Find Equivalent Expressions
Lesson Plans and Worksheets for Grade 5
Lesson Plans and Worksheets for all Grades
More Lessons for Grade 5
Common Core For Grade 5
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.
Problems 1–2
8 × 31
8 × 29
Problems 3–4
49 × 20
20 × 51
Problems 5–6
101 × 12
12 × 98
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 × _____)
= __________ – __________ = __________
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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