1. Vacaville USD December 8, 2014
KINDERGARTEN Session 2
Vacaville USD
December 8, 2014

2. AGENDA Problem Solving and Patterns
Math Practice Standards and High Leverage Instructional Practices
Number Talks
Dot Patterns, Ten Frames, and Rekenreks
Word Problems
Comparing Numbers
Addition

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. Cubes in a Line
How many face units (squares) can you see when cubes are put together?

5. Cubes in a Row
How many squares do you see on 1 cube?

6. Cubes in a Row
How many squares do you see on 2 cubes?

7. Cubes in a Row
You are going to be given 2 strips of paper like this:
_____________ _____________
number of cubes number of face units 7

8. Cubes in a Row What patterns do you see?
How could those patterns help you figure out how many squares you would see?

9. Hundred’s Charts What if we recorded the data on a hundred’s chart?
What patterns might Kindergarten students notice?

10. Cubes in a Row How many squares do you see on 1 cube?
Let’s mark that on a hundred’s chart.

11. Cubes in a Row How many squares do you see on 2 cubes?
Let’s mark that on a hundred’s chart.
How can you keep track of what sides you have counted?

12. Math Practice Standards
Remember the 8 Standards for Mathematical Practice

13. 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

14. High Leverage Instructional Practices

15. High-Leverage Mathematics Instructional Practices
An instructional emphasis that approaches mathematics learning as problem solving.
Make sense of problems and persevere in solving them.

16. An instructional emphasis on cognitively demanding conceptual tasks that encourages all students to remain engaged in the task without watering down the expectation level (maintaining cognitive demand)
Make sense of problems and persevere in solving them.

17. Instruction that places the highest value on student understanding
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively

18. Instruction that emphasizes the discussion of alternative strategies
Construct viable arguments and critique the reasoning of others

19. Instruction that includes extensive mathematics discussion (math talk) generated through effective teacher questioning
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning

20. Teacher and student explanations to support strategies and conjectures
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others

21. The use of multiple representations
Make sense of problems and persevere in solving them.
Model with mathematics
Use appropriate tools strategically

22. Number Talks

23. What is a Number Talk? Also called Math Talks
A strategy for helping students develop a deeper understanding of mathematics
Learn to reason quantitatively
Develop number sense
Check for reasonableness
Number Talks by Sherry Parrish

24. What is Number Talk?
A pivotal vehicle for developing efficient, flexible, and accurate computation strategies that build upon key foundational ideas of mathematics such as
Composition and decomposition of numbers
Our system of tens
The application of properties

25. Key Components Classroom environment/community Classroom discussions
Teacher’s role
Mental math
Purposeful computation problems

26. Classroom Discussions
What are the benefits of sharing and discussing computation strategies?

27. K.1 – Kindergarten Number Talk using ten frames and dot cards
Think about the following questions as you watch.

28. How does the teacher build students’ fluency with small numbers?
What questions does the teacher pose to build understanding?
What strategies are the students using to build meaning of the numbers?
How does the teacher support student communication during the number talk?

29. K.2 – Kindergarten Number Talk Using Rekenreks
Think about the following questions as you watch.

30. What instructional strategies does the teacher use to engage the students?
How does the teacher use rekenreks as a tool to build fluency with small numbers?
What role does the game “Can You Guess My Way?” play on the number talk?
What mathematical understandings and misconceptions are being addressed?

31. Do you see evidence of students demonstrating:
Developing number sense
Developing fluency with small numbers
Subitizing
Making tens

32. Tools for Solving Problems
Counters
Ten-frames
Rekenreks
Number Line / Hundred’s Chart

33. Solving Word Problems

34. 3 Benefits of Real Life Contents
Engages students in mathematics that is relevant to them
Attaches meaning to numbers
Helps students access the mathematics.

35. Word Problems Concrete Representational Abstract ACT IT OUT!!!
Draw a model
1 to 1 representation
Bar or scaled representation
Abstract
Write a number sentence
Use a strategy

36. Practice Problems
How could students act out these problems using manipulatives?
How could students begin to record (draw) the process of solving these problems?

37. Numbers, Bears, and Beds
Do you remember the song about 10 little monkeys jumping on the bed?

38. Numbers, Bears, and Beds
Well, my story is about bears jumping on the bed.

39. Comparing, Bears, and Beds
I see 4 bears on the bed and 1 bear on the floor.
Are there more bears on the bed or on the floor?

40. Comparing, Bears, and Beds
On the bed.
How do you know?

41. Comparing, Bears, and Beds

42. Addition, Bears, and Beds
I see 4 bears on the bed and 1 bear on the floor.
How many bears are there?

43. Addition, Bears, and Beds
How many bears are there? 5

44. Addition, Bears, and Beds
What addition sentence could I write?
4 + 1 = 5

45. 2 + 1 = 3

46. Addition

47. Addition, Bears, and Beds
Now I am going to give you an addition problem. I want you to build it using the beds and bears, draw a model of what you built (using a dot for each bear), and write the answer.

48. 3 + 1 = ____ 4

49. 3 + 1 = ____ 4    

50. Addition Strategies So what strategies did we just use?
What other strategies could we use?
What strategies do we want to encourage?