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 a Word Problem?

There are only two ways in which word problems can be solved.

Models You have already seen one way to solve word problems – in the examples on the previous page Trixie used physical materials (blocks in one case, rocks in the other) to make models of the problems. She solved the problems by manipulating the materials and counting.

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

The arguments can be more complex. Here Eva had 23 snakes. When 5 of them slithered away she used her ability to reason about the situation to figure out how many would be left.

And shortcuts can be even more complex as you will see in the example of "short division" on the next page.