Find Equivalent Expressions


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Lesson Plans and Worksheets for Grade 5
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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.
Convert Numerical Expressions

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




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 × _____)
    = _______ + _______ = _______


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 × _____)
    = __________ – __________ = __________

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 × _____)
= __________ – __________ = __________

  1. 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.


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.
Mathway Calculator Widget



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