Practical Activity: The Matchstick Tower

Objective: To physically build a growing pattern, record it as a number sequence, and predict future terms before verifying them by counting.

Materials Required: 40–50 matchsticks, ice-cream sticks, or small buttons; a ruled notebook page for recording observations.

Procedure

1.     Using your matchsticks or buttons, lay out Term 1 of a triangular number pattern: a single dot or stick.

2.     Build Term 2 by adding a row of two, so that your arrangement now forms a small triangle of three items.

3.     Continue building Term 3, Term 4, and Term 5, adding one more item to each new row than the row before it.

4.     After building each term, count the total number of matchsticks used so far and record it in the observation table below.

5.     Once you reach Term 5, do not build Term 6. Instead, use the rule you have discovered to predict how many matchsticks Term 6 would need.

6.     Finally, build Term 6 for real and count the matchsticks, to verify whether your prediction was correct.

Observation Table

Discuss with your group: did your prediction for Term 6 match what you built? If a classmate's group got a different answer, work together to find out at which step the disagreement began.