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Kingitanga Patterns and Algebra

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Kingitanga Patterns and Algebra

A robotics club is designing a repeating geometric border for a display about the Kīngitanga movement. The club is exploring mathematical ideas respectfully; its invented designs are not presented as traditional Māori designs. Use n for the step number and explain how you know.

Notice and describe

Use the club’s invented border patterns to solve the questions.

1.The border tiles go: triangle, square, triangle, square, triangle, ____. What shape comes next, and what is the repeating unit?

2.A growing border has 4 diamonds at step 1, 7 at step 2, and 10 at step 3. Which rule gives the number of diamonds, d, at step n?

d = 3n + 1
d = 4n + 3
d = n + 3
d = 3n + 4

3.Use the rule you identified for the diamond pattern to complete the missing counts.

Step number n

Number of diamonds d

_____

4.The diamond count starts at 4 for step 1 and increases by 3 at each step. How many diamonds will there be at step 12? Show or describe your calculation.

Build the algebra

Mere and Nikau test another invented tile pattern.

5.A second pattern has 5 tiles at step 1 and adds 4 tiles at every new step. Write the counts for steps 2, 3, and 4.

6.For the second pattern, let t be the number of tiles at step n. It starts with 5 tiles at step 1 and increases by 4 each step. Write an expression for t.

7.Use t = 4n + 1 to find the tile count at step 20.

8.Match each word to its meaning: sequence; variable; pattern rule; expression.

Sequence
Variable
Pattern rule
Expression

A letter that represents a number
An ordered list of numbers or shapes
Instructions for finding or continuing terms
A mathematical phrase that can include numbers, operations and variables

9.If a pattern increases by the same number each step, that increase can help you build an algebraic rule.

TrueFalse

10.Invent a simple geometric border that starts with 2 shapes and adds 3 shapes at each step. Sketch the first three steps, then state the number of shapes at step 3 and write a rule using s for shape count and n for step number.

11.In two or three sentences, explain how an algebra rule can help a robotics club plan how many tiles it needs for a much later step without drawing every earlier step.