2. Clarify Their Own Thinking Consider and Test Other Strategies Investigate and Apply Math Relationships Develop Multiple Strategies and Choose the Most Efficient One

3. Number Talks Strings- Give students a series of smaller problems that build on each other to teach a particular strategy. Focused Problem- 1 bigger problem that allows students to explore how to solve the problem in different ways- develops flexible and efficient thinking.

4. 5-15 minutes Think-Pair-Share Wait Time- Emphasize Thinking Over Speed Wait until most students feel they have at least one strategy Students who solve problem quickly are encouraged to solve problems in more than 1 way Accept All Ideas Different Strategies develop flexible thinking and build on understanding of number relationships Wrong answers lead discussion to focus on important strategies and clear up common misconceptions

5. Sample Prompts I agree with ____________ because__________. I disagree with__________ because__________. I do not understand____________. Can you please explain again? Why did you decide to_________________?

6. Getting Started Start with smaller problems Offer strategies from former students It’s ok to put an answer on the back burner 5-15 minutes Be patient

7. Building Mathematical Relationships Writing Problems Horizontally 199 + 199 +1 +1 200 + 200 = 400 -2 398 Vertical problems encourage standard algorithm

8. Building Mathematical Relationships Anticipate Student Answers and Name Them: 28+29 Friendly Numbers or Landmarks 25+23=25+25-2= 50-2=48 7x5= 5x5+2x5 Compensation 28+29 = (28-1) + (29+1)= 27+30 +10 +10 +10 27 37 47 57 Breaking Numbers Into Place Value (20+8)+ (20+9) = (20+20) + (8+9) = 40+17 = 40 +10 + 7 = 50 +7 = 57

9. Strings - a series of smaller problems that teach a pattern, strategy, etc…. 7+3 3+4 7+3+4 7+7

10. Strings - a series of smaller problems that teach a pattern, strategy, etc…. 3x5 Clarify Their Own Thinking Tyler realized his mistake and did the 2 nd one correctly Consider and Test Other Strategies Investigate and Apply Math Relationships Associative property Develop Multiple Strategies and Choose the Most Efficient One 3x (5x2) is more efficient than (3x5)x2 2x6 3x5x2 5x2x6

11. 1 Problem- Many Strategies 12+19 Compensation Make a 12 a friendly number by subtracting 2. Add 2 to 19 to compensate. 12+19= 10 + 21 (12-2) + (19+2)

12. 1 Problem- Many Strategies 12+19 Place Value Rewrite numbers in expanded form 12+19=( 10+2) +(10+9) Use associative property to add 10’s and 1’s 10+10=20 2+9=11 20+11=31

13. 1 Problem- Many Strategies 12+19 Friendly Landmarks Adjust 12 and 19 to make the friendly landmarks of 10 and 19. 12-2=10 and 19+1=20 10+20=30 Readjust numbers back 30+2=32 32-1=31

14. 1 Problem- Many Strategies 12x15 Decomposing and The Associative Property Decompose The Factors 12=3x4 15=3x5 12x15=3x4x3x5 Rearrange to friendlier numbers 12x15=(4x5)x (3x3) Recompose with friendlier numbers 12x15=20x9 12x15=180

15. 1 Problem- Many Strategies 12x15 Distributive Property Distribute 12 Groups of 15 Into Friendly Groups- 10 Groups of 15 +2 Groups of 15 12x15= (10 x 15) + (2 x 15) = 150+30=180 Or Distribute 15 Groups of 12 Into Friendly Groups- 10 Groups of 12 + 5 Groups of 12 12x15= (12 x 10) + (12 x 5)= 120 +60=180

16. 1 Problem- Many Strategies 12x15 Doubling and Halving Double 1 Factor and Halve The Other 12x15=6x30 Decompose 30 Into 3x10 6x30= 6x3x10 Use associative property to multiply a basic fact and multiple of 10 6x3=18 18x10=180

17. Accountability Smaller Number Talks Signal most efficient strategy Posters of Strategies Used Exit Problems Weekly Computation Assessment

18. Day 1 – Problem Talk Ted is saving money for a new bike. He deposits money at his bank three times a month. Each time he goes, he deposits $5. How much will he have saved in a year. First we have to figure out how much he saves in a month- 3x5 Then we have to find out he saves in a year- (3x5) x12 Day 2 – Number Talk 3x5 15x12

19. K-2 Classrooms: Big Ideas Developing Number Sense Relationships Magnitude Effect of operations Mental Math Estimation Conservation of # Developing Fluency With Small Numbers More than memorizing facts…understanding number relationships Subitizing Making 10’s

20. K-2 Classrooms: Tools Dot Cards Rekenreks (Bead models) 5 Frames and 10 Frames Number Lines Number Grids

21. K-2 Classrooms: Strategies Counting on/ Counting Back Counting chunks Finding 10’s Compose and Decompose Place Value Doubles/ Near Doubles Compensation

22. 3-5 Classrooms Developing Number Sense Relationships Magnitude Effect of operations Mental Math Estimation Conservation of # Place Value Developing Fluency More than memorizing facts…understanding number relationships Properties Connecting Mathematical Ideas

23. 3-5 Classrooms: Addition And Subtraction Strategies Counting on/ Counting Back Counting chunks Finding 10’s Compose and Decompose Place Value Doubles/ Near Doubles Compensation

24. 3-5 Classrooms: Multiplication Strategies Area Models Repeated addition Skip Counting Doubling and Halving and related relationships 5 x 4 = 10 x 2 Partial Products Landmarks and Friendly Numbers Decomposing Factors into Smaller Factors

25. 3-5 Classrooms: Division Strategies Area Models Repeated subtraction Sharing out (picture models) Multiplying Up (Partial products) Partial Quotients Proportional Reasoning (halving and halving) 200/4 = (200/2) / (4/2) = 100/2 = 50 Decomposing Factors into Smaller Factors 40/8 = 40 / (4x2) = (40/4) / 2 = 10/2 = 5