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Maths · Grade 4 · Set C
Rules, steps and reasons
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C
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Goal: 15 min
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Remember: Find the rule by looking at the jump between terms. Then use why: a start that is a multiple, plus a step that is the same multiple, keeps every term a multiple.

Find the rule and go further

1
Which rule makes this pattern? 4, 11, 18, 25
add 6add 7multiply by 3
2
The rule is start at 6 and add 7. What number comes next?
3
Each step has 5 more tiles than the step before. Step 1 has 3 tiles. How many tiles are in step 5?
4
The rule is start at 4 and add 9. What is the 6th term?
5
The bars show a pattern. What is the next term?

Reasons and spots

6
The rule is start at 5 and add 4. Will 100 be in the pattern?
Yes. The terms keep growing, so they reach 100.Yes. 5 is the start, and 100 is a multiple of 5.No. Every term is odd, and 100 is even.
7
The rule is start at 60 and subtract 6. Will 27 be in the pattern?
No. Every term is a multiple of 6, and 27 is not.Yes. The terms keep going down, so they reach 27.Yes. Every term is even, and 27 is even.
8
The terms are 6, 12, 18, 24. Why is every term a multiple of 6?
The start is a multiple of 6, and each step adds 6.Every number is a multiple of 6.It happens because the terms get bigger.
9
A pattern that starts at 10 and adds 10 has terms that all end in 0.
TrueFalse
10
Join each rule to its pattern.
  1. 1Start at 2, add 9
  2. 2Start at 80, subtract 15
  3. 3Start at 4, multiply by 2
  4. 4Start at 7, add 6
  • A7, 13, 19, 25
  • B80, 65, 50, 35
  • C4, 8, 16, 32
  • D2, 11, 20, 29
11
All four patterns start at 5. Put their 4th terms in order from least to greatest.
  • add 3 each step
  • add 10 each step
  • multiply by 2 each step
  • add 5 each step
12
Pip makes a pattern: start at 3 and add 6. Write the first five terms. Write one thing you notice that the rule did not say.
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Answer key · Set C
Rules, steps and reasons
1add 7 11 − 4 = 7, 18 − 11 = 7 and 25 − 18 = 7. Every step adds 7.
234 27 + 7 = 34.
323 Steps 1 to 3 have 3, 8 and 13 tiles. Step 4 has 18 and step 5 has 23.
449 4, 13, 22, 31, then 31 + 9 = 40 is the 5th term and 40 + 9 = 49 is the 6th.
518 The bars are 2, 6, 10, 14. Each step adds 4, so the next is 14 + 4 = 18.
6No. Every term is odd, and 100 is even. 5 is odd, and adding 4 keeps it odd. An even number like 100 can never be in the pattern.
7No. Every term is a multiple of 6, and 27 is not. 60, 54, 48, 42 are all multiples of 6, and the terms jump over 27. Also 27 is odd, so it is not even.
8The start is a multiple of 6, and each step adds 6. Start at a multiple of 6 and add 6 each time, and you land on multiples of 6. Not every number is one.
9True Adding 10 to a number that ends in 0 gives a number that ends in 0.
101-D, 2-B, 3-C, 4-A
111, 3, 4, 2 The 4th terms are 14, 20, 35 and 40.
12Your own words: a grown-up reads it.
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