1. Kindergarten and the CCSS–M
Vacaville USD
October 3, 2013

2. Demographic Form Name Email School

3. AGENDA The CCSS-M: Math Practice Standards Review Daily Math
The Bakery Problems
Word Problems
Concept of Number and Quantity
Planning/Discussions

4. 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.

5. 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 comment/ question/concern to share with the group.

6. Standards for Mathematical Practice

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

8. SMP Matrix

9. SMP Matrix Individual Reflection Look over the matrix
For each of the SMP’s,
where are your students on the matrix?
where are Kindergarten students at your site on the matrix?

10. 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 Kindergarten 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?

11. Review of Daily Math

12. Word Problems

13. 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?

14. 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?

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

16. How many two-foot boards can be cut from two five-foot boards
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?

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

18. 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.

19. 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.”

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

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

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

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

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

25. 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?

26. Juan has 9 marbles. He gives 5 marbles to Kim
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

27. Jon has 5 red blocks and 3 blue blocks
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?

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

29. Domains – Kindergarten
Counting and Cardinality
Operations and Algebraic Thinking
Number and Operations in Base Ten
Measurement and Data
Geometry

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

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

32. Word Problems

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

34. 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

35. 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

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

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

38. Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
2. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
Drawings need not show details, but should show the mathematics in the problem. (This applies wherever drawings are mentioned in the Standards)

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

41. Group Task
Work with your group to write a variety of problems appropriate for your grade level
Put one problem on each card
Label the problem type and write the problem on the front of the card
Show the model drawing representation and possible number sentences on the back.

42. Example
Put Together/Take Apart
Addend Unknown
I have 9 balloons. 3 of them are red and the rest are blue. How many balloons are blue?

43. The Number 7

44. Unit Planning
Topic: The Number 7
Content Standards:

45. Unit Planning Practice Standards:
What should students already know and how am I going to help them make connections to that prior knowledge?

46. Concrete – Representational – Abstract
Unit Planning
What will students learn and how will I know what they have learned?
Concrete – Representational – Abstract

47. Unit Planning
What will students learn and how will I know what they have learned?
Conceptual Understanding:

48. Unit Planning
What will students learn and how will I know what they have learned?
Conceptual Understanding:

49. Unit Planning
What will students learn and how will I know what they have learned?
Conceptual Understanding:

50. Unit Planning
What tools, models, and materials are necessary to fully address the standards for this unit?

51. Unit Planning
What will students learn and how will I know what they have learned?
Procedures and Skills:

52. Unit Planning
What will students learn and how will I know what they have learned?
Applications and Problem Solving:

53. Unit Planning
What will students learn and how will I know what they have learned?
Key Vocabulary

54. Unit Planning
What tools, models, and materials are necessary to fully address the standards for this unit?

55. Unit Planning Anticipated Number of Days: ______
Conceptual understanding: ____ days
Procedures and skills: ___ days
Applications and problem solving: ___ days

56. Unit Planning Sketch of Unit by Days (Overview)
Planning Actual Lessons

57. The Number 11

58. Developing Reasoning

59. Additional Planning Plan with your school/site for upcoming Units
Lessons