Discover Mathematics P5: Term 1, Unit 6, Lessons 5–7
GoalExtend a pattern, create patterns from a start number and a rule, and compare two patterns with different rules.
New words
extend · to write more terms of a patternterm number · the place of a term in the pattern: first, second, third …relationship · how two patterns are connected
Explanation
To create a pattern, choose a start number and a rule. Start at 3 and add 4: 3, 7, 11, 15, 19, 23. Two patterns can be compared term by term. Pattern A starts at 0 and adds 3; pattern B starts at 0 and adds 6. The terms are A: 0, 3, 6, 9, 12, 15 and B: 0, 6, 12, 18, 24, 30. Each B term is 2 times the A term in the same place, because B grows twice as fast. We can also use a letter n for the term number. For the pattern 5, 10, 15, 20 (start 5, add 5) the n-th term is 5 × n, so the 12th term is 5 × 12 = 60 without writing all terms.
Step
0
1
2
3
4
5
Pattern A (add 3)
0
3
6
9
12
15
Pattern B (add 6)
0
6
12
18
24
30
Worked examples
Create a pattern: start at 3, add 4. Terms: 3, 7, 11, 15, 19, 23. Each term is 4 more than the one before.
A
B
0
0
3
6
6
12
9
18
12
24
Compare A (start 0, add 3) and B (start 0, add 6). When A is 9, B is 18; when A is 12, B is 24. B is always 2 times A.
Term number n
1
2
3
4
n
Value
5
10
15
20
5 × n
Start at 5 and add 5. The n-th term is 5 × n. The 12th term is 5 × 12 = 60. Which term is 85? 85 ÷ 5 = 17, so the 17th term.
Class activity
Pattern workshop. Choose a start number and a rule and write six terms. Let the grown-up pick another rule with the same start and write six terms under yours. Compare the two rows: does one row grow faster? Is there a link, such as one row being double the other?
Practice
1
Write the first five terms: start at 10, add 7.
10, 17, 24, 31, 38.
2
Write the first five terms: start at 2, multiply by 2.
2, 4, 8, 16, 32.
3
Pattern A starts at 0 and adds 2. Pattern B starts at 0 and adds 10. Write five terms of each. How are the terms connected?
A: 0, 2, 4, 6, 8. B: 0, 10, 20, 30, 40. Each B term is 5 times the A term.
4
The n-th term of a pattern is 6 × n. Find the 9th term.
6 × 9 = 54.
5
In the same pattern (6 × n), which term number has the value 72?
