Lesson 3
Reasoning about Equations with Tape Diagrams
Problem 1
Solve each equation mentally.
 \(2x = 10\)
 \(\text3x = 21\)
 \(\frac13 x = 6\)
 \(\text\frac12x = \text7\)
Solution
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(From Unit 5, Lesson 15.)Problem 2
Complete the magic squares so that the sum of each row, each column, and each diagonal in a grid are all equal.
Solution
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(From Unit 5, Lesson 3.)Problem 3
Draw a tape diagram to match each equation.

\(5(x+1)=20\)

\(5x+1=20\)
Solution
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Problem 4
Select all the equations that match the tape diagram.
\(35=8+x+x+x+x+x+x\)
\(35=8+6x\)
\(6+8x=35\)
\(6x+8=35\)
\(6x+8x=35x\)
\(358=6x\)
Solution
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Problem 5
Each car is traveling at a constant speed. Find the number of miles each car travels in 1 hour at the given rate.

135 miles in 3 hours

22 miles in \(\frac12\) hour

7.5 miles in \(\frac14\) hour

\(\frac{100}{3}\) miles in \(\frac23\) hour

\(97\frac12\) miles in \(\frac32\) hour
Solution
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(From Unit 4, Lesson 2.)