Number Patterns
Primary 4 · Mathematics
Number Patterns
Lesson 3 of 4
20 min
Let's begin
Ishimwe makes a number pattern with cards on the classroom wall. Then the wind blows through the window, and two cards fall down!
Now the wall shows: 18, 25, ?, 39, ?, 53.
Can you work out which cards are missing? Today you will find the missing numbers in patterns.
Worked example 1
18, 25, ?, 39, ?, 53
Step 1 18 and 25 are neighbours: 25 − 18 = 7. The pattern adds 7.
Step 2 25 + 7 = 32. Check: 32 + 7 = 39. Yes!
Step 3 39 + 7 = 46. Check: 46 + 7 = 53. Yes!
The full pattern is 18, 25, 32, 39, 46, 53.
Worked example 2
40, ?, ?, 67 (the pattern adds the same number each time)
Step 1 From 40 to 67 there are 3 jumps (40 to the 1st card, to the 2nd card, to 67).
Step 2 The whole gap is 67 − 40 = 27. Share it among the jumps: 27 ÷ 3 = 9.
Step 3 40 + 9 = 49, 49 + 9 = 58. Check: 58 + 9 = 67.
Careful! Count the jumps, not the numbers. Four numbers have only three jumps between them.
Worked example 3
?, 45, 60, 75. The pattern adds 15. Go backwards: 45 − 15 = 30.
Worked example 4
What is the 10th term of 4, 7, 10, 13, …?
Step 1 The pattern adds 3.
Step 2 From the 1st term to the 10th term there are 9 jumps.
Step 3 4 + 9 × 3 = 4 + 27 = 31. You do not have to write out all ten terms!
Tip
Count the jumps, not the numbers. Find the gap between two terms you know, then share it equally among the jumps between them.
Work each one in your exercise book first. Then tap Show answer to check.
11, 19, ?, 35, 43
Answer: 27. The pattern adds 8: 19 + 8 = 27.
90, ?, 70, ?, 50
Answer: 80 and 60. The pattern subtracts 10.
?, 24, 36, 48
Answer: 12. The pattern adds 12, so go back: 24 − 12 = 12.
5, ?, ?, 26 (the same number is added each time)
Answer: 12 and 19. There are 3 jumps: (26 − 5) ÷ 3 = 21 ÷ 3 = 7.
What is the 6th term of 3, 8, 13, …?
Answer: 28. From the 1st to the 6th term is 5 jumps of 5: 3 + 25 = 28.
What you learned today
Sources and credits
The card and jump methods, the stories and the practice questions were written by Ganzaa.
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