REASONING STRATEGIES

ADDITION

• COMMUTATIVE PROPERTY - Students should be able to recognize that 4+7=11 is the same as 7+4 = 11, and that those facts are inverses of 11-7=4. Without an understanding this relationship, children need to memorize 100 facts (0-9). Truly understanding this relationship cuts the amount of facts to be remembered dramatically.

• DOUBLES & NEAR DOUBLES- Students use ‘doubles facts' to arrive at a sum. Ex) Students may think of 6+7 as "double 6 is 12, and one more is 13."

• MAKE A TEN (+) - Students mentally add to a group of ten, then add the remaining. Ex) Students may solve 6+7 by thinking "7 is 3 away from 10, so take3 away from 6 to put with the 7 to make 10, then add the remaining 3". OR "I can take 5 away from each addend to make 10, then add the remaining 1 and 2.

• USE A KNOWN FACT - Students use a fact they do know, to solve one they don't. Ex) Students may solve 7+5 by thinking "If 7+3=10, and 5 is two more than three, 7+5 must be two more than 7+3. 7+5 must be12.

SUBTRACTION

• MAKE A TEN (-) - Students mentally break two digit numbers into tens and ones, then subtract. Ex) Students may solve 17-8 by breaking 17 into 10 and 7, then subtract the 8 from the ten bundle, and add the leftover 2 and 7.

• THINK-ADDITION - Students think of the inverse addition fact that makes the subtraction problem true. Ex) When a student sees 9-4, they think "four and what makes nine?"

• USE A KNOWN FACT - Students use a fact they do know, to solve one they don't. Ex) Students may solve 14-9 by thinking "From 14 its 4 down to 10, then one more to 9 - for a total difference of 5.

MULTIPLICATION

• 2's: Use doubles facts for addition - or picture a real world situation - EX) an egg carton with 2 rows of 6, a spider with two sets of 4 legs, an 18 wheeler with two rows of 9 wheels.

• 3's: Double the factor, then add one more set Ex) 4 x 3 = (4 X2) + 4

• 4's: Double the factor twice. Ex) 8 x 4 = 16 + 16

• 5's: Picture the minute hand on a clock Ex) One set of 5 is equivalent to 5 past the hour; 8 sets of 5 is equivalent to 40 past the hour.

Multiply by 10, then take ½ the product, since 5 is ½ of 10.

• 6's: Multiply the factor by 3, then double. Ex) 4 x 6 = 12 + 12

• 7's: Add or subtract sets from a known fact. Ex) 7 x 10 = 70, so 7 x 9 must be two set less, or 70 - 7.

• 8's: Multiply by 4, then double. Ex) 7 x 8 = 28 + 28

• 9's: "Nifty Nines Rules" -
• o The tens place digit will always be one less than the factor you're multiplying by - EX) the tens digit for 9 x 4 will be 3; the tens digit for 9 x 8 will be 7.
• o The digits in the product will always have a sum of 9; allowing you to figure out the ones place digit. Ex) 9 x 6 = 54 (5+4 = 9); 9 x 4 = 36 (3 + 6 = 9)

• 12's: Use the Distributive Property - break 12 into 10 and 2 -

Ex) 12 x 6 = (10 x 6) + (2 x 6)