Isn't it wonderful when the grand kids first show off their ability to count? For the most part, kids learn to count on their own! That's why the set of numbers, 1, 2, 3, 4, 5, … are known as the

*natural*numbers. They just come naturally.

Early Greek mathematicians used the visual simplicity of geometric shape to discover and think about abstract number relationships.

Fish fifteen pennies out of your piggy bank, gather the kids
around the kitchen table, and let’s explore

*figurate*numbers.*natural*numbers.

Now this is so simple and obvious that my grand kids might
take it as an early sign that I am beginning to see profundity in the simplest
of situations. But, ah! It stays simple, but gets better.

Ask them to identify what shape the three coins form when
nudged close together (it helps to lay toothpicks or matches along the edges).

As the Greeks observed, the three coins (pebbles) form a
triangle. The natural number three is called a

The natural numbers
four and five are not triangular numbers because no matter how hard you try to
arrange five pennies in a snug, triangular form, there's always a hole (see
above picture) and we won't allow a hole to spoil our pattern.*triangular*number.
Have the kids fit the third row of pennies under the second
row and observe that the 6 pennies do form a triangular pattern with no holes.
The natural number 6 is a triangular number.

Now ask them to move the fourth row under the third row,
count the pennies in the four rows, and tell you if the sum is or is not a
triangular number (it is). Why? (The ten pennies fit snugly together to form a
triangle).

Finish by having them move the fifth row up, count the pennies, and decide if the sum is or is not a triangular number.

Now for the

*mathematics*. Ask the kids to predict the next triangular number (21) and explain how they got answer (15 + 6 in the sixth row = 21). If they want to keep going, let them. If not, that’s OK too.A good way to summarize the activity is to have the kids write down the natural numbers from 1 through 21 and to draw a triangle around those natural numbers that are also triangular numbers.

If you would like a free PDF file that let’s the kids
color and record the triangular numbers through row ten, simply email www.grandadscience@gmail.com.

There are so many directions we can go with this activity but let me just choose one other property of the triangular numbers. The Greeks quickly found that any two

*consecutive*triangular numbers form another class of figurate numbers, the

*square*numbers.

Watch this video to see the transformation of the two
consecutive triangular numbers, three and six.

The second figurate number post can be found by clicking on the following link.

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