Reasoning about Equations and Tape Diagrams (Part 2)
Grade 7
5.1
Warm-up
Solve each equation mentally.
5.2
Activity
5.3
Activity
Each situation in the previous activity is represented by one of the equations.
Match each situation to an equation.
Find the solution to each equation. Use your diagrams to help you reason.
What does each solution tell you about its situation?
Student Lesson Summary
Equations with parentheses can represent a variety of situations.
Lin volunteers at a hospital and is helping prepare 10 toy baskets for children who are patients. After Lin adds 2 items to each basket, the supervisor says 140 items have been equally placed in the baskets. Lin wants to know how many toys were in each basket before she added items.
A large store has the same number of workers on each of 2 teams to handle different shifts. The managers decide to add 10 workers to each team, bringing the total number of workers to 140. An executive at the company that runs this chain of stores wants to know how many employees were in each team before the increase.
Each basket in the first story has an unknown number of toys, , that is increased by 2. Then 10 groups of give a total of 140 toys. An equation representing this situation is . Since 10 times an amount is 140, that amount is 14, which is the total number of items in each basket. Before Lin added the 2 items there were or 12 toys in each basket.
The executive in the second story knows that the size of each team of employees has been increased by 10. There are now 2 teams of each. An equation representing this situation is . Since 2 times an amount is 140, that amount is 70, which is the new size of each team. The value of is or 60. There were 60 employees on each team before the increase.
None
Draw a tape diagram to represent each situation. For some of the situations, you need to decide what to represent with a variable.
Each of 5 gift bags contains pencils. Tyler adds 3 more pencils to each bag. Altogether, the gift bags contain 20 pencils.
Noah drew an equilateral triangle with sides of length 5 inches. He wants to increase the length of each side by inches so the triangle is still equilateral and has a perimeter of 20 inches.
An art class charges each student \$3 to attend plus a fee for supplies. Today, \$20 was collected for the 5 students attending the class.
Elena ran 20 miles this week, which was three times as far as Clare ran this week. Clare ran 5 more miles this week than she did last week.
Standards Alignment
Building On
Addressing
7.EE.4
Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.
Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?