Unit Title/Timeline:
6th grade Advanced Math Unit #4 Rates and Ratios (10 Weeks)
How can we use comparisons to describe and solve problems?
Priority Standard: the most complex comprehensive standard in a given set of 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 is not equal to 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.3.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.
6.RP.3.b Solve unit rate problems including those involving unit pricing and constant speed.
6.RP.3.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.
6.RP.3.d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.
7.RP.2 Recognize and represent proportional relationships between quantities.
7.RP.2.a 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.2.b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
7.RP.2.c Represent proportional relationships by equations.
7.RP.2.d 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.3 Use proportional relationships to solve multistep ratio and percent problems.
8.EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in
different ways.
7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a
scale drawing at a different scale
Essential Questions and Learning Goals
1. How can I compare quantities in meaningful ways?
•Students will understand that quantities can be compared using addition or subtraction in some situations while others require multiplication
or division (ratio).
•Students will know the notation and vocabulary associated with ratios. Sample vocabulary includes things such as for each, per, percent,
etc. and sample notation includes %, 1/5, 1:2, etc.
•Students will begin to develop the concept of unit rate.
•Students will know that any situation where the ratio between the related quantities remains constant is called a proportional relationship.
2. What is a proportional relationship and how can I recognize proportional relationships when looking at tables or graphs?
•Students will understand the connection between ratios and proportional relationships.
•Students will apply their knowledge of fractions (particularly the ability to write any value as a fraction with a denominator of one) to develop
the concept of a unit rate.
•Students will be able to create a table or graph to represent proportional relationships by making use of the ratio or unit rate.
•Students will be able to recognize proportional relationships in graphs and tables
•Students will apply their knowledge of visual representations to determine the unit rate for a proportional relationship.
•Students will compare the ratios for two situations represented in any form (graphs, tables, verbal situations), including those with equivalent
ratios.
•Students will recognize the special graphical features that occur for all proportional relationships. The point (0,0) appears on the graph of all
proportional relationships, the point (1, r) where r is the unit rate appears on the graph, and the graph is a line.
3. How can I apply ratio and rate reasoning to solve real world problems?
•Students will use multiple representations such as tape diagrams, double number line diagrams, or equations to solve rate and ratio
problems.
•Students will understand that a percent is a type of ratio that compares a quantity to 100
• Students will be able to use proportional reasoning, including unit rate and creating equivalent fractions, to find unknown values of interest.
•Students will apply their knowledge of proportions to solve problems involving a percent including simple interest, tax, markups, gratuities,
commissions, fees, percent error, and percent increase/decrease.
•Students will be able to use unit rates to write an equation for a proportional situation and will understand why the equation is useful.
•Students will make the connection between unit rate, rate of change, and slope.
•Students will make use of the connection specified in 3e to create a graph when given an equation for a proportional relationship.
•Use ratio reasoning to convert measurement units
•Students will apply their knowledge of ratios and proportions to create scale drawings and calculate scaled and actual measurements as well
as to alter the scale of a scaled drawing.
Academic Vocabulary:
Proportion, Proportional relationship, Ratio, Rate, Rate of change, Slope, Unit rate, Equivalent ratios, Constant of proportionality, Percent, Percent of
increase/decrease, Tape diagram, Double number line, Scale drawing, Scale factor
*assessments and additiona documents are linked on website
Cedar Springs Public Schools-Curriculum. Assessments, Instruction