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Step 1: Objective StatementStandard(s) for the grade level(s) before, same content areaStandard(s) for your grade level and content areaStandard(s) for the grade level(s) after, same content areaRatios and Proportional Relationships — 6.RP (M)Understand ratio concepts and use ratio reasoning to solve problems.Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” (6.RP.1)Understand the concept of a unit rate a/b associated with a ratio a:b with b 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” (6.RP.2)Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. (6.RP.3)Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. (6.RP.3a)Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? (6.RP.3b)Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. (6.RP.3c)Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. (6.RP.3d)Ratios and Proportional Relationships — 7.RP (M)Analyze proportional relationships and use them to solve real-world and mathematical pute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour. (7.RP.1)Recognize and represent proportional relationships between quantities. (7.RP.2)Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. (7.RP.2a)Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. (7.RP.2b)Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. (7.RP.2c)Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. (7.RP.2d)Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. (7.RP.3)Mathematical Practices 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique others’ reasoning. Expressions and Equations — 8.EE (M)Understand the connections between proportional relationships, lines, and linear equations.Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. (8.EE.5)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 the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. (8.EE.6)Objective Statement: All students will be able to analyze, use and represent proportional relationships to solve real world and mathematical problems. All students will be able to construct viable arguments and critique the reasoning of others verbally and in writing for problems that involve proportional relationships. Step 2: Performance CriteriaStudents will analyze, use and represent with equations proportional relationships to solve real-world and mathematical problems, including multi-step ratio/percent problems.Students will compute unit rates of quantities associated with ratios of fractions and explain the meaning in the context of the problem.Students will determine whether two quantities are in a proportional relationship and identify the constant of proportionality (unit rate) from tables, equations, diagrams, verbal descriptions and graphs.Students will interpret a point (x,y) on the graph of a proportional relationship in terms of the situation, with special attention to the points (0,0) and (1,r) where r is the unit rate.Students verbally and in writing justify their solutions and communicate their reasoning using a logical and complete response with correct use of grade-level vocabulary, symbols, and labels.Learning Progression RubricLimited CommandModerate CommandStrong Command(Performance Criteria)Distinguished CommandStudents will use proportional relationships to solve real-world and mathematical problems, including simple ratio/percent problems.Students will analyze and use proportional relationships to solve real-world and mathematical problems, including simple ratio/percent problems.Students will analyze, use and represent with equations proportional relationships to solve real-world and mathematical problems, including multi-step ratio/percent problems.Students will analyze and compare two related real-world proportional relationships represented in different ways.Students will compute unit rates of quantities associated with ratios of whole numbers.Students will compute unit rates of quantities associated with ratios of whole numbers and explain the meaning in the context of the problem.Students will compute unit rates of quantities associated with ratios of fractions and explain the meaning in the context of the problem.Students will determine when it is appropriate to compute a unit rate and understand which unit rate should be computed based on the context of the problem.Students will determine whether two quantities are in a proportional relationship from a graph and identify the constant of proportionality (unit rate).Students will determine whether two quantities are in a proportional relationship and identify the constant of proportionality (unit rate) from a table and a graph.Students will determine whether two quantities are in a proportional relationship and identify the constant of proportionality (unit rate) from tables, equations, diagrams, verbal descriptions and graphs.Students will compare the constants of proportionality in proportional relationships given in different forms (tables, equations, diagrams, verbal, graphs).Students will interpret a point (x,y) on the graph of a proportional relationship in terms of the situation.Students will interpret a point (x,y) on the graph of a proportional relationship in terms of the situation, with special attention to the points (0,0). Students will interpret a point (x,y) on the graph of a proportional relationship in terms of the situation, with special attention to the points (0,0) and (1,r) where r is the unit rate.Given a graph of a proportional relationship, students will create a situation that could be described by the graph and explain the meaning of key points.When given the grade-level vocabulary, symbols, and labels, students verbally and in writing construct a justification of their solutions. Responses may be incomplete or illogical.Using academic and content language with scaffolds and supports (e.g., sentence frames), students verbally and in writing justify their solutions and communicate their reasoning. Responses may be incomplete, but include a logical progression.Students verbally and in writing justify their solutions and communicate their reasoning using a logical and complete response with correct use of grade-level vocabulary, symbols, and labels.Students verbally and in writing construct and communicate a complete and efficient response using a logical and complete chain of reasoning, correctly using grade-level vocabulary, symbols, and labels; students evaluate and critique the validity and efficiency of others’ responses. ................
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