Matchstick Patterns

Introduction

In this task, we will practising the mathematical thinking outlined in the unit overview.  In particular, we will follow the following steps when investigating patterns.  Let's start with the matchstick pattern above.

Step 1: predict what the next patterns may be.  One good strategy is to draw out the next few patterns.

Step 2: organise your findings in a systematic way.  One good strategy is to put your observations in a table. 

Step 3: use your table to come up with some general rules (term to term rule and position to term rule).

Step 4: verify (a.k.a. check) that your rules work.  This can be achieved by comparing your drawings with the answers found using your rules.

Step 5: justify (a.k.a explain) why the rules work.

Here is a suggested answer for the pattern above for your reference.


Other questions:

Repeat steps 1-5 above with the 4 patterns below:

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Now try to make some matchstick patterns that fit the following rules:

Further Practice

Some of the essential skills introduced in this lesson are "linear/ arithmetic sequences", "position to term rule/ nth term" and "term to term rule".  The relevant skills can be found on DrFrostMaths, CorbettMaths, MyiMaths and Eedi.  Watch any video and/or go through any online lesson as you see fit.  


Transum


For more practice, try the questions:

More Matchstick Patterns.pdf
Pattern Investigation (good prep for assessment)

Above is a guided version

Extension

Transum

The following are things you will either learn in the next few lessons or are outside the scope of Year 7 Maths.  You may be interested in learning about them.


nRich

Here are some short problems and investigations on patterns and sequences


Don Steward

Look at Don Steward's Number Sequences ideas.


Try the two following investigations:

Matchstick Investigation.pdf
Lowry Squares.pdf