common Core Focus Lesson *May be helpful to make the connection that all sums of doubles facts are even since they are made up of two equal parts. Mental math: D 5.6 Math Message: Using unifix cubes find out if the digits 1-10 are even or odd. (in notebooks, list all even numbers- and their equal parts, then list the odd numbers) Then do some double digits: 18 (let students work with cubes- 10 is always even, so the ones place is what will help us know if number is even/odd) Try 15…etc Ind practice: P 5.6 and/or E 5.6 HW R 5.6 Manipulatives Unifix cubes **even/odd has been moved to 2nd grade

Numbers and Their Double: Odd or Even? 1 Odd 1+1=2 even

Problem Solving Activity

Lesson 2.4: Turn Around Facts and +9 Common Core Focus 2.OA.2. Fluently add and subtract within 20 using mental strategies.2 By end of Grade 2, know from memory all sums of two one-digit numbers Lesson Mental Math and Reflexes: use # line, discuss various strategies Part 3: Do FIRST with everyone! Use 10 Frames and counters (can be found on wiki, or can find various free books/ideas on google) Part 1: All Part 2: All: Instead of Beat Calc, play a Top-it Game: have students jot down every time they used doubles, doubles +1 or the +9 strategy to help them solve the problem Manipulatives 10 Frames, counters, cards

Using 10’s for +9 Facts Make It! Number Model _____+9 = _____+10-1 =

Number Grid- Subtraction (+9): +10, -1 Problem Start Number +10 -1 4+9=s 4 14 S=13

Using 10’s for +8 Facts Make It! Number Model _____+8 = _____+10+2 =

Number Grid- Subtraction (+8): +10, -2 Problem Start Number +10 -2 4+8=s 4 14 S=12

Lesson 2.5a: Addition Strategies That Use Double Facts Common Core Focus 2.OA.2. Fluently add and subtract within 20 using mental strategies.2 By end of Grade 2, know from memory all sums of two one-digit numbers Lesson Mental Math and Reflexes Part 1: All: as students find doubles +1,+2, have them write them out as 3 addends: 4+4+2=4+6…use counters or 10 Frames to show Part 2: All and can try all boxes (3) NO Manipulatives Counters 10 Frames

Use The Facts You know Like a Bridge To Solve The Facts You Don’t Know Use The Facts You know Like a Bridge To Solve The Facts You Don’t Know! Doubles Facts +1, +2 4 8 9 10 +4 5 +4 5 6 4+5=4+4+1 4+6=4+4+2

Doubles +1, Doubles +2 Original Number Double Fact Double Fact +1 4 4+4=8 4+5=4+4+1 4+4+1=8+1 8+1=9 4+6=4+4+2 4+4+2=8+2 8+2=10

Doubles -1, Doubles -2 Original Number Double Fact Double Fact +1 4 4+4=8 4+3=4+4-1 4+4+1=8-1 8-1=7 4+2=4+4-2 4+4-2=8-2 8-2=6

Double Fact +1 Bar Models

Double Fact +2 Bar Models

Lesson 2.5b: Adding 3 Numbers Common Core Focus 2.OA.2. Fluently add and subtract within 20 using mental strategies.2 By end of Grade 2, know from memory all sums of two one-digit numbers Lesson - Review strategies from previous day using 3 addends. Put 7+7+2 on board to solve. Discuss different strategies for solving: Why did some do 7+7 first, why might someone do 7+2 first then add on 7? (+9 strategy) Practice problems with 3 addends…discuss “easy” ways to solve: try to find a 10, try to find a double. Use 10 frames, counter to help solve Ind practice: D 2.5, P 2.5, (if some students are secure…they can work on E 2.5, but must WRITE about a strategy they used for each problem.) HW: R 2.5 Manipulatives 10 Frames, counters

Use The Facts You know Like a Bridge To Solve The Facts You Don’t Know Use The Facts You know Like a Bridge To Solve The Facts You Don’t Know! Making 10’s 4 10 11 12 +6 7 +6 7 8 4+7=4+6+1 4+8=4+6+2

Making 10’s Write It! Make It! Join Them- Total Smaller Part Larger Part

Make a 10, Add The Rest If you know your compliments of 10: And some of your basic facts: 1 2 3 4 5 6 7 8 9 10 3+0=3 3+1=4 3+2=5 3+3=6 3+4=7

Make A Ten, Add Some More 3 Addends 10 Fact Answer 4+6 4+6+0 10+0 10 4+7 4+6+1 10+1 11 4+8 4+6+2 10+2 12 4+9 4+6+3 10+3 13 4+10 4+10+0 10+4 14 4+11 4+10+1 10+5 15 4+12 4+10+2 10+6 16 4+17 4+16+1 17+3+1 20+1 21 4+18 4+16+2 18+2+2 20+2 22

It’s Easy To Make A 10 and Add The rest! 7+3 7+4 =7+ (3+1) 7+3+1=10+1 7+5 =7+3+2 7+3+2=10+2 7+6 =7+3+3 7+3+3=10+3 7+7=7+3+4 7+3+4=10+4

Make A 10, Add Some More Make It!

Number Grid- 3 Addends First Number + = Number Model ______+______+______=______

Lesson 2.6 Subtraction From Addition Common Core Focus 2.OA.2. Fluently add and subtract within 20 using mental strategies.2 By end of Grade 2, know from memory all sums of two one-digit numbers Lesson MMR Pt 3: Readiness only: use as warm up: discuss, write strategies Message Pt. 1: use bar modeling and dominoes Pt. 2 Boxes: no #2 Manipulatives Dominoes, Bar Model Flashcards

Problem Solving Activity

Lesson 2.7a: Fact Families Common Core Focus 2.OA.2. Fluently add and subtract within 20 using mental strategies.2 By end of Grade 2, know from memory all sums of two one-digit numbers Lesson MMR: discuss words that mean to “take away”, use counters to show the “take away” Part 3: Readiness: some who are ready could make stories to go with counter problems -Part 1 HW R 3.5

Part/Part/Whole Flashcards

Lesson 2.7b Fact Families Continued Common Core Focus 2.OA.2. Fluently add and subtract within 20 using mental strategies.2 By end of Grade 2, know from memory all sums of two one-digit numbers Lesson Warm up: write fact families using dominoes -Part 2 pg 37 model w/bar models and counters -Math box: no 4 HW: R 3.3 Manipulatives Dominoeas

Part/Part/Whole Flashcards

Lesson 2.9 Name Collection Boxes Common Core Focus 2.OA.2. Fluently add and subtract within 20 using mental strategies.2 By end of Grade 2, know from memory all sums of two one-digit numbers Lesson Warm up: write fact families using dominoes -Part 2 pg 37 model w/bar models and counters -Math box: no 4 HW: R 3.3

Name That Number Number Name #1 Name #2 Name #3

Equivalent Names For Numbers Draw It Expanded Form 3 Addends

Equivalent Names For Numbers Starting Number Equivalent Names Bar Model

Lesson 2.10: Frames and Arrows: Skip Counting Common Core Focus 2.NBT.2. Count within 1000; skip-count by 5s, 10s, and 100s. Lesson -No frames and arrows -part 3 do readiness -Practice counting by 5’s, 10’s and 100’s: 2.NBT.2: count by 5, 10,100 to 1000 -use number grids - use base 10 blocks to model…start from various numbers… - students should show/explain using both blocks and grid -do part 2, no box 4 HW: R 5.5 Manipulatives Number grids Base 10 blocks

Complete The Number Line Complete each number line below by skip counting from the beginning number 5 10 100

Counting by 10’s

Lesson 2.11 Function Machines Common Core Focus 2.NBT.5. Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Lesson MMR Message: use counters/10 frames to solve Part 1: Keep function boxes with emphasis on patterning and problem solving Part 2: Boxes: 2, 3,4, 6(can try 1 and 5) HW: 2.11

Number Grids In Rule Out

Lesson 2.12 Counting Strategies Common Core Focus 2.OA.2. Fluently add and subtract within 20 using mental strategies., know from memory all sums of two one-digit numbers. 2.NBT.5. Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. 2.NBT.9. Explain why addition and subtraction strategies work, using place value and the properties of operations. Lesson Part 3: Use this part for games -MMR -Math message- do multiples ex. Have kids write some sub. # stories to match a subtraction story -part 1 -part 2 -do boxes no #4 -Homelink

Subtraction- Counting Up and Down The Number Grid Start Number Count Back (-) End Number

Subtraction- Counting Up and Down On The Number Line Complete each number line below by skip counting from the beginning number 5 14 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 14-5=x 14-5=9

Subtraction- Counting Up and Down The Number Line Complete each number line below by skip counting from the beginning number

Lesson 2.13: Shortcuts For Harder Subtraction Facts Common Core Focus 2.OA.2. Fluently add and subtract within 20 using mental strategies., know from memory all sums of two one-digit numbers. 2.NBT.5. Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. 2.NBT.9. Explain why addition and subtraction strategies work, using place value and the properties of operations. Lesson MMR Message Pt 3 Readiness Pt 1 Pt 2 Boxes: #3- no roman numerals Homelink

10 Frame Subtraction- Make A 10, Count Some More Make It!

Using 10’s for -9 Facts Make It! Number Model _____-9 = _____-10+1 =

Number Grid- Subtraction (-9): -10, +1 Problem Start Number -10 +1 14-9=s 14 4 S=5

10 Frame Subtraction- Make A 10, Count Some More Make It!

Using 10’s for -8 Facts Make It! Number Model _____-8 = _____-10+2 =

Number Grid- Subtraction (-8): -10, +2 Problem Start Number -10 +2 14-8=s 14 4 S=6