Lesson 15

Off the Line

  • Let’s study solutions and non-solutions.

15.1: Estimation: Coin Weight

Photograph, 9 nickels and 7 picture hangers on a scale, weight 52 grams.

How much does a nickel weigh?

  1. Record an estimate that is:
     too low  about right   too high 
  2. Explain your reasoning.

 

15.2: Row Game: Equations

Work independently on your column. Partner A completes the questions in column A only and partner B completes the questions in column B only. Your answers in each row should match. Work on one row at a time and check if your answer matches your partner’s before moving on. If you don’t get the same answer, work together to find any mistakes.

Solve each equation.

row column A column B

1

\(3x-1=5\)

\(6x-2=10\)

2

\(4(x+1) = 3x - 12\)

 \(4x+4 = 3(x-4)\)

3

\(14x+10=4x+6\)

 \(7x+5 = 2x+3\)

4

 \(6x+3=33\) \(4x+2=22\)

5

 \(4x + 5y = 2 - 4x + 5y\) \(4x + 9y = 2 + 9y - 4x\)

6

 \(2x + 6y = 10\) \(5x + 15y = 25\)

 

15.3: What Were They Thinking?

Read each student’s reasoning and answer the questions.

Picture of 4 nickels and 7dollar coins on a scale, weight 76 point 7 grams.
Picture of 4 nickels and 5 dollar coins on a scale, weight 60 point 5 grams.

Jada says, “I know 4 nickels and 7 dollar coins weigh 76.7 grams. I know 4 nickels and 5 dollar coins weigh 60.5 grams. Here’s what else I can figure out based on that:

  • 2 dollar coins weigh 16.2 grams.
  • 1 dollar coin weighs 8.1 grams.
  • 5 dollar coins weigh 40.5 grams.
  • 4 nickels weigh 20 grams.
  • 1 nickel weighs 5 grams.”
  1. How did Jada figure out that 2 dollar coins weigh 16.2 grams?
  2. Why might Jada have done that step first?
  3. After Jada figured out how much 1 dollar coin weighed, why did she calculate how much 5 dollar coins weighed?
  4. Once Jada knew how much 5 dollar coins weighed, how did she figure out how much 4 nickels weighed?
Picture of 9 plastic building blocks and 3 number cubes on a scale, weight 39 grams.
Picture of 7 plastic building blocks and 6 number cubes on a scale, weight 50 point 5 grams.

Priya says, “I know 9 plastic bricks and 3 number cubes weigh 39 grams, and 7 plastic bricks and 6 number cubes weigh 50.5 grams. Here’s what I can figure out based on that:

  • The weight of 18 plastic bricks and 6 number cubes is 78 grams.
  • The weight of 11 plastic brick is 27.5 grams.
  • The weight of 1 plastic brick is 2.5 grams.
  • The weight of 9 plastic bricks is 22.5 grams.
  • The weight of 3 number cubes is 16.5 grams.
  • The weight of 1 number cube is 5.5 grams.”
  1. Why is Priya’s second step only about plastic bricks, not number cubes?
  2. How does it help Priya to have a statement that’s just about plastic bricks, and not number cubes?
  3. Why might Priya have started by finding the weight of 18 plastic bricks and 6 number cubes?
  4. After Priya figured out how much 1 plastic brick weighed, why did she calculate how much 9 plastic bricks weighed?

Summary