- Use the same three numbers as in the two given facts. - Think about another way to share the same total into equal groups.

1. The other division fact divides the same total by the other factor: \(12\div4=3\). 2. Check by multiplying: \(4\times3=12\).

\(12\div4=3\); check: \(4\times3=12\).

- How else could you describe the same \(12\) objects in equal groups? - If the total is already known, what might division find about those groups?

1. Switching the factors gives \(3\times4=12\). 2. Undoing four groups of three gives \(12\div4=3\).

\(3\times4=12\) and \(12\div4=3\).

- A fact family uses the same three numbers in every equation. - The greatest number is the product in the multiplication equations. - Each division equation starts with the greatest number. - Switch the two factors to write the second multiplication equation.

1. For \(7, 9, 63\), the equations are \(7 \times 9 = 63\), \(9 \times 7 = 63\), \(63 \div 9 = 7\), and \(63 \div 7 = 9\). 2. For \(4, 8, 32\), the equations are \(4 \times 8 = 32\), \(8 \times 4 = 32\), \(32 \div 8 = 4\), and \(32 \div 4 = 8\).

a) \(7 \times 9 = 63\), \(9 \times 7 = 63\), \(63 \div 9 = 7\), \(63 \div 7 = 9\) b) \(4 \times 8 = 32\), \(8 \times 4 = 32\), \(32 \div 8 = 4\), \(32 \div 4 = 8\)

- Read the number of rows and columns from the array. - The same three numbers appear in all four equations. - Two equations multiply to the total, and two divide the total.

1. The array has \(4\) rows and \(6\) columns, so it contains \(24\) squares. 2. The multiplication facts are \(4 \times 6 = 24\) and \(6 \times 4 = 24\). 3. The related division facts are \(24 \div 4 = 6\) and \(24 \div 6 = 4\).

\(4 \times 6 = 24\) \(6 \times 4 = 24\) \(24 \div 4 = 6\) \(24 \div 6 = 4\)

- Begin with the two ways to order the factors. - Make two division facts using the product as the number being divided.

1. Multiplication: \(5\times8=40\) and \(8\times5=40\). 2. Division: \(40\div5=8\) and \(40\div8=5\). 3. Both factor orders and both ways to undo the multiplication have been used.

\(5\times8=40\), \(8\times5=40\), \(40\div5=8\), and \(40\div8=5\). Both factor orders and both division facts are included.

- Try changing the order of the factors. - Decide whether that makes different numbers or the very same equation.

1. Switching the equal factors does not change the written equation \(6\times6=36\). 2. The two division equations are also identical: \(36\div6=6\). 3. There are only two different equations.

No. The two different equations are \(6\times6=36\) and \(36\div6=6\).

- In a fact family, two numbers are factors and the third is their product. - Use multiplication or division to find the missing number. - Then write two multiplication equations and two division equations with the same three numbers.

1. a) The missing number is \(48\): \(6 \times 8=48\), \(8 \times 6=48\), \(48 \div 6=8\), \(48 \div 8=6\). 2. b) The missing number is \(9\): \(9 \times 7=63\), \(7 \times 9=63\), \(63 \div 9=7\), \(63 \div 7=9\). 3. c) The missing number is \(9\): \(9 \times 4=36\), \(4 \times 9=36\), \(36 \div 9=4\), \(36 \div 4=9\). 4. d) The missing number is \(8\): \(4 \times 8=32\), \(8 \times 4=32\), \(32 \div 4=8\), \(32 \div 8=4\).

a) \(48\): \(6 \times 8=48\), \(8 \times 6=48\), \(48 \div 6=8\), \(48 \div 8=6\) b) \(9\): \(9 \times 7=63\), \(7 \times 9=63\), \(63 \div 9=7\), \(63 \div 7=9\) c) \(9\): \(9 \times 4=36\), \(4 \times 9=36\), \(36 \div 9=4\), \(36 \div 4=9\) d) \(8\): \(4 \times 8=32\), \(8 \times 4=32\), \(32 \div 4=8\), \(32 \div 8=4\)

- In each part, the greatest number is the product. - Which number multiplied by \(5\) gives \(45\)? - Which number multiplied by \(4\) gives \(28\)? - Use the two multiplication equations and the two related division equations.

1. For part a, \(45 \div 5 = 9\), so the missing number is \(9\). The fact family is \(5 \times 9 = 45\), \(9 \times 5 = 45\), \(45 \div 9 = 5\), and \(45 \div 5 = 9\). 2. For part b, \(28 \div 4 = 7\), so the missing number is \(7\). The fact family is \(7 \times 4 = 28\), \(4 \times 7 = 28\), \(28 \div 4 = 7\), and \(28 \div 7 = 4\).

a) Missing number: \(9\) \(5 \times 9 = 45\), \(9 \times 5 = 45\), \(45 \div 9 = 5\), \(45 \div 5 = 9\) b) Missing number: \(7\) \(7 \times 4 = 28\), \(4 \times 7 = 28\), \(28 \div 4 = 7\), \(28 \div 7 = 4\)

- Start with the two multiplication equations made from \(6\), \(8\), and \(48\). - Each related division equation starts with the product, \(48\). - Explain why dividing \(48\) by one factor gives the other factor.

1. The multiplication facts are \(6\times8=48\) and \(8\times6=48\). 2. The related division facts are \(48\div6=8\) and \(48\div8=6\). 3. Each division equation begins with \(48\) because \(48\) is the product. Dividing it by one factor gives the other factor.

\(6 \times 8=48\) \(8 \times 6=48\) \(48 \div 6=8\) \(48 \div 8=6\) Both division equations begin with \(48\) because \(48\) is the whole product. Dividing it by one factor gives the other factor.

- Check that every equation uses the same three numbers correctly. - In the multiplication equations, \(56\) is the whole product. - In the related division equations, start with that whole product.

1. The incorrect equation is \(8 \div 56 = 7\). 2. The correct fourth equation is \(56 \div 8 = 7\). 3. In both division facts, the product \(56\) is the number being divided because division starts with the whole product and separates it using one factor.

The incorrect equation is \(8 \div 56 = 7\). It should be \(56 \div 8 = 7\). The number being divided is \(56\) in both division facts.

- First use the two given numbers as factors. What product completes that fact family? - Then treat the larger given number as the product. What missing factor completes that fact family? - Check each third number with one multiplication equation and one related division equation.

1. For \(8\) and \(4\), one third number is \(32\): \(8 \times 4 = 32\) and \(32 \div 4 = 8\). Another third number is \(2\): \(2 \times 4 = 8\) and \(8 \div 4 = 2\). 2. For \(9\) and \(3\), one third number is \(27\): \(9 \times 3 = 27\) and \(27 \div 3 = 9\). Another third number is \(3\): \(3 \times 3 = 9\) and \(9 \div 3 = 3\). 3. For \(10\) and \(2\), one third number is \(20\): \(10 \times 2 = 20\) and \(20 \div 2 = 10\). Another third number is \(5\): \(5 \times 2 = 10\) and \(10 \div 2 = 5\).

a) \(32\): \(8 \times 4 = 32\), \(32 \div 4 = 8\); \(2\): \(2 \times 4 = 8\), \(8 \div 4 = 2\) b) \(27\): \(9 \times 3 = 27\), \(27 \div 3 = 9\); \(3\): \(3 \times 3 = 9\), \(9 \div 3 = 3\) c) \(20\): \(10 \times 2 = 20\), \(20 \div 2 = 10\); \(5\): \(5 \times 2 = 10\), \(10 \div 2 = 5\)