GoalFind the rule of a number pattern and use it to continue the pattern.
New words
pattern · numbers or pictures that follow a rulerule · what you do each time to get the next numberterm · one number in a pattern
Explanation
A pattern is a list of numbers or pictures that follows a rule. To find the rule, look at how much the numbers change from one to the next. In 14, 24, 34, 44 every number is 10 more than the one before, so the rule is add 10. The next numbers are 54 and 64. Check the rule on every pair of neighbours, not only the first pair. Dots can make patterns too. If picture 1 has 3 dots, picture 2 has 6 dots and picture 3 has 9 dots, each picture has 3 more dots than the last. Once you know the rule, you can say what a picture you have not drawn yet will look like.
Term
1
2
3
4
5
6
Number
14
24
34
44
?
?
Rule
+10
+10
+10
+10
+10
Worked examples
Week
1
2
3
4
5
Saved (LE)
25
35
45
55
65
Salma saves money for a bag. She puts in 25 LE in week 1, 35 LE in week 2 and 45 LE in week 3. The rule is add 10, so she saves 55 LE in week 4 and 65 LE in week 5.
Count the dots in each picture: 3, 6, 9. Each picture has 3 more dots, so picture 4 has 12 dots and picture 5 has 15 dots. To find picture 10, count by 3s ten times: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30. Picture 10 has 30 dots.
Term
1
2
3
4
5
6
Number
90
80
70
60
50
40
Rule
−10
−10
−10
−10
−10
Rahma counts back in tens: 90, 80, 70, 60. Each number is 10 less than the one before, so the rule is subtract 10. The next numbers are 50 and 40.
Class activity
Pattern game with beans or small stones. A grown-up makes piles of 2, 4 and 6 beans. The child says the rule and builds the next two piles. Then swap: the child invents a rule and makes three piles, and the grown-up has to guess the rule and continue.
Practice
1
Continue the pattern: 100, 110, 120, 130, __, __. What is the rule?
140 and 150. The rule is add 10.
2
Each picture has more stars than the one before. What is the rule, and how many stars will picture 4 have?
Add 4 stars each time: 4, 8, 12, so picture 4 has 16 stars.
3
Continue the pattern: 7, 12, 17, 22, __, __.
27 and 32. The rule is add 5.
4
Omar says the rule of 3, 6, 9, 12 is add 6. Is he right?
No. The numbers go up by 3 each time (6 − 3 = 3 and 9 − 6 = 3), so the rule is add 3.
5
Picture 1 has 2 squares, picture 2 has 4 and picture 3 has 6. How many squares will picture 10 have?
20 squares. Each picture has 2 more, so counting by 2s ten times gives 20.
