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
Worksheets for Grade 5

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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