1. Our Purpose and Agenda Important outcome for 2 nd grade Whole number addition and subtraction Two- and three-digit addition and subtraction Important outcomes for 3 rd grade Multiplication and division concepts Multiplication and division fluency

2. Adding single digits fluently Fluency develops over time, starting with word problems that are written to suggest strategies: 8 birds are sitting in a tree. 6 more birds fly into the tree. Now how many birds are in the tree? Students in 1 st grade should be doing many of these kinds of problems. They start with objects to model the action of the problem. See CGI Problem Types Then they might draw pictures. Eventually they use number strategies to get an answer. Number Talks: 8+6 CGI Strategies

3. 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?” 2 nd graders should know the single digit addition combinations from memory by the end of the year. Box and Books of Facts, ORIGO Mathematics

4. Addition Within 100 By the end of 1 st grade, students should be doing this: Leprechaun Traps: Addition Within 100Leprechaun Traps: Addition Within 100 (thru 4:49) 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.

5. 2 nd grade work What math abilities do your students have when they enter 2 nd grade that you see in this video?

6. Hundreds Chart Games

7. Two digit add & subtract There are 13 children on the playground. 24 more children come out to the playground. How many are now on the playground? How can you figure this out? What number strategies can you use in your head? Use base 10 blocks or linking cubes. Number Talks: 2 nd : 26+27 3 rd : 70-34

8. Concrete Concrete – Representational – Abstract Objects – Pictures – Symbols There are 17 children on the playground. 24 more children come out to the playground. How many are now on the playground? How can you figure this out? What number strategies can you use in your head? Use base 10 blocks or linking cubes.

9. Concrete There are 47 children on the playground. 24 go home. How many are left on the playground? How can you figure this out? What number strategies can you use in your head? Use base 10 blocks or linking cubes.

10. Concrete There are 53 children on the playground. 38 go home. How many are left on the playground? How can you figure this out? What number strategies can you use in your head? Use base 10 blocks or linking cubes.

11. Representational Concrete – Representational – Abstract Objects – Pictures – Symbols Base-ten placemat: The base-ten placemat is used to draw the graphic representation, which is simply a recording of what students did with unifix cubes. The base-ten placemat helps them maintain the correct place value during the problem.

12. Abstract Concrete – Representational – Abstract Objects – Pictures – Symbols Writing number sentences and using the formal algorithm: Eventually you can remove the base ten placemat and let them write the problem symbolically, using the formal algorithm that is the exact symbolic translation of the work they did with the concrete and representational materials.

13. Any twists? Is this how you do it? Do you have any enhancements or concerns about this approach? Remember C-R-A C: Problems worked out with unifix cubes (but try mental math first) R: Use a base-ten placemat to organize thinking A: Write the number sentence and formal algorithm

14. Common Core What do you find in the Common Core that supports this? What have you found in your enVision materials that supports this?

15. Add and subtract within 1000 Acquisition – Fluency – Generalization 2.NBT.7 Add and subtract within 1000, 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. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

16. Our Purpose and Agenda Important outcome for 2 nd grade Whole number addition and subtraction Two- and three-digit addition and subtraction Important outcomes for 3 rd grade Multiplication and division concepts Multiplication and division fluency

17. Understanding multiplication Leprechaun Traps: Addition Within 100 (after 4:49) Leprechaun Traps: Addition Within 100 2.OA.4 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

18. 2 nd grade What’s the total number of blocks? How did you get your answer? 2.OA.4 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

19. 3 rd grade What’s the total number of blocks? How did you get your answer? “I know that 4 x 5 is 20, and 4 x 2 is 8, so 4 x 7 is 28.” 3.OA.5 Apply properties of operations as strategies to multiply and divide. Examples…

20. Area Models Make a visual model of 9 x 4. Make a visual model of36 ÷ 9 Make up two word problems, one where 9 stands for the number of objects in each group, and one where 9 stands for the number of groups.

21. Multiplication and Division Problem types Equal size groups 5 groups with 4 in each group, the total is 5 x 4 Division is a “missing factor” problem. 20 cookies in 5 bags, how many in each bag? 20 cookies, 4 in each bag, how many bags? 20 = 5 x __ 20 = __ x 4 Partitive division Measurement division 44444 5 groups of 4 See handout

22. 2. Rate and price problems 7 bananas for 5 days? 8 pairs of socks at $3 each? 3. Combination problems The Friendly Old Ice Cream Shop has 3 types of ice cream cones. They also have 4 flavors of ice cream. How many different combinations of an ice cream flavor and cone type can you get at the Friendly Old Ice Cream Shop? How can we represent this visually?

23. How might children solve these? 1. Chad had 5 bags of candy with 7 pieces of candy in each bag. How many pieces of candy did Chad have? 2. At Sally ’ s birthday party there were 15 children and 3 blankets. If the same number of children sat on each blanket, how many children sat on each blanket? 3. Lee collects stamps. He has 45 stamps. If he sticks 9 stamps on each page, how many pages would he fill with stamps? 4. Mr. Wong has 4 children. He wants his children to share 12 marbles so that they each get the same amount. How many marbles should Mr. Wong give each child? 5. 19 children are going to the circus. 5 children can ride in each car. How many cars are needed so that all the children can go to the circus? 6. Maria has 17 fish. If 3 fish can be put into one fish bowl, how many bowls does she need to hold her fish?

24. Building fluency Provide LOTS of practice with these types of problems, letting children use strategies until they internalize the “fact”. Use games (see the fluency packet). 3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of one-digit numbers.

25. Building fluency Number Talks are helpful for seeing relationship that lead to quick strategies. Number Talks: 3 rd : 7x7 Doubling and Halving

26. 4 th Grade Multiplication Multiplicative Comparison The first-grade class has a hamster and a gerbil. The gerbil weighs 9 ounces. The hamster weighs 3 times as much as the gerbil. How much does the hamster weigh?

27. Common Core Checklist Read through the Common Core for both grades to see how what we’ve addressed fits with the core mathematics curriculum. Mark anything you have questions about or want to discuss further. Then create a checklist to help you monitor students’ progress on important math understandings and skills.

28. Your Curriculum As you teach from enVision, keep in mind these key goals for 2 nd and 3 rd grade mathematics.