Number Sense and Problem Solving Math Training Number Sense and Problem Solving

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

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

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?

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

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: 3 + 2 = 5 2 + 3 = 5 5 – 3 = 2 5 – 2 = 3 * It’s all about repeated practice! 5 3 2

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 50 + 7 = 57 5 tens + 7 ones = 57 57 50 7

Mental Math Strategies Making Tens 10 7 + 5 + 2 + 3 = 17 7 45 + 31 40 + 30 +5 + 1 = 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

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

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.

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.

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.