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6-8 Grade 7 Unit 6 Lesson 3

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Unit 6, Lesson 3

Reasoning about Equations with Tape Diagrams

Grade 7

Practice

Problem 1

ForLesson 15: Solving Equations with Rational Numbers

Solve each equation mentally.

\(2x = 10\)
\(\text-3x = 21\)
\(\frac13 x = 6\)
\(\text-\frac12x = \text-7\)

Problem 2

ForLesson 3: Changing Elevation

Complete the magic squares so that the sum of the three numbers in each row, each column, and each diagonal are all equal.

Square grid with 3 columns and 3 rows. Grid contains 0, 7, 2, blank, 3, blank, blank, blank, blank.

Square grid with 3 columns and 3 rows. Grid contains 1, blank, blank, blank, 3, negative 2, blank, blank, five.

Square grid with 3 columns and 3 rows. Grid contains blank, blank, blank, 4, 2, 0, negative 1, blank, blank.

Problem 3

Draw a tape diagram to match each equation.

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

Problem 4

Select all the equations that match the tape diagram.

Tape diagram, 1 part labeled 8, 6 parts labeled x, total 35.

\(35=8+x+x+x+x+x+x\)
\(35=8+6x\)
\(6+8x=35\)
\(6x+8=35\)
\(6x+8x=35x\)
\(35-8=6x\)

Problem 5

ForLesson 2: Ratios and Rates with Fractions

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