1. Number Sense and Problem Solving
Math Training
Number Sense and Problem Solving

2. Key Concepts Show Thinking! Focus on Numbers
Math talk -> Number Sense -> Place Value -> Problem Solving
Concrete  Pictorial  Abstract
Model! Model! Model!
Understanding + Practice = Speed
Utilize problem solving consistently

3. Scope and Sequence in Brief
Skill
Grade
Number Sense
Place Value
Problem Solving K
One – to – One
Numeral Recognition
Count Patterns (oral)
Number Bonds
(Whole / Part)
Number Stories
recognize 10’s and 1’s 1
Count Patterns (write)
Fact Families
Fact Fluency (add/sub)
to the 100’s place
-expanded notation as
number bonds and
number sentences
Pre – Model Drawing
(add / sub) 2
Rearranging/
Compatible Numbers
Regrouping
to the 1000’s place
-expanded notation
-cards and disks
Model Drawing
-add/sub with
regrouping 3
Fact Fluency
Mental Math
Multiply / Divide
to 10,000’s place
-use in computation
-multiply / divide

4. NUMBER SENSE: Begins with talking
Beginning Questions:
What do you see?
What can you count?
Intermediate Questions:
How many are _____?
How many _____?
Advanced Questions:
How many all together?
Tell me a number story
(begin number associations
for number bonds)
Challenging Questions:
How many groups of things?
Can we count another way?
If there was one more, how
many?

5. The Number Bond: Parts  Whole  Parts
Pennies for your thoughts
Double-sided Counters 5 5 5 3 2

6. Number Bond progression:
Number Stories   
Fact Families:
The Story of 5: 3 and 2 make 5 2 and 3 make 5 1 and 4 make 5 4 and 1 make 5 5 and 0 make 5 0 and 5 make 5
Fact Family for: = = 5 5 – 3 = 2 5 – 2 = 3 * It’s all about repeated practice! 5 3 2

7. Place Value 57 50 7 Begins with Number Bonds Then Expanded Notation
Use the number bond to identify 10’s and 1’s.
Create number sentences
= 57
5 tens + 7 ones = 57 57 50 7

8. Mental Math Strategies
Making Tens 10
= 17 7
= 76
Kids are taught to see 10’s
10 frame games
Rearranging / Compatible
Find 10’s
Find number bonds
Place Value Computation
Use place value knowledge

9. Problem Solving : Model Drawing
In 7 Steps
Read
Find the question. Write a sentence.
Label who and what
Draw bars
Read for clues. Fix the bar. Add a question mark.
Compute and Check
Answer

10. With Pictures : We see 9 fish.5 fish are big. The others are small.
How many fish are small?
There are _______ small fish.
There were 5 swans. Then 3 more swans came.
How many swans are there now?
There are ________ swans now.

11. With Boxes
8 boys were riding bikes. 6 were riding fast. How many boys ride slow? There were ______ boys riding slowly. I made 60 sandwiches to take camping. The boys ate 30 sandwiches. The girls ate 20 sandwiches. The squirrels ate 4 sandwiches. How many are left for me? There are _______ sandwiches left for me.

12. With Bars:
There are 18 ducks. Then 5 more swim over. How many ducks are there now? There are ________ ducks now. Jan has 12 cars. 6 of them are red. How many are not red There are ______ cars that are not red.