Goals - Part 3

My goals in helping children with arithmetic are simple. I want them

to be good at solving all different types of word problems,
to like solving word problems,
to understand the problem solving methods (shortcuts) that they use and
to be able to communicate their reasoning to others.

3. What Are The Different Ways to Solve Word Problems?*

Putting aside, for now, a lot of details, there are only two ways in which a word problem can be solved.

MODELS You can represent the problem with physical materials that you manipulate and count one-by-one. Here Trixie uses blocks to represent chickens.

SHORTCUTS Shortcuts are logical, reasoned arguments that solve word problems without physical models and/or without one-by-one counting.

These arguments can be very simple or rather complex.

Simple: Here Rose represents the legs on 4 lambs using only 8 fingers - not 16.

Complex: Here a student makes a very sophisticated argument to find 63 - 25.

*And, eventually, the equations that represent them.

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