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Division as an Unknown in the Array Model

Division as an Unknown in the Array Model . Lesson 1.6. Say the total as a repeated addition sentence. Write a division sentence for 15 divided into 3 equal groups. Divide Equal Groups . Say the total as a repeated addition sentence. Write a division sentence.

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Division as an Unknown in the Array Model

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  1. Division as an Unknown in the Array Model Lesson 1.6

  2. Say the total as a repeated addition sentence. • Write a division sentence for 15 divided into 3 equal groups. Divide Equal Groups

  3. Say the total as a repeated addition sentence. • Write a division sentence. • How are the two arrays similar and different? Divide Equal Groups

  4. Application Problem • 20 children play a game. There are 5 children on each team. How many teams play the game? • Write a division equation to represent the problem. • Solution • 20 ÷5 = 44 teams play the game.

  5. Guided Instruction Concept Development Problem 1 • Draw an array representing the application problem. • Talk to your partner, analyze the array and describe the following relationships: • Total number of children and total number of dots • Number of children on each team and number of dots in each row • Number of teams and number of rows

  6. Guided Instruction Concept Development Problem 1 • Draw the array from the division sentences below. • 8 ÷ 2 = 4 (Size of the groups is 2) • 18 ÷ 6 = 3 (Number of groups is 6)

  7. Guided Instruction Concept Development Problem 2 • Draw an array that shows the division sentence 15 ÷ 3 = 5, where the quotient (the answer) represents the size of the groups. • Write both a division and a multiplication sentence for the array. • 15 ÷ 3 = 5, 3 X 5 = 15 • Where do you find the quotient in our multiplication sentence? • It’s the second number, the size of the groups. It is a factor. • Circle the size of the groups in both problems.

  8. Guided Instruction Concept Development Problem 2 • Draw an array that shows: • 4 rows of 2 • 7 rows of 3 • Write the multiplication and division number sentences. • Explain to your partner how the factors in a multiplication problem can help you find the quotient in division.

  9. Guided Instruction Concept Development Problem 3 • _____ x 3 = 24 – Skip-count and track the number of threes to solve. • How many threes make 24? • Write a related division sentence where the quotient represents the unknown factor. • 24 ÷ 3 = 8 • 24 divided into threes makes how many groups? • How are the unknown factor and the quotient related in these equations? • The unknown factor represents the same as the quotient.

  10. Guided Instruction Concept Development Problem 3 • 2 x ___ = 18 and 18 ÷ 2 = _____ • How many twos make 18? • Write a related division sentence where the quotient represents the unknown factor. • 18 ÷ 2 = 9 • 18 divided into twos makes how many groups? • How are the unknown factor and the quotient related in these equations? • The unknown factor represents the same as the quotient.

  11. Guided Instruction Concept Development Problem 3 • ____ x 3 = 24 and 24 ÷ 3 = ____ • True or false? Both equations ask “How many threes are in 24?” • They look different, but they mean the same thing. In both we’re talking about 8 groups of 3 and a total of 24. So it’s true. • The quotient in a division problem is like finding the unknown factor in a multiplication problem.

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