1. Critical Outcomes 1 st grade Adding and subtracting situations Strategies for adding and subtracting Place value understanding (groups of tens and ones) 2 nd grade Fluency with single-digit numbers Two- and three-digit addition and subtraction

2. Basic assumptions about children’s learning of mathematics Very young children know how to solve math problems. Children develop mathematical understanding and acquire fluency with whole number computation by solving a variety of problems in any way that they choose. Children learn more advanced computational and problem solving strategies by watching their classmates solve problems.

3. CCSS 1 st Grade 1.OA.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

4. Adding to, taking from 1. Lucy has 8 fish. She wants to buy 5 more fish. How many fish would Lucy have then? 3. Janelle has 7 apples in her bag. How many more does she have to pick to have 11 apples? 2 TJ had 13 chocolate chip cookies. At lunch she ate 5 of those cookies. How many cookies did TJ have left? 4. Max had some money. He spent $9 on a video game. Now he has $7 left. How much money did Max have to start with?

5. Unknowns in all positions Result Change Start Unknown Unknown Unknown 8 + 5 =  7 +  = 11  + 2 = 7 13 – 5 =  8 –  = 5  – 9 = 7 Notice how these equations are shorthand for the action in the problem. Students should write equations to represent the problems in order to “decontextualize” the mathematics.

6. Part/whole problems Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. (K and 1 st ) 6 boys and 4 girls were playing soccer. How many children were playing soccer? (whole unknown) 10 children were playing soccer. 6 were boys and the rest were girls. How many girls were playing soccer? (part unknown)

7. No-action problems - comparing Mark has 3 mice. Joy has 7 mice. Joy has how many more mice than Mark? (comparing)

8. Other names for the same thing Equalizing: Abby has read 6 books so far this summer. Mollie has read 4. In order to have read as many books as Abby, how many more does Mollie need to read? (number sentence?) Missing part: There are 14 hats in the closet. 6 are red and the rest are green. How many green hats are in the closet? (number sentence?) Comparative subtraction: Jessica found 6 rocks on the trail and Tia found 7. How many more rocks did Tia find than Jessica? (number sentence?)

9. Solution Strategies There were 7 apples on the tree. A farmer came along and picked 5 of the apples. How many apples are still on the tree? 4 ladybugs were crawling in the grass. 3 more came to join them. How many ladybugs were there then?

10. Solution Strategies Direct modeling of the action in the problem Counting strategies Derived facts Fluency 4 ladybugs were crawling in the grass. 3 more came to join them. How many ladybugs were there then? CGI Interviews - Strategies

11. Children learn more advanced computational and problem solving strategies by watching their classmates solve problems.

12. Fluency with “math facts” The use of manipulatives, counting and derived-fact strategies eventually grows into knowledge of most math facts. Explicit instruction on strategies can be helpful for building math facts that haven’t come naturally through problem solving, but that isn’t necessary until 2 nd grade. K.OA.5 Fluently add and subtract within 5. 1.OA.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. 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.

13. Number Talks and Math Centers Number Talks and partner games don’t take the place of problem-solving, but they do supplement it and provide more opportunities for learning and practicing strategies. 8 birds are in a tree. 6 more birds fly up to the tree. Now how many birds are in the tree? Number Talks: 8+6

14. Encourage strategies Give your students these kinds of problems often. Let them tell the class what strategies they used. Students learn from each other. Instead of asking only “What’s the answer?” ask “How did you get your answer?”

15. Critical Outcomes 1 st grade Adding and subtracting situations Strategies for adding and subtracting Place value understanding (groups of tens and ones) 2 nd grade Fluency with single-digit numbers Two- and three-digit addition and subtraction

16. Important tools 1.NBT.5 Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. 1.NBT.6 Subtract multiples of 10 in the range 10- 90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

17. Addition Within 100

18. Two digit add & subtract Concrete – Representational – Abstract Objects – Pictures – Symbols There are 24 children on the playground. 13 more children come out to the playground. How many are now on the playground? Do this with mental math. Use base 10 blocks or linking cubes. How does this translate into a written method?

19. A progression of problems There are 17 children on the playground. 24 more children come out to the playground. How many are now on the playground? Do this with mental math. Use base 10 blocks or linking cubes. How does this translate into a written method?

20. A progression of problems There are 47 children on the playground. 24 go home. How many are left on the playground? There are 53 children on the playground. 38 go home. How many are left on the playground? Do this with mental math. Use base 10 blocks or linking cubes. How does this translate into a written method?

21. Representational – Abstract

22. Related problems 2.MD.5 Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. 2.MD.4 Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.

23. 2.MD.6 Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, …, and represent whole-number sums and differences within 100 on a number line diagram. 2.MD.10 Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph.