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Presentation transcript:

Goals for this presentation Learn how the philosophical shift in the way we teach math affects the way we teach basic facts Learn some effective strategies for teaching basic facts to students

Philosophical shift Focus on number sense Focus on mental math and estimation

The Nature of Mathematics Number Sense Rote Memory versus committing isolated facts to memory one after another drill and practice Automaticity relies on thinking, using relationships among the facts focusing on relationships

What are the basic facts? The Alberta Program of Studies defines them as: Addition and Subtraction to 18 Multiplication and Division to 81

The Power of Thinking Strategies + 1 2 3 4 5 6 7 8 9 1+1 1+2 1+3 1+4 1+5 1+6 1+7 1+8 1+9 2+1 2+2 2+3 2+4 2+5 2+6 2+7 2+8 2+9 3+1 3+2 3+3 3+4 3+5 3+6 3+7 3+8 3+9 4+1 4+2 4+3 4+4 4+5 4+6 4+7 4+8 4+9 5+1 5+2 5+3 5+4 5+5 5+6 5+7 5+8 5+9 6+1 6+2 6+3 6+4 6+5 6+6 6+7 6+8 6+9 7+1 7+2 7+3 7+4 7+5 7+6 7+7 7+8 7+9 8+1 8+2 8+3 8+4 8+5 8+6 8+7 8+8 8+9 9+1 9+2 9+3 9+4 9+5 9+6 9+7 9+8 9+9 The Power of Thinking Strategies

+ 1 2 3 4 5 6 7 8 9 1+1 1+2 1+3 1+4 1+5 1+6 1+7 1+8 1+9 2+1 2+2 2+3 2+4 2+5 2+6 2+7 2+8 2+9 3+1 3+2 3+3 3+4 3+5 3+6 3+7 3+8 3+9 4+1 4+2 4+3 4+4 4+5 4+6 4+7 4+8 4+9 5+1 5+2 5+3 5+4 5+5 5+6 5+7 5+8 5+9 6+1 6+2 6+3 6+4 6+5 6+6 6+7 6+8 6+9 7+1 7+2 7+3 7+4 7+5 7+6 7+7 7+8 7+9 8+1 8+2 8+3 8+4 8+5 8+6 8+7 8+8 8+9 9+1 9+2 9+3 9+4 9+5 9+6 9+7 9+8 9+9 Count On

+ 1 2 3 4 5 6 7 8 9 Doubles Count On 1+1 1+2 1+3 1+4 1+5 1+6 1+7 1+8 1+9 2+1 2+2 2+3 2+4 2+5 2+6 2+7 2+8 2+9 3+1 3+2 3+3 3+4 3+5 3+6 3+7 3+8 3+9 4+1 4+2 4+3 4+4 4+5 4+6 4+7 4+8 4+9 5+1 5+2 5+3 5+4 5+5 5+6 5+7 5+8 5+9 6+1 6+2 6+3 6+4 6+5 6+6 6+7 6+8 6+9 7+1 7+2 7+3 7+4 7+5 7+6 7+7 7+8 7+9 8+1 8+2 8+3 8+4 8+5 8+6 8+7 8+8 8+9 9+1 9+2 9+3 9+4 9+5 9+6 9+7 9+8 9+9 Count On Doubles

+ 1 2 3 4 5 6 7 8 9 Doubles Near Doubles Count On 1+1 1+2 1+3 1+4 1+5 1+6 1+7 1+8 1+9 2+1 2+2 2+3 2+4 2+5 2+6 2+7 2+8 2+9 3+1 3+2 3+3 3+4 3+5 3+6 3+7 3+8 3+9 4+1 4+2 4+3 4+4 4+5 4+6 4+7 4+8 4+9 5+1 5+2 5+3 5+4 5+5 5+6 5+7 5+8 5+9 6+1 6+2 6+3 6+4 6+5 6+6 6+7 6+8 6+9 7+1 7+2 7+3 7+4 7+5 7+6 7+7 7+8 7+9 8+1 8+2 8+3 8+4 8+5 8+6 8+7 8+8 8+9 9+1 9+2 9+3 9+4 9+5 9+6 9+7 9+8 9+9 Count On Doubles Near Doubles

+ 1 2 3 4 5 6 7 8 9 Doubles Near Doubles Names of 10 Count On 1+1 1+2 1+3 1+4 1+5 1+6 1+7 1+8 1+9 2+1 2+2 2+3 2+4 2+5 2+6 2+7 2+8 2+9 3+1 3+2 3+3 3+4 3+5 3+6 3+7 3+8 3+9 4+1 4+2 4+3 4+4 4+5 4+6 4+7 4+8 4+9 5+1 5+2 5+3 5+4 5+5 5+6 5+7 5+8 5+9 6+1 6+2 6+3 6+4 6+5 6+6 6+7 6+8 6+9 7+1 7+2 7+3 7+4 7+5 7+6 7+7 7+8 7+9 8+1 8+2 8+3 8+4 8+5 8+6 8+7 8+8 8+9 9+1 9+2 9+3 9+4 9+5 9+6 9+7 9+8 9+9 Count On Doubles Near Doubles Names of 10

+ 1 2 3 4 5 6 7 8 9 Doubles Near Doubles Names of 10 Names of 5 1+1 1+2 1+3 1+4 1+5 1+6 1+7 1+8 1+9 2+1 2+2 2+3 2+4 2+5 2+6 2+7 2+8 2+9 3+1 3+2 3+3 3+4 3+5 3+6 3+7 3+8 3+9 4+1 4+2 4+3 4+4 4+5 4+6 4+7 4+8 4+9 5+1 5+2 5+3 5+4 5+5 5+6 5+7 5+8 5+9 6+1 6+2 6+3 6+4 6+5 6+6 6+7 6+8 6+9 7+1 7+2 7+3 7+4 7+5 7+6 7+7 7+8 7+9 8+1 8+2 8+3 8+4 8+5 8+6 8+7 8+8 8+9 9+1 9+2 9+3 9+4 9+5 9+6 9+7 9+8 9+9 Count On Doubles Near Doubles Names of 10 Names of 5

+ 1 2 3 4 5 6 7 8 9 Doubles Near Doubles Names of 10 Nine strategies 1+1 1+2 1+3 1+4 1+5 1+6 1+7 1+8 1+9 2+1 2+2 2+3 2+4 2+5 2+6 2+7 2+8 2+9 3+1 3+2 3+3 3+4 3+5 3+6 3+7 3+8 3+9 4+1 4+2 4+3 4+4 4+5 4+6 4+7 4+8 4+9 5+1 5+2 5+3 5+4 5+5 5+6 5+7 5+8 5+9 6+1 6+2 6+3 6+4 6+5 6+6 6+7 6+8 6+9 7+1 7+2 7+3 7+4 7+5 7+6 7+7 7+8 7+9 8+1 8+2 8+3 8+4 8+5 8+6 8+7 8+8 8+9 9+1 9+2 9+3 9+4 9+5 9+6 9+7 9+8 9+9 Count On Doubles Near Doubles Names of 10 Nine strategies

+ 1 2 3 4 5 6 7 8 9 Doubles Near Doubles Names of 10 Nine strategies 1+1 1+2 1+3 1+4 1+5 1+6 1+7 1+8 1+9 2+1 2+2 2+3 2+4 2+5 2+6 2+7 2+8 2+9 3+1 3+2 3+3 3+4 3+5 3+6 3+7 3+8 3+9 4+1 4+2 4+3 4+4 4+5 4+6 4+7 4+8 4+9 5+1 5+2 5+3 5+4 5+5 5+6 5+7 5+8 5+9 6+1 6+2 6+3 6+4 6+5 6+6 6+7 6+8 6+9 7+1 7+2 7+3 7+4 7+5 7+6 7+7 7+8 7+9 8+1 8+2 8+3 8+4 8+5 8+6 8+7 8+8 8+9 9+1 9+2 9+3 9+4 9+5 9+6 9+7 9+8 9+9 Count On Doubles Near Doubles Names of 10 Nine strategies Making 10

+ 1 2 3 4 5 6 7 8 9 Doubles Near Doubles Names of 10 Nine strategies 1+1 1+2 1+3 1+4 1+5 1+6 1+7 1+8 1+9 2+1 2+2 2+3 2+4 2+5 2+6 2+7 2+8 2+9 3+1 3+2 3+3 3+4 3+5 3+6 3+7 3+8 3+9 4+1 4+2 4+3 4+4 4+5 4+6 4+7 4+8 4+9 5+1 5+2 5+3 5+4 5+5 5+6 5+7 5+8 5+9 6+1 6+2 6+3 6+4 6+5 6+6 6+7 6+8 6+9 7+1 7+2 7+3 7+4 7+5 7+6 7+7 7+8 7+9 8+1 8+2 8+3 8+4 8+5 8+6 8+7 8+8 8+9 9+1 9+2 9+3 9+4 9+5 9+6 9+7 9+8 9+9 Count On Doubles Near Doubles Names of 10 Nine strategies Making 10 Skip count by 2

+ 1 2 3 4 5 6 7 8 9 Doubles Near Doubles Names of 10 Nine strategies 1+1 1+2 1+3 1+4 1+5 1+6 1+7 1+8 1+9 2+1 2+2 2+3 2+4 2+5 2+6 2+7 2+8 2+9 3+1 3+2 3+3 3+4 3+5 3+6 3+7 3+8 3+9 4+1 4+2 4+3 4+4 4+5 4+6 4+7 4+8 4+9 5+1 5+2 5+3 5+4 5+5 5+6 5+7 5+8 5+9 6+1 6+2 6+3 6+4 6+5 6+6 6+7 6+8 6+9 7+1 7+2 7+3 7+4 7+5 7+6 7+7 7+8 7+9 8+1 8+2 8+3 8+4 8+5 8+6 8+7 8+8 8+9 9+1 9+2 9+3 9+4 9+5 9+6 9+7 9+8 9+9 Count On Doubles Near Doubles Names of 10 Nine strategies Making 10 Skip count by 2 Number in Middle

+ 1 2 3 4 5 6 7 8 9 Doubles Near Doubles Names of 10 Nine strategies 1+1 1+2 1+3 1+4 1+5 1+6 1+7 1+8 1+9 2+1 2+2 2+3 2+4 2+5 2+6 2+7 2+8 2+9 3+1 3+2 3+3 3+4 3+5 3+6 3+7 3+8 3+9 4+1 4+2 4+3 4+4 4+5 4+6 4+7 4+8 4+9 5+1 5+2 5+3 5+4 5+5 5+6 5+7 5+8 5+9 6+1 6+2 6+3 6+4 6+5 6+6 6+7 6+8 6+9 7+1 7+2 7+3 7+4 7+5 7+6 7+7 7+8 7+9 8+1 8+2 8+3 8+4 8+5 8+6 8+7 8+8 8+9 9+1 9+2 9+3 9+4 9+5 9+6 9+7 9+8 9+9 Count On Doubles Near Doubles Names of 10 Nine strategies Making 10 Skip count by 2 Number in Middle Commutativity

+ 1 2 3 4 5 6 7 8 9 Doubles Near Doubles Names of 10 Nine strategies 1+1 1+2 1+3 1+4 1+5 1+6 1+7 1+8 1+9 2+1 2+2 2+3 2+4 2+5 2+6 2+7 2+8 2+9 3+1 3+2 3+3 3+4 3+5 3+6 3+7 3+8 3+9 4+1 4+2 4+3 4+4 4+5 4+6 4+7 4+8 4+9 5+1 5+2 5+3 5+4 5+5 5+6 5+7 5+8 5+9 6+1 6+2 6+3 6+4 6+5 6+6 6+7 6+8 6+9 7+1 7+2 7+3 7+4 7+5 7+6 7+7 7+8 7+9 8+1 8+2 8+3 8+4 8+5 8+6 8+7 8+8 8+9 9+1 9+2 9+3 9+4 9+5 9+6 9+7 9+8 9+9 Count On Doubles Near Doubles Names of 10 Nine strategies Making 10 Skip count by 2 Number in Middle Commutativity

Multiplication Talk about ‘groups of ‘ Talk about ‘families’ Give strategies for when we don’t know what to do There is NOT an endless supply of basic facts

Start in grade 3 Learn up to 5 x 5 What do we already know? Start in grade 3 Learn up to 5 x 5

x 1 2 3 4 5 6 7 8 9 10 Zero groups of

x 1 2 3 4 5 6 7 8 9 10 Zero groups of 1 group of

x 1 2 3 4 5 6 7 8 9 10 15 20 25 Zero groups of 1 group of 1 2 3 4 5 6 7 8 9 10 15 20 25 Zero groups of 1 group of Counting by 5’s

x 1 2 3 4 5 6 7 8 9 10 15 20 25 Zero groups of 1 group of 1 2 3 4 5 6 7 8 9 10 15 20 25 Zero groups of 1 group of Counting by 5’s Counting by 2’s

x 1 2 3 4 5 6 7 8 9 10 15 16 20 25 Zero groups of 1 group of 1 2 3 4 5 6 7 8 9 10 15 16 20 25 Zero groups of 1 group of Counting by 5’s Counting by 2’s Doubles

x 1 2 3 4 5 6 7 8 9 10 12 15 16 20 25 Zero groups of 1 group of 1 2 3 4 5 6 7 8 9 10 12 15 16 20 25 Zero groups of 1 group of Counting by 5’s Counting by 2’s Doubles Families

Important to remember Teach through families 2 x 3 = 6 3 x 2 = 6 6 ÷ 3 = 2 6 ÷ 2 = 3 Work the teaching of division right into the teaching of the multiplication….

So that is it for Grade 3 Let’s move on to grade 4…… Coming Later!