40 Smart Activities and Ideas for Teaching Division | WeAreTeachers - Free Printable
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Step-by-step solution for: 40 Smart Activities and Ideas for Teaching Division | WeAreTeachers
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Show Answer Key & Explanations
Step-by-step solution for: 40 Smart Activities and Ideas for Teaching Division | WeAreTeachers
To solve the "Division Squares" problem, we need to ensure that each row and column in the grid represents a valid division problem. Let's go through each grid step by step.
---
```
8 ? 2
? 1 ?
4 ? ?
```
#### Step 1: Analyze the first row.
The first row is `8 ÷ ? = 2`. To find the missing number:
\[
8 ÷ x = 2 \implies x = 8 ÷ 2 = 4
\]
So, the first row becomes:
\[
8 ÷ 4 = 2
\]
#### Step 2: Analyze the second column.
The second column is now `? ÷ 1 = ?`. Since the middle cell is `1`, the division must be:
\[
x ÷ 1 = y \implies x = y
\]
We already know the bottom cell of the second column must be `4` (from the third row). So, the second column becomes:
\[
? ÷ 1 = 4 \implies ? = 4
\]
Thus, the second column is:
\[
4 ÷ 1 = 4
\]
#### Step 3: Analyze the third row.
The third row is `4 ÷ ? = ?`. We know the first cell is `4` and the last cell is `?`. Since the second column is `4 ÷ 1 = 4`, the third row must be:
\[
4 ÷ 4 = 1
\]
So, the third row becomes:
\[
4 ÷ 4 = 1
\]
#### Step 4: Analyze the third column.
The third column is now `2 ÷ ? = 1`. To find the missing number:
\[
2 ÷ x = 1 \implies x = 2
\]
So, the third column becomes:
\[
2 ÷ 2 = 1
\]
#### Final Grid 1:
\[
\begin{array}{|c|c|c|}
\hline
8 & 4 & 2 \\
\hline
4 & 1 & 4 \\
\hline
4 & 4 & 1 \\
\hline
\end{array}
\]
---
```
24 3 ?
6 ? 2
? 1 ?
```
#### Step 1: Analyze the first row.
The first row is `24 ÷ 3 = ?`. To find the missing number:
\[
24 ÷ 3 = 8
\]
So, the first row becomes:
\[
24 ÷ 3 = 8
\]
#### Step 2: Analyze the second row.
The second row is `6 ÷ ? = 2`. To find the missing number:
\[
6 ÷ x = 2 \implies x = 6 ÷ 2 = 3
\]
So, the second row becomes:
\[
6 ÷ 3 = 2
\]
#### Step 3: Analyze the third column.
The third column is now `? ÷ 2 = ?`. We know the top cell is `8` and the middle cell is `2`. Since the third row must complete the division, let's denote the bottom cell as `x`:
\[
8 ÷ 2 = 4
\]
So, the third column becomes:
\[
8 ÷ 2 = 4
\]
#### Step 4: Analyze the third row.
The third row is `? ÷ 1 = ?`. We know the last cell is `4` (from the third column). So, the third row must be:
\[
4 ÷ 1 = 4
\]
#### Final Grid 2:
\[
\begin{array}{|c|c|c|}
\hline
24 & 3 & 8 \\
\hline
6 & 3 & 2 \\
\hline
4 & 1 & 4 \\
\hline
\end{array}
\]
---
```
2 ? 2
4 ? 2
4 ? 4
```
#### Step 1: Analyze the first column.
The first column is `2 ÷ 4 = ?`. To find the missing number:
\[
2 ÷ 4 = 0.5
\]
So, the first column becomes:
\[
2 ÷ 4 = 0.5
\]
#### Step 2: Analyze the second column.
The second column is `? ÷ ? = ?`. We know the top cell is `?` and the bottom cell is `?`. Since the middle cell is `?`, let's denote the middle cell as `x`:
\[
x ÷ x = 1
\]
So, the second column becomes:
\[
x ÷ x = 1
\]
#### Step 3: Analyze the third column.
The third column is `2 ÷ 2 = 4`. To find the missing number:
\[
2 ÷ 2 = 1
\]
So, the third column becomes:
\[
2 ÷ 2 = 1
\]
#### Final Grid 3:
\[
\begin{array}{|c|c|c|}
\hline
2 & 1 & 2 \\
\hline
4 & 1 & 2 \\
\hline
4 & 1 & 4 \\
\hline
\end{array}
\]
---
```
32 ? 8
? 2 8
? ? ?
```
#### Step 1: Analyze the first row.
The first row is `32 ÷ ? = 8`. To find the missing number:
\[
32 ÷ x = 8 \implies x = 32 ÷ 8 = 4
\]
So, the first row becomes:
\[
32 ÷ 4 = 8
\]
#### Step 2: Analyze the second row.
The second row is `? ÷ 2 = 8`. To find the missing number:
\[
x ÷ 2 = 8 \implies x = 8 × 2 = 16
\]
So, the second row becomes:
\[
16 ÷ 2 = 8
\]
#### Step 3: Analyze the third column.
The third column is now `8 ÷ 8 = ?`. To find the missing number:
\[
8 ÷ 8 = 1
\]
So, the third column becomes:
\[
8 ÷ 8 = 1
\]
#### Step 4: Analyze the third row.
The third row is `? ÷ ? = ?`. We know the last cell is `1` (from the third column). So, the third row must be:
\[
4 ÷ 4 = 1
\]
#### Final Grid 4:
\[
\begin{array}{|c|c|c|}
\hline
32 & 4 & 8 \\
\hline
16 & 2 & 8 \\
\hline
4 & 4 & 1 \\
\hline
\end{array}
\]
---
```
6 3 ?
9 ? 3
? ? ?
```
#### Step 1: Analyze the first row.
The first row is `6 ÷ 3 = ?`. To find the missing number:
\[
6 ÷ 3 = 2
\]
So, the first row becomes:
\[
6 ÷ 3 = 2
\]
#### Step 2: Analyze the second row.
The second row is `9 ÷ ? = 3`. To find the missing number:
\[
9 ÷ x = 3 \implies x = 9 ÷ 3 = 3
\]
So, the second row becomes:
\[
9 ÷ 3 = 3
\]
#### Step 3: Analyze the third column.
The third column is now `2 ÷ 3 = ?`. To find the missing number:
\[
2 ÷ 3 = \frac{2}{3}
\]
So, the third column becomes:
\[
2 ÷ 3 = \frac{2}{3}
\]
#### Step 4: Analyze the third row.
The third row is `? ÷ ? = ?`. We know the last cell is `\frac{2}{3}` (from the third column). So, the third row must be:
\[
6 ÷ 9 = \frac{2}{3}
\]
#### Final Grid 5:
\[
\begin{array}{|c|c|c|}
\hline
6 & 3 & 2 \\
\hline
9 & 3 & 3 \\
\hline
6 & 9 & \frac{2}{3} \\
\hline
\end{array}
\]
---
\[
\boxed{
\begin{array}{|c|c|c|}
\hline
8 & 4 & 2 \\
\hline
4 & 1 & 4 \\
\hline
4 & 4 & 1 \\
\hline
\end{array}
\quad
\begin{array}{|c|c|c|}
\hline
24 & 3 & 8 \\
\hline
6 & 3 & 2 \\
\hline
4 & 1 & 4 \\
\hline
\end{array}
\quad
\begin{array}{|c|c|c|}
\hline
2 & 1 & 2 \\
\hline
4 & 1 & 2 \\
\hline
4 & 1 & 4 \\
\hline
\end{array}
\quad
\begin{array}{|c|c|c|}
\hline
32 & 4 & 8 \\
\hline
16 & 2 & 8 \\
\hline
4 & 4 & 1 \\
\hline
\end{array}
\quad
\begin{array}{|c|c|c|}
\hline
6 & 3 & 2 \\
\hline
9 & 3 & 3 \\
\hline
6 & 9 & \frac{2}{3} \\
\hline
\end{array}
}
\]
---
Grid 1:
```
8 ? 2
? 1 ?
4 ? ?
```
#### Step 1: Analyze the first row.
The first row is `8 ÷ ? = 2`. To find the missing number:
\[
8 ÷ x = 2 \implies x = 8 ÷ 2 = 4
\]
So, the first row becomes:
\[
8 ÷ 4 = 2
\]
#### Step 2: Analyze the second column.
The second column is now `? ÷ 1 = ?`. Since the middle cell is `1`, the division must be:
\[
x ÷ 1 = y \implies x = y
\]
We already know the bottom cell of the second column must be `4` (from the third row). So, the second column becomes:
\[
? ÷ 1 = 4 \implies ? = 4
\]
Thus, the second column is:
\[
4 ÷ 1 = 4
\]
#### Step 3: Analyze the third row.
The third row is `4 ÷ ? = ?`. We know the first cell is `4` and the last cell is `?`. Since the second column is `4 ÷ 1 = 4`, the third row must be:
\[
4 ÷ 4 = 1
\]
So, the third row becomes:
\[
4 ÷ 4 = 1
\]
#### Step 4: Analyze the third column.
The third column is now `2 ÷ ? = 1`. To find the missing number:
\[
2 ÷ x = 1 \implies x = 2
\]
So, the third column becomes:
\[
2 ÷ 2 = 1
\]
#### Final Grid 1:
\[
\begin{array}{|c|c|c|}
\hline
8 & 4 & 2 \\
\hline
4 & 1 & 4 \\
\hline
4 & 4 & 1 \\
\hline
\end{array}
\]
---
Grid 2:
```
24 3 ?
6 ? 2
? 1 ?
```
#### Step 1: Analyze the first row.
The first row is `24 ÷ 3 = ?`. To find the missing number:
\[
24 ÷ 3 = 8
\]
So, the first row becomes:
\[
24 ÷ 3 = 8
\]
#### Step 2: Analyze the second row.
The second row is `6 ÷ ? = 2`. To find the missing number:
\[
6 ÷ x = 2 \implies x = 6 ÷ 2 = 3
\]
So, the second row becomes:
\[
6 ÷ 3 = 2
\]
#### Step 3: Analyze the third column.
The third column is now `? ÷ 2 = ?`. We know the top cell is `8` and the middle cell is `2`. Since the third row must complete the division, let's denote the bottom cell as `x`:
\[
8 ÷ 2 = 4
\]
So, the third column becomes:
\[
8 ÷ 2 = 4
\]
#### Step 4: Analyze the third row.
The third row is `? ÷ 1 = ?`. We know the last cell is `4` (from the third column). So, the third row must be:
\[
4 ÷ 1 = 4
\]
#### Final Grid 2:
\[
\begin{array}{|c|c|c|}
\hline
24 & 3 & 8 \\
\hline
6 & 3 & 2 \\
\hline
4 & 1 & 4 \\
\hline
\end{array}
\]
---
Grid 3:
```
2 ? 2
4 ? 2
4 ? 4
```
#### Step 1: Analyze the first column.
The first column is `2 ÷ 4 = ?`. To find the missing number:
\[
2 ÷ 4 = 0.5
\]
So, the first column becomes:
\[
2 ÷ 4 = 0.5
\]
#### Step 2: Analyze the second column.
The second column is `? ÷ ? = ?`. We know the top cell is `?` and the bottom cell is `?`. Since the middle cell is `?`, let's denote the middle cell as `x`:
\[
x ÷ x = 1
\]
So, the second column becomes:
\[
x ÷ x = 1
\]
#### Step 3: Analyze the third column.
The third column is `2 ÷ 2 = 4`. To find the missing number:
\[
2 ÷ 2 = 1
\]
So, the third column becomes:
\[
2 ÷ 2 = 1
\]
#### Final Grid 3:
\[
\begin{array}{|c|c|c|}
\hline
2 & 1 & 2 \\
\hline
4 & 1 & 2 \\
\hline
4 & 1 & 4 \\
\hline
\end{array}
\]
---
Grid 4:
```
32 ? 8
? 2 8
? ? ?
```
#### Step 1: Analyze the first row.
The first row is `32 ÷ ? = 8`. To find the missing number:
\[
32 ÷ x = 8 \implies x = 32 ÷ 8 = 4
\]
So, the first row becomes:
\[
32 ÷ 4 = 8
\]
#### Step 2: Analyze the second row.
The second row is `? ÷ 2 = 8`. To find the missing number:
\[
x ÷ 2 = 8 \implies x = 8 × 2 = 16
\]
So, the second row becomes:
\[
16 ÷ 2 = 8
\]
#### Step 3: Analyze the third column.
The third column is now `8 ÷ 8 = ?`. To find the missing number:
\[
8 ÷ 8 = 1
\]
So, the third column becomes:
\[
8 ÷ 8 = 1
\]
#### Step 4: Analyze the third row.
The third row is `? ÷ ? = ?`. We know the last cell is `1` (from the third column). So, the third row must be:
\[
4 ÷ 4 = 1
\]
#### Final Grid 4:
\[
\begin{array}{|c|c|c|}
\hline
32 & 4 & 8 \\
\hline
16 & 2 & 8 \\
\hline
4 & 4 & 1 \\
\hline
\end{array}
\]
---
Grid 5:
```
6 3 ?
9 ? 3
? ? ?
```
#### Step 1: Analyze the first row.
The first row is `6 ÷ 3 = ?`. To find the missing number:
\[
6 ÷ 3 = 2
\]
So, the first row becomes:
\[
6 ÷ 3 = 2
\]
#### Step 2: Analyze the second row.
The second row is `9 ÷ ? = 3`. To find the missing number:
\[
9 ÷ x = 3 \implies x = 9 ÷ 3 = 3
\]
So, the second row becomes:
\[
9 ÷ 3 = 3
\]
#### Step 3: Analyze the third column.
The third column is now `2 ÷ 3 = ?`. To find the missing number:
\[
2 ÷ 3 = \frac{2}{3}
\]
So, the third column becomes:
\[
2 ÷ 3 = \frac{2}{3}
\]
#### Step 4: Analyze the third row.
The third row is `? ÷ ? = ?`. We know the last cell is `\frac{2}{3}` (from the third column). So, the third row must be:
\[
6 ÷ 9 = \frac{2}{3}
\]
#### Final Grid 5:
\[
\begin{array}{|c|c|c|}
\hline
6 & 3 & 2 \\
\hline
9 & 3 & 3 \\
\hline
6 & 9 & \frac{2}{3} \\
\hline
\end{array}
\]
---
Final Answer:
\[
\boxed{
\begin{array}{|c|c|c|}
\hline
8 & 4 & 2 \\
\hline
4 & 1 & 4 \\
\hline
4 & 4 & 1 \\
\hline
\end{array}
\quad
\begin{array}{|c|c|c|}
\hline
24 & 3 & 8 \\
\hline
6 & 3 & 2 \\
\hline
4 & 1 & 4 \\
\hline
\end{array}
\quad
\begin{array}{|c|c|c|}
\hline
2 & 1 & 2 \\
\hline
4 & 1 & 2 \\
\hline
4 & 1 & 4 \\
\hline
\end{array}
\quad
\begin{array}{|c|c|c|}
\hline
32 & 4 & 8 \\
\hline
16 & 2 & 8 \\
\hline
4 & 4 & 1 \\
\hline
\end{array}
\quad
\begin{array}{|c|c|c|}
\hline
6 & 3 & 2 \\
\hline
9 & 3 & 3 \\
\hline
6 & 9 & \frac{2}{3} \\
\hline
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of division projects grade 4.