# Shortcuts - Hard Addition

Eva was 8 years and 7
months at the time that this video was made.

**The Problem**

I have 3 pennies and you have 5 more pennies than I have.
How many pennies do you have?

**What To Look For In This Video**

- Eva holds up 3 fingers on one hand and 5 fingers on the other hand - representing only the pennies that she has. (By not representing the pennies that I have she is taking a shortcut. Her model is the model for Easy Addition, not Hard Addition. No one taught her to do this - it is her own ability to reason that she is using.)
- She solves the problem by counting on, "5, (pause), 6, 7, 8."
- Eva solves the problem by a second method. She realizes that 3 +
5 is the same as 4 + 4. Since she remembers that 4 + 4 = 8 she reasons
that 3 + 5 must also equal 8. More technically, she reasons as follows:
3 + 5 = 3 + (1 + 4) = (3 + 1) + 4 = 4 + 4 = 8.
^{1} - Too many children think that there is one and only one right way to solve every problem. You should encourage your child to look for a variety of shortcuts. A method that is good for one problem (e.g. counting on to compute 98 + 3) is not so good for another (e.g. 98 + 98).