Find Equivalent Expressions

Examples, solutions and videos to help Grade 5 students learn how to convert numerical expressions into unit form as a mental strategy for multi-digit multiplication.

Common Core Standards: 5.OA.1, 5.OA.2, 5.NBT.5

New York State Common Core Math Grade 5, Module 2, Lesson 4
Grade 5, Module 2, Lesson 4 Worksheets (pdf)

The following figure shows how to convert numerical expressions to simplify multi-digit multiplications. Scroll down the page for more examples and solutions.

Lesson 4 Concept Development
Problems 1–2
8 × 31
8 × 29
Problems 3–4
49 × 20
20 × 51
Problems 5–6
101 × 12
12 × 98

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Lesson 4 Problem Set

1. Circle each expression that is not equivalent to the expression in bold.
   a. 16 × 29
   29 sixteens
   16 × (30 – 1)
   (15 – 1) × 29
   (10 × 29) – (6 × 29)
   b. 38 × 45
   (38 + 40) × (38 + 5)
   (38 × 40) + (38 × 5)
   45 × (40 + 2)
   45 thirty-eights
2. Solve using mental math. Draw a tape diagram and fill in the blanks to show your thinking.
   c. 79 × 14 = _____ fourteens
   Think: ____ fourteens – 1 fourteen
   = (____ × 14) – (___ × 14)
   = ______ - ______ = ______.
   
   d. 21 × 75 = ____ seventy-fives
   Think: ___ seventy-fives + ___ seventy-five
   = (___ × 75) + (___ × 75)
   = ______ + ______ = _____
3. Define the unit in word form and complete the sequence of problems as was done in Problems 3–4 in the lesson.
   a. 19 × 15 = 19 __________
   Think: 20 _______ – 1 __________
   = (20 × ____) – (1 × ___)
   = _______ – _______ = _______
   
   b. 14 × 15 = 14 ________
   Think: 10 _________ + 4 _________
   = (10 × ____) + (4 × _____)
   = _______ + _______ = _______

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Lesson 4 Homework

1. Circle each expression that is not equivalent to the expression in bold.
   a. 37 × 19
   37 nineteens
   (30 × 19) – (7 × 29)
   37 × (20 – 1)
   (40 – 2) × 19
2. Solve using mental math. Draw a tape diagram and fill in the blanks to show your thinking.
   b. 11 × 26 = ________ twenty-sixes
   
   Think: _______ twenty-sixes + ____ twenty-sixes
   = (_____ × 26) + (_____ × 26)
   = __________ + __________ = _________ 3. Define the unit in word form and complete the sequence of problems.
   c. 19 × 11 = 19 ____________________
   
   Think: 20 ________ – 1 ________
   = (20 × ______) – (1 × _____)
   = __________ – __________ = __________

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This video demonstrates how to use mental math to evaluate expressions involving multiplication.

3. Define the unit in word form and complete the sequence of problems.

a. 29 × 12 = 29 ____________________ Think: 30 _____________ – 1 _____________
= 30 × ______) – (1 × _____)
= __________ – __________ = __________

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6. Joy is helping her father to build a deck that measures 14 ft by 19 ft. Find the area of the deck using a mental strategy. Explain your thinking.

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Try the free Mathway calculator and problem solver below to practice various 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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