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Unknown in Multiplication and Division


Videos and solutions to help Grade 3 students learn how to interpret the unknown in multiplication and division to model and solve problems.

Common Core Standards: 3.OA.3, 3.OA.4, 3.OA.5, 3.OA.7, 3.OA.1, 3.OA.2, 3.OA.6, 3.OA.8

New York State Common Core Math Module 3, Grade 3, Lesson 11

Decompose the Multiplication Sentence

8 × 8 = (5 + 3) × 8

= (5 × 8) + (3 × 8)

= 40 + 24

= 64

Concept Development

Problem 1: Interpret the unknown in multiplication.
Asmir buys 8 boxes of 9 candles for his dad’s birthday. After putting some candles on the cake, there are 28 candles left. How many candles does Asmir use?
Problem 2: Interpret the unknown in division.
Write the following problem: The fabric store sells 1 meter of cloth for $8. Maria buys some cloth that costs a total of $56. She then uses 3 meters to sew a dress. How many meters of cloth does she have left?

Interpret the Unknown in Multiplication and Division to Model and Solve Problems

Lesson 11 Problem Set

1. Ms. Santor divides 32 students into 8 equal groups for a field trip. Draw a tape diagram and label the number of students in each group as n. Write an equation and solve for n.
2. Tara buys 6 packs of printer paper. Each pack of paper costs $8. Draw a tape diagram and label the total amount she spends as m. Write an equation and solve for m.
3. Mr. Reed spends $24 on coffee beans. How many kilograms of coffee beans does he buy? Draw a tape diagram and label the total amount of coffee beans he buys as c. Write an equation and solve for c.

Lesson 11 Problem Set

4. Eight boys equally share 4 packs of baseball cards. Each pack contains 10 cards. How many cards does each boy get?
5. There are 8 bags of yellow and green balloons. Each bag contains 7 balloons. If there are 35 yellow balloons, how many green balloons are there?
6. The fruit seller packs 72 oranges into bags of 8 each. He sells all the oranges at $4 a bag. How much money did he receive?


Lesson 11 Homework
1. Jenny bakes 10 cookies. She puts 7 chocolate chips on each cookie. Draw a tape diagram and label the total of amount of chocolate chips as c. Write an equation and solve for c.
3. There are 35 computers in the lab. Five students each turn off an equal number of computers. How many computers does each student turn off? Label the unknown as m, then solve.
5. There are 8 trail mix bags in one box. Clarissa buys 5 boxes. She gives an equal number of bags of trail mix to 4 friends. How many bags of trail mix does each friend receive?

Lesson 11 Homework

6. Leo earns $8 a week for doing chores. After 7 weeks, he buys a gift and has $38 left. How much does he spend on the gift?

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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