EAST ALLEN COUNTY SCHOOLS
Bundle 4
Grade 6
Math
Ratios and
Proportions
Big Idea: Interpretations
Enduring Understandings
Essential Questions
Part-whole relationships can be expressed in equivalent fraction, decimal,
percent, or ratio forms.
Mastery of proportional reasoning allows one to solve a variety of problems.
Ratios and proportions are parts of a whole that can be represented in a
variety of ways.
What are different comparisons that can be made using ratios?
How can ratios be used to find unknown quantities or inaccessible
measurements?
How are ratio, unit rate, and proportion related to real life occurrences?
How does a proportion compare two equivalent ratios?
Multiplication and division mastery is required when analyzing ratios and
proportions.
CC/Learning Targets
6.1.6
6.2.6
6.2.7
6.7
6.RP.3b
6.EE.7
6.EE.9
Core Vocabulary
proportions
unit rate
Links to Technology
-Math!!! (app)
-Whiteboard (app)
-Show Me (app)
-SAS Flashcards (app)
Bundle Performance Task(s)
The PTO in your school has decided to have the 6th graders publish a cookbook. There has been a decision to include 100 recipes, one on each page. This
cookbook needs to be divided into three main sections: appetizers, main dishes, and desserts. Before you begin this task, you need to refer to other cookbooks to
determine how many recipes are needed per category. If 20 recipes are used for dessert, the ratio would be 20:100, or in simplest form 1:5. You also need to
explain how you determine the total amount of recipes in each category. Make a table including the following information:
• Type of recipe
• Ratio to total recipes
• Number of recipes per category
• Ratios represented in simplest form
• Photographs evenly proportioned throughout cookbook
• Three real example recipes must be included, with correct fractional measurements, such as 1/3 cup of sugar.
As an extension, use DaVinci's ratio or Black Death .
Grade 6
Math Bundle 4
Quarter 2
Nov.-Dec.
Recommended Read-Alouds
Title
Big Idea: Interpretations
Author
Relates to…
Chasing Vermeer
Blue Balliett
Patterns
Extreme Temperatures: Learning About Positive and Negative Numbers
John Strazzabosco
Temperatures
If You Hopped Like A Frog
David Schwartz
Ratios and Proportions
Jim and the Beanstalk
Raymond Briggs
Proportions
L.A. Bundle 4
Read-Alouds
Page 2 of 4
Math
G6 - Bundle 4
CC/Learning Targets
6.1.6
Model ratios using objects, drawings, or other
concrete or pictorial representations.
Resource of Ideas
-If You Hopped Like A Frog by David Schwartz (ratios/proportions)
-Jim and the Beanstalk by Raymonf Briggs (ratio/proportions)
Evidence of Learning
-Models to represent ratios
-Calculating ratios of height to
width in famous architecture
-Ratio!!! (apps) (Now costs $3.99)
-Ratio of Golden Rectangle (play spiral, measure ratio)
-Holt Math Hands-On Lab pp. 396-397
6.2.6
a. Define ratio using the notations: a/b, a to b,
a:b.
b. Interpret ratios to represent the relative size
of two quantities. Include situations involving
part to part (girls to boys) and part to whole
(girls to total students). Connect part to whole
situations to prior work with fractions.
(6.PR.1)
Understand the concept of a ratio and
use ratio language to describe a ratio
relationship between two quantities. For
example, “The ratio of wings to beaks in
the bird house at the zoo was 2:1,
because for every 2 wings there was 1
beak.” “For every vote candidate A
received, candidate C received nearly
three votes.”
(6.RP.2)
(6.RP.3)
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. For example, “This
recipe has a ratio of 3 cups of flour to 4
-Holt Middle School Math, Lessons 8-1, 8-2, 8-3, 8-4, 8-5, 8-6
-Unit rates
-Finding Unit Rates (video from Khan Academy)
-Unit Rate using IXL Activity (could be an assessment)
- Holt Middle School Math, pp. 392-395
-Holt Math Corresponding Lesson
Resources
-Unit Rate using IXL Activity
Math
G6 - Bundle 4
cups of sugar, so there is ¾ cup of flour
for each cup of sugar.” “We paid $75 for
15 hamburgers, which is a rate of $5 per
hamburger.”
Use ratio and rate reasoning to solve realworld and mathematical problems, e.g., by
reasoning about tables of equivalent
ratios, tape diagrams, double number line
diagrams, or equations1.
6.2.7
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? (Notes: The
CCSS includes unit rates, the use of
tables and the coordinate plane with
ratios, solving problems involving
finding the whole given a part and the
percent, using ratio reasoning to do
measurement conversions, and
manipulating and transforming units)
a. Define proportion. Connect proportions to
prior work with equivalent fractions.
b. Write proportions based on problem
situations, using a variable as the unknown.
c. Solve problems involving proportions. Solve
proportions mentally (connecting to the
concept of equivalent fractions) as well as
solving for the unknown using an equation.
-If You Hopped Like A Frog by David Schwartz (ratios/proportions)
-Jim and the Beanstalk by Raymonf Briggs (ratio/proportions)
-Proportional triangles lesson (interactive practice at bottom of page)
-Proportions lesson (interactive practice at bottom of page)
-Holt Middle School Math, Lessons 8-2, 8-3, 8-4, 8-5, 8-6, 11-2
-Holt Hands-On Lab, pp. 396-397
-Holt Math Corresponding Lesson
Resources
-Proportional triangles quiz
(interactive)
-Proportions quiz (interactive)
-Calculate proportions of houses
or local buildings
Math
6.7
G6 - Bundle 4
Problem Solving
-The Problem Solver 6: Activities for Learning Problem-Solving
Strategies
-Five Easy Steps to a Balanced Math Program for Secondary Grades
pp.29-73
-Problem Solver Activities
-See Problem Solving Template
in Appendix.
-Math Curse by Jon Scieszka (problem solving)
6.EE.7
6.EE.9
Solve real-world and mathematical
problems by writing and solving
equations of the form x + p = q and px
= q for cases in which p, q and x are
all nonnegative rational numbers.
Use variables to represent two
quantities in a real-world problem that
change in relationship to one another;
write an equation to express one
quantity, thought of as the dependent
variable, in terms of the other quantity,
thought of as the independent
variable. Analyze the relationship
between the dependent and
independent variables using graphs
and tables, and relate these to the
equation. For example, in a problem
involving motion at constant speed, list
and graph ordered pairs of distances
and times, and write the equation d =
65t to represent the relationship
between distance and time.
-Holt Middle School Math, pp. 604-605
-Problem Solver Activities
-See Problem Solving Template
in Appendix.
-Variables (independent/dependent)
-Problem Solver Activities
-See Problem Solving Template
in Appendix.
-Variables video
Math
G6 - Bundle 4
Correlating CC/Learning Targets
6.1.7
6.2.4
6.3.1
6.3.2
6.5.10
Teacher Notes
-Due to ISTEP, probability, mean, mode, median and range need to be incorporated into DMR and
Problem Solving. These are yellow standards addressed in Bundle 8.
-Problem Solving indicators need to be embedded in each Bundle
-Nlvm.usu.edu (huge library of virtual manipulatives for all standards!)
-Studyzone.com (huge library of process and content activities; many are interactive)
-Onlinemathlearning (huge library of online videos for all standards)
-Study Jams (huge resource of interactive lessons and activities)
-Five Easy Steps to a Balanced Math Program for Secondary Grades, pp. 75-100
-All embedded apps included in this curriculum are free.