**Addition and
Subtraction Concepts ****
**

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**Math
Models Home Page**

**Modeling Addition and
Subtraction**

**Modeling
Multiplication and Division**

**Using a base five model for
exploring basic operations helps illustrate the importance of
regrouping in addition and subtraction. The meanings of the basic
operations themselves help develop the models. Here's a couple of
examples:**

**14**_{five} +
23_{five}
**301**_{five} -
134_{five}

**First, the addition
problem...**

**Notice that the units had to be
regrouped into one strip and two units...**

**Addition is, quite simply, a
process of combining and regrouping!**

**Now, for the subtraction
problem. Here we have two meanings to explore, the ***take-away*
model and the *difference* model.

**These simple models will work
in any base, including our own base ten. Here are some more problems
to try. See if you can picture the pieces that represent the numbers
in your imagination.**

**224**_{five} +
303_{five} =
**301**_{five} -
244_{five} =
**45**_{six} +
123_{six} =
**111**_{three} -
22_{three} =
**304**_{ten} -
167_{ten} =

**Our ****next
lesson**** takes a look
at multiplication and division concepts with base five models. See
you there!**