1. Welcome!

2. Helping Your Child With Mathematics
1. Pose open questions.
2. Use verbs that encourage higher level thinking.
3. Provide wait time.

3. Questioning to Stimulate Thinking
Our goal in posing questions to children is not to lead our students to a predetermined solution. Rather, the goal is to help students clearly identify their thinking about the problem.

4. Questions and Prompts for Math Thinking
"What information are you/we going to use to solve this problem?"
"How is this like something you have done before?"
"How have you shown your thinking?"
"How could you arrive at the same answer but in a different way?"

5. Manipulatives

6. Frog Problem Instructions
Work in small partners (one partner is the parent and one is the student)
Record your solution and thinking on the paper provided.
Try to solve the problem in at least two different ways

7. Frog Problem
There were 57 frogs in the pond. Some were swimming and some were sunning. There are about twice as many frogs swimming as were sunning. How many frogs were swimming and how many frogs were sunning? Use pictures, numbers, and/or words to prove that your answer makes sense.

10. Making Sense of Number Sense
Students with number sense:
Develop multiple meanings of numbers
Know how operations work
How to apply them
Use numbers fluently (accurately, efficiently, flexibly)

11. CPR C–Conceptual Understanding
What students will be expected to KNOW. These are the ideas that students should be developing. 
P–Procedural Understanding 
What students will be expected to DO. These are the procedures and skills that enable students to access the ideas of mathematics.  
R – Representational Understanding  
How students will SHOW what they know and can do. These are the drawings, models, and ways that students make their thinking visible.

12. BUILDING CONCEPTUAL UNDERSTANDING

13. Climbing the Number Sense Ladder
Step 1 Rote Counting

14. Example: Kindergarten StandardK.CC.1. COUNT TO 100 BY ONES AND BY TENS
Conceptual:
count by ones in sequence from 1 to 10.
count by ones in sequential progression from 11 to 20.
count by ones in sequential progression from 21 to 100.
count by tens in sequence from 10 to 100.
Procedural:
rote counting by ones up to 10.
rote counting by ones up to 20 and continue in sets of 10 to 100.
rote counting by tens up to 100.
Representational:
use kinesthetic movements to represent counting connectionsn (e.g., clapping, jumping, etc.).

15. Climbing the Number Sense Ladder
Step 2 One to One Correspondence
Step 1 Rote Counting

16. Example: Kindergarten Standard K. CC
Example: Kindergarten Standard K.CC.4 UNDERSTAND THE RELATIONSHIP BETWEEN NUMBERS AND QUANTITIES; CONNECT COUNTING TO CARDINALITY.
Conceptual:
develop strategies for keeping track of counted
objects.
accurately count objects with one-to-one correspondence up to 20.
count various groupings and arrays up to 20.
identify “how many” objects they counted.
understand quantities of “one more” up to 20 (e.g., 7 is one more than 6).
Procedural:
touch, slide, tap, drop, color, etc. to accurately count objects.
identify the last number counted as the quantity of objects.
create groups of 10 and some quantity for easier counting of teen numbers.
create a given number of objects and one more.
Representational:
color, slide, tap, drop, and move, objects as they count.
use ten frames, dot cards, domino, dice, or other arrangements to assist counting. Students can use cards, dice, dominoes, written numerals, etc. to name quantities.
demonstrate an understanding of quantities of one more.

17. Climbing the Number Sense Ladder
Step 3 Subsitizing
Step 2 One to One Correspondence
Step 1 Rote Counting

18. How many?

19. Climbing the Number Sense Ladder
Step 4 Complements of Ten
Step 3 Subsitizing
Step 2 One to One Correspondence
Step 1 Rote Counting

20. Complements of five

21. How many?

22. Climbing the Number Sense Ladder
Step 5 Counting Strategies
Step 4 Complements of Ten
Step 3 Subsitizing
Step 2 One to One Correspondence
Step 1 Rote Counting

23. Important Counting Strategies
Counting on
Counting back
Skip counting
Counting up to subtract
Using doubles
Using commutative property
Using fact families*

24. Climbing the Number Sense Ladder
Step 6 Conservation of Numbers
Step 5 Counting Strategies
Step 4 Complements of Ten
Step 3 Subsitizing
Step 2 One to One Correspondence
Step 1 Rote Counting

25. CONSERVATION OF NUMBERS
A “number” means an “amount”. That amount does not change no matter how you arrange the objects.

26. Climbing the Number Sense Ladder
Step 7 Compensation
Step 6 Conservation of Numbers
Step 5 Counting Strategies
Step 4 Complements of Ten
Step 3 Subsitizing
Step 2 One to One Correspondence
Step 1 Rote Counting

27. Compensation IMPORTANT conceptual skill.
Referred to as “compose and decompose” numbers.
Flexibility with numbers

28. Compensation Example 1:
When working with numbers, you can take an amount from one set and add it to another, the total amount does not change.

29. Compensation Example 2:
Suppose the problem is Many problems with give us the same answer.

30. Compensation Example 3:
Shift both numbers to amounts that don’t require regrouping.
➔ 46-30
Students MUST understand a strategy to be competent with it.

31. Climbing the Number Sense Ladder
Step 8 Fact Families
Step 7 Compensation
Step 6 Conservation of Numbers
Step 5 Counting Strategies
Step 4 Complements of Ten
Step 3 Subsitizing
Step 2 One to One Correspondence
Step 1 Rote Counting

32. Pete's Problem
Work in partners (one partner is the parent and one is the student)
Record your solution and thinking on the paper provided.
Try to solve the problem in at least 2 different ways

33. Pete's Problem
Pete has some cookies. He divided each cookie into thirds. He ate seven pieces. How many cookies did he eat?