Summary
In this lesson, students will be able to identify the family to which a function belongs using characteristics of graphs. This is a great lesson to use at the beginning of Algebra 2, before students begin to study any of the specific function families (absolute value, quadratic, radical, exponential, logarithmic) or transformations. Alternatively, this lesson can be used later in the year as an introduction to transformations.
Essential Question(s)
What is a family of functions? How can we identify the family a function belongs to?
Snapshot
Engage
Students decide which graph they believe is not like the others and justify their thinking.
Explore
Students sort cards into sets based on common characteristics they see in the graphs.
Explain
Students share how they grouped their cards and formalize the meaning of family of functions and parent functions.
Extend
Students sketch a graph for each given story and then identify which family of functions the graph belongs to.
Evaluate
Students demonstrate their understanding by creating Anchor Charts for different families of functions.
Materials
Lesson Slides (attached)
Not Like the Others signs (attached; one set; print one-sided)
Function Cards (attached; one set per group; print two-sided)
Card Sort Sets handout (attached; one per group; print one-sided)
Modeling the Story handout (attached; one per student; print two-sided)
Chart paper (seven sheets)
Pencils
Markers
Paper
Document camera (to display cards; alternative option provided)
Preparation
Before you begin, print the attached Function Cards (one set per small group of 2–3). Print these two-sided while selecting the “flip on long edge” setting, which is typically the default printer setting. This printer setup ensures that each function appears on the back of its corresponding graph. There are 35 unique cards across the 12-page document, resulting in 6 printed pages when printed two-sided.
Consider printing on cardstock, especially if you plan to reuse these cards. Once printed, cut out the cards. All of these cards are the same size for easy cutting.
Engage
15 Minute(s)
Introduce the lesson using the attached Lesson Slides. Display slide 3 to share the lesson’s essential questions, and then move to slide 4 to review the lesson’s learning objective. Review each of these with your class to the extent you feel necessary.
Display slide 5 and introduce the Not Like the Others strategy. Ask students to identify which graph does not match the others. Ask them to be ready to explain why. After a minute of wait time, direct students to move to the sign to indicate which graph is not like the others. Invite each group to discuss among themselves why they think this graph is not like the others. Allow 1–2 minutes for this discussion, then have each corner select a spokesperson to share their reasoning.
Explore
20 Minute(s)
Explain to students that they will be examining many different kinds of graphs in class. To be able to describe graphs efficiently, they will need to categorize graphs, just like shapes can be categorized by their dimensions, number of sides, or angle properties. Then show slide 6.
Have students get in small groups of 2–3 or assign groups. Give each group a set of the attached Function Cards, graph-side up. Introduce the Card Sort strategy and direct students to sort the cards into sets. Students can group cards however they wish, as long as they follow the rules (shown on the slide):
Each set must have more than one card in it.
All cards within a set must share a single characteristic. For example, they are all lines; they all contain the point (0, 3); etc.
No card may belong to more than one set.
As students near the end of their Card Sort activity, transition to slide 7 and give each group a copy of the attached Card Sort Sets handout.
Explain
45 Minute(s)
Taking turns, have each group bring one set of their sorted cards to the front. Have them place their cards under the document camera, graph-side up, and explain what all of their graphs in the set have in common. Ask students to confirm that these cards all have this common characteristic and that no other cards share the characteristic. Use the hidden slide 8 as a reminder to have students share their card sets. This slide also has the link for a digital option for displaying card sets (see details in the note below).
If the class agrees that the group has found a correct set, have the group flip their cards over to display the equations of the graphs on the back. Ask the class what the equations have in common and what conclusions they can form based on their observations. As a group is sharing, have those at their desks arrange their cards to follow along. Remind them that this is the reason they took notes on their Card Sort Sets handout.
Ask students to write down the conclusion they formed as an if-then conditional statement. Follow classroom norms for this, whether that is having students write in their math notebook or on a piece of notebook paper.
Record conclusions, using academic vocabulary, on the board or on chart paper. Once the conclusions have been written for the seven sets of cards, based on the seven families of functions, display slide 9. Ask groups to discuss what they think a family of functions is.
After several minutes, ask for volunteers to share their answers. Explain that the class should create one definition for a family of functions. Discuss with students what this definition should be, questioning them as necessary until a sufficiently precise definition is formed.
Show slide 10 and tell students that each family of functions has one parent function. Ask students to look at the equations (not the graphs) in each group and see if they can determine which equation is the parent function. Ask groups to think about how they would define parent function as they are looking for the parent function for each set. Give students several minutes to think about this.
Ask different groups to each share examples of parent functions (the cards they selected for each family of functions). Then ask for volunteers to share their definitions of what a parent function may be. Again, discuss the definition and question students until a sufficiently precise definition of parent function is created.
Display slide 11 and confirm with students that they have all identified the parent functions for each family of functions. Direct students to set aside those cards to use for the next activity. The rest of the cards can be put away.
Extend
15 Minute(s)
Show slide 12 and give each student a copy of the attached Modeling the Story handout. Here students are asked to sketch graphs based on the information provided in each story and then identify the family of functions each graph belongs to. Display slide 13 for students to use as a quick reference while they complete their handout. Alternatively, you could have students complete this handout at home.
Once students complete their handout, have them check their results with a partner.
Evaluate
15 Minute(s)
Divide the class into seven groups, one for each family of functions, and show slide 14. Introduce the Anchor Chart strategy and give each group chart paper and markers. Assign each group one of the following families of functions: quadratic, square root, cubic, cube root, exponential, logarithmic, and absolute value. Use the slide to communicate your expectations for the anchor charts.
Each anchor chart should include the following:
Function name
Equation of parent function
Sketch of parent graph with labeled key characteristics, such as intercepts and asymptotes
Resources
Eike, M., & Matchell, C. (n.d.) Amplify Classroom: Card Sort Sets [Interactive activity]. Amplify Classroom. https://classroom.amplify.com/activity/6a75edd076083fe50900e1d0
K20 Center. (n.d.). Anchor chart. Strategies. https://learn.k20center.ou.edu/strategy/58
K20 Center. (n.d.). Canva. Tech Tools. https://learn.k20center.ou.edu/tech-tool/612
K20 Center. (n.d.). Card sort. Strategies. https://learn.k20center.ou.edu/strategy/147
K20 Center. (n.d.). Google drawing. Tech Tools. https://learn.k20center.ou.edu/tech-tool/629
K20 Center. (n.d.). Not like the others. Strategies. https://learn.k20center.ou.edu/strategy/77