Population Density �
The population density is
the average number of
things per unit of area
(people per square mile)
Proportion � An equation
stating that two ratios are
equal.
Rate �A rate can be
thought of as a direct
comparison of two sets
(20 cookies for 5 children)
Ratio -A ratio is a com-parison of two quantities that tells the scale be-
tween them. Ratios may
be expressed as quotients,
fractions, decimals, per-
cents or given in the form
a:b. Unit Rate -A unit rate compares an amount to a single unit. For example,
1.9 children per family;
32 mpg.
Comparing and Scaling
Glossary
Connected Mathematics
Project
Everett Public Schools
Mathematics Program
Proposed Time Frame:
Approximately 6 weeks
Comparing and
Scaling
Ratio, Proportion, and
Percent
Unit Goals :
Explore proportional
relationships betw een
quantities
Interpret fractions as r atios
as rates, or as comparisons
of a part to a whole Scaling ratios up or down Compare quantities using ratios, rates, or percent s
Web Resources
You will find the Factor
Game and the Product Game
at:
www.illuminations.nctm.org
Paper Pool
Tips for Helping at
Home
Good questions and
good listening will help
children make sense of mathematics
and build self-confidence. A good
question opens up a problem and
supports different ways of thinking
about it. Here are some questions
you might try, notice that none of
them can be answe red with a simple
�yes� or �no�.
Getting Started
What do you need to find out?
What do you need to know?
What terms do you understand
or not understand?
While Working
How can you organize the info r-
mation?
Do you see any patterns or rela-
tionships that w ill help solve this?
What would happen if�?
Reflecting about the Solution
How do you know your answer is
reasonable?
Has the question been an-
swered?
Can you explain it another way ?
At Home:
1 Talk with your child about
what�s going on in mathematics
class.
2 Look for ways to link mathe-
matical learning to daily activi-
ties. Encourage your child to
figure out the amounts fo r halv-
ing a recipe, esti mating gas
mileage, or fi guring a restau-
rant tip.
3 Encourage your child t o sched-
ule a regular ti me for home-
wo rk and provide a comfortable
place for their study, free from
distractions.
4 Monitor your child�s homework
on a regular basis by looking at
one problem or asking your
child to briefly describe the fo-
cus of the homework. When
your child asks for help, w ork
with them instead of doing the
problem for t hem.
At School
1 Attend Open House, Back to
School Night, and afte r school
events.
2 Join the parent-teacher organi-
zation
Investigation 1 Making Comparisons
Make comparisons
Develop ways to use ratios, fracti ons,
rates, and unit rates, to answer ques-
ti ons involving proportional reasoning
Investigation 2 Comparing by Finding
Percents
Make sensible comparisons of data
using ratios, fractions, and decimal
rates, with a fo cus on percents
Make judgments about rounding data
to estimate ratio comparisons
Investigation 3 Comparing by Using Ra-
tios
Recognize situations in which rati os are
a useful form of com parison
Form, label, and interpret ratios fr om
numbers given or im plied in a situation
Solve scaling problems involving rat ios
(solving proportions)
Investigation 4 Comparing by Finding
Rates
Find unit rates
Represent data in tables and graphs
Find the missing value in a proporti on
Investigation 5 Estimating Populat ions
and Population Densit ies
Use geometric scaling to estimate
population counts
Apply proportional reasoning
Use ratios to find mi ssing values in a
proportion
Use rates to describe populat ion and
traffic density (space per person or car)
Connected Mathematics Pr oject
Mathematics in
Investigations
Phone: 425-385-4062
Fax: 425-385-4092
Email: mstine@everett.wednet.edu