Repeating patterns worksheet

Part A: Working out and filling in

1. 1. 14

   Start from 14 and see after how many numbers it begins again; the 9th follows that group.

   The numbers repeat in groups of 4, so the 9th is the same as the 1st: 14.

2. 2. 12

   Start from 12 and see after how many numbers it begins again; the 9th follows that group.

   The numbers repeat in groups of 4, so the 9th is the same as the 1st: 12.

3. 3. 20

   The numbers repeat every 3. Work out 46 ÷ 3 and look at the remainder.

   Groups of 3: 46 ÷ 3 = 15 r 1, so the 46th is the 1st of a group: 20.

4. 4. 1

   The numbers repeat every 4. Work out 45 ÷ 4 and look at the remainder.

   Groups of 4: 45 ÷ 4 = 11 r 1, so the 45th is the 1st of a group: 1.

5. 5. 8

   Count the 🐰 in one group of 3, then use 23 ÷ 3 to see how many whole groups there are and how many are left.

   Groups of 3, each with 1 🐰. 23 ÷ 3 = 7 r 2: 7 groups hold 7, and the 2 left over hold 1, so 8 in all.

6. 6. 9

   Count the 🐸 in one group of 3, then use 25 ÷ 3 to see how many whole groups there are and how many are left.

   Groups of 3, each with 1 🐸. 25 ÷ 3 = 8 r 1: 8 groups hold 8, and the 1 left over hold 1, so 9 in all.

7. 7. 10

   Count the 📏 in one group of 4, then use 19 ÷ 4 to see how many whole groups there are and how many are left.

   Groups of 4, each with 2 📏. 19 ÷ 4 = 4 r 3: 4 groups hold 8, and the 3 left over hold 2, so 10 in all.

Part B: Choose, or true or false

1. 8. B. 📎

   Find the group that repeats and how many are in it, then see which place in the group comes after the 10th.

   It repeats in groups of 3. After the 10th comes the 11th, which by the pattern is 📎.

2. 9. False

   Count how many are in the repeating group, divide 25 by it, and see which place in the group the 25th is.

   Groups of 4; 25 ÷ 4 leaves 1, so the 25th is the 1st of a group: 🐵.

3. 10. A. 📏

   Count how many are in the repeating group, then divide 35 by that number and look at the remainder.

   Groups of 3: 35 ÷ 3 = 11 r 2, so the 35th is the 2nd of a group: 📏.

4. 11. A. 🐰

   Count how many are in the repeating group, then divide 34 by that number and look at the remainder.

   Groups of 2: 34 ÷ 2 = 17 r 0, so the 34th is the 2nd of a group: 🐰.

5. 12. False

   Count how many are in the repeating group, divide 30 by it, and see which place in the group the 30th is.

   Groups of 3; 30 ÷ 3 leaves 0, so the 30th is the 3rd of a group: 📎.

Part C: Word problems

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

1. 13. 9

   Each group has 1 + 2 + 1 posts, with yellow first. How many whole groups come before the 3rd yellow?

   Groups of 4, with yellow first in each. Before it come 2 whole groups, 8 posts, so the 3rd yellow is post 9.

2. 14. 50 people

   Every 3 tables make a group with one 6-seat table. First count how many 6-seat tables there are among the 15.

   Groups of 3 tables: the first 15 have 5 tables for 6 and 10 for 2: 6 × 5 + 2 × 10 = 50.

3. 15. A. Wednesday

   The week repeats every 7 days. Find the remainder of 20 ÷ 7; whole weeks don't change the day.

   The week repeats every 7 days. 20 ÷ 7 = 2 r 6: after 2 weeks it is Thursday again; count on 6 from there to reach Wednesday.

4. 16. 9 red beads

   4 red and 3 white make one group. Work out how many whole groups 15 beads make, then look at what is left.

   Groups of 7, each with 4 red. 15 ÷ 7 = 2 r 1: 2 groups hold 8; the 1 left over start with red, giving 1. 9 in all.

5. 17. 53

   Each group has 1 + 2 + 1 posts, with yellow first. How many whole groups come before the 14th yellow?

   Groups of 4, with yellow first in each. Before it come 13 whole groups, 52 posts, so the 14th yellow is post 53.

6. 18. 64 people

   Every 3 tables make a group with one 4-seat table. First count how many 4-seat tables there are among the 19.

   Groups of 3 tables: the first 19 have 7 tables for 4 and 12 for 3: 4 × 7 + 3 × 12 = 64.