Ratio and Proportional Relationships UbD Unit

Unit Understanding: Ratio & Proportional Relationships Subject/Grade/Year: 6th grade Math
Stage 1 - Desired Results (Standards)
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Power Standard(s): What CCSS/ISBE/National Standards(s)
will address this unit?
CC.6.RP.1 Understand ratio concepts and use ratio reasoning to
solve problems. Understand the concept of a ratio and use ratio
language to describe a ratio relationship between two quantities.
CC.6.RP.2 Understand ratio concepts and use ratio reasoning
to solve problems. Understand the concept of a unit rate a/b
associated with a ratio a:b with b ≠ 0 (b not equal to zero), and
use rate language in the context of a ratio relationship.
CC.6.RP.3a Make tables of equivalent ratios relating quantities
with whole-number measurements, find missing values in the
tables, and plot the pairs of values on the coordinate plane. Use
tables to compare ratios.
CC.6.RP.3b Solve unit rate problems including those involving
unit pricing and constant speed.
CC.6EE.6 Use variables to represent numbers and write
expressions when solving a real-world or mathematical problem;
understand that a variable can represent an unknown number,
or, depending on the purpose at hand, any number in a specified
set.
CC.6.EE.9 Represent and analyze quantitative relationships
between dependent and independent variables. 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.
CC.6.NS.4 Compute fluently with multi-digit numbers and find
common factors and multiples. Find the greatest common factor
of two whole numbers less than or equal to 100 and the least
common multiple of two whole numbers less than or equal to 12.
Transfer Goal: Applies the Power Standard to a “novel” real world
situation. A statement of what students should be able to do with
the standard knowledge in other contexts. Students will be able to
independently use their learning on a long-term basis to...
● Apply ratios and rates to different situations, such as unit pricing
and constant speed.

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Essential Understandings: What specific understandings can
be predicted from the Power Standard(s)?
● Students will understand that a proportion involves
multiplicative thinking, not additive.
● Students will understand that ratios compare two
quantities.
Essential Questions: What thought provoking questions would foster
inquiry, understanding and transfer of learning?
How can we model, represent and tell the difference between rates and
ratios?
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Knowledge: What should students know as a result of this unit?
What can be studied? (Theory/Concepts/Mental Coordination)
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I can understand a ratio as a way to compare two
quantities.
I can use ratio language to describe ratio relationships.
I can understand a unit rate of a:b as a ratio of a:b.
I can solve unit rate problems involving unit pricing.
I can make a table of equivalent ratios.
I can determine missing values in a table of equivalent
ratios.
I can use tables to compare ratios.
I can plot pairs of values on a coordinate plane.
I can solve unit rate problems involving constant speed.
Skills: What should students be able to do as a result of this unit?
What can be practiced? (Application of Theory/Concepts/Physical
Coordination)
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Students will be able to define ratio as a distinctive relationship
between two pieces of data.
Students will be able to create and manipulate ratios and utilize
ratio language to problem solve (find & apply unit rates, create,
extend & graph tables).
Stage 2 - Evidence

Summative Performance Assessment(s): Is each standard and transfer goal being assessed? An authentic assessment(s) designed to show
how students demonstrate their understanding of essential questions and transfer goals when applied to a new, varied, or realistic situation.
Should be written in the GRASPS format and reflect the UbD “Six Facets of Understanding”.
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Complete a table of proportional values (not in order), find unit rate, graph results, use graph to predict, make a general statement about
what is happening in the table/graph (rule).
Write a letter to the person who shops and prepares meals for your family. In it explain how using ratios might assist them in saving
money or prepare the right amount of food. Cite two different and specific examples using the words per, for every, each, unit rate, ratio,
rate (i.e. buying an item in bulk as opposed to a more convenient size, planning a large dinner).
○ Rubric?
Assessment Criteria: What criteria will be used in each assessment to evaluate attainment of each desired result? What are the qualities by
which learning is judged? Think rubric components!!! (Content, Process, Product, knowledge, skill)
Constructively aligned assessment criteria begin with a noun that complements the verb in the assessment tasks objective. If the objective is for
students to "explain how concepts in the subject interrelate" one of the criteria might be "Clarity of explanation". That is, the criterion describes
the quality in the assessment task that will be judged as an assessment. Other commonly used quality words used in criteria include: Accuracy,
Currency, Depth, Impact, Legibility, Originality, Succinctness, and Relevance.
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Formative Assessment Evidence: What daily evidence has been collected to determine goal attainment? Tests, quizzes, discussions,
homework, exit slips, graphic organizers, note-taking, etc…
Pre-assessment:
● Timed Test: Multiplication
● Math Talk/Socrative/Warm-Up: Point plotting/giving coordinates
● Using a table with a given unit rate, determine unknown values of equivalent ratios
Formative Assessments:
● Recess Games
● Using a table with a given unit rate, determine unknown values of equivalent ratios, state rule that makes the two quantities relate
● Given a ratio, determine its unit rate and use this information to answer questions about better buy, speed, etc..
● MARS Task - Cans of Kola
Stage 3 - Learning Plan (Activity)
Pre-Assessment: What will be done to determine students’ background knowledge, skill level, and possible misconceptions? (K-W-L) How will
students be grouped? What opportunities for differentiation will take place?
● Multiplication Timed Test - repeat periodically
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Aligned Learning Activities: What will be done each day to foster student success at transfer, meaning, and acquisition? How will critical
thinking, problem solving, and systems thinking be incorporated? Consider the “Gradual Release of Responsibility Model” and “WHERETO”
format when developing daily experiences linked to Stages 1 and 2.
Date(s)
“We Will…” Objective:
How are action verbs
used to link content to the
Power Standard for each
learning experience?
Procedures:
What is the daily lesson plan process? What is the step-bystep
path of learning? How are learning activities prioritized
and sequenced in an engaging and time sensitive manner?
How are learning experiences differentiated or modified to meet
assessed learning needs? How are the daily products connected to
Summative Performance Tasks?
Progress Monitoring:
How is progress toward transfer,
meaning, and acquisition regularly
monitored?
What are the misunderstandings?
How will students receive relevant
feedback?

Social Studies:
Science:
P.E.:
Health:
Art:
Incorporate scale activities (Hot on the Trail/Sundae Delivery)
Latitude/Longitude (desk maps)
Food Webs and Food Chains - calories burned moving through the
food chain
Heart rate
Nutritional values
Scale drawings
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I can understand
a ratio as a way
to compare two
quantities.
I can use ratio
language to
describe ratio
relationships.
For daily consideration...
● Timed Test: Need to be able to multiply
● Math Talk/Socrative/Warm-Up: Point plotting/giving
coordinates
Math Talk:
Display ratio drawings (Van de Walle pg 302) and ask students to
make comparisons among the objects shown
Extension: Are any two pictures showing the same thing? Match
them up? What are you comparing?
(1st slide - show one picture, then after show all)
Vocabulary: each, per, ratio, every

Explain: The ratio of wings to beaks in the bird house at the zoo
was 2:1.
How can this be represented in a chart? Headings? What is being
compared?
A ratio is the comparison of two quantities or measures. The
comparison can be part-to-whole (ratio of guppies to all fish
in an aquarium) or part-to-part (ratio of guppies to goldfish).
Students need to understand each of these ratios when
expressed in the following forms: 6/15 , 6 to 15, or 6:15.
These values can be reduced to 2/5, 2 to 5, or 2:5; however,
students would need to understand how the reduced values
relate to the original numbers.
A chart will be formed to show the relationship. Show how
multiplication and division can be used to find ratios.
(can use fish slides from last year)
HW: Express using chart with correct headings. Extend chart for 5
number pairs. Explain in words what is being compared.
For every vote candidate A received, candidate C received nearly
three votes.
Use sentence frames when writing sentences using ratios as
comparison.
Example: For every _____ girls playing soccer, _____ boys played
soccer.
Use iPod and Book problems before formative assessment.
Formative Assessment: Recess Games
TUESDAY
● Differentiate or Math Talk using student samples of correct/
incorrect work: students using additive thinking (who
used multiplicative thinking: Chaska & Mika?; students
using incorrect order; student using incorrect format;
understanding meaning of “difference”
● Fish Slides

● I can understand
a unit rate of a:b
as a ratio of a:b.
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I can derive a unit
rate from a given
ratio.
I can solve unit
rate problems
involving unit
pricing.
WEDNESDAY LATE START
Math Talk:
If the ratio of girls to boys is 2:1 and there are 6 people in the room,
how many girls are there? How many boys? (Consider making a
chart and expanding it)
● Refer to examples of unit rate we’ve already seen (trucks,
beaks, hot dogs, laps)
● “Per serving” investigation: HW for Wed.
THURSDAY
● Per Serving Investingation
○ Teacher will model finding and using unit rate in a
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per serving situation (calories per serving)
Students will work in small groups to determine
and present to one another their per serving
examples
THURSDAY/FRIDAY/MONDAY
During Compelling Conversation THEN...video (remediation) and
Bean Bag/Teacher Shortage (advanced)
● 8.2 slides on Unit Rate
*Possible Warm-ups/Exit Slips*
● What are some other amounts of boys and girls that fit
this ratio? or worded as: If the ratio of girls to boys in the
room (or at the party) is 2:1, make a chart showing different
combinations of boys and girls at the party.
● If you paid $75 for 15 hamburgers, how much did each
burger cost? ($5 per hamburger)
● Complete this statement: If a recipe calls for 3 cups of flour
and 4 cups of sugar, there is (3/4) cup of flour for each cup
of sugar.
TUESDAY
Writing Unit Rates when costing
Mangos for Sale (mangos per $1 or dollars per mango)
● Consider rephrasing question: Which ratio is more
appropriate?
H.W.: Beans for Sale (beans per $1 or dollars per pound)
WEDNESDAY(late start schedule)

Formative Assessment Option: Consider Socrative
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?

● I can solve unit
rate problems
involving unit
pricing. (Better
buy)
Rates, a relationship between two units of measure, can be written
as ratios, such as miles per hour, ounces per gallon and students
per bus. For example, 3 cans of pudding cost $2.48 at Store A and
6 cans of the same pudding costs $4.50 at Store B. Which store
has the better buy on these cans of pudding? Various strategies
could be used to solve this problem:
· A student can determine the unit cost of 1 can of pudding
at each store and compare.
· A student can determine the cost of 6 cans of pudding at
Store A by doubling $2.48.
· A student can determine the cost of 3 cans of pudding at
Store B by taking 1⁄2 of $4.50.
Using ratio tables develops the concept of proportion. By
comparing equivalent ratios, the concept of proportional thinking is
developed and many problems can be easily solved.
Store A
3 cans 6 cans
$2.48
Store B
6 cans 3 cans
$4.50
THURSDAY
Review Pudding responses
MARS Task: Cans of Kola

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I can solve unit
rate problems
involving constant
speed.
I can plot pairs
I can determine
missing values
in a table of
equivalent ratios.
I can use tables
to compare ratios.
of values on a
coordinate plane.
FRIDAY
Debrief on Kola Task -address misconceptions
HW:
Pasta Problem (from last year’s slides)
A store sells the same pasta following two ways: 10lbs of bulk
pasta for $15.00 and 2 pounds of packaged pasta for $3.98. To
determine which is the better buy, find the unit rate for both types.
Battery Problem (from last year’s slides)
Which of the following is a better buy? 2AA batteries for $1.50 or
6AA batteries for $4.80
Monday: Debrief Pasta & Battery
Monday
Math Talk: Explore Cups of Peanuts: Cups of Chocolate (pg. 4)
Extension: Graph results AND use graph to determine unknown
values.
Tuesday
Math Talk: Running at a Constant Speed
● Use proportions to solve for unknown
● Put data into table
● Graph

● LOOK AT
ALL “I CAN”
STATEMENTS
● I can plot pairs
of values on a
coordinate plane.
Wednesday
Formative Assessment:
Books Unlimited Tables (pg. 3) (have students graph results?)
During MAP testing, work more on constant speed