# Lesson 15

Off the Line

• Let’s study solutions and non-solutions.

### 15.1: Estimation: Coin Weight

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.

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?

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?