Fun, Fun Function Tables
Students will be able to generate arithmetic patterns within the context of a function table and determine rules based on the patterns therein.
- Place a stack of books at the front of the room (about 12 books). Count the books aloud for student reference.
- Draw a t-chart on the board and label the left column ‘stacked books.’ Write 12 in the column to denote the total number of books.
- Invite a student to come to the front of the room and tell them to take one book from the pile. Then ask the class, "How many books are there left in the pile?" The answer is 11.
- Label the right column of the t-chart ‘what’s left.’ Point out that after the student came up and took a book, there were only 11 books left in the pile (write 11 in the right column).
- Invite a second student to come to the front of the room. Point out that there are now only 11 books stacked (write 11 in the left column), then tell them to take one book. Ask the class, "How many books are left now?" The answer is 10. Add to the t-chart.
- Repeat until there are four students holding one book each and only eight books left in the pile.
- Ask, "How many books would there be if we had five students who each took a book? How about 10 students?" Ask students to explain how they know (i.e. if every student who came up took one book, we can subtract one from the remaining books each time a new student comes up).
- Explain to the class that this is an example of a pattern. Then, define the pattern’s rule. (i.e. in this pattern, we subtracted one each time a new student came up. We call that the rule.) Write ‘minus one’ or ‘subtract one’ on the board.
- Tell students that today we are going to create number patterns and rules for the patterns.
Explicit Instruction/Teacher modeling(12 minutes)
- Draw a picture of a car on the board and ask students how many tires a car has. Then, write ‘4’ on the car.
- Provide context for the car problem (i.e. Darla owns a tire shop and she is trying to figure out how many tires she will sell if each customer buys a full set).
- Draw three more cars and write ‘4’ on each. Then explain to students that for each car that comes to Darla’s shop, she will sell four tires.
- Create a t-chart with the headings ‘cars’ and ‘tires.’ Complete the first two rows of the t-chart (1,4 and 2,8). Then have students help complete the next two rows (3,12 and 4,16).
- Explain that a t-chart that shows a pattern is called a function table. Function tables show patterns that follow a rule.
- Point out the pattern and rule in the ‘cars’ function table. (i.e. This pattern follows the rule ‘times four’ because for each car there are four tires. So, when Darla replaces the tires on five cars, she will sell 20 tires altogether because 5 x 4 is 20.) Add (5,20) to the table. Then, write ‘times four’ on the board.
- Write 10 in the ‘cars’ column and ask, :How many tires would Darla sell if there were 10 cars?" The answer is 40. Write the answer in the ‘tires’ column.
Guided Practice(10 minutes)
- Draw a function table with a simple pattern (i.e. [1,4] [2,5] [3,6] [4, 7] [5,8]).
- Ask students to come up with a rule for the table. Have students discuss with an elbow partner and then come up with a rule as a class (add three).
- Hand out the Funky Function Tables worksheet. Go over the example problem with students.
- Guide students through the first exercise on the worksheet. Then have students complete the remainder of the worksheet with a partner or small group.
- Circulate and check in with groups to offer support and guidance as needed.
Independent working time(15 minutes)
- With your students, brainstorm several scenarios in which a pattern might occur (i.e. scoops of ice cream in a sundae, a spider’s legs, ounces left in a water bottle over a period of time). Write the generated scenarios on the board for student reference.
- Hand out piece of white paper to each student and have students come up with their own pattern using the scenario of their choice. Then, instruct them to make a function table showing their pattern with at least six rows.
- Hand out one sticky note per student and instruct them to write their pattern on the sticky note (students should not write their pattern on the paper with their function table).
- Circulate and offer support as needed. Check for and help correct mistakes in student work.
- Provide partially completed function tables for students to complete.
- Provide a specific rule for students before asking them to create a function table (i.e. add two or times five).
- Provide scaffolded practice problems, like the First Function Tables worksheet, in place of the guided practice worksheet.
- Show students more complex, two-step patterns (i.e. times two, plus one) and encourage students to come up with a complex pattern of their own.
- Have students apply the skills learned to solve word problems (see the Function Tables & Word Problems worksheet).
- Instruct students to leave the function tables they created displayed on their desk.
- Collect students’ sticky notes. Mix them up and randomly hand out the sticky notes with pattern rules, ensuring that students do not get their own sticky note.
- Instruct students to walk around the classroom and find the function table that matches the rule they have on the sticky note they were given. They should then stick their note to the function table. (Note: some students may generate the same rule. For the purpose of this activity, each rule should be matched with a coordinating function table, but does not need to originate back to same author).
- Observe student responses for understanding.
Review and closing(5 minutes)
- Ask and discuss: How might a function table be useful in the real world? How can a function table help us continue a pattern? What was the easiest way to figure out a rule when looking at a given pattern?