Lesson 04: Reasoning About Equations and Tape Diagrams (Part 1) | Unit 6: Expressions, Equations, and Inequalities

Multiple Choice

Here are three stories: * A family buys 6 tickets to a show. They also pay a $$3 parking fee. They spend$$ 27 to see the show. * Diego has 27 ounces of juice. He pours equal amounts for each of his 3 friends and has 6 ounces left for himself. * Jada works for 6 hours preparing for the art fair. She spends 3 hours on a sculpture and then paints 27 picture frames. She spends the same amount of time painting each frame. Here are three equations: * $$3x+6=27$$ * $$6x+3=27$$ * $$27x+3=6$$ Which equation represents each story? What does $$x$$ represent in each equation?

• 27x + 6 = 3
• 1: 3x + 6 = 27 (x = cost of each ticket); 2: 6x + 3 = 27 (x = amount of juice per friend); 3: 27x + 3 = 6 (x = time spent on each frame).
• 6x + 27 = 3
• 3x + 27 = 6

Open Ended

Here are three equations: * $$3x+6=27$$ * $$6x+3=27$$ * $$27x+3=6$$ Find the solution to each equation. Explain or show your reasoning.

Multiple Choice

Here are three equations: * $$3x+6=27$$ * $$6x+3=27$$ * $$27x+3=6$$ What does each solution tell you about its situation?

• x = 5 for the first equation
• x = 10 for the second equation
• x = 2 for the third equation
• x = 7 for the first equation, x = 4 for the second equation, x = 1/9 for the third equation.

Open Ended

Here is a diagram and its corresponding equation. Find the solution to the equation and explain your reasoning. Equation: $$6x+11=21$$ Image URL: https://media.quizizz.com/_mdserver/main/media/resource/gs/quizizz-media/quizzes/b6722425-6726-42ba-aa5c-1d34cc8d5119-v2

Multiple Select

Select **all** the stories that can be represented by the diagram.

• Andre studies 7 hours this week for end-of-year exams. He spends 1 hour on English and an equal number of hours each on math, science, and history.

• Lin spends $$3 on 7 markers and a$$ 1 pen.

• Diego spends $1 on 7 stickers and 3 marbles.

• Noah shares 7 grapes with 3 friends. He eats 1 and gives each friend the same number of grapes.

• Elena spends $$7 on 3 notebooks and a$$ 1 pen.