This is a level 2 algebra strand activity from the Figure It Out series.

A PDF of the student activity is included.

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find rules for sequential patterns

matchsticks

#### Activities One and Two

Many students will need to use matchsticks or similar equipment to build the patterns. Copying is an important initial behaviour if visual patterns are to help develop algebraic thinking. Encourage students to look for systematic counting strategies to find the total number of matchsticks in each pattern. Below are some useful methods commonly used by students:

1. Add-on Counting

2. Using the whole figure but taking off the joins

3. Parting the whole figure

Where students use methods you are unsure of, ask them to explain their reasoning: “Where did you get these numbers from? Can you show me how you did it?”

You can use a variety of strategies to find the number of matchsticks needed to build a 20-object pattern. Such strategies include:

1. Use matchsticks to build the actual pattern

2. Use a table and look for the pattern:

3. Write an equation:

Be aware that some students will make a “ratio error”, believing that the number of matchsticks required to make a 20-object pattern will be twice that required for a 10-object pattern. The error ignores the effect of joining, but you can correct it by modelling with equipment. For example:

41 matchsticks 41 matchsticks

Joining these two sets gives a total of 81 matchsticks (rather than 41 + 41 = 82) because one middle arm is lost in the join.

#### Answers to Activities

**Activity One**

a. 31 matchsticks

b. 42 matchsticks

c. 41 matchsticks

d. 54 matchsticks**Activity Two**

a. 61 matchsticks

b. 82 matchsticks

c. 81 matchsticks

d. 104 matchsticks**Activity Three**

Answers will vary.