1
SFUSD Mathematics Core Curriculum Development Project
2014–2015
Creating meaningful transformation in mathematics education
Developing learners who are independent, assertive constructors of their own understanding
SFUSD Mathematics Core Curriculum, Grade 6, Unit 6.3: Ratio, 2014–2015
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Grade 6
Unit 6.3: Ratio
Number
of Days
Lesson
Reproducibles
Number of
Copies
1
Entry Task
Family Party
1 per student
4
Lesson Series 1
CPM CCC1 Lesson 3.1.6 (4 pages)
HW: CPM CCC1 Lesson 3.1.6
Games at Recess/Walkathon (2 pages)
Friends Meeting on Bicycles/Jim and Jesse’s Money (2
pages)
1 per pair
CPM eBook
1 per pair
1 per pair
1 per pair
1
Apprentice Task
Snail Pace
1 per student
3
Lesson Series 2
CPM CCC1 Lesson 3.1.2 (4 pages)
Resource Page 3.1.2A
HW: CPM CCC1 Lesson 3.1.2
CPM CCC1 Lesson 4.2.4 (3 pages)
HW: CPM CCC1 4.2.4
Candies/Mixing Paints (2 pages)
1 per pair
1 per pair
CPM eBook
1 per pair
CPM eBook
1 per student
1
Expert Task
Mid-Module Assessment Task – Engage NY (2 pages)
1 per student
4
Lesson Series 3
CPM CCC1 Lesson 7.1.1 (3 pages)
HW: CPM CCC1 Lesson 7.1.1
CPM CCC1 Lesson 7.1.2 (3 pages)
Resource Pages 7.1.2A
Resource Page 7.1.2B
The Escalator/Running at a Constant Speed (2 pages)
Overlapping Squares/Shirt Sale (2 pages)
1 per pair
CPM eBook
1 per pair
1 per pair
1 per pair
1 per pair
1 per pair
2
Milestone Task
End of Module Assessment Task – Engage NY (5
pages)
1 per student
Materials
Large jar full of white and brown
beans
Colored pencils or markers
SFUSD Mathematics Core Curriculum, Grade 6, Unit 6.3: Ratio, 2014–2015
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Unit Overview
Big Idea
A ratio represents a comparison of two quantities, which can be expressed by “part to part,” “part to whole,” and “whole to part” relationships. Equivalency of two
or more ratios establishes a framework for a proportional relationship.
Unit Objectives
Students will be able to define and write ratios in three ways (a:b, a/b, a to b). Students will describe the difference between a ratio and a fraction (fractions
always name part to whole, while ratios may name part to whole, part to part, or whole to part.) They will represent proportional relationships by constructing
function tables, graphs, tape diagrams, and double number lines. Students will use these diagrams to compare, solve, and explain real-world problems involving
unit rates, percents, and measurement conversions by using the concepts of equivalency in ratio relationships.
Unit Description
Throughout the scope of the unit we will be touching on the following concepts:
• Interpreting and modeling ratios.
• Comparing ratio relationships and building concepts of equivalency.
• Extending ratio relationships to calculate unknown quantities.
• Applying concepts of equivalent ratios to apply ratios to percents, unit conversions, and scale.
The unit is designed to help students interpret and model ratios, and to use ratio relationships to solve problems, in terms of calculating unknown quantities and
equivalent ratios, and to apply concepts of equivalent ratios to articulating percents, unit conversions, and scale.
SFUSD Mathematics Core Curriculum, Grade 6, Unit 6.3: Ratio, 2014–2015
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CCSS-M Content Standards
Ratios and Proportional Relationships
Understand ratio concepts and use ratio reasoning to solve problems.
6.RP.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.3 Use ratio and rate reasoning to solve real-world problems, e.g. by reasoning about tables of equivalent ratios, tape diagrams, double number line
diagrams, or equations.
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
6.RP.3b 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?
6.RP.3c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole,
given a part and the percent.
6.RP.3d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
SFUSD Mathematics Core Curriculum, Grade 6, Unit 6.3: Ratio, 2014–2015
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Progression of Mathematical Ideas
Prior Supporting Mathematics
Current Essential Mathematics
Future Mathematics
Students connect their understanding of
multiplication and division with ratios and rates.
Thus students expand the scope of problems
for which they can use multiplication and
division to solve problems, and they connect
ratios and fractions. Students will continue to
build on the conceptual idea of fraction
equivalence, the idea that the different
numerical representations ultimately represent
the same quantity.
Students will understand ratio relationships and use
ratio reasoning to solve problems using reasoning
about multiplication and division. They will be able to
recognize and describe ratios and unit rates as
building blocks for proportional reasoning, while
understanding how ratios differ from fractions.
Students will use models to represent collections of
ratios as equivalent quantities using double number
lines, tape diagrams, and functions tables as a
framework for proportional relationships.
In seventh grade, students will analyze proportional
relationships and use them to solve real-world and
mathematical problems. Students will graphically
represent ratios as sets of coordinates understanding
that the ratio represents the slope of a line on a linear
function. Students will use their understanding of
ratios and proportionality to solve a wide variety of
percent problems, including those involving discounts,
interest, taxes, tipping, and percent increase or
decrease. They will distinguish proportional
relationship from other relationships.
SFUSD Mathematics Core Curriculum, Grade 6, Unit 6.3: Ratio, 2014–2015
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Unit Design
All SFUSD Mathematics Core Curriculum Units are developed with a combination of rich tasks and lessons series. The tasks are both
formative and summative assessments of student learning. The tasks are designed to address four central questions:
1 day
4 days
1 day
3 days
1 day
Lesson Series 3
Milestone
Task
Lesson Series 2
Expert
Task
Lesson Series 1
What do you already know?
What sense are you making of what you are learning?
How can you apply what you have learned so far to a new situation?
Did you learn what was expected of you from this unit?
Apprentice
Task
Entry Task
Entry Task:
Apprentice Task:
Expert Task:
Milestone Task:
4 days
2 days
Unit length: 16 Days (1 day = 50 minute period)
SFUSD Mathematics Core Curriculum, Grade 6, Unit 6.3: Ratio, 2014–2015
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Entry Task
Family Party
Apprentice Task
Snail Pace and Truffles
Expert Task
Mid-Module Assessment Task
Milestone Task
End-of-Module Assessment Task
CCSS-M
Standards
6.RP.1, 6.RP.3a
6.RP.1, 6.RP.3a
6.RP.1, 6.RP.3a
6.RP.1, 6.RP.2, 6.RP.3
Brief
Description
of Task
Students work with commonly
used fractions and percentages in
a real context.
Students work with distances,
time, and speeds in inches and
minutes. In Truffles, they use
ratios in a recipe context and
interpret a graph.
Students use multiple strategies,
including tables, graphs, and
diagrams, to solve real-world
problems involving ratios.
Students use multiple strategies,
including tables, graphs, and
diagrams, to solve real-world
problems involving ratios and
percents.
Source
MARS: Family Party (2006)
MARS: Snail Pace (2008)
Mid-Module Assessment Task
(NYS Common Core
Mathematics Curriculum Unit
6.1), www.engageny.org
End of Module Assessment Task
(NYS Common Core Mathematics
Curriculum Unit 6.1),
www.engageny.org
Lesson Series 1
Lesson Series 2
Lesson Series 3
CCSS-M
Standards
6.RP.1, 6.RP.3.a
6.RP.1, 6.RP.3, 6.RP.3a, 6.RP.3.c
6.RP.3a, 6.RP.3b, 6.RP.3.c
Brief
Description
of Lessons
Students create tables, number lines, tape
diagrams; transfer ratio relationships to plot
points on simple graphs.
Students learn how to find a percent of a quantity
as a ratio per 100 to solve problems involving
finding the whole, given part and the percent.
Then they solve real world and mathematical
problems, involving ratios and percent. Work with
ratios in non-geometric contexts and use them to
solve problems.
Lesson series introduces rates and guides
students to compare rates through tables and
graphs. Students continue to solve real-world
problems involving ratios, rate, and percent.
Sources
CPM CCC1 Lesson 3.1.6
Illustrative Mathematics
CPM CCC1 Lesson 3.1.2
MARS: Candies (2007) and Mixing Paint (2003)
CPM CCC1 Lessons 7.1.1, 7.1.2
Illustrative Mathematics
MARS: Sewing (2009)
SFUSD Mathematics Core Curriculum, Grade 6, Unit 6.3: Ratio, 2014–2015
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Entry Task
Family Party
What will students do?
Mathematics Objectives and Standards
Math Objectives:
• Students will work with benchmark fractions and percents.
CCSS-M Standards Addressed:
6.RP.3c
Potential Misconceptions:
● Students may struggle with the concept of percent.
● Students may struggle with the fact that Andrea should be included in
the calculations.
Framing Student Experience
Launch:
•
•
•
•
Ask students to name a fraction of boys to students in the classroom.
Ask students to name a fraction of girls to students in the classroom.
Ask students what a class would look like if it were 25%, 50%, 75%, or
100% boys.
Ask students what a class would look like if it were 25%, 50%, 75%, or
100% girls.
During:
Have student work with partners to solve the problems in this task. Circulate
around the room noticing how students are working together as well as the
strategies they use to solve these problems. Note particularly interesting
strategies that you want to be sure to share with the class to build a deeper
understanding of the fraction-percent relationship.
Closure/Extension:
• Ask specific students to share their solutions. These students should be
chosen based on how they solved the problem, either correctly or
incorrectly. The goal is to have a shared understanding of the fractionpercent relationship.
SFUSD Mathematics Core Curriculum, Grade 6, Unit 6.3: Ratio, 2014–2015
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Family Party
How will students do this?
Focus Standards for Mathematical Practice:
1. Make sense of problems and persevere in solving them.
4. Model with mathematics.
Structures for Student Learning:
Academic Language Support:
Vocabulary: fraction, numerator, denominator, percent, ratio
Sentence frames:
The fraction of cousins to guests is ___________.
The percent of cousins to guests is __________.
The ratio of cousins to guests is ____________.
Differentiation Strategies:
Students may use realia, such as counters or coins, to assist with concept understanding.
Participation Structures (group, partners, individual, other):
Partners or individual
SFUSD Mathematics Core Curriculum, Grade 6, Unit 6.3: Ratio, 2014–2015
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Lesson Series #1
Lesson Series Overview: In this lesson series, students develop their part-to-whole fraction understanding. Students will learn how to create tables, double
number lines, and tape diagrams. Students will learn how to transfer ratio relationships to plot points on simple graphs.
CCSS-M Standards Addressed: 6.RP.1, 6.RP.3a
Time: 4 days
Lesson Overview – Days 1 & 2
Resources
Description of Lesson:
Students will be presented with ratios from different contexts. Students will define and
represent a ratio in three ways: a/b, a:b, and a to b.
CPM CCC1, Lesson 3.1.6
Notes:
Read the CPM Teacher Notes for Lesson 3.1.6. You may want to lead Problems 3-78 and
3-79 as full-class discussions, with careful attention to new vocabulary. Problem 3-80
refers to work on a problem from Chapter 1, but that problem isn’t needed to do 3-80. Just
let students know that the problem was about using diagrams to help organize information
and make quick estimates. The problems in this section have a lot of reading, so be
prepared to assist with vocabulary and helping students decode the problems.
Classwork 3-78 to 3-83
Ratio of Boys to Girls (Illustrative Mathematics) – project or copy
this problem onto the board
Homework: 3-84, 3-85, 3-87
Post or display the focus questions to consider as they work through the problems, and
use these questions as prompts while you are circulating to monitor pairs or groups.
1. How do the quantities compare?
2. What quantities am I comparing?
3. How can I represent the relationship?
4. Can I represent it in another way?
For the Ratio of Boys to Girls, ask pairs or groups to solve it using as many methods as
they can. Circulate as students work, and choose groups to share their solution method
with the class. If none of the groups use a diagram, share the tape diagram and ask
students to help you connect that diagram to the other solution methods. Do the same
with the table.
SFUSD Mathematics Core Curriculum, Grade 6, Unit 6.3: Ratio, 2014–2015
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Lesson Overview – Day 3
Resources
Description of Lesson:
Students will describe the difference between a fraction and ratio. While fractions only
describe part to whole, ratios may describe part to part, part to whole, and whole to part.
Students will build and model equivalent ratios using a table and tape diagram. Students
will then interpret and represent ratio relationships on a double number line.
Games at Recess (Illustrative Mathematics)
Walkathon (Illustrative Mathematics)
Notes:
In this lesson you will focus students’ attention on expressing ratio relationships in a
variety of ways: verbally, symbolically (3:1), in table form, in graphical form, with a double
number line, and with a tape diagram. Help students make connections among these
representations, and focus on precision in language and representations.
Lesson Overview – Day 4
Resources
Description of Lesson:
Students solve real-world problems involving ratios, and interpret and represent ratio
relationships in a variety of representations.
Friends Meeting on Bicycles (Illustrative Mathematics)
Jim and Jesse’s Money (Illustrative Mathematics)
Notes:
Use a Think-Pair-Share for part a of the Bicycles problem so that each students has time
to make sense of the problem and attempt to solve it before working with a partner. If
students finish quickly, ask them to solve the problem another way.
SFUSD Mathematics Core Curriculum, Grade 6, Unit 6.3: Ratio, 2014–2015
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Apprentice Task
Snail Pace
What will students do?
Mathematics Objectives and Standards
Math Objectives:
● Students will be able to define and represent a ratio in three ways.
● Students will be able to use ratio language to describe a ratio
relationship.
● Students will be able to describe the difference between a fraction and
a ratio.
● Students will be able to build a model of equivalent ratios using a
table and tape diagram.
● Students will be able to interpret and represent ratio relationships on a
double number line.
CCSS-M Standards Addressed:
6.RP.1, 6.RP.3a
Potential Misconceptions:
● TIME: What is inch? What is minute? What is half an hour?
● DISTANCE: What does that mean?
● SPEED: What does that mean?
Framing Student Experience
Launch:
Ask students:
• What is a race?
• What are different types of races?
• Have you participated in a race?
• Are there different ways to determine a winner of a race?
During:
• Have students work with partners to answer the questions from Snail
Pace.
• Help students set up a table for each snail.
• Help students fill in the partial values on the chart.
Closure/Extension:
• Ask students to describe the winner.
• Ask students to describe proof that a winner has been decided. Ask
students to articulate 2nd, 3rd, and 4th place.
• You can use a second day to have students share and discuss their
solutions.
SFUSD Mathematics Core Curriculum, Grade 6, Unit 6.3: Ratio, 2014–2015
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Snail Pace
How will students do this?
Focus Standards for Mathematical Practice:
1. Make sense of problem and persevere in solving them.
4. Model with mathematics.
Structures for Student Learning:
Academic Language Support:
Vocabulary: minutes, hours, half an hour, inches, feet, travel, speeds
Sentence frames:
Compare feet and inches.
Compare minutes and hours.
Snail __________ is traveling faster than snail ___________.
Snail _________ is traveling slower than snail __________.
The difference between inches and feet is _________________.
The difference between distance and speed is ______________.
Differentiation Strategies:
• Organize.
• Count.
• Make a table
• Add equal amounts (repeated addition).
• Make a conclusion.
• Explain your answer.
• Use a watch.
• Convert minutes to hours, ½ hours.
• Convert inches to feet.
• Teach time and distance.
• Use a stop-watch.
• Count minutes, seconds.
• Use a ruler.
Participation Structures (group, partners, individual, other):
• A + B Partners
• Numbered-Heads together
• Think-Pair-Share
• Safe Shout-out
Individual
SFUSD Mathematics Core Curriculum, Grade 6, Unit 6.3: Ratio, 2014–2015
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Lesson Series #2
Lesson Series Overview: In this lesson series, students learn how to find a percent of a quantity as a ratio per 100 to solve problems involving finding the
whole, given part and the percent. Then they solve real-world and mathematical problems, involving ratios and percents.
CCSS-M Standards Addressed: 6.RP.1, 6.RP.3, 6.RP.3a, 6.RP.3c
Time: 3 days
Lesson Overview – Day 1
Resources
Description of Lesson:
Students develop an understanding of percent and solve problems involving finding the
whole given a part and the percent. The context used is sampling from a mixture of
peanuts and raisins to estimate the amount of each. Students also build their intuition for
how large a given percentage is compared to the whole.
CPM CCC1, Lesson 3.1.2
Resource page 3.1.2
Percent Ruler – project or draw onto board
Materials:
Glass jar with mix of beans, small scoop
Resource Page 3.1.2A, one page for each pair of groups, cut in half
Resource Page 3.1.2B for display
Classwork: Problems 3-22 to 3-30
Large jar full of white and brown beans
Homework: Problems 3-31 to 3-33, and choose from 3-34, 3-35.
Notes:
Read the Teacher Notes for Lesson 3.1.2. You will need a large glass jar full of a mix of
white and brown (or another contrasting color) beans. These represent the raisins and
peanuts described in Problem 3-22.
Problem 3-24 is essential for introducing percent; you might lead this as a class. This
lesson is supposed to be completed in one day, but you may need extra time to help
students make sense of the context and for discussion.
SFUSD Mathematics Core Curriculum, Grade 6, Unit 6.3: Ratio, 2014–2015
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Lesson Overview – Day 2
Resources
Description of Lesson:
Students solve real-world problems involving ratios. Problem contexts include making
drinks from a powdered mix, trail mix, toys in a carnival game, and a score on a test.
CPM CCC1, Lesson 4.2.4
Notes:
Read the Teacher Notes for Lesson 4.2.4, which contain suggestions for opening the
lesson as well as strategies for universal access and teamwork. Students get additional
practice with percents in this lesson.
Homework: Problem 4-80, and choose from Problems 4-81 to 4-84
for review of other concepts.
Classwork: Problems 4-75 to 4-79
Lesson Overview – Day 3
Resources
Description of Lesson:
This is an optional re-engagement lesson. The MARS Candies Task is designed for fifth
th
grade but addresses the standards of this unit. Mixing Paints is designed from 7 grade
and applies concepts of ratios and percents in a difficult problem. You will need to
choose to do one of the lessons, not both of them.
th
Candies (5 grade MARS)
th
Mixing Paints (7 grade MARS)
Student work examples are provided electronically
Notes:
Augment the task by asking extension questions such as:
• What percent of the candies did Amy eat?
• If Anthony has 3 cups of chocolate, how much cream will he need to make his
candies?
• Can you use a diagram to solve?
• Can you solve it another way?
• Can you write another problem about paint using the same information? Trade
problems with another group.
SFUSD Mathematics Core Curriculum, Grade 6, Unit 6.3: Ratio, 2014–2015
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Expert Task
Mid-Module Assessment Task (NYS Common Core Math Curriculum)
What will students do?
Mathematics Objectives and Standards
Math Objectives:
• Students will compare ratios and describe differences in the
relationships.
• Students will represent the ratio relationship in a table to a group and
make predictions.
CCSS-M Standards Addressed:
6.RP.1, 6.RP.3a
Potential Misconceptions:
● Students may give a ratio associated with the numbers in the problem
but not the ratio asked for.
● Errors in graphing, such as not putting a line through the origin.
Framing Student Experience
Launch:
Ask students:
• What are shoe sizes?
• How many of you know your shoe size?
• What is the most common shoe size in the class?
• What is the biggest shoe size in the class? The smallest?
During:
•
•
•
Help student complete the table.
Add extra values to the table to help students understand the concept.
Help students label the axes and plot the points on the graph.
Closure/Extension:
• Ask students to give the coordinates for the points.
• Ask students to name four more coordinate on the graph.
• Ask students to explain the meaning of the graph in relation to the
table.
SFUSD Mathematics Core Curriculum, Grade 6, Unit 6.3: Ratio, 2014–2015
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Mid-Module Assessment Task (NYS Common Core Math Curriculum)
How will students do this?
Focus Standards for Mathematical Practice:
1. Make sense of problems and persevere in solving them.
6. Attend to precision.
Structures for Student Learning:
Academic Language Support:
Vocabulary: plot values, coordinate plane, points, complete a table of values, label the axes, shoe sizes, common shoe sizes
Sentence frames:
The ratio of ______ to ______ (Illustrative Mathematics)
Differentiation Strategies:
Participation Structures (group, partners, individual, other):
SFUSD Mathematics Core Curriculum, Grade 6, Unit 6.3: Ratio, 2014–2015
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Lesson Series #3
Lesson Series Overview: This lesson series introduces rates (though rates did appear in the Snail Pace entry task) and guides students to compare rates
through tables and graphs. Students continue to solve real-world problems involving ratio, rate, and percents. Depending on student progress, you may choose
from a variety of activities for re-engagement, challenge, or review.
CCSS-M Standards Addressed: 6.RP.3a, [6.RP.3b], 6.RP.3c
Time: 4 days
Lesson Overview – Days 1 & 2
Resources
Description of lesson:
Students will compare ratios and describe differences in the relationships. They will
convert units. They will compare rates using tables and graphs. Note that students will
explore rate and unit rate more deeply in a subsequent unit.
CPM CCC1, Lessons 7.1.1 and 7.1.2
Day 1:
Classwork: Problems 7-1, 7-2, 7-7 (add 7-3 to 7-6 for more guidance)
Homework: Problems 7-9 to 7-11; optional 7-12, 7-13
Notes:
Read the Teacher Notes for Lessons 7.1.1 and 7.1.2. You might post the focus
questions for 7.1.2 and refer to them as you circulate among the teams.
1. Which quantities can we compare?
2. Are the ratios equivalent?
3. How else can the ratio be expressed?
Day 2:
Classwork: Problems 7-14 to 7-18
Resource Pages 7.1.2
Colored pencils or markers, several of different colors per team
You can use Problem 7-18 as closure for the second day.
Homework: Problems 7-19, 7-21, 7-23
Lesson Overview – Day 3
Resources
Description of lesson:
Students work more deeply on rate in the context of distance-time.
The Escalator, Assessment Variation (Illustrative Mathematics)
Running at a Constant Speed (Illustrative Mathematics)
Notes:
You might do these activities as Think-Ink-Pair-Share. First have students work
individually, writing down their solutions. Then have them pair up to share their thinking
and revise their solutions.
SFUSD Mathematics Core Curriculum, Grade 6, Unit 6.3: Ratio, 2014–2015
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Lesson Overview – Day 4
Description of lesson:
Re-engage students with any topics they are struggling with, or go deeper with the
application of the standards.
Resources
Overlapping Squares (Illustrative Mathematics)
Shirt Sale (Illustrative Mathematics)
Notes:
You may have pairs or trios prepare a poster and give a presentation on a problem
(assign different problems to each group.) You can also use the suggested Illustrative
Mathematics problems to give students a chance to work with percent in more
challenging problems.
SFUSD Mathematics Core Curriculum, Grade 6, Unit 6.3: Ratio, 2014–2015
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Milestone Task
End of Module Assessment Task (NYS Common Core Math Curriculum)
What will students do?
Mathematics Objectives and Standards
Math Objectives:
● Interpret graphs, tables, and verbal descriptions to solve problems
involving ratios.
● Solve real-world problems involving ratio and percents using a variety
of methods.
● Explain reasoning about ratios using precision in language and
symbols.
Time: 2 days
CCSS-M Standards Addressed:
6.RP.1, 6.RP.2 (not explicitly addressed in this unit), 6.RP.3
Note: This assessment covers some standards not included in the Scope and
Sequence standards for this unit (6.RP.2, 6.RP.3b, 6.RP.3d). You may want to
choose just some of the problems, or provide some scaffolding for questions
that involve unit rate. Lesson Series 3 does give students some experience
with unit rate, so you should decide based on your students’ comfort level.
There will be a later unit that focuses on rate, so students should not be
expected to have mastery of unit rate at this time.
Potential Misconceptions:
Framing Student Experience
Launch:
Connect prior knowledge: What do you already know about ratios? What do
you already know about ratio as a rate? How can you represent percents as
ratios?
Support ELL students by introducing important vocabulary before the task:
• Word Wall
• Vocabulary Chart
• Provide sentence starters w for students to practice orally and in
writing.
• Brainpop.com: Ratio Video
During:
Students will use the SOLVE method from KEMS to examine and restate each
word problem.
Students will then work individually to solve the End of Module Assessment
task individually by using tables, diagrams, or equations to justify their answer
in written form.
Closure/Extension:
Grade and assess the task and provide opportunities for students to revisit the
End of Module Assessment to identify misconceptions. Have students analyze
other students’ work in a group to explain the process to correctly calculating
the answer, or the errors involved in miscalculations.
SFUSD Mathematics Core Curriculum, Grade 6, Unit 6.3: Ratio, 2014–2015
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End of Module Assessment Task (NYS Common Core Math Curriculum)
How will students do this?
Standards for Mathematical Practice:
4. Model with mathematics.
6. Attend to precision.
Structures for Student Learning:
Academic Language Support:
Vocabulary: safety course, exam, progress bar, complete, justify, court, approximately, feet, hardware store, signs on pallets, rate, unit rate, better value,
brand, cubic foot, pounds, constant rate, income.
Sentence frames:
This question is asking me to find _____________________________.
Twenty % can be written as a ratio as _______________________.
My calculations can be justified by ______________________.
Problem # 3:F Julie works 1/12 hours/dollar. This rate means ________________________________.
It will take Julie __________________ hours to earn $228.
Differentiation Strategies:
• Drawing conclusion/making inferences.
• Keeping track of materials/assignments.
• Paying attention to the written word.
Participation Structures (group, partners, individual, other):
• A + B Partners
• Individual
SFUSD Mathematics Core Curriculum, Grade 6, Unit 6.3: Ratio, 2014–2015