Absolute Value Functions (Part 1)
5 min
Teacher Prep
Required Preparation
Prepare a jar that contains about 30–50 small objects, or display a picture of such a jar, such as the one in the activity’s Launch.
Narrative
In this Warm-up, students compute absolute guessing errors using class data. The absolute errors they find here will be plotted in the next activity.
The absolute errors could be calculated and compiled in different ways, by hand or using technology, including a spreadsheet tool (MP5). For example, students could:
- Complete a table of values individually.
- Complete a table in groups of 2–4, with the calculations done by hand but divided among group members.
- Complete a table as a class, with each student calculating only one absolute guessing error and sharing it with the class.
Launch
Tell students to guess the number of objects in the collection. If no collection is available, display the image and ask students to guess the number of snap cubes in the jar.
Collect all of the guesses from the students, and display them for all to see.
Read the Task Statement with the class. Make sure students understand what they are asked to compute. Consider arranging students in groups of 2–4 so students can split up the calculations, if desired. Provide access to calculators and spreadsheet technology.
Give each student a copy of the blackline master to record their calculations, then reveal the actual number of items in the collection. If using the image given in this lesson, the actual number of snap cubes in the jar is 47.
Students should compute at least 12 absolute guessing errors, and more if time permits.
Student Task
Use the actual number of items to calculate the absolute guessing error of each guess, or how far the guess is from the actual number. For example, suppose the actual number of objects is 100.
- If a guess is 75, then the absolute guessing error is 25.
- If a guess is 110, then the absolute guessing error is 10.
Record the absolute guessing error of at least 12 guesses in Table A of the handout (or elsewhere, as directed by your teacher).
Sample Response
Sample response for 20 guesses, when the actual number of objects is 47:
| guess | absolute guessing error |
|---|---|
| 27 | 20 |
| 44 | 3 |
| 46 | 1 |
| 59 | 12 |
| 53 | 6 |
| 36 | 11 |
| 35 | 12 |
| guess | absolute guessing error |
|---|---|
| 65 | 18 |
| 50 | 3 |
| 62 | 15 |
| 58 | 11 |
| 28 | 19 |
| 38 | 9 |
| 30 | 17 |
| guess | absolute guessing error |
|---|---|
| 55 | 8 |
| 37 | 10 |
| 57 | 10 |
| 41 | 6 |
| 40 | 7 |
| 60 | 13 |
Activity Synthesis (Teacher Notes)
If desired, display a completed table for all to see, or simply invite students to share some observations about the absolute guessing errors they found. If no one mentioned that all the values are positive, ask them about it and solicit some ideas about why this is the case.
Also ask students if they could tell from the data how good the guesses were. (Were the guesses close? Were there a lot of overestimates or underestimates?)
Tell students that they will plot the data next.
Anticipated Misconceptions
Some students may record negative values for the absolute guessing errors of guesses that are lower than the actual number, not realizing that the term “absolute error” refers to “how far away” and, therefore, cannot be negative. Suggest that they revisit the examples in the Task Statement, and clarify the term as needed.
Standards
- F-IF.7.b·Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
- F-IF.7.b·Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
- F-IF.7.b·Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
- F-IF.7.b·Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
- F-IF.7.b·Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
- HSF-IF.C.7.b·Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
15 min
15 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Absolute Value Functions (Part 1)
5 min
Teacher Prep
Required Preparation
Prepare a jar that contains about 30–50 small objects, or display a picture of such a jar, such as the one in the activity’s Launch.
Narrative
In this Warm-up, students compute absolute guessing errors using class data. The absolute errors they find here will be plotted in the next activity.
The absolute errors could be calculated and compiled in different ways, by hand or using technology, including a spreadsheet tool (MP5). For example, students could:
- Complete a table of values individually.
- Complete a table in groups of 2–4, with the calculations done by hand but divided among group members.
- Complete a table as a class, with each student calculating only one absolute guessing error and sharing it with the class.
Launch
Tell students to guess the number of objects in the collection. If no collection is available, display the image and ask students to guess the number of snap cubes in the jar.
Collect all of the guesses from the students, and display them for all to see.
Read the Task Statement with the class. Make sure students understand what they are asked to compute. Consider arranging students in groups of 2–4 so students can split up the calculations, if desired. Provide access to calculators and spreadsheet technology.
Give each student a copy of the blackline master to record their calculations, then reveal the actual number of items in the collection. If using the image given in this lesson, the actual number of snap cubes in the jar is 47.
Students should compute at least 12 absolute guessing errors, and more if time permits.
Student Task
Use the actual number of items to calculate the absolute guessing error of each guess, or how far the guess is from the actual number. For example, suppose the actual number of objects is 100.
- If a guess is 75, then the absolute guessing error is 25.
- If a guess is 110, then the absolute guessing error is 10.
Record the absolute guessing error of at least 12 guesses in Table A of the handout (or elsewhere, as directed by your teacher).
Sample Response
Sample response for 20 guesses, when the actual number of objects is 47:
| guess | absolute guessing error |
|---|---|
| 27 | 20 |
| 44 | 3 |
| 46 | 1 |
| 59 | 12 |
| 53 | 6 |
| 36 | 11 |
| 35 | 12 |
| guess | absolute guessing error |
|---|---|
| 65 | 18 |
| 50 | 3 |
| 62 | 15 |
| 58 | 11 |
| 28 | 19 |
| 38 | 9 |
| 30 | 17 |
| guess | absolute guessing error |
|---|---|
| 55 | 8 |
| 37 | 10 |
| 57 | 10 |
| 41 | 6 |
| 40 | 7 |
| 60 | 13 |
Activity Synthesis (Teacher Notes)
If desired, display a completed table for all to see, or simply invite students to share some observations about the absolute guessing errors they found. If no one mentioned that all the values are positive, ask them about it and solicit some ideas about why this is the case.
Also ask students if they could tell from the data how good the guesses were. (Were the guesses close? Were there a lot of overestimates or underestimates?)
Tell students that they will plot the data next.
Anticipated Misconceptions
Some students may record negative values for the absolute guessing errors of guesses that are lower than the actual number, not realizing that the term “absolute error” refers to “how far away” and, therefore, cannot be negative. Suggest that they revisit the examples in the Task Statement, and clarify the term as needed.
Standards
- F-IF.7.b·Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
- F-IF.7.b·Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
- F-IF.7.b·Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
- F-IF.7.b·Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
- F-IF.7.b·Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
- HSF-IF.C.7.b·Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.