Algebra games - Offline & online maths ideas for KS2-4 - Teachwire - Free Printable

Explanation:
We have a “Function Machine” with two steps:
1. Multiply by 3 (purple robot)
2. Then add 5 (green robot)

So the full rule is:
Input → ×3 → +5 → Output

We are given some inputs and outputs, and need to fill in the missing ones.

Let’s go row by row.

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Row 1: Input = 9
Step 1: 9 × 3 = 27
Step 2: 27 + 5 = 32
→ Output = 32

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Row 2: Output = 35
We need to find the input. Work backwards.

Let input be *x*.
Then:
x × 3 + 5 = 35
Subtract 5: x × 3 = 30
Divide by 3: x = 10
→ Input = 10

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Row 3: Input = 5
Step 1: 5 × 3 = 15
Step 2: 15 + 5 = 20
→ Output = 20

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Row 4: Input = 8
Step 1: 8 × 3 = 24
Step 2: 24 + 5 = 29
→ Output = 29

Now let’s list all the filled values:

- Row 1: Input 9 → Output 32
- Row 2: Input 10 → Output 35
- Row 3: Input 5 → Output 20
- Row 4: Input 8 → Output 29

The blanks in the diagram are:
- Left column (inputs): one blank — that’s row 2 → 10
- Middle column (the circles, probably just connectors — no numbers needed)
- Right column (outputs): three blanks — rows 1, 3, 4 → 32, 20, 29

Since the question asks to solve the problem (and the image shows boxes to fill), we need to provide the missing numbers in order from top to bottom for the empty boxes:

Looking at the layout:
- Left side (input column): second box is empty → 10
- Right side (output column): first, third, fourth boxes are empty → 32, 20, 29

So the missing values (in reading order: top-left blank, then top-right, middle-right, bottom-right) are:
- Top-left: 10
- Top-right: 32
- Middle-right (row 3 output): 20
- Bottom-right (row 4 output): 29

But wait — the diagram shows:
- Left column has 4 boxes: 9, [blank], 5, 8
- Right column: [blank], 35, [blank], [blank]

So positions:
1. Left, row 2 → ?
2. Right, row 1 → ?
3. Right, row 3 → ?
4. Right, row 4 → ?

We found:
- Left row 2 = 10
- Right row 1 = 32
- Right row 3 = 20
- Right row 4 = 29

All correct.

Let me double-check each:

- 9 → ×3 = 27 → +5 = 32 ✔
- 10 → ×3 = 30 → +5 = 35 ✔
- 5 → ×3 = 15 → +5 = 20 ✔
- 8 → ×3 = 24 → +5 = 29 ✔

All match.

Final Answer:
10, 32, 20, 29