# Lesson 4

Interpret This, Interpret That

These materials, when encountered before Algebra 1, Unit 3, Lesson 4 support success in that lesson.

## 4.1: Math Talk: Units (5 minutes)

### Warm-up

The purpose of this Math Talk is to elicit strategies and understandings students have for mentally finding the unit rate. These understandings help students develop fluency.

### Launch

Display one problem at a time. Give students quiet think time for each problem and ask them to give a signal when they have an answer and a strategy. Keep all problems displayed throughout the talk. Tell students that if their answer is a decimal, round to the nearest whole number that is realistic for the context. Follow with a whole-class discussion.

### Student Facing

Mentally calculate each value.

5 granola bars cost $20. How much is 1 worth?

A car travels at a constant speed and goes 100 miles in 2.5 hours. How fast is the car travelling in miles per hour?

Tyler can do 50 sit-ups in 4 minutes. What is his average sit-ups per minute?

3 ounces of yeast flakes costs $4.29. What is the cost for 1 ounce?

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

Ask students to share their strategies for each problem. Record and display their responses for all to see. To involve more students in the conversation, consider asking:

- “Who can restate \(\underline{\hspace{.5in}}\)’s reasoning in a different way?”
- “Did anyone have the same strategy but would explain it differently?”
- “Did anyone solve the problem in a different way?”
- “Does anyone want to add on to \(\underline{\hspace{.5in}}\)’s strategy?”
- “Do you agree or disagree? Why?”

## 4.2: Absences and Scores (15 minutes)

### Activity

The goal of this activity is for students to practice interpreting points in a scatter plot. Students also practice using the trend from data in a scatter plot to estimate outcomes in the data.

### Launch

Allow students to work individually.

### Student Facing

Here are a table and scatter plot representing the number of students’ absences and their final exam scores.

student | number of absences | final exam score |
---|---|---|

A | 1 | 94 |

B | 5 | 71 |

C | 1 | 98 |

D | 5 | 70 |

E | 3 | 67 |

F | 2 | 94 |

G | 6 | 71 |

H | 4 | 89 |

I | 5 | 77 |

J | 0 | 90 |

K | 2 | 91 |

L | 11 | 60 |

student | number of absences | final exam score |
---|---|---|

M | 7 | 68 |

N | 8 | 65 |

O | 20 | 42 |

P | 10 | 63 |

Q | 11 | 63 |

R | 20 | 50 |

S | 15 | 67 |

T | 16 | 40 |

U | 4 | 86 |

V | 8 | 82 |

W |

- What are the coordinates of the point in the scatter plot that represents student \(G\)?
- What are the coordinates of the point in the scatter plot that represents student \(R\)?
- What is the final exam score of the student who has perfect attendance?
- What are the final exam scores of the students with the most absences?
- How many absences does the student with the highest score have?
- How many absences does the student with the lowest score have?
- If student \(W\) has 12 absences, what final exam score do you estimate the student will have? Plot this point on the scatter plot.

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

The goal of this discussion is for students to interpret data from a scatter plot and table. Discuss the ways students accomplish this. Here are sample questions for discussion:

- “How do you determine the coordinates for student \(R\) and student \(G\)” (I use the table to see what numbers are listed in the same row as each student. You can also find the point labeled as \(G\) or \(R\) on the scatter plot and estimate the coordinates by looking at the lines on the graph.)
- “When given one of the values for a student, how do you find the other value for the same student?” (When the problem gives me one value for a variable, I find it on the scatter plot or table. Then, I look to see the other value that is matched with the given value. In a table, it is the value next to the given value. In a scatter plot, it is the value on the opposite axis that meets the given value at a plotted point.)
- “How do you come up with the value for the question about student \(W\)?” (I look to see if there was a pattern. I notice that, in general, the more absences a student has the lower the final exam score is. Student \(W\) missed more days than any other student, so I would expect that student to do worse than anyone else on the final exam.)

## 4.3: Elevator Weights (20 minutes)

### Activity

The purpose of this activity is for students to understand that the slope and \(y\)-intercept of a linear model can be used to interpret a situation.

### Launch

Allow students to work individually or with a partner to complete the activity.

### Student Facing

Here is a linear model of the weight of an elevator and the number of people on the elevator.

- Find these values. Explain your reasoning.
- the weight of the elevator when 6 people are on it
- the number of people on the elevator when it weighs 1,400 kg
- the weight of the elevator when no people are on it
- the increase in elevator weight for each additional person according to the model

- Which of your answers corresponds to the slope of the line in the graph?
- Which of your answers corresponds to the \(y\)-intercept of the line in the graph?
- This model can be represented with the equation \(y = 1,\!200 + 50x\). An equation for a different model is written \(y = 70x + 1,\!000\). What are some things you can say about this new model?

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

The goal of this lesson is for students to interpret the slope and \(y\)-intercept of a line. Discuss how students are able to recognize and understand the meaning of slope and \(y\)-intercept** **from the given model in the situation. Here are sample questions to promote class discussion:

- “What does slope represent in any given model?” (How steep a line is or the rate of change in a given situation.)
- “How do you determine which quantity represents the slope?” (I thought about what is changing in the model, and that is how the weight of the elevator changes based on the number of people in it. So, I know the slope is the number that represents the increase in weight of the elevator for each person because it represents the rate of change.)
- “What does the \(y\)-intercept represent in any given model?” (In the graph, it represents where the line crosses the \(y \)-axis or the value of \(y\) when \(x\) is equal to 0.)
- “How do you determine which quantity represents the \(y\)-intercept?” (I use the graph to see the value of \(y\) when \(x\) is 0. I also know that the \(y\)-intercept represents the weight of the elevator when no one is on it, so the \(y\)-intercept should be the elevator’s weight by itself.)