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Common Core for Grade 8

Common Core for Mathematics

More Math Lessons for Grade 8

Videos, examples, solutions, and lessons to help Grade 8 students learn how to describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

Common Core: 8.F.5

### Suggested Learning Targets

**[8.F.5-1.0] Interpreting Functions - Common Core Standard**

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear).

Example:

The graph below represents how far Jackie has climbed up a mountain in the last few hours. During which part was she climbing the flattest part of the mountain?

**Interpreting and Sketching Graphs (Part 1)**

We analyze and describe simple time/distance graphs and learn how to draw simple graphs from a description.

Example:

1. A Scuba Diver's Dive

a) How many minutes did the dive last?

b) At what time did the diver stop her descent?

c) What was the greatest depth the diver reached? For how many minutes sis she stay at that depth?

2. Each point on the graph represents a bag of popping corn. Explain the answers to the questions below.

a) Which bag is the most expensive? What does it cost?

b) Which bag has the least mass? What is this mass?

c) What bags have the same mass? What is this mass?

d) Which bags cost the same? What is this cost?

e) Which of bags C or D has the better value for the money?

3. Each point on this graph represents a person. Explain your answer to the question below.

a) Which person is the oldest? What is his or her age?

b) Which two people have the same height? What is this height?

c) Which two people have the same age? What is this age?

d) Which person B or C is taller for his or her age?

**Interpreting and Sketching Graphs (Part 2)**

Examples:

1. Describe the journey for each segment of the graph.

2. This graph represents a day trip from Athabasca to Kikino in Alberta, a distance of approximately 140 km. Describe the journey for each segment of the graph.

3. Samuel went on a bicycle ride. He accelerated until he reached a speed of 20 km/h, then he cycled for 30 min at approximately 20 km/h. Samuel arrived at the bottom of a hill, and his speed decreased to approximately 5 km/h for 10 min as he cycled up the hill. He stopped at the top of the hill for 10 min.

Sketch a graph of speed as a function of time. Label each section of the graph, and explain what it represents.

**Interpreting Functions - Common Core Standard**

Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

Example:

Your family is driving from Los Angeles to San Francisco at 60 miles per hour. Draw a graph showing how far you are from Los Angeles over time. In the last hour of the ride, your family sped up to 80 miles per hour. Would the slope of the graph be higher or lower during the last hour?

**Describing Function Graphs (8.F.5)**

Describe the following graphs as increasing or decreasing, linear or non-linear.

**CCSS 8.F.5 - video 1 - Describing Functional Relationships**

Examples:

1. Look at the graph and answer the following:

a) Identify the interval(s) over which the function is increasing.

b) Identify the interval(s) over which the function is decreasing.

c) Identify the interval(s) over which the function is constant.

d) Identify the interval(s) over which the function is linear.

e) Identify the interval(s) over which the function is nonlinear.

2. Taylor walks to and from school. During science, her class walks to a nearby park to collect insects. Then they return to the school for the rest of the school day. The graph shows the relationship between time (x) and her distance (y) from home. Describe the relationship between time and distance as shown in the graph.

**How to describe the relationship between two quantities by analyzing the graph?**

Example:

Using the graph to the right, answer the following questions:

a) In which section(s) of the graph has John stopped? Circle all that apply.

b) In which section is John walking at the slowest rate?

**Interpret the y-intercept and Slope of a Linear Model**

This video provides an example of how to interpret the real life meaning of the y-intercept and slope of a linear model.**Given Linear Function, Find the Rate of Change and Initial Value**

This video explains how to find the rate of change and initial value from the equation of a given linear function. The results mean of each is explained as part of an application problem.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

Common Core for Grade 8

Common Core for Mathematics

More Math Lessons for Grade 8

Videos, examples, solutions, and lessons to help Grade 8 students learn how to describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

Common Core: 8.F.5

- I can sketch a graph given a verbal description of its qualitative features.
- I can interpret the relationship between x and y values by analyzing a graph.
- I can analyze a graph and describe the functional relationship between two quantities using the qualities of the graph.

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear).

Example:

The graph below represents how far Jackie has climbed up a mountain in the last few hours. During which part was she climbing the flattest part of the mountain?

We analyze and describe simple time/distance graphs and learn how to draw simple graphs from a description.

Example:

1. A Scuba Diver's Dive

a) How many minutes did the dive last?

b) At what time did the diver stop her descent?

c) What was the greatest depth the diver reached? For how many minutes sis she stay at that depth?

2. Each point on the graph represents a bag of popping corn. Explain the answers to the questions below.

a) Which bag is the most expensive? What does it cost?

b) Which bag has the least mass? What is this mass?

c) What bags have the same mass? What is this mass?

d) Which bags cost the same? What is this cost?

e) Which of bags C or D has the better value for the money?

3. Each point on this graph represents a person. Explain your answer to the question below.

a) Which person is the oldest? What is his or her age?

b) Which two people have the same height? What is this height?

c) Which two people have the same age? What is this age?

d) Which person B or C is taller for his or her age?

Examples:

1. Describe the journey for each segment of the graph.

2. This graph represents a day trip from Athabasca to Kikino in Alberta, a distance of approximately 140 km. Describe the journey for each segment of the graph.

3. Samuel went on a bicycle ride. He accelerated until he reached a speed of 20 km/h, then he cycled for 30 min at approximately 20 km/h. Samuel arrived at the bottom of a hill, and his speed decreased to approximately 5 km/h for 10 min as he cycled up the hill. He stopped at the top of the hill for 10 min.

Sketch a graph of speed as a function of time. Label each section of the graph, and explain what it represents.

Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

Example:

Your family is driving from Los Angeles to San Francisco at 60 miles per hour. Draw a graph showing how far you are from Los Angeles over time. In the last hour of the ride, your family sped up to 80 miles per hour. Would the slope of the graph be higher or lower during the last hour?

Describe the following graphs as increasing or decreasing, linear or non-linear.

Examples:

1. Look at the graph and answer the following:

a) Identify the interval(s) over which the function is increasing.

b) Identify the interval(s) over which the function is decreasing.

c) Identify the interval(s) over which the function is constant.

d) Identify the interval(s) over which the function is linear.

e) Identify the interval(s) over which the function is nonlinear.

2. Taylor walks to and from school. During science, her class walks to a nearby park to collect insects. Then they return to the school for the rest of the school day. The graph shows the relationship between time (x) and her distance (y) from home. Describe the relationship between time and distance as shown in the graph.

Example:

Using the graph to the right, answer the following questions:

a) In which section(s) of the graph has John stopped? Circle all that apply.

b) In which section is John walking at the slowest rate?

This video provides an example of how to interpret the real life meaning of the y-intercept and slope of a linear model.

This video explains how to find the rate of change and initial value from the equation of a given linear function. The results mean of each is explained as part of an application problem.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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