Grade 6 MSM I (Common Core Mathematics 6 (CCM-6)) Starting Points
Unit 1: Ratios and Proportional Relationships
Essential Questions:
o What is the connection between a ratio and a fraction?
o Why is it important to know how to solve for unit rates?
o How is a ratio or rate used to compare two quantities or values?
o How and where are ratios and rates used in the real world?
o How can I model and represent rates and ratios?
o What are similarities and differences between fractions and ratios?
Curriculum Standards:
Understand ratio concepts and use ratio reasoning to solve problems.
1. Understand the concept of a ratio and use ratio language to describe a ratio relationship
between two quantities.
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.
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.
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?
c. 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.
d. Use ratio reasoning to convert measurement units; manipulate and transform units
appropriately when multiplying or dividing quantities.
Approximate Length of Unit: 25 days
Standard(s)
6.RP.A.1
Days
3
Notes
Big ideas:
Develop understanding of ratio, representing ratios in
various forms, comparing quantities with ratios
Comparing types of ratios (part to part, part to whole)
Representing ratios with tape diagrams
Resources:
This document represents one sample starting points for the unit. It is not all-inclusive and is only one
planning tool. Please refer to the wiki for more information and resources.
 Lesson: Ratio Relationships
 Lesson: Which Cup has a Lighter Color?
Assessment Items:
 Illustrative Mathematics: Ratio of Boys to Girls
 Illustrative Mathematics: Voting for Two
 Illustrative Mathematics: Games at Recess
 Illustrative Mathematics: The Escalator:
Assessment Variation
6.RP.A.3a
8
Big ideas:
Introduction of ratio table, using ratio tables to find
values, using ratios tables to compare ratios
Using tape diagrams to find compare ratios, using tape
diagrams to find values
Plot pairs on coordinate plane and notice patterns
Resources:
 Van de Walle, J (2010). “Chapter 18:
Proportional Reasoning.” Elementary & Middle
School Mathematics: Teaching Developmentally.
Pgs. 356-358. (Ratio Tables) Activities 18.4 and
18.5. (Ratio Relationships)
 Lobato, J.E., Ellis, A.B, Charles, R.I., & Zbiek, R.M.
(2010). Developing Essential Understanding of
Ratios, Proportions & Proportional Reasoning
for Teaching Mathematics in Grades 6-8. Reston,
VA: NCTM. Pgs 36. (Ramp Activity)
 Lesson: “What’s My Grade” (6.RP.3c)
Assessment Items:
 Illustrative Mathematics: Running at a Constant
Speed: Assessment Variation
 Illustrative Mathematics: Mixing Concrete
 Illustrative Mathematics: Walk-a-thon
 Task: World Series of Pop Culture
6.RP.A.2
6.RP.A.3b
5
Big ideas:
Understanding unit rates
Solving problems for a given unit (using ratio tables,
This document represents one sample starting points for the unit. It is not all-inclusive and is only one
planning tool. Please refer to the wiki for more information and resources.
tape diagrams, division)
Resources:
 Lesson: Gas Mileage
 NCTM Illuminations Lesson: What’s Your Rate
 UEN Lesson: Trundle Wheel
 Task: Neighborhood Snow Removal
Assessment Items:
 Illustrative Mathematics: Price per pound and
pounds per dollar
 Illustrative Mathematics: Mangoes for Sale
 Illustrative Mathematics: Running at a Constant
Speed
 Illustrative Mathematics: Friends Meeting on
Bicycles
6.RP.3c
5
Big ideas:
Finding solutions to percent problems in context (using
ratio tables, tape diagrams, etc.)
Resources:
 NCTM Illuminations Lesson: Shopping Mall Math
 NCTM Illuminations Lesson: Big Math and Fries
Assessment Items:
 Task: Designing a Kitchen Backsplash
 Illustrative Mathematics: Shirt Sale
 Illustrative Mathematics: Overlapping Squares
6.RP.3d
4
Big ideas:
Converting between standard units of measure.
Comparing measurements represented with different
units.
Resources:
 Lesson: Huckleberry Trail Mix Recipe
 Lesson: Maps
 Lesson: Conversions with Inches
Assessment Items:
 Illustrative Mathematics: Dana’s House
This document represents one sample starting points for the unit. It is not all-inclusive and is only one
planning tool. Please refer to the wiki for more information and resources.
 Illustrative Mathematics: Converting Square
Units
 Illustrative Mathematics: Currency Exchange
 PARCC Prototype Assessment Item: Slide Ruler
Culminating Task: World Series of Pop Culture, Designing a Kitchen Backsplash
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.
This document represents one sample starting points for the unit. It is not all-inclusive and is only one
planning tool. Please refer to the wiki for more information and resources.