Algebra and equations · Ages 9–10
Growing patterns worksheet
Part of: Patterns and rules
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Growing patterns worksheet
Algebra and equations · Ages 9–10
Numsprite
numsprite.com
Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.These dot patterns grow by a rule. How many dots does pattern 4 have?
Answer:
2.Matchstick patterns grow by a rule; three of them are shown. How many matchsticks does pattern 5 need?
Answer:
3.Matchstick patterns grow by a rule; three of them are shown. How many matchsticks does pattern 6 need?
Answer:
4.Matchstick patterns grow by a rule; patterns 1 to 3 are shown. How many matchsticks does pattern 11 need?
Answer:
5.Matchstick patterns grow by a rule; patterns 1 to 3 are shown. How many matchsticks does pattern 14 need?
Answer:
6.Matchstick patterns grow by a rule; patterns 1 to 3 are shown. How many matchsticks does pattern 12 need?
Answer:
7.These dot patterns grow by a rule; patterns 1 to 3 are shown. How many dots does pattern 10 have?
Answer:
8.These dot patterns grow by a rule; patterns 1 to 3 are shown. How many dots does pattern 6 have?
Answer:
Part B: Choose, or true or false (2 marks each)
9.The matchstick patterns keep growing by the rule (patterns 1 to 3 shown), and pattern 5 needs 25 matchsticks.
True or false?
Answer:
10.Matchstick patterns grow by a rule; patterns 1 to 3 are shown. Which picture is pattern 5?
- A
- B
- C
- D
Choose the right picture
Answer:
11.Matchstick patterns grow by a rule; patterns 1 to 3 are shown. Which picture is pattern 4?
- A
- B
- C
- D
Choose the right picture
Answer:
12.The matchstick patterns keep growing by the rule (patterns 1 to 3 shown), and pattern 6 needs 22 matchsticks.
True or false?
Answer:
Part C: Word problems (4 marks each)
13.Ming builds a row of houses from lolly sticks: 1 house uses 6, 2 houses use 11, 3 houses use 16. With 67 sticks, how many houses can Ming build at most?
Working:
Answer:
14.Ming builds stairs from blocks: 1 step takes 1 block, 2 steps take 3, 3 steps take 6. Carrying on, how many blocks do 12 steps take?
Working:
Answer:
15.A plant is 9 cm tall in week 1, 14 cm in week 2 and 19 cm in week 3. If it keeps growing like this, how tall is it in week 6?
Working:
Answer:
16.A cha chaan teng pushes tables together in a row: 1 table seats 6, 2 tables seat 10, 3 tables seat 14. Carrying on, how many can 20 tables seat?
Working:
Answer:
17.A cha chaan teng pushes tables together in a row: 1 table seats 4, 2 tables seat 6, 3 tables seat 8. Carrying on, how many can 16 tables seat?
Working:
Answer:
18.Ka-lok builds stairs from blocks: 1 step takes 1 block, 2 steps take 3, 3 steps take 6. Carrying on, how many blocks do 12 steps take?
Working:
Answer:
Show the answers and working
Growing patterns worksheet: Answers and working
Part A: Working out and filling in
1. 20
Count the dots in the three patterns and write them in a row. Is the increase the same each time?
Write the counts in a row: 2, 6, 12. See how many more each time and how the picture is built: pattern 4 has 20.
2. 16
Count the sticks in each pattern shown and see how many more each time. How many patterns on from pattern 3 is pattern 5?
Each pattern has 3 more sticks than the one before. Pattern 3 has 10; add 3 another 2 times: 16.
3. 19
Count the sticks in each pattern shown and see how many more each time. How many patterns on from pattern 4 is pattern 6?
Each pattern has 3 more sticks than the one before. Pattern 4 has 13; add 3 another 2 times: 19.
4. 56
Count the sticks in pattern 1 and how many each new pattern adds. How many times do you add them to reach pattern 11?
Each pattern adds 5 sticks. Pattern 1 has 6; pattern 11 adds 5 another 10 times: 6 + 10 × 5 = 56.
5. 71
Count the sticks in pattern 1 and how many each new pattern adds. How many times do you add them to reach pattern 14?
Each pattern adds 5 sticks. Pattern 1 has 6; pattern 14 adds 5 another 13 times: 6 + 13 × 5 = 71.
6. 61
Count the sticks in pattern 1 and how many each new pattern adds. How many times do you add them to reach pattern 12?
Each pattern adds 5 sticks. Pattern 1 has 6; pattern 12 adds 5 another 11 times: 6 + 11 × 5 = 61.
7. 100
Look at how the dots are laid out: how many rows, and how many in each, in patterns 1, 2 and 3? Then picture pattern 10.
The counts go up by 3, 5, … and each increase is 2 more. Quicker to look at the layout: pattern 10 has 10 rows, which add up to 10 + 10 + … + 10 = 100 dots.
8. 21
Look at how the dots are laid out: how many rows, and how many in each, in patterns 1, 2 and 3? Then picture pattern 6.
The counts go up by 2, 3, … and each increase is 1 more. Quicker to look at the layout: pattern 6 has 6 rows, which add up to 6 + 5 + … + 1 = 21 dots.
Part B: Choose, or true or false
9. False
Count the sticks in pattern 1 and how many each new pattern adds, then work up to pattern 5 and compare with 25.
Each pattern adds 5 sticks. Counting on from pattern 1, pattern 5 needs 27.
10. B
See how many sticks each new pattern adds and work out how many pattern 5 needs; then count each picture's sticks and check its shape.
Each pattern adds 5 sticks, so pattern 5 needs 26, in the same shape.
11. D
See how many sticks each new pattern adds and work out how many pattern 4 needs; then count each picture's sticks and check its shape.
Each pattern adds 2 sticks, so pattern 4 needs 9, in the same shape.
12. False
Count the sticks in pattern 1 and how many each new pattern adds, then work up to pattern 6 and compare with 22.
Each pattern adds 3 sticks. Counting on from pattern 1, pattern 6 needs 19.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 13 houses
How many more sticks does each house add? Work out what n houses use, then see how many 67 sticks can make.
Each house adds 5 sticks: n houses use 5 × n + 1. 13 houses use 5 × 13 + 1 = 66; one more would need 71, more than 67.
14. 78 blocks
How many more blocks does each new step need? See how the increase changes from 1 to 3 to 6.
Each new step adds a column as tall as the number of steps: 1 + 2 + 3 + … + 12 = 78.
15. 34 cm
How many cm does it grow each week? And how many weeks after week 1 is week 6?
It grows 5 cm a week. From week 1, another 5 weeks: 9 + 5 × 5 = 34.
16. 82 people
How many more people does each extra table seat? Compare 6, 10 and 14.
Each extra table seats 4 more (the joined sides lose seats). 1 table seats 6; add 4 another 19 times: 6 + 19 × 4 = 82.
17. 34 people
How many more people does each extra table seat? Compare 4, 6 and 8.
Each extra table seats 2 more (the joined sides lose seats). 1 table seats 4; add 2 another 15 times: 4 + 15 × 2 = 34.
18. 78 blocks
How many more blocks does each new step need? See how the increase changes from 1 to 3 to 6.
Each new step adds a column as tall as the number of steps: 1 + 2 + 3 + … + 12 = 78.
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