A homeowner wants to build a garden with concrete tiles around the outside. He has room for the garden to vary in length but not width. He’s not sure what size he wants the garden to be. Here are sketches of gardens that are 1, 2, and 3 meters long. The homeowner needs to know how many concrete tiles will be needed for different possible garden lengths.
Complete the table to show how many tiles will be needed if the garden is 1, 2, 3, 4, or 5 meters long.
garden length
number of tiles
1
2
3
4
5
Describe the way the pattern is growing.
Are You Ready for More?
2.2
Activity
Representing Relationships
Standards Alignment
Building On
Addressing
8.F.4
Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
The equation describes the relationship between temperatures in degrees Celsius and degrees Fahrenheit.
Describe the relationship in words.
Complete the table showing corresponding temperatures in degrees Celsius and degrees Fahrenheit.
Make a graph that represents the relationship.
temperature ()
temperature ()
23
-5
41
5
50
104
40
122
212
100
Which representation would you use to answer each question (the equation, table, or graph)? Be prepared to explain your reasoning.
What is the temperature of an oven in degrees Fahrenheit when it is set to ?
You are in Canada, and the forecast is . Will it be cold, warm, or hot outside?
The outside temperature is . How would this temperature be reported in degrees Celsius?
2.3
Activity
Card Sort: Whose Representation Is That?
Standards Alignment
Building On
Addressing
6.EE.9
Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.
Your teacher will give you a set of cards. Each card has either a verbal description, a table, or a graph. Find the three cards that represent the same situation. If one of the three representations for a situation is missing, use the blank cards to create that representation.
Glossary
None
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Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.
For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.