Worksheets for practicing algebraic expressions through visual patterns of shapes and circles.

Let’s solve each pattern one by one. We’ll count the number of Squares (S) and Circles (C) in each step, then find a rule (formula) that tells us how many S and C there are for any step number — we’ll call the step number “n”.

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Pattern 1:

Look at the shapes:

- Step 1: 1 square, 4 circles → S=1, C=4
- Step 2: 2 squares, 6 circles → S=2, C=6
- Step 3: 3 squares, 8 circles → S=3, C=8

We can see:
- Squares = n (just the step number)
- Circles = 2n + 2? Let’s check:
- n=1 → 2(1)+2 = 4 ✔️
- n=2 → 2(2)+2 = 6 ✔️
- n=3 → 2(3)+2 = 8 ✔️

✔ Formula:
S = n
C = 2n + 2

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Pattern 2:

Shapes:

- Step 1: 1 square, 3 circles → S=1, C=3
- Step 2: 2 squares, 5 circles → S=2, C=5
- Step 3: 3 squares, 7 circles → S=3, C=7

Squares = n
Circles: 3, 5, 7 → increases by 2 each time → starts at 3 when n=1 → so C = 2n + 1
Check:
- n=1 → 2(1)+1 = 3 ✔️
- n=2 → 2(2)+1 = 5 ✔️
- n=3 → 2(3)+1 = 7 ✔️

✔ Formula:
S = n
C = 2n + 1

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Pattern 3:

Shapes:

- Step 1: 1 square, 6 circles → S=1, C=6
- Step 2: 2 squares, 8 circles → S=2, C=8
- Step 3: 3 squares, 10 circles → S=3, C=10

Squares = n
Circles: 6, 8, 10 → increases by 2 → starts at 6 → C = 2n + 4
Check:
- n=1 → 2(1)+4 = 6 ✔️
- n=2 → 2(2)+4 = 8 ✔️
- n=3 → 2(3)+4 = 10 ✔️

✔ Formula:
S = n
C = 2n + 4

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Pattern 4:

Shapes:

- Step 1: 4 squares, 4 circles → S=4, C=4
- Step 2: 8 squares, 6 circles → S=8, C=6
- Step 3: 12 squares, 8 circles → S=12, C=8

Squares: 4, 8, 12 → multiples of 4 → S = 4n
Circles: 4, 6, 8 → increases by 2 → starts at 4 → C = 2n + 2
Check:
- n=1 → S=4(1)=4, C=2(1)+2=4 ✔️
- n=2 → S=8, C=6 ✔️
- n=3 → S=12, C=8 ✔️

✔ Formula:
S = 4n
C = 2n + 2

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Final Answer:

Pattern 1:
S = n
C = 2n + 2

Pattern 2:
S = n
C = 2n + 1

Pattern 3:
S = n
C = 2n + 4

Pattern 4:
S = 4n
C = 2n + 2