Functions: Grade 8
Hook 1 8.F.A.1
Prompt 1: Split the items into two groups and write a definition for each group.
This hook aims to introduce the idea of a function to students. Putting the words "Number of" in front of each output makes the connection much more apparent, perhaps, even too easy; which is why I leave it off, let the kids bounce some ideas around and then suggest they think of the "number of" each output. By using non-mathematical, real-world examples of functions, the hook allows students to think critically about functions before they are given the formal definition. It's also a good reference point to circle back to when kids are struggling to remember the one input-one output nature of functions.
Video: Functions of Love? (3:12)
Hook 2 8.F.A.1
Prompt: What is my function?
This hook is a popular game to play with students being introduced to functions. Students are challenged to guess the function that creates each input/ouput table. It's a great way to have students practice, or learn, to write equations to represent function tables. The difficulty level increases with each example and should be customized to the level of your class. Be aware of how confusing function notation can be for students and take some time to discuss it. The notation is not a part of the 8th grade standards yet it's often used by textbooks. I've found the diagram of the "function machine" used in the hook to be a useful reminder of the notation for students as well as the labels "input" and "output" in tables.
Hook 1 8.F.A.2
Prompt: Which representation, table, graph or equation, would be the most useful to determine the fastest bird?
This hook differs from most activities connected to this standard by not offering any of the representations students are asked to consider. There is not a correct answer to the prompt as an argument can be made for the ease of using each representation. Graphs provide a clear visual, tables would indicate the unit rate as would the equation in the form of the coefficient of the independent variable. Whether or not your students can make these arguments will tell you a lot about the depth of their knowledge of each representation.
Video: Data of the World
Hook 2 8.F.A.2
Prompt: Rank these birds in terms of speed.
Students should be familiar with all three representations of linear functions and comparing functions in these different representations will spark important mathematical discussions that can provide valuable formative assessment. It's worthwhile to take apart each representation piece by piece to ensure students have a solid understanding of what each value, variable, coordinate and point represent. There's a lot of places where students can go astray so look for common errors and conduct a class discussion that addresses these concerns while offering students opportunities to articulate their understanding of linear functions. Offering a word bank with words like constant rate, variables, coefficient, slope and coordinates is one way to encourage and highlight the importance of vocabulary use in their conversations.
Hook 1 8.F.A.3
Prompt: Match each species in column A to its growth rate equation in Column B. Then create an equation for the missing match.
For this standard, we want students to discuss constant rate and the y-intercept even if they are not yet familiar with the this vocabulary. By matching the first three equations, students should have a strong inkling of the slope-intercept form even if they have not yet articulated this concept in class. By asking students if they expect either measure to change in the animals lifetime (or the nature of the relationship itself), teachers can deepen the discussion and understanding of slope-intercept form and its components.
Hook 2 8.F.A.3
Prompt : Which table's rule does not fit with the others?
Students have the opportunity to see that each linear relationship can be represented by the form y = mx+b while also working with an exponential relationship that does not fit into the pattern. For more advanced groups, tables without the "0" x coordinate and/or having irregular x intervals could make identifying the non-linear relationship more challenging.
Hook 1 8.F.B.4
Prompt: Match the linear relationship in column A with the correct equation in column B.
The standard asks students to write functions, by identifying the rate of change and y-intercept, from tables, graphs, two given points and a description of the function. Watching where your students begin looking for rates of change and y-intercepts and listening to how they describe these concepts in context of each representation will be powerful formative assessment for your lesson.
Video: Fibonacci's Sequence in Nature (2:28)
Hook 1 8.F.B.5
Prompt: Use the order of activities and times in the table to draw a graph of the relationship between time and heartbeat.
This prompt is an opportunity to get kids out of their seats and moving. Have students follow the prompts in small units of time and monitor their pulse for changes in their heartbeat. Discussions of how heartbeat levels rise and fall for each exercise and the nature of those changes (linear vs. non-linear) will allow students to think deeply about the qualitative features of graphs.
Video: Data in sports (1:20)