Sailing the Seas of BDS CCSS Math K-5

# Sailing the Seas of BDS CCSS Math K-5

## Sailing the Seas of BDS CCSS Math K-5

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1. Sailing the Seas of BDS CCSS Math K-5

2. Our Objectives: • To increase K-5 teachers understanding of the Mathematical Practice Standards and the Mathematical Content Standards specific to their grade band.

3. You would never hear someone say: I am not very good at reading. I can’t read.

4. You do hear people say: I am not good at math. I can’t do math. When I was a kid math was my worst subject

5. What is the difference? The difference between the USA and other higher performing nations is that a culture of learning math is established from the beginning of a students career in school. Students are informed and taught everyone can do math.

6. Essential Question #1 • How do the Mathematical Practice Standards help me to improve my math instruction?

7. Common Core Standards for Mathematical Practice • Make sense of problems and persevere in solving them • Reason abstractly and quantitatively • Construct viable arguments and critique the reasoning of others • Model with mathematics • Use appropriate tools strategically • Attend to precision • Look for and make use of structure • Look for and express regularity in repeated reasoning http://www.corestandards.org/the-standards/mathematics/introduction/standards-for-mathematical-practice

8. SMP 1 - Make sense of problems and persevere in solving them. • Students: • make sense of the meaning of the task • find an entry point or a way to start the task • focus on concrete manipulatives before moving to pictorial representations • develop a foundation for problem solving strategies • reexamine the task when they are stuck • ask, “Does my answer make sense?”

9. CCSS Practice #1

10. What does SMP1 look like in a K-2 classroom? • “Old” problem (little or no rigor) Tina had 10 balloons. She gave 7 of them away. How many balloons did Tina have then? • “New” problem (with rigor) Burger Barn has 1 small table that can seat 4 people. They also have 1 large table that can seat double that amount. 15 people came in at lunch time. How many people did not get a seat?

11. SMP 2 - Reason abstractly and quantitatively. • Students: • make sense of quantities and the relationships • decontextualize • contextualize • use abstract reasoning: • when they measure and compare lengths of objects • when they partition 2-D geometric figures into halves and fourths • as they begin to use standard measurement units

12. CCSS Practice #2

13. Math StringsMental Math • The number of fingers on two human hands • Subtract the number of toes on one human foot • Multiply it by the number doughnuts in a half dozen • Divide by the number of eyes on a human face • Add to it the number of hearts in a human body • The answer is? 16

14. What does SMP2 look like in a K-2 classroom? • I had two pencils. My mom gave me some more. Now I have five pencils. How many pencils did my mom give me? • Decontextualize: 2 + □ = 5

15. SMP 3 - Construct viable arguments and critique the reasoning of others. • Students: • use mathematical terms to construct arguments • use definitions and previously established solutions in their arguments • engage in discussions about problem solving strategies • recognize and discuss reasonableness of strategies • recognize and discuss similarities and differences between strategies

16. CCSS Practice #3

17. Find the Fiction • My number is 100. • I can be broken into 4 parts equally • I represent a millennium • My quantity in pennies is equal to a dollar

18. Find the Fiction • On your board write the number of the statement that is fiction and write the word fiction next to that number (DO NOT SHOW ANYONE) • Example: 4 Fiction • When you hear the signal word discuss with your group one at a time your answer. Come to a consensus • Answer: 2 is the Fiction • Praise: Expert Thinking

19. Farmer Fred looks in his field, but can only see feet. He knows that he has four animals. He knows that he has cows and chickens. Farmer Fred sees 14 feet. What are his four animals?

20. A model of mathematical modeling (pg. 72, CCSSM) • Identifying important quantities in a practical situation • Making assumptions and approximations to simplify a complicated situation • Mapping relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas • Analyzing relationships mathematically to draw conclusions • Interpreting mathematical results in the context of the situation • Reflecting on whether the results make sense • Improving the model if it has not served its purpose.

21. SMP 4 - Model with mathematics. • Students: • Apply math to solve problems in everyday life. • Represent math by using symbols, pictures, concrete representation, graphs or equation writing. • Analyze relationships and draw conclusions • Interpret results in context • Reflect if results make sense

22. CCSS Practice #4

23. What does this Array tell us?

24. Why Arrays?

25. SMP 5 - Use appropriate tools strategically. • Students: • have access to a variety of tools • counters, place value blocks, hundred boards, number lines, geometric shapes, paper/pencil, etc. • determine which tools are most appropriate to use • explain why they used a specific tool • use tools appropriately • have experiences with educational technology • Calculators, virtual manipulatives, games that support conceptual understanding or higher order thinking skills

26. CCSS Practice #5

27. Number Lines

28. What does SMP5 look like in a K-2 classroom? • Students have easy access to math tools. • Students select their own tools.

29. SMP 6 – Attend to precision. • Students: • are precise in their communication • are precise in their calculations • are precise in their measurements (no gaps or overlaps) • describe their actions and strategies clearly • use grade-level appropriate mathematical vocabulary accurately • give precise explanations and reasoning • check their work for accuracy and reasonableness of solutions

30. CCSS Practice #6

31. Equality Insert link from cpalms

32. What does SMP6 look like in a K-2 classroom? • How does a student (or teacher) talk through a subtraction with regrouping model? 413 -168

33. SMP 7 - Look for and make use of structure. • Students: • look for patterns and structures in the number system and other areas of mathematics • begin to recognize the commutative property • begin to recognize that numbers can be decomposed into tens and leftovers (ones) • work with subtraction as missing addend problems (How much more do I need to get to ___?) • skip count by tens off the decade to solve addition and subtraction problems • recognize that ten ones equals a ten, and ten tens equals a hundred

34. CCSS Practice #7

35. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 What does SMP7 look like in a K-2 classroom? 82 - 14 = 68 53 + 23 = 76 82 - 14 = ? 53 + 23 = ?

36. Word ProblemTake a Deep Breath! • Mr. Centeno had a fruit fly problem. • On day 1 there were two fruit flies. • On day 2 there were four fruit flies. • On day 3 there were six fruit flies. • How many fruit flies would Mr. Centeno have on day 5? • Answer: 10 • What was the pattern? +2

37. SMP 8 - Look for and express regularity in repeated reasoning. • Students: • look for regularity in problem structures when solving mathematical tasks • compose and decompose numbers in different ways • use composition to make a ten and add the extras • use decomposition and composition to break apart numbers by place value to add and subtract larger numbers • look for the most efficient strategies for computations (including doubles, doubles 1 or 2, make a ten, counting on, etc.) • use repeated reasoning when solving a task with multiple correct solutions • check for reasonableness during and after task

38. What does SMP7 look like in a K-2 classroom? • Addition facts that equal ten • How does a student know they have found them all? 0 + 10 = 10 • Equivalent Representations 4 + 6 = 10 8 + 2 = 10 3 + 7 = 10 10 + 0 = 10 4 + 6 = 10 6 + 4 = 10 3 + 7 = 10 6 + 4 = 10 7 + 3 = 10 7 + 3 = 10 8 + 2 = 10 9 + 1 = 10 0 + 10 = 10 9 + 1 = 10 10 + 0 = 10

39. CCSS Practice #8

40. What does SMP8 look like in a K-2 classroom? What is ten more than …… 3? 13? 23? 33? 43? 53?

41. What does SMP8 look like in a K-2 classroom? • Make a Ten (Add the Extra) 6 + 7 = 13 4 3 10 + 3 = 13

42. Repeated Pattern Activity Directions. Multiply the middle number by itself. Multiply the outer numbers to each other. Compare the products 5,6,7 3,4,5 6,7,8 What conjecture can you come up with? What is 29x31 and why? What would the Algebraic formula look like?

43. Mathematics – Grades K - 5 • 5 Domains • Counting and Cardinality • Operations and Algebraic Thinking • Number and Operations in Base Ten • Measurement and Data • Geometry

44. Mathematics – Grades 1st – 5th • 4 Domains • Operations and Algebraic Thinking(OA) • Number and Operations in Base Ten(NBT) • Measurement and Data(MD) • Geometry(G)