- Think about what the two factors mean. - Which factor describes the number in one group?

1. Three groups of four make twelve. 2. Dividing twelve into three equal groups gives four in each group, so \(12\div3=4\).

\(12\div3=4\). The multiplication fact gives the size of each group.

- Find the number of dots in one row. - Ask how many such rows make the total.

1. There are \(4\) rows with \(5\) dots in each. 2. \(20\div5=4\), so the answer counts the rows.

\(20\div5=4\). The answer counts rows.

- Use a multiplication fact that has the same total as each division fact. - Your multiplication check must make the number being divided. - Write the multiplication check after each division answer.

1. Since \(7 \times 9 = 63\), \(63 \div 9 = 7\). 2. Since \(8 \times 4 = 32\), \(32 \div 4 = 8\). 3. Since \(9 \times 9 = 81\), \(81 \div 9 = 9\).

a) \(63 \div 9 = 7\); check: \(7 \times 9 = 63\) b) \(32 \div 4 = 8\); check: \(8 \times 4 = 32\) c) \(81 \div 9 = 9\); check: \(9 \times 9 = 81\)

- Think of a multiplication fact that uses the same two numbers. - Write the related multiplication fact to check each answer. - Your multiplication check should make the starting total.

1. \(32 \div 4 = 8\) because \(8 \times 4 = 32\). 2. \(42 \div 7 = 6\) because \(6 \times 7 = 42\). 3. \(45 \div 5 = 9\) because \(9 \times 5 = 45\). 4. \(56 \div 8 = 7\) because \(7 \times 8 = 56\).

a) \(32 \div 4 = 8\); check: \(8 \times 4 = 32\) b) \(42 \div 7 = 6\); check: \(6 \times 7 = 42\) c) \(45 \div 5 = 9\); check: \(9 \times 5 = 45\) d) \(56 \div 8 = 7\); check: \(7 \times 8 = 56\)

- Read the number of rows and the number of dots in each row from the array. - The multiplication equation should describe the whole array. - Use the same three numbers to write the related division equations.

1. The array has \(4\) rows with \(8\) dots in each row, for \(32\) dots altogether. 2. The multiplication equation is \(4 \times 8 = 32\). 3. The related division equations are \(32 \div 4 = 8\) and \(32 \div 8 = 4\).

a) \(4\) rows and \(8\) dots in each row b) \(4 \times 8 = 32\) c) \(32 \div 4 = 8\) and \(32 \div 8 = 4\)

- Use the image to find how many equal sections there are. - Think of the total as being shared equally among those sections. - Use the same three numbers in both the multiplication and division equations.

1. The image shows \(3\) equal sections. 2. Dividing \(54\) tracks among \(3\) equal sections gives \(54 \div 3 = 18\) tracks per section. 3. The matching multiplication equation is \(3 \times 18 = 54\).

a) \(3\) sections b) \(18\) tracks in each section c) \(3 \times 18 = 54\) and \(54 \div 3 = 18\)

- Count the rows and the dots in one row. - Use the array to write a multiplication equation for the whole. - For each division equation, start with the whole and divide by one of the two factors to find the other.

1. The array has \(3\) rows with \(4\) dots in each row, so \(3 \times 4 = 12\). 2. Dividing the total by the number of rows gives the number in each row: \(12 \div 3 = 4\). 3. Dividing the total by the number in each row gives the number of rows: \(12 \div 4 = 3\).

\(3 \times 4 = 12\) \(12 \div 3 = 4\) \(12 \div 4 = 3\)

- What is being shared equally among the rows? - Which multiplication equation would rebuild the total after you divide?

1. \(24\div6=4\), so each row has \(4\) cars. 2. The matching multiplication check is \(6\times4=24\).

\(24\div6=4\) cars per row; check: \(6\times4=24\).

- Test what would happen if you made \(6\) groups of Eli's answer. - If your check does not give the total, how could you change the number in each group?

1. Check Eli's answer: \(6\times7=42\), not \(48\). 2. Find the factor that works: \(6\times8=48\). 3. The correct division equation is \(48\div6=8\).

No. \(6\times7=42\), not \(48\). Since \(6\times8=48\), the correct equation is \(48\div6=8\).

- Use the same three numbers in a related multiplication equation. - In the multiplication check, the product should be the number that was divided. - Use the multiplication equation to justify the missing number, not just to check it afterward.

1. a) Since \(7 \times 6=42\), the completed division equation is \(42 \div 6=7\). 2. b) Since \(9 \times 7=63\), the completed division equation is \(63 \div 7=9\). 3. c) Since \(4 \times 8=32\), the completed division equation is \(32 \div 8=4\). 4. d) Since \(9 \times 9=81\), the completed division equation is \(81 \div 9=9\). 5. In every part, the multiplication equation rebuilds the number being divided from the number you divide by and answer.

a) \(42 \div 6=7\); \(7 \times 6=42\) b) \(63 \div 7=9\); \(9 \times 7=63\) c) \(32 \div 8=4\); \(4 \times 8=32\) d) \(81 \div 9=9\); \(9 \times 9=81\)

- Count the rows and the dots in each row of the array. - In part b), you know the total number of dots and the number of equal rows. - For part c), use the number of rows and the number of dots in each row. - Compare the three numbers in your division and multiplication equations.

1. The array has \(6\) rows with \(6\) dots in each row, so \(6 \times 6 = 36\). 2. The same \(36\) dots are arranged into \(4\) equal rows. \(36 \div 4 = 9\), so each row has \(9\) dots. 3. The multiplication check is \(4 \times 9 = 36\). 4. The division equation and multiplication equation use the same three numbers. Multiplication checks or undoes the division.

a) \(6 \times 6 = 36\) b) \(36 \div 4 = 9\) c) \(4 \times 9 = 36\) d) They use the same three numbers. Multiplication checks the division.