Math Games 4th Grade - Free Printable

This is a "Salamander Big Multiplication Game", where the goal is to choose two numbers — one from the top row and one from the bottom row — and multiply them. Then, you mark the product on the grid below. The objective is to get four in a line (horizontally, vertically, or diagonally) to win.

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🔢 Step 1: Understand the Numbers

You are given:

- Top row: `3, 4, 7, 8, 9`
- Bottom row: `20, 30, 40, 50, 60`

You must pick one number from each row, multiply them, and then check if that product appears on the grid.

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🧠 Step 2: Strategy – Find Products That Appear on the Grid

Let’s calculate all possible products:

| Top × Bottom | Result |
|--------------|--------|
| 3 × 20 | 60 |
| 3 × 30 | 90 |
| 3 × 40 | 120 |
| 3 × 50 | 150 |
| 3 × 60 | 180 |
| 4 × 20 | 80 |
| 4 × 30 | 120 |
| 4 × 40 | 160 |
| 4 × 50 | 200 |
| 4 × 60 | 240 |
| 7 × 20 | 140 |
| 7 × 30 | 210 |
| 7 × 40 | 280 |
| 7 × 50 | 350 |
| 7 × 60 | 420 |
| 8 × 20 | 160 |
| 8 × 30 | 240 |
| 8 × 40 | 320 |
| 8 × 50 | 400 |
| 8 × 60 | 480 |
| 9 × 20 | 180 |
| 9 × 30 | 270 |
| 9 × 40 | 360 |
| 9 × 50 | 450 |
| 9 × 60 | 540 |

Now let's see which of these appear on the grid:

We'll go through the grid and identify which numbers from our list are present.

The grid:

```
Row 1: 350 210 1500 240 1800 80
Row 2: 420 160 400 280 600 360
Row 3: 90 180 140 2400 540 60
Row 4: 120 240 1800 160 1200 3000
Row 5: 320 480 200 180 2400 120
Row 6: 450 270 1000 420 2000 800
```

Now cross-reference our multiplication results with the grid.

Valid products on the grid:

- 60 → yes (row 3, col 6)
- 90 → yes (row 3, col 1)
- 120 → yes (row 4, col 1 & row 5, col 6)
- 150 → ✘ not on grid
- 180 → yes (row 3, col 2 & row 5, col 4)
- 80 → yes (row 1, col 6)
- 160 → yes (row 2, col 2 & row 4, col 4)
- 200 → yes (row 5, col 3)
- 240 → yes (row 1, col 4 & row 4, col 2)
- 140 → yes (row 3, col 3)
- 210 → yes (row 1, col 2)
- 280 → yes (row 2, col 4)
- 350 → yes (row 1, col 1)
- 420 → yes (row 2, col 1 & row 6, col 5)
- 320 → yes (row 5, col 1)
- 480 → yes (row 5, col 2)
- 400 → yes (row 2, col 3)
- 270 → yes (row 6, col 2)
- 360 → yes (row 2, col 6)
- 450 → yes (row 6, col 1)
- 540 → yes (row 3, col 5)
- 1800 → yes (row 1, col 5 & row 4, col 3)
- 2400 → yes (row 3, col 4 & row 5, col 5)
- 1200 → yes (row 4, col 5)
- 3000 → yes (row 4, col 6)
- 2000 → yes (row 6, col 5)
- 800 → yes (row 6, col 6)

So most of our products are on the grid — except 150.

---

✔ Step 3: Try to Get Four in a Line

Let’s look for potential lines of four matching numbers.

We’ll scan rows, columns, and diagonals.

#### 🔹 Check Rows:
- Row 1: 350, 210, 1500, 240, 1800, 80 → no clear pattern
- Row 2: 420, 160, 400, 280, 600, 360 → all different
- Row 3: 90, 180, 140, 2400, 540, 60 → mixed
- Row 4: 120, 240, 1800, 160, 1200, 3000 → no repeats
- Row 5: 320, 480, 200, 180, 2400, 120 → mixed
- Row 6: 450, 270, 1000, 420, 2000, 800 → all unique

No row has four same values.

But wait — maybe we can make a line by marking products as we go?

Ah! This is a game — so players take turns choosing pairs and marking their product on the board.

Our job here is to find a winning combination — i.e., find a sequence of four numbers in a line that can be formed by multiplying the available numbers.

Let’s look at columns.

#### 🔹 Check Columns:

- Col 1: 350, 420, 90, 120, 320, 450 → no obvious pattern
- Col 2: 210, 160, 180, 240, 480, 270 → many multiples of 30?
- 210 = 7×30
- 160 = 4×40
- 180 = 9×20 or 3×60
- 240 = 4×60 or 8×30
- 480 = 8×60
- 270 = 9×30
→ Not a straight line of same product

Wait — let’s try to find a column or diagonal where four products are achievable and form a line.

Let’s consider Column 4:

- 240 (row 1)
- 280 (row 2)
- 2400 (row 3)
- 160 (row 4)
- 180 (row 5)
- 420 (row 6)

No pattern.

How about diagonals?

Try top-left to bottom-right:

- 350 → 160 → 140 → 160 → 180 → 800 → no
- 210 → 400 → 2400 → 1200 → 2000 → ? → too big

Alternatively, let’s look for a set of four products that form a line and can be made from valid multiplications.

Let’s look at column 6:

- 80 → 360 → 60 → 3000 → 120 → 800

Not helpful.

Wait — notice something interesting:

Look at column 5:

- 1800
- 600
- 540
- 1200
- 2400
- 2000

Hmm.

But here’s a better idea:

Let’s look at column 3:

- 1500
- 400
- 140
- 1800
- 200
- 1000

Still messy.

Wait — what about row 4?

Row 4: 120, 240, 1800, 160, 1200, 3000

No.

But let’s think differently.

Maybe we can simulate a winning move.

Let’s suppose we want to get four in a line.

Let’s look at column 1:

- 350
- 420
- 90
- 120
- 320
- 450

Can we make any of these?

Yes — 350 = 7×50 → both available!
420 = 7×60 or 8×50? 8×50=400, 7×60=420 → yes
90 = 3×30 → yes
120 = 3×40 or 4×30 → yes
320 = 8×40 → yes
450 = 9×50 → yes

So column 1 has:

- 350 → 7×50
- 420 → 7×60 or 8×50
- 90 → 3×30
- 120 → 3×40 or 4×30
- 320 → 8×40
- 450 → 9×50

But they’re not the same product — so we can’t get four identical numbers.

Wait — the game likely allows marking a cell when its product is achieved, and the goal is to get four marked cells in a line.

So it's like connect four — but using multiplication.

So the strategy is to choose pairs whose products form a line.

Let’s look for a line where all four numbers can be produced from the given factors.

Let’s try column 2:

- 210 → 7×30
- 160 → 4×40 or 8×20
- 180 → 3×60 or 9×20
- 240 → 4×60 or 8×30
- 480 → 8×60
- 270 → 9×30

All of these are achievable!

So column 2: 210, 160, 180, 240, 480, 270

But we need four in a line — so if someone marks all four of these in column 2, they win.

But they don't have to be consecutive? No — “four in a line” usually means consecutive.

So let’s check if there’s a straight line of four cells where each can be formed from the multiplication table.

Let’s examine row 6:

- 450 → 9×50
- 270 → 9×30
- 1000 → 8×125? But 125 not available. 10×100? Not in list.
- 1000 = 20×50? But 20 and 50 are in the bottom row, but 20×50 = 1000 → YES!
- Wait: top row: 3,4,7,8,9 → 8 is in top row
- bottom row: 20,30,40,50,60 → 50 is there
- So 8×50 = 400 → no, 8×50 = 400
- 20×50 = 1000 → but 20 is in bottom row, 50 is also in bottom row → we need one from top, one from bottom
- So we can only use one from top row, one from bottom row

So 1000 = ?
- 20×50 = 1000 → but both are in bottom row → invalid
- 5×200 → not allowed
- 10×100 → not in lists

Is 1000 achievable?

Check: 1000 ÷ 3 ≈ 333.3 → not integer
÷4 = 250 → not in bottom row
÷7 ≈ 142.8 → no
÷8 = 125 → not in bottom row
÷9 ≈ 111.1 → no

So 1000 cannot be made from the given numbers.

So 1000 is not a valid product — even though it's on the grid, it might be a red herring.

Wait — this is a problem.

Let’s double-check: Is 1000 achievable?

We need:
- One factor from {3,4,7,8,9}
- One from {20,30,40,50,60}

Try:
- 3×?=1000 → 333.3 → no
- 4×?=1000 → 250 → not in bottom row
- 7×?=1000 → ~142.8 → no
- 8×?=1000 → 125 → not in bottom row
- 9×?=1000 → ~111.1 → no

So 1000 is NOT achievable — but it’s on the grid.

Similarly, 1500:
- 1500 ÷ 3 = 500 → not in bottom row
- ÷4 = 375 → no
- ÷7 ≈ 214 → no
- ÷8 = 187.5 → no
- ÷9 ≈ 166.7 → no

So 1500 is not achievable

Similarly, 3000:
- 3000 ÷ 3 = 1000 → not in bottom
- ÷4 = 750 → no
- ÷7 ≈ 428.6 → no
- ÷8 = 375 → no
- ÷9 ≈ 333.3 → no

So 3000 not achievable

Also 1800:
- 1800 ÷ 3 = 600 → not in bottom
- ÷4 = 450 → no
- ÷7 ≈ 257 → no
- ÷8 = 225 → no
- ÷9 = 200 → not in bottom row

Wait — 9×200 = 1800 → but 200 not in bottom row

But 3×600 → 600 not in bottom

Is 1800 achievable?

Try:
- 3×600 → 600 not in bottom
- 4×450 → no
- 7×257 → no
- 8×225 → no
- 9×200 → no

So 1800 not achievable

But wait — earlier we had 7×50 = 350, etc.

But 1800 is listed twice — row 1 and row 4.

But cannot be formed from the given numbers.

So perhaps some numbers on the grid are not reachable — meaning they're just distractors.

So only the reachable products matter.

Let’s go back to our list of valid products that can be formed:

From earlier:

- 60 → 3×20
- 90 → 3×30
- 120 → 3×40 or 4×30
- 180 → 3×60 or 9×20
- 80 → 4×20
- 160 → 4×40 or 8×20
- 200 → 4×50
- 240 → 4×60 or 8×30
- 140 → 7×20
- 210 → 7×30
- 280 → 7×40
- 350 → 7×50
- 420 → 7×60 or 8×50? 8×50=400 → no, 7×60=420 → yes
- 320 → 8×40
- 480 → 8×60
- 400 → 8×50
- 270 → 9×30
- 360 → 9×40
- 450 → 9×50
- 540 → 9×60
- 2400 → 8×300? 300 not in bottom → 8×300 = 2400 → but 300 not in bottom
- 8×300 → no
- 9×266.7 → no
- 3×800 → no
- 4×600 → no
- 7×342.8 → no
- So 2400 not achievable
- Similarly, 1200: 8×150 → no, 9×133.3 → no, 7×171.4 → no → not achievable
- 3000: no
- 2000: 8×250 → no, 9×222.2 → no → not achievable
- 800: 8×100 → no, 9×88.9 → no → not achievable

So only achievable products are those from the multiplication table we did earlier.

Let’s list all achievable ones:

| Product | How to make |
|--------|-------------|
| 60 | 3×20 |
| 90 | 3×30 |
| 120 | 3×40 or 4×30 |
| 180 | 3×60 or 9×20 |
| 80 | 4×20 |
| 160 | 4×40 or 8×20 |
| 200 | 4×50 |
| 240 | 4×60 or 8×30 |
| 140 | 7×20 |
| 210 | 7×30 |
| 280 | 7×40 |
| 350 | 7×50 |
| 420 | 7×60 |
| 320 | 8×40 |
| 480 | 8×60 |
| 400 | 8×50 |
| 270 | 9×30 |
| 360 | 9×40 |
| 450 | 9×50 |
| 540 | 9×60 |

Now, let’s see which of these appear on the grid.

Go through the grid and mark which cells contain achievable products.

Grid:

```
Row 1: 350 ✔, 210 ✔, 1500 ✘, 240 ✔, 1800 ✘, 80 ✔
Row 2: 420 ✔, 160 ✔, 400 ✔, 280 ✔, 600 ✘, 360 ✔
Row 3: 90 ✔, 180 ✔, 140 ✔, 2400 ✘, 540 ✔, 60 ✔
Row 4: 120 ✔, 240 ✔, 1800 ✘, 160 ✔, 1200 ✘, 3000 ✘
Row 5: 320 ✔, 480 ✔, 200 ✔, 180 ✔, 2400 ✘, 120 ✔
Row 6: 450 ✔, 270 ✔, 1000 ✘, 420 ✔, 2000 ✘, 800 ✘
```

Now let’s look for four in a line among the ✔ cells.

Let’s scan:

#### 🔹 Column 1:
- 350 ✔
- 420 ✔
- 90 ✔
- 120 ✔
- 320 ✔
- 450 ✔

All six are ✔! And all are achievable.

So column 1 has six achievable products.

So if you mark all of them, you get six in a column — definitely four in a line.

But can you get them all? Only if you can make each product.

Let’s verify:

- 350 = 7×50 → yes
- 420 = 7×60 → yes
- 90 = 3×30 → yes
- 120 = 3×40 → yes
- 320 = 8×40 → yes
- 450 = 9×50 → yes

All valid!

So column 1 is a winning line.

Therefore, if you can get all six cells in column 1 marked, you win.

But you don’t need all six — just four in a line.

So even if you only get four of them, you win.

For example, if you play:

- 7×50 = 350 → mark row 1, col 1
- 7×60 = 420 → row 2, col 1
- 3×30 = 90 → row 3, col 1
- 3×40 = 120 → row 4, col 1

That’s four in a column — win!

Or even better, you could get:

- 7×50 = 350
- 7×60 = 420
- 8×40 = 320
- 9×50 = 450

But they are not consecutive — so not a line unless in a row.

But in column 1, all are in the same column, so any four consecutive would win.

So column 1 is a potential winning line.

Are there others?

Let’s check column 2:

- 210 ✔
- 160 ✔
- 180 ✔
- 240 ✔
- 480 ✔
- 270 ✔

All ✔!

And all achievable:

- 210 = 7×30
- 160 = 4×40 or 8×20
- 180 = 3×60 or 9×20
- 240 = 4×60 or 8×30
- 480 = 8×60
- 270 = 9×30

All valid!

So column 2 is also a full winning column.

Similarly, column 3:

- 1500 ✘
- 400 ✔
- 140 ✔
- 1800 ✘
- 200 ✔
- 1000 ✘

Only three ✔: 400, 140, 200 — not enough.

Column 4:

- 240 ✔
- 280 ✔
- 2400 ✘
- 160 ✔
- 180 ✔
- 420 ✔

So: 240, 280, 160, 180, 420 — five ✔

But not all in a row.

But look: row 4, col 4: 160
row 5, col 4: 180
row 6, col 4: 420

But not aligned.

But column 4 has: 240, 280, ?, 160, 180, 420

Not a clean line.

But column 1 and column 2 are both fully filled with achievable products.

Now check row 6:

- 450 ✔
- 270 ✔
- 1000 ✘
- 420 ✔
- 2000 ✘
- 800 ✘

Only three ✔: 450, 270, 420 — not enough.

Row 3:

- 90 ✔
- 180 ✔
- 140 ✔
- 2400 ✘
- 540 ✔
- 60 ✔

So: 90, 180, 140, 540, 60 — five ✔

But not in a straight line of four.

But column 1 and column 2 are both complete and valid.

So the best strategy is to aim for column 1 or column 2, since they are fully achievable.

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✔ Final Answer:

Yes, it is possible to win.

A winning strategy is to aim for column 1 or column 2, since all entries in these columns can be formed by multiplying one number from the top row (3,4,7,8,9) and one from the bottom row (20,30,40,50,60).

For example, to win via column 1:

- Choose 7 and 50 → 350 (row 1, col 1)
- Choose 7 and 60 → 420 (row 2, col 1)
- Choose 3 and 30 → 90 (row 3, col 1)
- Choose 3 and 40 → 120 (row 4, col 1)

This gives four in a vertical line — you win!

Similarly, column 2 offers another winning path.

Thus, the solution is to choose combinations that fill a column (especially column 1 or 2), and you will achieve four in a line.

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🎯 Summary:

- Winning condition: Get four marked cells in a line (row, column, or diagonal).
- Best strategy: Focus on column 1 or column 2, as all their values are achievable.
- Example winning move: Mark 350, 420, 90, 120 in column 1 → four in a line.

✔ Answer: You can win by selecting products that form a vertical line in column 1 or column 2.