Concepts that use
Proportional Reasoning
Grade 8
Number Concepts/Number and
Relationship Operations
(GCO A)
• A7 – when comparing and ordering fractions,
one strategy is to use common denominators.
Proportional reasoning can be used to create
equivalent fractions.
• Chapter 6, pages 262–267
• A9 – this outcome introduces the conceptual
understanding needed for proportional
reasoning.
• Students use the typical problems (If a 3-pack
of juice costs $1.10, what would 12 juice
cost?) to help explore the relationships found
“within” and “between” ratios.
• This outcome should be addressed in
connection with B2 and D1.
• Chapter 4, pages 158–167
Number Concepts/Number and
Relationship Operations
(GCO B)
• B2 – this outcome, a continuation of A9, is
where students learn various strategies to
solve proportions.
• Cross multiplication should be used only when
the numbers involved do not lend themselves
to more intuitive methods.
• Understanding and being able to use the
multiplicative relationship is essential in
proportional reasoning.
• Chapter 4, pages 158–177
• B3 – some percent problems can be solved
using proportions.
• Example: If 20% of a number is 0.46, what
would 110% of the number be?
• Chapter 4, pages 148–157, 168–177
• B5/B6 – When adding and subtracting
fractions, it might be necessary to use
equivalent fractions to get a common
denominator.
• Chapter 2, pages 56–69, 101–103
Patterns and Relations
(GCO C)
• C1 – this outcome is about representing a
relationship between 2 quantities in a variety
of formats. There are many opportunities
when working with the table of values, graph
and when making generalizations (predicting
the nth term) to use proportional reasoning.
• Chapter 8, pages 330–340, 368–375
• C2 – when working with linear relationships,
there are opportunities within the table of
values and the graph to use proportional
reasoning.
• Chapter 8, pages 341–347, 368–375
• C4 – this outcome introduces the conceptual
understanding of slope. Students should
recognize that for linear relationships, the
ratio of the vertical change to the horizontal
change is consistent anywhere along the line.
• Chapter 8, pages 348–360
• C6 – students should be able to solve
a c
equations of the type  as long as the
b d
unknown is in the numerator.
• Chapter 7, pages 310–321, 325, 38–381
Measurement
(GCO D)
• D1 – this outcome addresses contexts that
encourage the use of Proportional
Reasoning—scale drawings and other
measurement problems as well as
enlargements and reductions.
If problems include the conversion of SI units,
then D2 is being addressed.
• Chapter 4, pages 158–177
Geometry
(GCO E)
• E2 – this outcome addresses the development
of the properties of dilatations.
Developmental work for and problems that
apply these properties use proportional
reasoning.
• Chapter 9, pages 388–394, 410–417
• E3 – the development of the properties of
similar 2-D shapes and applications of these
properties provide many opportunities to use
proportional reasoning.
• Chapter 9, pages 395–402
Data Management
(GCO F)
• F3 – in this outcome students are learning to
construct circle graphs. Students would use
proportional reasoning if they determine the
a
c
size of the sectors using 
b 360
• Chapter 5, pages 220–225
Probability
(GCO G)
• In the G outcomes, there are applications of a
concept that require students to gather
information and extend that information to
solve a problem.
• Conducting surveys and using experimental
probability to predict theoretical probably are
examples of these applications. Students
would likely set up proportions to solve these
problems.
• Chapter 5