Curriculum / Math / 3rd Grade / Unit 2: Multiplication and Division, Part 1 / Lesson 5
Math
Unit 2
3rd Grade
Lesson 5 of 21
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Relate multiplication and division and understand that division can represent situations of unknown group size or an unknown number of groups.
The core standards covered in this lesson
3.OA.A.1 — Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
3.OA.A.2 — Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.
3.OA.A.3 — Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
3.OA.B.6 — Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.
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Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding
a. Match each situation with one of the drawings below. Explain your reasoning.
A
B
b. What is the same and what is different about these situations?
c. Both of these situations are division situations. How would you define division based on these situations?
d. We can represent both situations with the equation $$10 \div 2 = 5$$. What do the 10, 2, and 5 represent in Presley's situation? In Antonia's situation?
Markers in Boxes, accessed on Oct. 10, 2018, 2:32 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
Suppose that there are 4 tanks and 3 fish in each tank, as shown in the picture below. The total number of fish in this situation can be expressed as 4 $$\times$$ 3 = 12.
a. Describe what is meant in this situation by 12 $$\div$$ 3 = 4.
b. Describe what is meant in this situation by 12 $$\div$$ 4 = 3.
Fish Tanks, accessed on Oct. 10, 2018, 2:35 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
Write a multiplication equation and a division equation to represent each of the following situations. Then find the number that makes the equations true.
a. Ross has 15 flowers that he wants to make into flower arrangements. Each flower arrangement will use 5 flowers. How many flower arrangements can he make?
b. Heidi passes out 8 cards to 4 students so that they each get an equal number of cards. How many cards does each student get?
Problem Set
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Cesar says that he can solve the equation $$35 \div 5$$ by thinking about the multiplication problem $$5\:\times$$ ___$$=35$$. Do you agree or disagree? Explain.
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The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.
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Lesson 4
Lesson 6
Topic A: The Meaning of Multiplication and Division
Identify and create situations involving equal groups and describe these situations using the language and notation of multiplication.
3.OA.A.1
Identify and create situations involving arrays and describe these situations using the language and notation of multiplication.
Identify and create situations involving unknown group size and find group size in situations.
3.OA.A.1 3.OA.A.2 3.OA.A.3
Identify and create situations involving an unknown number of groups and find the number of groups in situations.
3.OA.A.1 3.OA.A.2 3.OA.A.3 3.OA.B.6
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Topic B: Multiplication and Division by 2, 5, and 10
Build fluency with multiplication facts using units of 2, 5, and 10.
3.OA.A.1 3.OA.C.7
Demonstrate the commutativity of multiplication.
3.OA.B.5
Build fluency with division facts using units of 2, 5, and 10.
3.OA.A.2 3.OA.B.6 3.OA.C.7
Solve one-step word problems involving multiplication and division using units of 2, 5, and 10.
Topic C: Multiplication and Division by 3 and 4
Build fluency with multiplication and division facts using units of 3.
3.OA.A.1 3.OA.A.2 3.OA.B.5 3.OA.B.6 3.OA.C.7
Build fluency with multiplication and division facts using units of 4.
Solve one-step word problems involving multiplication and division using units of 3 and 4.
Topic D: More Complex Multiplication and Division Problems
Determine the unknown whole number in a multiplication or division equation relating three whole numbers, including equations with a letter standing for the unknown quantity.
3.OA.A.4 3.OA.C.7 3.OA.D.8
Solve one-step word problems involving multiplication and division and write problem contexts to match expressions and equations.
Solve two-step word problems involving multiplication and division.
3.OA.D.8
Solve two-step word problems involving all four operations.
Topic E: Scaled Picture and Bar Graphs
Create scaled picture graphs where the scale is provided.
3.MD.B.3
Create scaled picture graphs where the scale must be determined.
Create scaled bar graphs where the scale is provided.
Create scaled bar graphs where the scale must be determined.
Solve one- and two-step word problems using information presented in scaled picture and bar graphs.
3.MD.B.3 3.OA.D.8
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