HCPSS Curriculum Framework
Common Core Mathematics 7
Unit 2: Ratios & Proportional Relationships
Overview (Big Ideas):
Students extend their understanding of ratios and develop understanding of proportionality to
solve single- and multi-step problems. Students use their understanding of ratios and
proportionality to solve a wide variety of percent problems, including those involving discounts,
interest, taxes, tips, and percent increase or decrease. Students solve problems about scale
drawings by relating corresponding lengths between the objects or by using the fact that
relationships of lengths within an object are preserved in similar objects. Students graph
proportional relationships and understand the unit rate informally as a measure of the steepness
of the related line, called the slope. They distinguish proportional relationships from other
relationships. Students will extend their understanding of proportional relationships to similar
figures. (adapted from CCSC Grade 7 page 46)
Enduring Understandings:
1. Reasoning with ratios involves attending to and coordinating two quantities.
2. A ratio is a multiplicative comparison of two quantities, or it is a joining of two quantities in
a composed unit.
3. Forming a ratio as a measure of a real-world attribute involves isolating that attribute from
other attributes and understanding the effect of changing each quantity on the attribute of
interest.
4. A number of mathematical connections link ratios and fractions:
o Ratios are often expressed in fraction notation, although ratios and fractions do not have
identical meaning.
o Ratios are often used to make “part-part” comparisons, but fractions are not.
o Ratios and fractions can be thought of as overlapping sets.
o Ratios can often be meaningfully reinterpreted as fractions.
5. Ratios can be meaningfully reinterpreted as quotients.
6. A proportion is a relationship of equality between two ratios. In a proportion, the ratio of two
quantities remains constant as the corresponding values of the quantities change.
7. Proportional reasoning is complex and involves understanding that o Equivalent ratios can be created by iterating and/or partitioning a composed unit;
o If one quantity in a ratio is multiplied or divided by a particular factor, then the other
quantity must be multiplied or divided by the same factor to maintain the proportional
relationship; and
o The two types of ratios - composed units and multiplicative comparisons - are related.
8. A rate is set of infinitely many equivalent ratios.
9. Several ways of reasoning, all grounded in sense making, can be generalized into algorithms
for solving proportion problems.
10. Superficial cues present in the context of a problem do not provide sufficient evidence of
proportional relationships between quantities.
11. Geometric images provide the content in relation to which properties can be noticed,
definitions can be made, and invariances can be discerned.
12. Geometric awareness develops through practice in visualizing, diagramming, and
constructing.
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.
Sources:
Lobato, J. E. (2010). Developing essential understanding of ratios, proportions & proportional
reasoning for teaching mathematics in grades 6-8. Reston, VA: The National Council of
Teachers of Mathematics, Inc.
Sinclair, N., Pimm, D., & Skelin, M. (2012). Developing essential understanding of geometry for
teaching mathematics in grades 6-8. Reston, VA: The National Council of Teachers of
Mathematics, Inc.
Essential Questions:
o What are the types/varieties of situations in life that depend on or require the application
of ratios and proportional reasoning?
o How can a complex fraction be simplified?
o What is the difference between a unit rate and a ratio?
o What is a proportion?
o Why are multiplicative relationships proportional?
o How are equivalent ratios, values in a table, and ordered pairs connected?
o What characteristics define the graphs of all proportional relationships?
Curriculum Standards:
7.RP.A Analyze proportional relationships and use them to solve real-world and
mathematical problems.
1. Compute 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 ½/¼ miles per hour,
equivalently 2 miles per hour.
2. Recognize and represent proportional relationships between quantities.
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.
b. Identify the constant of proportionality (unit rate) in tables, graphs, equations,
diagrams, and verbal descriptions of proportional relationships.
c. 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.
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.
3. Use the 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.G.A Draw, construct, and describe geometrical figures and describe the relationships
between them.
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.
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.
Common Misconceptions:
o Students may confuse the significance of the numerator compared to the denominator.
o Students may believe that a denominator with a greater digit automatically has a greater
value than a fraction with a lesser denominator, e.g., ,1-8. > ,1-3. .
o Students may rely on one configuration for setting up proportions without realizing that
other configurations may also be correct (see discussion of within ratios and between
ratios on page 2).
o Students may have difficulty calculating unit rate, recognizing unit rate when it is
graphed on a coordinate plane, and realizing that unit rate is also the slope of a line.
o Students may misinterpret or not have mastery of the precise meanings and appropriate
use of ratio and proportion vocabulary.
o Students may miscomprehend the difference between additive reasoning versus
multiplicative reasoning.
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.