Welcome!

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

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.

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?"

Manipulatives

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

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.

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)

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.

BUILDING CONCEPTUAL UNDERSTANDING

Climbing the Number Sense Ladder Step 1 Rote Counting

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.).

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

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.

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

How many?

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

Complements of five

How many?

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

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

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

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

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

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

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.

Compensation Example 2: Suppose the problem is 44 - 28. Many problems with give us the same answer. 43 - 27 39 - 23 42 - 26 38 -22 41 - 25 37 - 21 40 - 24 36 - 20

Compensation Example 3: Shift both numbers to amounts that don’t require regrouping. 45 + 29 ➔ 46-30 Students MUST understand a strategy to be competent with it.

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

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

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