Connections to the Mathematical Practices Make sense of problems and persevere in solving them Students make sense of ratio and unit rates in real-world contexts. They 1 persevere by selecting and using appropriate representations for the given contexts. Reason abstractly and quantitatively Students will reason about the value of the rational number in relation the 2 models that are created to represent them. Construct viable arguments and critique the reasoning of others Students use arguments to justify their reasoning when creating and solving 3 proportions used in real-world contexts. Model with mathematics Students create models using tape diagrams, double number lines, manipulatives, tables and graphs to represent real-world and mathematical 4 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 Use appropriate tools strategically Students use visual representations such as the coordinate plane to show the 5 constant of proportionality. Attend to precision Students attend to the ratio and rate language studied in grade 6 to represent 6 and solve problems involving rates and ratios. Look for and make use of structure Students look for patterns that exist in ratio tables in order to make connections 7 between the constant of proportionality in a table with the slope of a graph. Look for and express regularity in repeated reasoning Students formally begin to make connections between covariance, rates, and 8 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 =
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 =
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