Counting on:
A. Example: to find 8+3 or 3+8, you
would say: 8...9, 10, 11 and the answer is 11 (count 3 more, starting
with 8)
*Counting on is broken up into counting on from first, and counting on
from higher
*To count on, a child must first know how to count forward starting
with any number
B. Counting on is easier to do with 8+2 than with 8+6 because you are
doing less counting with 8+2.
C. Counting on is an efficient thing to do
if: one of the addends (numbers being added) is 1, 2, or 3.
Using 10:
A. Example: to find 9+4, you take 1
from the 4 and give it to the 9, so the problem becomes:
9+4=9+1+3=10+3=13
*To use use this strategy, children must first know some facts that
equal 10 (such as 9+1=10 and 8+2=10), they must know how break up a
number by separating out 1 and 2 from the number (in this example, the
child needed to know 4=1+3), and the child needs to know how to
efficiently add a 1 digit number to 10 (10+3=13)
*This strategy is sometimes called a bridging with 10 strategy because
the child adds to get to 10, and then adds on from 10.
B. This strategy is easier to use with 9+5 than with 7+5 because
changing 5 into 1+4 is easier than changing 5 into 3+2. It's also
easier to imagine when it's 9+ because 9 is so close to 10.
C. Using 10 is an efficient strategy if one of the addends is nearly 10
(9, 8, maybe 7)
Using doubles
A. Example: 5+6=5+5+1=10+1=11.
*In order to use this strategy, a child must know some doubles facts
(such as 5+5=10 or 6+6=12), and the child must recoginize when a
pair of addends are almost a double (recognizing that 5+6 is almost 5+5
or that it is almost 6+6)
*This strategies is composed of a lot of smaller sub-strategies:
doubles plus 1, doubles -1, doubles +2, doubles -2 and what I was
calling the sandwich strategy.
B. Using doubles is easier with 6+7 than with 6+9 because 7 is only one
away from 6, and 9 is 3 away from 6.
C. Using doubles is an efficient strategy if the addends are 1 or 2
apart
(so the addends are nearly the same)
Count back
Count up to subtract
Use 10
You can find descriptions of the strategies
and what facts they are efficient
for by reading the
FAQ
on the Thinking with Numbers site. You should be following the
subtraction links under
What are the
thinking strategies?
You can see me explaining subtraction strategies in these videos:
Write up and
turn
in:
For each of the 3 strategies: count
back, count up to subtract, and use 10:
A. Give an example of how to use the strategy to solve a basic fact
computation
B. Give an example of a fact that the strategy would be efficient for
(easy to use), and an example of a fact the strategy would be
inefficient for (harder to use).
C. Describe the kinds of facts that the strategy works best for.
I have assigned A, B, and C to my explanations in the addition section,
so you can see which parts I expect you to do. The parts marked
with a * are things I hope you will pay attention to as you read and
watch, but I do not expect you to include them in this assignment.