6th Grade Ratios & ProportionsJoana Wu, Krista Milroy, Chelsea Keen, Becki Schwindt, and Erin Craig

Progressions

Standards 6.RP.1: Understand the concept of a ratio and use ratio language

to describe a ratio relationship between two quantities

1 2

3

6.RP.2: 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.

6.RP.3 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.3a 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.3b 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.3c 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.3d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Anticipated Student Errors, Misconceptions, and Preconceptions

 More than half the population of adults is not proportional thinkers Student ErrorsStudents may think Ratios and Fractions are the same thing – they are related, but not necessarily the same

Ratios can be part-to-part and fractions are part-to-wholeRatios can be part-to-wholeFractions of a length are not ratios – not a multiplicative

comparison Students can struggle determining which features to compare to which  Have students write about their reasoning to assess how they are reasoning

Resources

Dan Meyer Video

Assessment Rubric Checklist6.RP. 1 – Concept of Ratios

Students can understand that ratios are different than fractions

Students can use ratio language to describe the relationship between two quantities

Students can make and use tables to compare ratios and analyze patterns/relationships 4.MD.1 - Know relative sizes of measurement units within one system of

units; record measurement equivalents in a two column table 5.OA.3 - Identify apparent relationships between corresponding terms to

form ordered pairs and graph the ordered pairs on a coordinate plane 5.NF.5 - Interpret multiplication as scaling (resizing) by comparing the

size of a product to the size of one factor on the basis of the size of the other factor

Assessment Rubric Checklist6.RP.2 – Unit Rates

Students can understand that a rate is a ratio that compares quantities in different units and that unit rate compares quantities in units of one

Students can use rate language in context of the ratio relationship 7.RP.1 - Compute unit rates associated with ratios of

fractions, including ratios measured in like or different units 7.RP.2a - Decide whether two quantities are in a

proportional relationship 7.RP.2c - Represent proportional relationships by equations

Assessment Rubric Checklist6.RP.3 – Ratios, Tables, & Graphs

Students can solve unit rate problems Students can solve problems finding the

whole, given part, and the percent Students can use ratio reasoning to convert

measurements and transform other units 7.RP.2b - Identify the constant of proportionality (unit rate) in

tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships

7.RP.2d - Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation

7.RP.3 - Use proportional relationships to solve multistep ratio and percent problems