Fishtank Learning

5th Grade Math
Unit 7: Patterns and the Coordinate Plane
Lesson 11

Objective

Represent real-world problems by graphing information represented on a table in the coordinate plane and interpret coordinate values of points in the context of a situation.

Criteria for Success

Graph points represented in a table on a coordinate plane.
Contextualize and decontextualize a coordinate pair based on the situation, e.g., the point (0, 4) in Anchor Task #1 represents how much a typical male greyhound weighs (4 pounds) when he’s born (0 months) (MP.2).
Solve real-world problems involving information represented on a coordinate plane, including interpreting relationships between coordinate values of points, e.g., a typical male greyhound in Anchor Task #1 grows 26 pounds in its first 4 months of life (MP.4) (optional).
Understand the steepness of a line graph is related to the rate of it, e.g., how quickly or slowly change is happening (optional).
Make conjectures about information that aren’t explicitly represented in the graph or table itself (optional).
Understand the limitations of conjectures or conclusions drawn from information represented in a line graph (optional).
See the advantages of representing a situation on a graph, e.g., it helps to see the magnitude of the numbers in relation to one another (optional).

Anchor Tasks - Problem 1

a. The data table below shows the weight of a typical male greyhound, a breed of dog, during the first 28 months of his life. Graph the corresponding points, then connect the points in the order they are given to form a line graph.

Age (in months)	Weight (in pounds)
0	4
4	30
8	55
12	66
16	69
20	72
24	72
28	72

b. What do you notice? What do you wonder?

Guiding Questions

How did you decide what scale to use for the x-axis? The y-axis?
How can you label the x-axis? The y-axis? What title can you give it to convey what is represented on the coordinate grid?
What do you notice about the points you plotted? What do you wonder?
What can we learn about the typical male greyhound’s weight by looking at the graph, especially compared with looking at the same information in the table?

Notes

An example of the coordinate grid displaying the greyhound data is shown below:

The last question is also included in Anchor Task #3. You could ask it in both places, or strategically ask it once when you think students are ready to discuss the advantages of a graph over a table as a way to display the same information. Students will also see the limitations of conjectures or conclusions drawn from data represented in a line graph (e.g., one cannot use given data on male greyhounds’ weight to draw conclusions about female greyhounds’ weight).

Anchor Tasks - Problem 2

Using the information about a typical male greyhound’s weight from Anchor Task #1, answer the following questions.

a. How much does a typical male greyhound weigh when he is born?

b. What does the coordinate pair (12, 66) mean in the context of this graph?

c. How much weight does the typical male greyhound gain in the first 4 months of his life? How do you know? What about between 4 months and 8 months? How do you know?

d. How long does it take the typical male greyhound to grow from 55 to 72 pounds?

e. Challenge: When does the typical male greyhound gain weight the fastest? How do you know? What about the slowest?

Guiding Questions

What coordinate pair can you write to correspond to the information discussed in Part (a)?
How can you determine how much weight is gained in Part (c)? If I think a typical greyhound gains 30 pounds in the first 4 months of life, what mistake have I made?
Which questions are more difficult to answer using the table? The graph? Which questions are easiest to answer using the table? The graph? In particular, how does the graph help you answer Part (e) more easily than the table?

Notes

Part (e) is optional, since students do not need to understand the idea of slope, even informally, until Grade 6. Parts (c) and (d) can be cut, as well, depending on timing, though students will see some questions like this on the Problem Set and Extra Practice Problems. They are included here more as an exploration than an expectation of the grade level.

Anchor Tasks - Problem 3

Using the information about the typical male greyhound’s weight from Anchor Task #1, answer the following questions.

a. How heavy do you think a typical male greyhound gets? How do you know from the graph?

b. At what age do male greyhounds reach their full weight? Why?

c. How heavy do you think a typical female greyhound gets? Why?

Guiding Questions

Do you think all male greyhounds weigh 72 pounds when they are fully grown? Why or why not?
Do you think the typical male dog of any breed is fully grown at 20 months? Why or why not?
What conclusions about female greyhounds can you draw from this graph, if any? Why?
What can we learn about a typical male greyhound’s weight by looking at the graph, especially compared with looking at the same information in the table?

Notes

This Anchor Task is optional. It asks students to interpret the meaning of points displayed on a coordinate grid, including building a basic understanding of rate of change, which connects to work in the RP and EE domains in the middle grades.

Problem Set

View Problem Set

Discussion of Problem Set

How did you find the answer to #1(a) in the graph?
What is the meaning of the coordinate point (4, 5) in #1(c)?
How did you determine at what time the hot air balloon rose to 400 yards in #2(b)? How did you determine what height the balloon was at 5:50 in #2(c)?
How did you determine on what date Howard had $2,000 in his checking account in #3(b)?
When did Howard likely get paid in #3(f)? Why do you think that? When did Howard likely buy a television? How do you know?
How did you determine how much rain had fallen by 5:00 p.m. in #4(b)?
How did you find the answer for #4(f)? Did you use subtraction or just look for the steepest line?
How did you set up your work when solving for #4(h)?
Would the graph of a different rainy day have the same shape as the graph in #4? How might it be the same? Different?

Target Task

January 31, 2019 was the coldest day of the year in Boston, MA. The hourly temperature for the first 12 hours of that day is shown in the graph below.

a. What was the temperature 3 hours after midnight?

b. When was the temperature the lowest?

c. Explain what the point (9, 6) represents in this situation.

Word Problem

The following graph shows some data for the age and weight of children who went to Dr. Shastri’s office today.

Kamiyah is 3 years old. Label the point on the coordinate grid above that represents Kamiyah with the letter K.
Kamiyah is half as old as her sister, Mercy. She also weighs 15 pounds less than Mercy. Plot a point on the coordinate grid above to represent Mercy’s age and weight, and label it with the letter M.

Fishtank Learning

5th Grade MathUnit 7: Patterns and the Coordinate PlaneLesson 11

Objective

Anchor Tasks - Problem 1

Anchor Tasks - Problem 2

Anchor Tasks - Problem 3

Problem Set

Target Task

Word Problem

5th Grade Math
Unit 7: Patterns and the Coordinate Plane
Lesson 11