Mathematics Content Framework - Chicago Public Schools

Grade 6 Mathematics Planning Guide – SY12-13
Big Idea: Expressions and Equations
Big Idea Assessment: Expressions and Equations
See 6th Grade Toolset*: Sample 6th Grade assessment (collection of problems from Illustrative Math)
Topic: Using Ratio Reasoning to Solve Problems
CCSS-M Content Standards
6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
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.
a. 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.
b. Solve unit rate problems including those involving unit pricing and constant speed.
c. Find a percent of a quantity as a rate per 100; solve problems involving finding the whole, given a part and the percent.
d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
Standards for Mathematical Practice How it applies…
Connections to Standards
for Mathematical Practice
Especially in unit conversion (6.RP.3d) - creating a symbolic representation
of the problem and contextualizing the result of the calculations back to the
MP2 – Reason abstractly and quantitatively.
context of the problem.
Students are able to identify important quantities in a practical situation
and map their relationships using diagrams, two way tables, graphs, flowcharts,
etc. and use this info to derive a formula.
MP4 – Modeling with mathematics.
Key Ideas Key Terms
• Understand and use rational reasoning to calculate a unit rate Ratio, proportion, unit rate, equivalent
• Apply a ratio to calculate the composition of a set
Terms should be deeply understood within the context of their use. Not to
• Use ratio reasoning to derive a generalized description of a set be considered standalone vocabulary exercises.
Key Ideas and Terms
for “Using Ratio Reasoning
to Solve Problems“
• Use equivalent fractions as a strategy to add and subtract fractions
• Multiply and divide fractions
Prior Knowledge
CPS Mathematics Content Framework_Version 1.0 Page 35
• Simplify fractions into lowest terms
• Create tables of equivalent ratios.
• Use ratio relationships to determine percent, part, or whole given the
others.
• Apply ratio reasoning when converting units of measurement.
• Create and describe a ratio relationship between two quantities.
• Express ratios in different forms.
• Understand and derive unit rate.
• Determine equivalent ratios.
Students will be able to:
MARS Task: Candies; Elevators; Boys and Girls Task; Sugar Cookies; Shades of Blue
Possible tasks*
*The Grade 6 mathematics toolset includes this and other resources and can be found online at https://ocs.cps.k12.il.us/sites/IKMC/default.aspx and on the Department of Mathematics and Science website (cmsi.cps.k12.il.us).
Planning Guides