🎯 Learning outcomes
- Describe and extend number and shape patterns with a rule
- Find a missing number in a number sentence
- Use a letter or box to stand for an unknown number
Before you start: The four operations.
📖 Explanation
Number patterns grow or shrink by a rule: 3, 7, 11, 15 adds 4 each time. Some patterns multiply: 2, 4, 8, 16 doubles.
A number sentence with a missing number is like a puzzle: 7 + □ = 15 means □ = 8. We can use a letter instead of a box: 7 + n = 15, so n = 8.
Patterns in shapes can be described with numbers: if each triangle in a row uses 3 matchsticks, 5 triangles use 5 × 3 = 15 matchsticks, so n triangles use 3 × n.
Seats in an auditorium increase by 2 in each row: 20, 22, 24 … The 10th row has 20 + 9 × 2 = 38 seats.
✗ In 5 + n = 12, n can be any number
✓ A letter in a number sentence stands for the one number that makes it true; here n = 7.
🧪 Try this activity
Build squares in a row with matchsticks. Record the number of squares and sticks in a table and find the rule.
✍️ Question bank with answers
Tap an option to check multiple-choice answers. Open “Answer” or “Marking points” for the others.
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Next number: 5, 10, 20, 40, __
Answer
D. 80
The rule is to double.
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If 9 × □ = 72, then □ =
Answer
D. 8
72 ÷ 9 = 8.
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Matchstick triangles in a row use 3 sticks each, separately. For 6 triangles you need
Answer
B. 18
6 × 3 = 18.
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Find n: n − 6 = 14
Answer
n = 20
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Continue: 100, 90, 80, __
Answer
70
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Write the rule and the next two terms: 1, 4, 9, 16
Marking points
- Square numbers: 1×1, 2×2, 3×3, 4×4
- 25, 36
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A taxi charges ₹50 plus ₹15 per km. Write a rule for the cost of k km and find the cost for 12 km.
Marking points
- Cost = 50 + 15 × k
- For 12 km: 50 + 180 = ₹230
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A plant is 4 cm tall and grows 3 cm a week. How tall after 6 weeks?
Answer
- 4 + 6 × 3
- 22 cm
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Draw the next shape in a pattern of squares: 1, 3, 5 squares in an L-shape.
Answer
An L-shape of 7 squares
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