8th Grade Task: Speed Limit
8th Grade Task: Speed Limit
- Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships...
- Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive...
- Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal...
- Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For...
- Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a...
- Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or...
- Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe...
- Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For...
- GLE 0806.3.4
- Translate among verbal, tabular, graphical and algebraic representations of linear functions.
- GLE 0806.5.2
- Select, create, and use appropriate graphical representations of data (including scatterplots with lines of best fit) to make and test conjectures.
- SPI 0806.1.3
- Calculates rates involving cost per unit to determine the best buy.
- SPI 0806.3.4
- Translate between various representations of a linear function.
- SPI 0806.3.7
- Identify, compare and contrast functions as linear or nonlinear.
- SPI 0806.5.3
- Generalize the relationship between two sets of data using scatterplots and lines of best fit.
- Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in...
- Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; know and derive...
- Know and interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.
- Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a...
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Essential and guiding questions:
- Is it necessary to use the same units of measure in comparing the speeds Kana traveled on her way home? Why or why not?
- How did you determine if the speed was 100 mph or over?
- What is the relationship between the speed at which Kana traveled and the slopes of the graphs?
Blooms taxonomy level:
If students can’t get started….
- You might ask them to think about a simpler problem such as how can you compare the value of 20 cents to 1 dollar and 75 cents to 100 pennies?
- Would one penny be the same as 1 dollar? How could you use a fraction to describe the differences in the use of the “ones” in this comparison?
In an advancing question….
- How could the fractional value help to find the slope of the equation when modeling the different speeds Kana may be driving?
If students finish early….
- Ask the students to graph hours per mile. Then have the students compare and contrast the two graphs.