Unit 1- Ratios and Proportional Relationships
Unit 1 Lesson 3 – Rates-Unit Rates
Learning Goals for this Lesson: Understand
unit rate.
Students Will Know:
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.
Standards: MAFS.6.RP.1.2, MAFS.6.RP.1.3,
LAFS.68.WHST.1.1, MAFS.K12.MP.2.1,
MAFS.K12.MP.6.1
Students Will Be Able To:
Describe a unit rate in words. Write a unit rate in
a/b and a: b form. Give examples of rates and
write rates as unit rates. Use rates and unit rates
to solve real-world mathematical problems.
Lesson Essential Question:
How are cross products and unit rates helpful in determining whether two ratios are equivalent?
Activating Strategy:
Have student’s complete pg.31 “What You’ll Learn”, Vocabulary Start Up, and Real-world Link.
As a class discuss what scenarios students found throughout the chapter that demonstrate rates used
in the real world. Discuss the vocabulary terms that are used within the lesson. Ask students to
collaborate with their partners and find out if their partner found similar examples or different
examples within the lesson.
Key Vocabulary to Preview and Vocabulary Strategy:
rate, unit rate, unit price, constant speed
Lesson Instruction:
Learning Activity 1:
Have students begin Cornell notes on Rates. Students will begin by defining the
word “Rate” in their notes. Give examples on finding Unit Rates and have
students record these examples in their Cornell Notes. Review what it means to
simplify ratios (dividing numerator by denominator). Continue Cornell Notes
using EXAMPLE 1 on pg. 32 to illustrate how to write a rate and simplify it to a
unit rate. Use the scaffolding extensions on pg. 32 to build students’ knowledge
on solving problems with unit rates. Have students record the answers to
extension questions on processing page of their interactive notebook. Then,
have students in collaborative pairs discuss how they think a unit rate and unit
cost are related. Allow time for students to agree, disagree, or amend. Have
students begin Cornell Notes on Unit Price beginning with defining the term Unit
Price. Give examples on finding Unit Prices and have students record these
examples in their Cornell Notes. EXAMPLE 2 illustrates how finding a unit price
can determine if an item is a better buy.
Assessment Prompt for LA 1:
CHECK FOR UNDERSTANDING: Have students complete the “Got it” question
on pg. 32 (a & b). Have students pairs check each other’s work to determine if
students correctly solved problem. Allow time for student pairs to discuss any
questions they have about their partner’s answers and time for partners to
justify their answers or revise as needed. Review the answer together, with
students presenting their work to the class.
Graphic Organizer:


students will use a Frayer model
on word rate
Cornell Notes
Differentiation:
(Approaching Level):
 Have students highlight, underline, circle, or otherwise mark important
information in Cornel Notes
 Have students summarize paragraphs, draw pictures of concepts
 Provide copy of cloze notes as needed
 Provide vocabulary word bank (SLM)
 Use visuals: pictures, graphs, charts within Cornell Notes instruction
 Verbal reinforcement of key concepts
 Write key points on the board while working through examples
 Write a list of the sequential steps to solve each example given in
Cornell Notes.
 Use mnemonics to reinforce concepts (KFC)
 Display/clarify key vocabulary during Cornell Note instruction
 Give cues for what to write/what’s important to remember during
Cornell Note instruction
 Provide teach created study guides for lower level students
 Use maps, charts, graphic organizers, illustrations, pictures to convey
concepts, skill or subject matter.
(On Level)/ Beyond Level): Have students create a HOT question using their
Cornell Notes.
Learning Activity 2:
Assignment:
Have students begin by creating 3 questions about Unit Rate and Unit Price
(See Cmaps Resources for
from the previous Cornell Notes. Have students mark the text using HOTS
Original)
questions from within the lesson. The first example will be EXAMPLE 3 on
Common Core 6.RP.2 Minitextbook pg.33. Students will record the example and mark the text as teacher
models the steps of how to solve the problem. Have students complete the “Got Culminating Activity – Factory
Production:
it” problem on pg. 33 as an extension to the example. Have student’s record
answers on the processing page. Student will continue marking the text activity
with teacher modeling word problems from pg. 36 problems 10 & 11.
Adv: Use the same teaching method but include examples that have students
compute fractions within the rates.
Assessment Prompt for LA 2:
CHECK FOR UNDERSTANDING: Have student’s complete guided practice on
pg.34 and remainder of HOTS Questions from pg.36. Students will then silently
complete error analysis by switching partners and comparing answers. Students
will mark problems that they have different answers and then redo them to
determine who is correct and where the mistake is.
Advanced Students: Assign 3 own your own problems that include fractions
within the rates.
Differentiation:
(Approaching Level) - Alternate Teaching Strategy
If students struggle with determining unit rates,
Then use one of these reteach options:
1. Quick Review Math Handbook, p. 237
2. Problem-Based Learning Book 1, Unit D: Ratios and Rates,
Investigation 4: Comparison Shopping
3. Have students use two-color counters to model rates and unit
rates. For example, students can model
by using red
A table is given which shows the
production results for three factories.
Students are asked to answer the
following questions:
1. Write a unit rate that represents the
total vehicle production at each
factory.
2. Which factory has the fastest rate of
production?
3. How many vehicles are
manufactured at each factory in one
year? How many more vehicles does
Factory C produce than Factory A in
one year?
4. Suppose Factory A manufactures
500 more cars in their 10-month time
period. How many more trucks would
Factory A need to manufacture in
those 10 months to equal the rate of
total vehicle production at Factory C?
Rubric:
See Attached
counters for miles and yellow counters for hours.
Ask students to regroup the counters so there are an equal
number of red counters per yellow counter. Explain that this is
the unit rate.
If some of your students are not ready for assignments, use the differentiated
activities below.
 (Approaching Level/ELL) Think-Pair-Share: Give students a few
minutes to think through their solutions for Exercises 1–6. Then ask
pairs of students to work together to determine the solution. Call on
one pair of students to share their solutions with the class for each
exercise.
 (Beyond Level/ELL) Find the Fib: Have students work with a partner
to write two facts and one fib for Exercise 6. Then have them exchange
facts and fibs with another pair of students. Each pair identifies the
other pair’s facts and fib.
Suggested Assignments:
You can use the table below that includes exercises of all complexity levels to
select appropriate exercises for your students' needs.
Differentiated Homework Options
Approaching Level
1–7, 9, 11, 13, 23, 24
On Level
1–5 odd, 7–11, 13, 23, 24
Beyond Level
7–13, 23, 24
(Beyond Level) Create Your Own Homework Online: eSolutionsManual™ can
be used to create worksheets for the suggested assignments above, or to
create your own worksheets for differentiated homework or review.
Learning Activity 3: Have students watch video on
determining if two proportions are equivalent:
http://www.virtualnerd.com/pre-algebra/ratiosproportions/proportionality/determine-proportionality/crossproduct-check-proportionality The teacher will then model how to
solve a proportion using the cross products rule. Students will
then complete a Justify and Prove activity requires students to show written
and numerical evidence that ratios are equivalent when cross products are
equal.
Assessment Prompt for LA 3:
Students will complete “find the missing number game” with their shoulder
partner. Students will be given a pair of dice. They will each roll the dice to
determine the first rate. Then students will be required to roll the dice to
determine the denominator of the second rate. Together they will have to
figure out the number they can use for the missing numerator to make the
ratios equivalent. If students are unable to make ratios equivalent they need to
explain why and show their work.
Hw: http://www.teach-nology.com/worksheets/math/ratios/ratioandprop7.pdf
Differentiation:
(Approaching Level)
The Reteach Worksheet provides additional examples and practice for students
who may have difficulty in grasping the math concepts in this lesson.
(On Level)
Option 1: Naturalistic Learners - Have students research animal facts, such as
speed, longevity, or heart rate. Then ask them to use the facts to write rates
problems. For example, a dolphin can swim 28 miles in 2 hours. How many
miles can a dolphin swim in one hour? Have students exchange problems and
solve.
(Beyond Level)
Option 2: Intrapersonal Learners - Have students choose one grocery item such
as cereal, toothpaste, trash bags, or dishwashing soap. Using grocery ads,
students should find the cost of three different sizes of their item. For example,
they could find the cost of an 11-ounce, 18-ounce, and 21-ounce box of cereal.
Students should then find the unit rate for each and rank them in order from
least unit rate to greatest unit rate. Then have them discuss how the unit rate
would or would not affect the size of the item they would buy.
Option 3: Logical Learners - Have students research real-world examples of
rates, such as birth rates, death rates, or population growth rates for two cities
or counties of their choice. Ask them to prepare a short presentation
interpreting and comparing the rate information they have found. Have them
give their presentations to the class.
The Enrich Worksheet provides students with valuable opportunities for
extending this lesson.
Summarizing Strategy:
Students will complete a Dear Absent Letter explaining how to tell if two rates are equivalent.
Students will have to include vocabulary terms.
Student
Modification/Accommodations
1. Seat student near teacher.
2. Stand near student when giving
directions/presenting.
3. Provide visual aids/graphic organizers.
4. Ensure oral directions are understood.
5. Allow extra time to complete tasks.
6. Simplify complex written directions.
7. Give test items orally.
8. Provide peer assistance/study groups.