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Multiples Pattern Exploration
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Multiples Pattern Exploration
Explore how multiplication describes and predicts patterns. Show your working where needed.
Build and record patterns
1.The numbers of small triangles in Patterns 1–4 are 1, 3, 6 and 10. Complete the table for Patterns 1–6 by finding the next two totals.
Pattern
1
2
3
4
5
6
Triangles
1
3
6
10
2.A row of separate squares arranged in a row, with no sides shared, uses 4 matchsticks for each square. How many matchsticks are needed for 1, 2, 3, 4, 5 and 6 squares? Record the square number and matchstick total in a table.
Describe multiples with multiplication
3.The sequence 4, 8, 12, 16, 20, 24 lists the first six positive multiples of 4. Describe how multiplication generates each term.
4.The sequence 9, 18, 27, 36, 45 shows consecutive positive multiples of 9. Explain the relationship between each term and the position it occupies.
5.Complete the statement for the sequence 6, 12, 18, 24, 30: These are multiples of . The term at position n is multiplied by n.
Write and use multiplication rules
Position (n)
1
2
3
4
5
Value
7
14
21
28
35
6.For the table above, write a rule connecting position n to value. Use the form Value = k × n.
7.A pattern has the rule Value = 8 × n. Complete its values for positions 1, 2, 3, 4 and 5, then write the rule in words.
8.Use the rule Value = 8 × n to find the value at position n = 14. Show the multiplication you use.
9.Why can a multiplication rule be quicker than adding the same amount again and again to find a far-away term? Give one example using the rule Value = 5 × n to find the value at position 20.
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