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6-8 Accelerated 7 Unit 3 Lesson 5

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IM K-5 Math
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Unit 3, Lesson 5

Reasoning about Equations and Tape Diagrams (Part 2)

Accelerated 7

Practice

Problem 1

Here are two stories:

A family buys 6 tickets to a show. They also each spend \$3 on a snack. They spend a total of \$24 for tickets and snacks.
Diego has 24 ounces of juice. He pours equal amounts for each of his 3 friends, and then adds 6 more ounces for each.

Here are two equations:

\(3(x+6)=24\)
\(6(x+3)=24\)

Which equation represents which story?
What does \(x\) represent in each equation?
Find the solution to each equation. Explain or show your reasoning.
What does each solution tell you about its situation?

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Lesson 5 Resources

Student Materials

Problem 2

Here is a diagram and its corresponding equation. Find the solution to the equation and explain your reasoning.

Tape diagram, 6 equal parts labeled x + 1, total 24.

\(\displaystyle 6(x+1)=24\)

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Problem 3

Match each equation to a story. (Two of the stories match the same equation.)

\(3(x+5)=17\)
\(3x+5=17\)
\(5(x+3)=17\)
\(5x+3=17\)

Jada’s teacher fills a travel bag with 5 copies of a textbook. The weight of the bag and books is 17 pounds. The empty travel bag weighs 3 pounds. How much does each book weigh?
A piece of scenery for the school play is in the shape of a 5-foot-long rectangle. The set designer decides to increase the length. There will be 3 identical rectangles with a total length of 17 feet. By how much did the designer increase the length of each rectangle?
Elena spends \$17 on gifts for her 5 cousins. Each cousin gets a book that costs \$3 and the same bookmark. How much does each bookmark cost?
Noah packs bags at the food pantry to deliver to families. He packs 5 bags that weigh a total of 17 pounds. Each bag contains 3 pounds of groceries and a packet of papers with health-related information. How much does each packet of papers weigh?
Andre has 3 times as many pencils as Noah and 5 pens. He has 17 pens and pencils all together. How many pencils does Noah have?

to access Practice Problem Solutions.

Problem 4

ForLesson 3: Reasoning about Equations with Tape Diagrams

The diagram can be represented by the equation \(25=2+6x\). Explain where you can see the 6 in the diagram.

Tape diagram, 1 part labeled 2, 6 parts labeled x, total 25.

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Problem 5

ForLesson 16: Writing Equations for Lines

Select all the pairs of points so that the line between those points has slope \(\frac 2 3\).

\((0,0)\) and \((2,3)\)
\((0,0)\) and \((3,2)\)
\((1,5)\) and \((4,7)\)
\((\text-2,\text-2)\) and \((4,2)\)
\((20,30)\) and \((\text-20,\text-30)\)

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Problem 6

from an earlier course

The markings on the number line are evenly spaced. Label the other markings on the number line.

A number line.

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