1. Grade 3 Instructional Focus Four critical areas: Developing understanding of: multiplication & division and strategies of multiplication & division within 100 fractions, especially unit fractions the structure of rectangular arrays and of area Describing and analyzing 2-dimensional shapes

2. Grade 4 Instructional Focus Three critical areas: Developing an understanding: of and fluency with multi-digit multiplication, and dividing to find quotients involving multi-digit dividends fraction equivalence, addition & subtraction of fractions with like denominators, and multiplication of fractions by whole numbers That geometric figures can be analyzed & classified based on their properties (parallel sides, perpendicular sides, particular angle measures, & symmetry

3. Grade 5 Instructional Focus Three critical areas: Developing fluency with addition and subtraction of fractions and developing understanding of the multiplication of fractions and of division of fractions in limited cases* Extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations Developing an understanding of volume.

4. Grade 6 Instructional Focus Four critical areas: connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems; completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers; writing, interpreting, and using expressions and equations; and developing understanding of statistical thinking.

5. Grouping the practice standards 1. Make sense of problems andpersevere in solving them 6. Attend to precision Problem solving with precision 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others 4. Model with mathematics 5.Use appropriate tools strategically 7.Look for and make use of structure 8.Look for and express regularity in repeated reasoning Reasoning and Explaining Modeling and using tools Seeing structure and generalizing

6. Use this site for more information: http://dpi.state.nc.us/acre/standards/co mmon-core-tools/#unela Math Unpacking Standards

7. Levels of Learning: Think about how people learn. Concrete > Pictures > Abstract

8. Division of whole numbers Create a story for this division problem. Solve by drawing a picture. 14 3

9. Grade 3

10. 3.OA.2 Partitive and Measurement (Quotative) Models

11. Two Types of Division Partitive Division (equal sharing) Mark picked 24 apples. He wants to put them equally into 4 bags. How many apples can each bag hold?  You are answering “how many in each group”. Measurement Division (repeated subtraction) Mark picked 24 apples. He put them into bags containing 6 apples each. How many bags did Mark use?  You are answering “how many groups?"

12. 3.OA.3 Let’s share our division stories and solutions. Decide if the story represents that partitive or measurement model.

13. 3.OA.4 Finding the whole using the inverse relationship of multiplication and division 8 x ? = 48 5 = 3

14. 3.OA.5 Use your number sense and apply properties of operations! One example > 8 x 7 can be thought of as 8 x 5 = 40 + 8 x 2 = 16 The sum is 56

15. 3.OA.6 Division as an unknown-factor problem.

16. 3.OA.7 FLUENCY! FLUENCY! FLUENCY! Fluently divide within 100.

17. Grade 4

18. 4.OA.3 Talking about remainders Recall the earlier problem> 14 3 What does the remainder 2 mean?

19. 4.OA.3 Talking about remainders Write different word problems involving 14 3 = ? where the answers are best represented as: Problem A: 4 Problem B: 4 r 2 Problem C: 5 Problem D: 4 2/3

20. 4.NBT.6 This standard calls for students to explore division through various strategies. What are some ways to solve 120 4?

21. Concrete? Picture? Algorithm?

22. Grade 5

23. 5.NBT.6 Let’s talk about your solutions tomorrow. There are 1, 716 students participating in Field Day. They are put into teams of 16 for the competition. How many teams are created? Are any students left over? If so, what do you do with them. Think of 3 different ways to solve.

24. 5. NBT.7 Dividing decimals to hundredths. A relay race lasts 4.65 miles. The relay team has 3 runners. If each runner goes the same distance, how far does each member run? Make an estimate, find the actual answer, and then compare them.

25. Grade 5 Day 2

26. 5.NBT.6 Let’s talk about your solutions tomorrow. There are 1, 716 students participating in Field Day. They are put into teams of 16 for the competition. How many teams are created? Are any students left over? If so, what do you do with them. Think of 3 different ways to solve.

27. Partitive or Measurement (Quotative)?

32. Sharing Sub Sandwiches Draw pictures to solve the following problem: A baseball team is carpooling to a game. They stop to get some submarine sandwiches, and each car gets a certain number of subs to share. Assuming that the subs are shared equally, which car would you want to be in (to get the biggest piece of sandwich?) Car A: 2 subs for 3 people Car B: 3 subs for 5 people Car C: 2 subs for 4 people Car D: 4 subs for 6 people

37. The student concludes that the answer is Car A. Imagine that you were evaluating this student’s understanding. Would you say that he: has a full understanding of the problem, and uses fractions appropriately to describe the amount each child gets. has a good understanding of the problem, but needs to convert his answer into a single fraction. has drawn an appropriate picture, but something is wrong with how he is using fractions to describe the amount each child gets. has drawn an inappropriate picture which cannot be used to solve the problem. does not understand this problem or fractions at all.

38. Division of Fractions Let’s Take a Look

39. Write a problem and use a drawing to help this student understand the meaning of 1 1/3

40. Pat discovers that she has only 1 cup of brown sugar, and her recipe calls for 1/3 cup of brown sugar. Now how many recipes can she make? – Imagine a child who correctly solves the problem but has yet to learn an algorithm for dividing fractions. How might the child solve the problem? – How many 1/3s are in 1?

41. Let’s Help Tonya and Chris

43. Write a problem and use a drawing to help this student understand the meaning of ½ 3

44. Fraction Strips

45. Recall the whole