Second Grade and the CCSS–M

1. Second Grade and the CCSS–M Vacaville USD September 23, 2013

2. AGENDA • The CCSS-M: Math Practice Standards • Review Daily Math • Word Problems • Place Value • Planning/Discussions

3. Expectations • We are each responsible for our own learning and for the learning of the group. • We respect each others learning styles and work together to make this time successful for everyone. • We value the opinions and knowledge of all participants.

4. Sharing • At your tables, discuss • What you have tried since our first session • What successes you have had • What questions and/or concerns you have? • Pick one success and one question/concern to share with the group.

5. Standards for Mathematical Practice

6. CCSS Mathematical Practices REASONING AND EXPLAINING Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others MODELING AND USING TOOLS Model with mathematics Use appropriate tools strategically OVERARCHING HABITS OF MIND Make sense of problems and persevere in solving them Attend to precision SEEING STRUCTURE AND GENERALIZING Look for and make use of structure Look for and express regularity in repeated reasoning

7. SMP Matrix

8. SMP Matrix Individual Reflection • Look over the matrix • For each of the SMP’s, • where are your students on the matrix? • where are 2ndgrade students at your site on the matrix?

9. SMP Matrix Site Reflection: Based on your individual reflections with regards to the SMP’s, • Discuss as a group • Where do you believe most of your 2ndgrade students are on the matrix? • Plan as a group • What SMP do you want to work on as a team? • What are your next steps?

10. Review of Daily Math

11. Word Problems

12. Bakery Problem #1 A bakery sold 235 boxes of cookies. They sold 119 more boxes of cookies than cupcakes. How many boxes of cupcakes were sold?

13. Bakery Problem #2 Another bakery sold 3 times as many boxes of cookies than cupcakes. If they sold 126 more boxes of cookies than cupcakes, how many boxes of cookies were sold?

14. Lessons Learned From Research Sense-making is important! • In learning and remembering mathematics • In developing mathematical thinking and reasoning

15. How many two-foot boards can be cut from two five-foot boards? (Verschaffel, 2007) Nearly 70% of the upper elementary school students given this problem say that the answer is “five” Why?

16. How many two-foot boards can be cut from two five-foot boards? (Verschaffel, 2007) Because 5 + 5 = 10 and 10 ÷ 2 = 5. What did the students forget? the “real world” context

17. Kurt Reusser asked 97 1st and 2nd graders the following question: There are 26 sheep and 10 goats on a ship. How old is the captain? 76 of the 97 students “solve” this problem - by combining the numbers.

18. H. Radatz gave students non-problems such as: Alan drove 50 miles from Berkeley to Palo Alto at 8 a.m. On the way he picked up 3 friends. NO QUESTION IS ASKED! Yet, from K-6, an increasing % of students “solve” the problem by combining the numbers and producing an “answer.”

19. The Serious Question Where does such behavior come from?

20. A Serious Answer • Students develop their understanding of the nature of the mathematical enterprise from their experience with classroom mathematics.

21. Therefore….. • If the curriculum doesn’t induce them to see mathematics as a sense-makingactivity, they won’t engage with mathematics in sensible ways.

22. What about using “key words” to help elementary school kids solve word problems? For example…….

23. Using Key Words. John had 7 apples. He gave 4 apples to Mary. How many apples did John have left? 7 - 4 = 3

24. Nick Branca gave students problems like these: • John had 7 apples. He left the room to get another 4 apples. How many apples does John have? • Mr. Left had 7 apples… Can you guess what happened?

25. Juan has 9 marbles. He gives 5 marbles to Kim. How many marbles does he have now? • Juan has 9 marbles. Kim gives 5 marbles to him. How many marbles does he have now? ** Problems can use the same key words but have different meanings

26. Jon has 5 red blocks and 3 blue blocks. How many blocks does he have in all? • Jon has 5 bags with 3 red blocks in each bag. How many blocks does he have in all?

27. Key Word Strategies • Biggest concern – Research shows that students stop reading for meaning • Students need to be taught to reason through a problem – to makesense of what is happening

28. Personal Example • Mary practiced the piano for 2 hours on Monday. This was 20% of her total practice time for the week. How many hours does Mary practice the piano each week?

29. Personal Example • Mary practiced the piano for 2 hours on Monday. This was 20% of her total practice time for the week. How many hours does Mary practice the piano each week?

30. Domains – 2nd Grade • Operations and Algebraic Thinking • Number and Operations in Base Ten • Measurement and Data • Geometry

31. Key to algebraic thinking is developing representations of the operations using • Objects • Drawing • Story contexts And connecting these to symbols

32. Such manipulatives or pictures are not merely “crutches” but are essential tools for thinking

33. Word Problems and Model Drawing

34. Model Drawing • A strategy used to help students understand and solve word problems • Pictorial stage in the learning sequence of concrete – pictorial – abstract

35. Model Drawing • Develops visual-thinking capabilities and algebraic thinking. • If used regularly, helps students spiral their understanding and use of mathematics

36. Steps to Model Drawing • Read the entire problem, “visualizing” the problem conceptually • Decide and write down (label) who and/or what the problem is about H

37. Steps to Model Drawing • Rewrite the question in sentence form leaving a space for the answer. • Draw the unit bars that you’ll eventually adjust as you construct the visual image of the problem H

38. Steps to Model Drawing • Chunk the problem, adjust the unit bars to reflect the information in the problem, and fill in the question mark. • Correctly compute and solve the problem. • Write the answer in the sentence and make sure the answer makes sense.

39. Representation • Getting students to focus on the relationships and NOT the numbers!

40. Problem #1 Tyrone had $17 in his piggy bank. He added $10 more. What is his total savings now? H

41. Problem #2 Ray has 465 tractors and his brother Ben has 289. How many tractors do they have altogether?

42. Problem #3 Jennifer went shopping with $42. She came home with $9. How much money did she spend?

43. Problem #4 Hansel read 235 pages of his book over the weekend. Gretel read 198 pages of her book over the weekend. How many more pages did Hansel read than Gretel?

44. Problem #5 A total of 100 raffle tickets were sold over a 3-day period. If 21 raffle tickets were sold on Monday, and 67 tickets were sold on Tuesday, how many raffle tickets were sold on Wednesday?

45. Problem #6 There are 5 plates of cookies on the shelf. If there are 4 cookies on each plate, how many cookies are there in all?

46. Problem #7 There are 20 chairs. Kayla wants to put the chairs into 4 rows. How many chairs will be in each row?

47. Problem #8 12 students need rides to an after school event. If only 4 students can ride in each car, how many cars are needed to transport the students?

48. 2.OA.1. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1

50. Word Problems • What can we do when to make word problems more interesting and engaging for our students?