Unit of Study- Grade 7 Math- Comparing & Scaling
Stage 1-Desired Results
GLE’s Number and Operations
7-1: Demonstrate conceptual understanding of rational numbers with respect to square roots of
perfect squares, rates, and proportional reasoning.
7-4: Accurately solves problems involving proportional reasoning; percents including discounts,
tax, or tips; and rates.
7-6: Uses a variety of mental computation strategies to solve problems and to determine the
reasonableness of answers; and mentally calculates benchmark perfect squares and related square
roots; determines the part of a number using benchmark percents and related fractions.
7-7: Makes estimates in a given situation (including tips, discounts, and tax) by identifying when
estimation is appropriate, selecting the appropriate method of estimation, determining the level of
accuracy needed given the situation, analyzing the effect of the estimation method on the accuracy
of results, and evaluating the reasonableness of solutions appropriate to grade level GLE’s across
the standards.
Understandings
Students will understand that…
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We use comparisons in daily life to
make decisions.
We have many different ways to
mathematically compare quantities or
things (percent, ratios, rates, unit rates,
proportions, differences)
Students will know…
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How do compare items to find the best
buy
The different ways to mathematically
compare things or quantities.
Students will know which comparison
is the best way to effectively convey
information.
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Essential Questions
What quantities should be compared?
What types of comparisons will give the
most useful information?
How can the comparison be expressed in a
different but useful way?
How can given comparison data be used
to make predictions about unknown
quantities?
Students will be able to…
 Determine the best type of comparison to use
in a given situation.
 Solve problems which involve making
comparisons and reasoning with rates, ratios,
and proportions.
 Determine which is the “best buy” thereby
allowing student to make connections to real
life math.
Stage 2- Assessment Evidence
Performance Tasks:
Other Evidence:
 Quiz: Ratios and Percents, Cross Products
& Benchmark Fractions
 Open ended PBA allowing student to
choose which comparison works best
 Quiz: Percents, Better Deal, Cross
and supporting answer with evidence.
Products, Unit Price
 Quiz: Proportions, Rates, Discount
 Quiz: Multiplication & Long Division
using decimals
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End of Unit Test- Summative Assessment
End of Unit Writing Reflection
Stage 3- Learning Plan
Learning Activities:
 Introduce the book
Day 1- Use alpha Box as students complete a Book Preview. Talk about the essential
questions which are listed on the front bulletin board. Show grocery store ads and discuss
diet coke sales. What commercials on TV show comparisons? (Progressive Insurance)
Tool box items: Benchmark Fractions & Fraction, Decimals & Percents. HomeworkFinish Toolbox Items.
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Investigation 1- Making Comparisons is the introduction to the unit. Students will see that
there are many ways to compare the same data and they will determine which way is the
best type of comparison given what you are looking for. We will also conduct a class
survey (what is your favorite type of pizza?) to support the investigation. (Introduce: Ratio,
Difference, Fractions, Rates, Unit Rates, and Percent)
Day 2- Classwork- Investigation 1.1-Writing Ads-Page 5-6 in student book. Backside is 1.1
ACE (# 7-11). Homework- Skill 1- Ratios
Day 3- Classwork- Investigation 1.2- Targeting an Audience- Page 7 in the book. We will
then conduct a class survey on the backside and have students manipulate their class data in ratios,
differences, fractions, and percents.
Day 4- Classwork 1.2 ACE (#1-5). Homework- Skill 2- Equal Ratios
Day 5- Writing Math Reflection- modified from page 15 in the book. Homework: Skill 10
(Meaning of Percent)
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Investigation 2- Comparing by Finding Percents. Students will conduct a class survey on
leisure activities and will use percents do make comparisons. Student will develop the
ability to make judgments about rounding data to estimate ratio comparisons. Students
should notice that percents are only used to compare part to whole. (Essential VocabularyPercent)
Day 6- Classwork- Modified Investigation 2.2- In Class Survey about leisure activities.
Homework: Skill 11 (Fractions, Decimals, and Percents)
Day 7- 2.1 ACE and 2.2 ACE. Homework: Study for Quiz
Day 8- Quiz on Equal Fractions, Changing Fractions to Decimals, Changing Decimals to
Percents, and Benchmark Fractions.
Day 9- Comparison Review/Notes on Percent, etc. Homework: Mrs. Petonitos Class.
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Investigation 3- Comparing by Using Ratios. In these investigations students recognize
situations in which ratios are a useful form of comparison. They will form, label, and
interpret ratios from numbers given or implied in a situation. They will explore several
strategies for solving scaling problems involving ratios, or solving proportions. Students
will notice that a ratio can be part to part, part to whole, or 2 different things. They will
also find there’s 3 ways to write a ratio. (Essential Vocabulary- Ratio, Equivalent
Ratios, Proportion)
Day 10- Read Intro to Investigation 3- Discuss Ratios- Note text features. Investigation 3.1
Orange Juice Concentrate- Be sure if they use percents they do part to whole!!! Homework:
Skill 5- Proportion
Day 11- Investigation 3.2- Making spaghetti sauce. Homework- Skill 6- Using Cross
Products
Day 12- Investigation 3.3- Choose the best table. Homework- 3.1 ACE
Day 13- Classwork 3.2 ACE and 3.3 ACE; Quiz: Percent, Better Deal, and Cross Products
Day 14- Model Frayer Model using Scale factor from last unit. Students do Percent and
Ratio. Homework- Proportion Practice.
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Investigation 4- Comparing by Find Rates. Students will find unit rates, represent data in
tables and graphs, and look for patterns in tables in order to make predictions beyond the
tables. They will also connect unit rates with the rule describing the situation, find the
missing value in a proportion, and they will begin to recognize that constant growth in a
table will give a straight-line graph. (Essential Vocabulary: Rate, Unit Rate)
Day 15- Read Introduction to Investigation 4- Do Investigation comparing prices as Stop &
Shop vs. Shaws. Homework: Percent, Taxes, and Tips
Day 16- Solving Proportions, page 56/57. Homework: Multiplication/Division Practice
Day 17- Investigation 4.2- Rate Table for Madeline and Luis’ gas mileage. Homework: 3.4
Both sides (Rates/Unit Rates)
Day 18- 4.2 ACE, # 6, 10,11, 18 and Quiz on Proportions, Rates, and Discounts
Day 19- Investigation 4.3 – Sascha’s bike Trip. Homework- Finding rates, page 52
Day 20- Investigation 4.4- Craft Beads- Unit Price- Homework: Frayer Model on Rate and
Unit Rate
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Investigation 5- Estimating Populations and Population Densities. Students will use rates
to describe population and traffic density; they will use ratios and scaling up or down to find
the missing value in a proportion.
Day 21- Investigation 5.1 Estimating Population and 5.1 ACE. Homework- Writing
Reflection page 51
Day 22- Modified Investigation 5.3 Population Density using local towns and cities.
Homework: Check up 2
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Game- Wheel of Proportion- to practice various types of comparisons.
Day 23- Review Study Guide. Quiz on multiplication and division with decimals. Start
wheel of proportion game to review for unit test.
Day 24- Review for test using Wheel of Proportion game.
Day 25-27- Part 1 of unit test: NECAP no calculator, Part 2: Multiple choice. Part 3: Short
constructed answer. Part 4: Writing Reflection. Part 5: Performance Task