Connections to the Mathematical Practices 1 Make sense of problems and persevere in solving them Students make sense of ratio and unit rates in real-world contexts. They persevere by selecting and using appropriate representations for the given contexts. 2 Reason abstractly and quantitatively Students will reason about the value of the rational number in relation the models that are created to represent them. 3 Construct viable arguments and critique the reasoning of others Students use arguments to justify their reasoning when creating and solving proportions used in real-world contexts. 4 Model with mathematics Students create models using tape diagrams, double number lines, manipulatives, tables and graphs to represent real-world and mathematical situations involving ratios and proportions. For example, students will examine the relationships between slopes of lines and ratio tables in the context of given situations 5 Use appropriate tools strategically Students use visual representations such as the coordinate plane to show the constant of proportionality. 6 Attend to precision Students attend to the ratio and rate language studied in grade 6 to represent and solve problems involving rates and ratios. 7 Look for and make use of structure Students look for patterns that exist in ratio tables in order to make connections between the constant of proportionality in a table with the slope of a graph. 8 Look for and express regularity in repeated reasoning Students formally begin to make connections between covariance, rates, and representations showing the relationships between quantities. Vocabulary Term Definition Constant of Constant value of the ratio of proportional quantities x and y. Written as y =
b. This got Travis wondering how he could remedy similar mistakes if he were to dump in a single cup of some of the other ingredients. Assume he wants to keep the ratios the same. many cups of sugar are needed if a single cup of blueberries is used in the mix? many cups of butter are needed if a single cup of sugar is used in the mix? many cups of blueberries are needed for each cup of sugar? Track Practice (7.RP.1) Part A. Angel and Jayden were at track practice. The track is 2/5 kilometers around. Angel ran 1 lap in 2 minutes. Jayden ran 3 laps in 5 minutes. How many minutes does it take Angel to run one kilometer? What about Jayden? How far does Angel run in one minute? What about Jayden? Who is running faster? Explain your reasoning. Part B. Molly runs 1/3 of a mile in 4 minutes. If Molly continues at the same speed, how long will it take her to run one mile? Draw and label a picture showing why your answer to part (a) makes sense. Coffee Cost (7.RP.2) Coffee costs $18.96 for 3 pounds. What is the cost for one pound of coffee? At this store, the price for a pound of coffee is the same no matter how many pounds you buy. Let x be the number of pounds of coffee and y be the total cost of x pounds. Draw a graph of the relationship between the number of pounds of coffee and the total cost. Where can you see the cost per pound of coffee in the graph? What is it? Art Class (7.RP.2) The students in Ms. Baca’s art class were mixing yellow and blue paint. She told them that two mixtures will be the same shade of green if the blue and yellow paint are in the same ratio. The table below shows the different mixtures of paint that the students made.