Doubles Plus and other shortcuts

One of the things that we must help children do is recognize when to use a particular strategy. For the Doubles Plus One strategy, tell the children "when the numbers are next door neighbors (the numbers are consecutive like 6 and 7) then we can use the doubles plus one strategy."

Doubles Plus Two
If a child is faced with a problem like 5 + 7, think through the same steps as Doubles Plus One except add 2 instead of one. This works for facts that have number that are separated by two.

When helping a child to recognize when to use this strategy tell them to use it "when the numbers are NOT next door neighbors, but two doors down from each other."

Plus 9 Shortcut
If your child is learning a fact like 9 + 5 these are the steps to think through:
* Think 10 + 5 = (which is much easier to add)
* Now minus 1 (Think 15 - 1 + 14)
* Now say the fact: 9 + 5 = 14
* Remind your child that you added 10 + 5 instead of 9 + 5. That's one more than you started with, so you have to take that one away to get to the correct answer.

Minus 9 Shortcut
If your child is trying 17 - 9, these are the steps to think through:
* Change the 9 to 10 ( Think 17 - 10 = 7, which is much easier to subtract)
* Now add 1 ( Think 7 + 1 = 8)
* Now say the fact: 17 - 9 = 8
* Now remind your child that you subtracted 17 - 10 instead of 17 - 9 . That's taking one more away then you started with, so you have to add that one back to get the right answer.

Minus 8 shortcut
If your child is learning 15 - 8, these are the steps to think through:
* Change the 8 to 10 (Think 15 - 10, which is much easier to subtract)
* Now add 2 (Think 5 + 2 =7)
* Say the whole fact now: 15 - 8 = 7
* Remind your child that you took two extra away when you changed to 8 to 10 in the first step, and you must add it back to get the right answer.

What is Multiplication?

Keith Devlin claims

“Multiplication simply is not repeated addition, and telling young pupils it is inevitably leads to problems when they subsequently learn that it is not.”

http://letsplaymath.net/2008/07/28/whats-wrong-with-repeated-addition/

Addition requires identical units.

The sum must always have the same units as the addends.

Multiplication requires different units.

The product does not have the same units as either the multiplier or the multiplicand.

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Multiplication: multiplier X multiplicand = product. 

The multiplier and multiplicand have different names, even though many of us have trouble remembering which is which.

• multiplier= “how many or how much”
• multiplicand= the size of the “unit” or “group”