6th Grade Mathematics
Ratios and Proportions
Unit 1 Curriculum Map: September 9th – October 9th
ORANGE PUBLIC SCHOOLS
OFFICE OF CURRICULUM AND INSTRUCTION
OFFICE OF MATHEMATICS
6th Grade Unit 1: Ratios and Proportions
September 9th – October 9th
Table of Contents
I.
Unit Overview
II.
CMP Pacing Guide
III.
Pacing Calendar
IV.
Math Background
V.
PARCC Assessment Evidence Statement
VI.
Connections to Mathematical Practices
VII.
Vocabulary
VIII.
Potential Student Misconceptions
IX.
Teaching to Multiple Representations
X.
Unit Assessment Framework
XI.
Performance Tasks
XII.
Assessment Check
XIII.
Summative Task
XIV.
Extensions and Sources
p. 2
p. 3
p. 4-5
p. 6
p. 7-9
p. 10
p. 11
p. 12
p. 13-15
p.16
p.17-21
p. 22
p. 23
p. 24
1
6th Grade Unit 1: Ratios and Proportions
September 9th – October 9th
2
6th Grade Unit 1: Ratios and Proportions
September 9th – October 9th
Unit Overview
In this unit students will …
-
Strengthen sense of and understanding of proportional reasoning
-
Develop and use multiplicative thinking
-
Develop the understanding that a ratio is a comparison of two numbers or quantities
-
Find percents using the same processes for solving rates and proportions
-
Solve real-life problems involving measurement units that need to be converted
Enduring Understandings
-
A ratio is a number that relates two quantities or measures within a given situation in a
multiplicative relationship (in contrast to a difference or additive relationship).
-
Ratios can express comparisons of a part to whole, (a/b with b ≠ 0)
-
Fractions are part-whole ratios, meaning fractions are also ratios. Percentages are
ratios and are sometimes used to express ratios.
-
Both part-to-whole and part-to-part ratios compare two measures of the same type of
thing. A ratio can also be a rate.
-
A rate is a comparison of the measures of two different things or quantities; the
measuring unit is different for each value.
-
Ratios use division to represent relations between two quantities.
3
6th Grade Unit 1: Ratios and Proportions
September 9th – October 9th
CMP Pacing Guide
Activity
Common Core Standards
Estimated Time
Unit Readiness Assessment
(CMP3)
5.NBT.A.1, 4.NBT.A.2, 5.NF.B.3,
5.NF.B.7, 5.NBT.A.3b
1 Block
Comparing Bits and Pieces
(CMP3) Investigation 1
6.RP.A.1, 6.RP.A.3, 6.RP.A.3a,
6.NS.B.4
4 Blocks
Assessment: Partner Quiz
(CMP3)
6.RP.A.1, 6.RP.A.3, 6.RP.A.3a,
6.NS.B.4
½ Block
Comparing Bits and Pieces
(CMP3) Investigation 2
6.RP.A.1, 6.RP.A.2, 6.RP.A.3,
6.RP.A.3b, 6.NS.B.4
2 Blocks
Assessment: Check Up 1
(CMP3)
6.RP.A.1, 6.RP.A.2, 6.RP.A.3,
6.RP.A.3b, 6.NS.B.4
½ Block
Performance Task 1
6.RP.A.2
½ Block
Comparing Bits and Pieces
(CMP3) Investigation 3
6.NS.C.6a, 6.NS.C.6c, 6.NS.C.7b,
6.NS.C.7c
4 Blocks
Assessment: Check Up 2
(CMP3)
6.NS.C.6a, 6.NS.C.6c, 6.NS.C.7b,
6.NS.C.7c
½ Block
Comparing Bits and Pieces
(CMP3) Investigation 4
6.RP.A.1, 6.RP.A.3, 6.RP.A.3b,
6.RP.A.3c, 6.NS.B.2
2 Blocks
Assessment: Check Up 3
(CMP3)
6.RP.A.1, 6.RP.A.3, 6.RP.A.3b,
6.RP.A.3c, 6.NS.B.2
½ Block
Decimal Ops
(CMP3) Investigation 4
6.RP.A.1, 6.RP.A.2, 6.RP.A.3c,
6.NS.B.2, 6.NS.B.3
2½ Blocks
Unit 1 Assessment
6.RP.A.1, 6.RP.A.2, 6.RP.A.3a,
6.RP.A.3b, 6.RP.A.3c
1 Block
Performance Task 2
6.RP.A.3c
½ Block
Total Time
19 ½ Blocks
4
September 9th – October 9th
6th Grade Unit 1: Ratios and Proportions
Pacing Calendar
SEPTEMBER
Sunday
Monday
1
Labor Day
Tuesday
2
OPENING
DAY
SUP. FORUM
PD DAY
9
1st Day for
students
7
8
PD DAY?
14
15
16
21
22
Assessment:
Check Up 1
23
28
29
30
Wednesday
Thursday
Friday
Saturday
3
4
5
6
PD DAY
PD DAY
PD DAY
10
Unit 1:
Ratios &
Proportions
Readiness
Assessment
17
Assessment:
Partner Quiz
11
12
13
18
19
Performance
Task 1 Due
20
24
12:30 pm
Dismissal for
students
25
26
Assessment:
Check Up 2
27
5
September 9th – October 9th
6th Grade Unit 1: Ratios and Proportions
OCTOBER
Sunday
5
Monday
6
Assessment:
Unit 1
Assessment
Tuesday
7
Wednesday
Thursday
Friday
Saturday
1
Assessment:
Check Up 3
2
3
4
8
9
Unit 1
Complete
10
11
17
18
25
Performance
Task 2 Due
16
12
13
14
15
19
20
21
22
23
12:30 pm
Dismissal for
students
24
26
27
28
29
30
12:30 pm
Dismissal for
students
31
6
6th Grade Unit 1: Ratios and Proportions
September 9th – October 9th
Unit 1 Math Background
Rational numbers are a focal point for middle school students. The goal of this unit is to help
students deepen their understanding of equivalent fractions and develop this understanding as
they explore ratios. Throughout the unit students will learn to compare with ratios for specific
cases. This will assist them in improving their multiplicative thinking and prepare them for
proportional reasoning.
During their elementary mathematics education, students were exposed to the area model for
fractions. In this unit the students work with more linear models in order to extend the manner
in which they reason about rational numbers, understand equivalence, as well as perform
operations on rational numbers which is explored further in a later unit. These models include
fraction strips, percent bars, and number lines.
Throughout the unit, students use rate tables as a way to express equivalent ratios and
compute unit rates. For most of this unit, ratios are not written as fractions. The intent is to
keep the notation for part–whole fractions and rational numbers apart from the notation for
ratio comparisons to help develop understanding. When the word fraction appears, it is used to
represent part of a whole. The learning here will help lay the foundation for the work on ratios
and unit rates that will come later in the year as well as the following year. In grade 7, students
will use fraction notation to express ratios and will explore ratios in more detail.
7
September 9th – October 9th
6th Grade Unit 1: Ratios and Proportions
PARCC Assessment Evidence Statements
CCSS
Evidence Statement
Clarification
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.”
i) Expectations for ratios in this
grade are limited to ratios of
non-complex fractions. (See
footnote, CCSS p 42.) The
initial numerator and
denominator should be whole
numbers.
6.RP.2
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. For example,
“This recipe has a ratio of 3
cups of flour to 4 cups of sugar,
so there is 3/4 cup of flour for
each cup of sugar.” “We paid
$75 for 15 hamburgers, which
is a rate of $5 per hamburger.”
Use ratio and rate reasoning to
solve real-world and
mathematical problems, e.g., by
reasoning about tables of
equivalent ratios, tape
diagrams, double number line
diagrams, or equations.
i i) Expectations for unit rates
in this grade are limited to noncomplex fractions. (See
footnote, CCSS p 42.)
The initial numerator and
denominator should be whole
numbers.
2
No
The testing interface can
provide students with a
calculation aid of the specified
kind for these tasks.
2, 4, 5, 7,
8
Yes
2, 8, 5
Yes
6.RP.3a
a. 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.
Math
Calculator?
Practices
2
No
i) Expectations for ratios in this
grade are limited to ratios of
non-complex fractions. (See
footnote, CCSS p 42.) The
initial numerator and
denominator should be whole
numbers.
Use tables to compare ratios.
6.RP.3b
Use ratio and rate reasoning to
solve real-world and
mathematical problems, e.g., by
reasoning about tables of
equivalent ratios, tape
diagrams, double number line
diagrams, or equations.
i) See ITN Appendix F, Table
F.c, “Minimizing or avoiding
common drawbacks of
selected response,”
specifically, Illustration 1 (in
contrast to the problem
“A bird flew 20 miles in 100
8
6th Grade Unit 1: Ratios and Proportions
b. 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?
September 9th – October 9th
minutes. At that speed, how
long would it take the bird to fly
6 miles?”)
ii) The testing interface can
provide students with a
calculation aid of the specified
kind for these tasks.
iii) Expectations for unit rates in
this grade are limited to noncomplex fractions. (See
footnote, CCSS p 42)
iii) The initial numerator and
denominator should be whole
numbers.
6.RP.3c
1
Use ratio and rate reasoning to
solve real-world and
mathematical problems, e.g., by
reasoning about tables of
equivalent ratios, tape
diagrams, double number line
diagrams, or equations.
i) The testing interface can
provide students with a
calculation aid of the specified
kind for these tasks.
c. Find a percent of a quantity
as a rate per 100 (e.g., 30% of
a quantity means 30/100 times
the quantity).
iii) Expectations for ratios in
this grade are limited to ratios
of non-complex fractions. (See
footnote, CCSS
2, 7, 5, 8
Yes
2, 7, 5, 8
Yes
2, 6, 7, 5,
8
Yes
ii) Pool should contain tasks
with and without contexts
p 42.) The initial numerator and
denominator should be whole
numbers.
6.RP.3c2
Use ratio and rate reasoning to
solve real-world and
mathematical problems, e.g., by
reasoning about tables of
equivalent ratios, tape
diagrams, double number line
diagrams, or equations.
c. Solve problems involving
finding the whole, given a part
and the percent.
6.RP.3d
i) The testing interface can
provide students with a
calculation aid of the specified
kind for these tasks.
ii) Expectations for ratios in this
grade are limited to ratios of
non-complex fractions. (See
footnote, CCSS
p 42.) The initial numerator and
denominator should be whole
numbers.
Use ratio and rate reasoning to i) Pool should contain tasks
solve real-world and
with and without contexts
mathematical problems, e.g., by
reasoning about tables of
ii) Tasks require students to
9
6th Grade Unit 1: Ratios and Proportions
equivalent ratios, tape
diagrams, double number line
diagrams, or equations.
d. Use ratio reasoning to
convert measurement units;
manipulate and transform units
appropriately when multiplying
or dividing quantities.
September 9th – October 9th
multiply and/or divide
dimensioned quantities
iii) 50% of tasks require
students to correctly express
the units of the result.
The testing interface can
provide students with a
calculation aid of the specified
kind for these tasks.
iv) Expectations for ratios in
this grade are limited to ratios
of non-complex fractions. (See
footnote, CCSS p 42.) The
initial numerator and
denominator should be whole
numbers.
10
6th Grade Unit 1: Ratios and Proportions
September 9th – October 9th
Connections to the Mathematical Practices
1
2
3
4
5
6
7
8
Make sense of problems and persevere in solving them
- Make sense of real-world rate and proportion problem situations by representing the
context in tactile and/or virtual manipulatives, visual, or algebraic models
- Understand the problem context in order to translate them into ratios/rates
Reason abstractly and quantitatively
- Understand the relationship between two quantities in order to express them
mathematically
- Use ratio and rate notation as well as visual models and contexts to demonstrate
reasoning
Construct viable arguments and critique the reasoning of others
- Construct and critique arguments regarding the proportion of a whole as
represented in the context of real-world situations
- Construct and critique arguments regarding appropriateness of representations
given ratio and rate contexts, EX: does a tape diagram adequately represent a
given ratio scenario
Model with mathematics
- Model a problem situation symbolically (tables, expressions, or equations), visually
(graphs or diagrams) and contextually to form real-world connections
Use appropriate tools strategically
- Choose appropriate models for a given situation, including tables, expressions or
equations, tape diagrams, number line models, etc.
Attend to precision
- Use and interpret mathematical language to make sense of ratios and rates
- Attend to the language of problems to determine appropriate representations and
operations for solving real-world problems.
- Attend to the precision of correct decimal placement used in real-world problems
Look for and make use of structure
- Use knowledge of problem solving structures to make sense of real world problems
- Recognize patterns that exist in ratio tables, including both the additive and
multiplicative properties
- Use knowledge of the structures of word problems to make sense of real-world
problems
Look for and express regularity in repeated reasoning
- Utilize repeated reasoning by applying their knowledge of ratio, rate and problem
solving structures to new contexts
- Generalize the relationship between representations, understanding that all formats
represent the same ratio or rate
- Demonstrate repeated reasoning when dividing fractions by fractions and connect
the inverse relationship to multiplication
- Use repeated reasoning when solving real-world problems using rational numbers
11
September 9th – October 9th
6th Grade Unit 1: Ratios and Proportions
Vocabulary
Term
Absolute Value
Equivalent
Fractions
Definition
The absolute value of a number is its distance from 0 on a number line. Numbers
that are the same distance from 0 have the same absolute value. For
example, −3 and 3 both have an absolute value of 3.
Fractions that are equal in value, but may have different numerators and
2
14
denominators. For example, 3 and 21 are equivalent fractions. The shaded part of
2
3
this rectangle represents both and
Mixed Number
14
.
21
A number that is written with both a whole number and a fraction. A mixed number
1
is the sum of the whole number and the fraction. The number 2 2 represents 2
1
1
wholes and a 2 and can be thought of as 2 + 2
Opposite
Percent
Proportion
Rate
Rate Table
Ratio
Rational Number
Tape Diagram
Unit Rate
Unit Ratio
Two numbers whose sum is 0. For example, −3 and 3 are opposites. On a number
line, opposites are the same distance from 0 but in different directions from 0. The
number 0 is its own opposite.
A fraction or ratio in which the denominator is 100; a number compared to 100
An equation which states that two ratios are equal
A comparison of two quantities that have different units of measure
A table that shows the value of a single item in terms of another item. It is used to
show equivalent ratios of the two items.
Compares quantities that share a fixed, multiplicative relationship
A number that can be written as a/b where a and b are integers, but b is not equal
to 0
A thinking tool used to visually represent a mathematical problem and transform the
words into an appropriate numerical operation. Tape diagrams are drawings that
look like a segment of tape, used to illustrate number relationships. Also known as
Singapore Strips, strip diagrams, bar models or graphs, fraction strips, or length
models.
A unit rate is a rate in which the second number (usually written as the
denominator) is 1, or 1 of a quantity. For example, 1.9 children per family, 32 miles
3 𝑓𝑙𝑎𝑣𝑜𝑟𝑠 𝑜𝑓 𝑖𝑐𝑒 𝑐𝑟𝑒𝑎𝑚
per gallon, and
are unit rates. Unit rates are often found by
1 𝑏𝑎𝑛𝑎𝑛𝑎 𝑠𝑝𝑙𝑖𝑡
scaling other rates.
Ratios written as some number to 1
12
6th Grade Unit 1: Ratios and Proportions
September 9th – October 9th
Potential Student Misconceptions
-
Often there is a misunderstanding that a percent is always a natural number less than or equal
to 100. Provide examples of percent amounts that are greater than 100%, and percent amounts
that are less than 1%.
-
Students may not distinguish between proportional situations and additive situations.
Students may not realize that although they may have added to find equivalent ratios,
they did not add the same amount on both sides.
-
Students may still not understand the need to keep the same rate when thinking
proportionally.
13
6th Grade Unit 1: Ratios and Proportions
September 9th – October 9th
Teaching Multiple Representations
14
6th Grade Unit 1: Ratios and Proportions
September 9th – October 9th
15
6th Grade Unit 1: Ratios and Proportions
September 9th – October 9th
16
6th Grade Unit 1: Ratios and Proportions
September 9th – October 9th
Assessment Framework
Unit 1 Assessment Framework
Assessment
CCSS
Estimated
Time
Format
Graded
?
Unit Readiness Assessment
(Beginning of Unit)
CMP3
Assessment: Partner Quiz
(After Investigation 1)
CMP3
Assessment: Check Up 1
(After Investigation 2)
CMP3
Assessment: Check Up 2
(After Investigation 3)
CMP3
Assessment: Check Up 3
(After Investigation 4)
CMP3
Unit 1 Assessment
(Conclusion of Unit)
Model Curriculum
5.NBT.A.1, 4.NBT.A.2,
5.NF.B.3, 5.NF.B.7,
5.NBT.A.3b
6.RP.A.1, 6.RP.A.3,
6.RP.A.3a, 6.NS.B.4
1 Block
Individual
No
½ Block
Group
Yes
6.RP.A.1, 6.RP.A.2,
6.RP.A.3, 6.RP.A.3b,
6.NS.B.4
6.NS.C.6a, 6.NS.C.6c,
6.NS.C.7b, 6.NS.C.7c
½ Block
Individual
Yes
½ Block
Individual
Yes
6.RP.A.1, 6.RP.A.3,
6.RP.A.3b, 6.RP.A.3c,
6.NS.B.2
6.RP.A.1, 6.RP.A.2,
6.RP.A.3a, 6.RP.A.3b,
6.RP.A.3c
½ Block
Individual
or Group
Yes
1 Block
Individual
Yes
Unit 1 Performance Assessment Framework
Assessment
CCSS
Estimated
Time
Format
Graded
?
Performance Task 1
(Mid-September)
Mangos for Sale
6.RP.A.2
½ Block
Group
Yes; Rubric
Performance Task 2
(Early October)
Gianna’s Job
6.RP.A.3, 6.RP.A.3a
½ Block
Yes: rubric
Assessment Check 1
(optional)
6.RP.A.1, 6.RP.A.3a,
6.RP.A.3b, 6.RP.A.3c,
6.NS.C.6c
Teacher
Discretion
Individual
w/
Interview
Opportunity
Teacher
Discretion
Yes, if
administered
6.RP.A.1, 6.RP.A.2,
6.RP.A.3
Teacher
Discretion
Teacher
Discretion
Yes, if
administered
Summative Tasks
(optional)
17
6th Grade Unit 1: Ratios and Proportions
September 9th – October 9th
Performance Tasks
Performance Task 1:
Mangos for Sale (6.RP.A.2)
A store was selling 8 mangos for $10 at the farmers market.
Keisha said,
“That means we can write the ratio 10 : 8, or $1.25 per mango.”
Luis said,
“I thought we had to write the ratio the other way, 8 : 10, or 0.8 mangos per dollar."
Can we write different ratios for this situation? Explain why or why not.
18
6th Grade Unit 1: Ratios and Proportions
September 9th – October 9th
Solution:
Yes, this context can be modeled by both of these ratios and their associated unit rates. The context
itself doesn’t determine the order of the quantities in the ratio; we choose the order depending on what
we want to know.
Performance Task Scoring Rubric:
3-Point Response
The response shows complete understanding of the problem’s
essential mathematical concepts. The student executes
procedures completely and gives relevant responses to all parts of
the task. The response contains few minor errors, if any. The
response contains a clear, effective explanation detailing how the
problem was solved so that the reader does not need to infer how
and why decisions were made.
2-Point Response
The response shows nearly complete understanding of the
problem’s essential mathematical concepts. The student executes
nearly all procedures and gives relevant responses to most parts of
the task. The response may have minor errors. The explanation
detailing how the problem was solved may not be clear, causing
the reader to make some inferences.
1-Point Response
The response shows limited understanding of the problem’s
essential mathematical concepts. The response and procedures
may be incomplete and/or may contain major errors. An incomplete
explanation of how the problem was solved may contribute to
questions as to how and why decisions were made.
0-Point Response
The response shows insufficient understanding of the problem’s
essential mathematical concepts. The procedures, if any, contain
major errors. There may be no explanation of the solution or the
reader may not be able to understand the explanation. The reader
may not be able to understand how and why decisions were made.
19
6th Grade Unit 1: Ratios and Proportions
September 9th – October 9th
Performance Task 2:
Gianna’s Job (6.RP.A.3, 6.RP.A.3a)
Gianna is paid $90 for 5 hours of work.
a. At this rate, how much would Gianna make for 8 hours of work?
b. At this rate, how long would Gianna have to work to make $60?
20
6th Grade Unit 1: Ratios and Proportions
September 9th – October 9th
Solutions:
Solution: Making a table
a. This method uses a ratio table:
Time Worked
(hours)
Gianna's Earnings
(dollars)
5
90
10
180
20
360
40
720
8
144
b. The first row is the given information and to get to the second row we multiply both entries of the
first row by 2. To get from the second to the third row of the table we multiply by 2 again. From
the third to the fourth for we multiply by 2 for a third time. Now 40 hours can be divided by 5 to
give 8 hours so this is the last step. There are many other possible ways to arrive at the answer
with a table. For example, since
8
8=( )×5
5
8
we could move from the first row to the last in one step, multiplying the first row by 5 .
c. We again make a table and this time the goal is to get $60 in the earnings column and find out
how many hours it takes for Gianna to earn this amount of money. We see that 60 is not a factor
of 90 so we can’t get to 60 directly by dividing by a whole number. But 60 is a factor of 180
which is 2 × 90 so we use this:
Time Worked
(hours)
Gianna's Earnings
(dollars)
5
90
10
180
10
3
60
d. It takes Gianna
10
3
hours or 3 hours and 20 minutes to make $60.
21
6th Grade Unit 1: Ratios and Proportions
September 9th – October 9th
Solution: Making a double number line
a. We are given that Gianna makes $90 in 5 hours. We can plot this information on a double
number line, with money plotted on one line and time on the other:
The goal is to use the information given to work out what dollar amount will go along with 8
hours. One way to do this would be to work out the hourly wage and then multiply by 8. This is
shown below with the first step drawn in purple and the second step in blue:
To find the hourly wage we have to divide the number of given hours by 5 and so we also divide the
wages by 5. Next, to find the wages for 8 hours we multiply the hourly wage by 8. There are many
other alternatives. The quickest method would be to multiply the given values of money and time
8
by 5 .
2
b. To find how long Gianna has to work to make $60 notice that $60 is 3 of $90. So we can first
take one third of the given values (in purple below) and then double these new values (in blue):
It takes Gianna
10
3
hours or 3 and a third hours to earn $60.
Solution: Using a unit rate
a. In order to find out how much Gianna makes in 8 hours, we can first find her hourly rate and
then multiply by 8. Since Gianna makes $90 in 5 hours she will make $90 ÷ 5 in 1 hour. This
means that Gianna makes $18 per hour. So in 8 hours she will make
8 × $18 = $144.
b. To find out how long it takes Gianna to make $60 we can find out how long it take her to
make $1 and then multiply by 60. Since Gianna makes $90 in 5 hours she will make $1 in
1
1
5 ÷ 90 hours. This is 18 of an hour. Since Gianna makes $1 in 18 of an hour she will make $60
60
in 18 hours. This is three and a third hours.
Although the solutions to (a) and (b) are conceptually similar, (a) feels more natural because we use
the units of dollars per hour frequently when thinking of wages. For part (b), we use the units of hours
per dollar which feel less familiar
22
6th Grade Unit 1: Ratios and Proportions
September 9th – October 9th
Performance Task Scoring Rubric:
3-Point Response
The response shows complete understanding of the problem’s
essential mathematical concepts. The student executes
procedures completely and gives relevant responses to all parts of
the task. The response contains few minor errors, if any. The
response contains a clear, effective explanation detailing how the
problem was solved so that the reader does not need to infer how
and why decisions were made.
2-Point Response
The response shows nearly complete understanding of the
problem’s essential mathematical concepts. The student executes
nearly all procedures and gives relevant responses to most parts of
the task. The response may have minor errors. The explanation
detailing how the problem was solved may not be clear, causing
the reader to make some inferences.
1-Point Response
The response shows limited understanding of the problem’s
essential mathematical concepts. The response and procedures
may be incomplete and/or may contain major errors. An incomplete
explanation of how the problem was solved may contribute to
questions as to how and why decisions were made.
0-Point Response
The response shows insufficient understanding of the problem’s
essential mathematical concepts. The procedures, if any, contain
major errors. There may be no explanation of the solution or the
reader may not be able to understand the explanation. The reader
may not be able to understand how and why decisions were made.
23
6th Grade Unit 1: Ratios and Proportions
September 9th – October 9th
Assessment Check
Assessment Check 1
1. The table below shows the 2009 population of Tennessee represented by different age
groups.
Based on this information, which ratio represents the percent of the total population who
were over 65 and over age group to the percent of the total population who were in the
0 to 18 age group in Tennessee in 2009?
a. 1:8
b. 1:5
c. 13: 24
d. 13:17
2. Fill in the chart comparing slices per pizza.
3. A farmer was selling corn to the market. He sold it by the ton (2000 lbs.)
a. If he sold 12 tons for $3600, then how much did one pound of corn cost the market?
b. After purchasing the corn, the market found that one ton of corn equaled 6000 ears
of corn averages. How many ears per pound does that compute to?
4. Jack ran 4 miles in 45 minutes. Jill ran 7 miles in 64.5 minutes.
a. How many miles/hour did each person run?
b. Who ran faster? Explain how you know.
5. Kendall bought a vase that was priced at $450. In addition, she had to pay 3% sales
tax. How much did she pay for the vase?
6. A submarine was situated 800 feet below sea level. If it ascends 250 feet, what is the
new position?
7. One day in July, the temperature at ground level at the airport was 90°. A pilot reported
the temperature at 10,000 feet was 50°. How much did the temperature drop per 1000
feet?
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6th Grade Unit 1: Ratios and Proportions
September 9th – October 9th
Summative Tasks
Summative Task
6.RP.A.1, 6.RP.A.2, 6.RP.A.3
1. John, Marie, and Will all ran for 6th grade class president. Of the 36 students, 16 voted for
John, 12 for Marie, and 8 for Will. What was the ratio of votes for John to votes for Will? What
was the ratio of votes for Marie to votes for Will? What was the ratio of votes for Marie to votes
for John?
2. Because no one got half the votes, they had to have a run-off election. Marie dropped out
and convinced all her voters to vote for Will. What is the new ratio of Will’s votes to John’s?
3. John and Will also ran for Middle School Council President. There are 90 students voting in
middle school. If the ratio of Will’s votes to John’s votes remains the same as it was in part (b),
how many more votes will Will get than John?
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6th Grade Unit 1: Ratios and Proportions
September 9th – October 9th
Extensions and Sources
Online Resources
http://www.illustrativemathematics.org/standards/k8
- Performance tasks, scoring guides
http://www.ixl.com/math/grade-6
- Interactive, visually appealing fluency practice site that is objective descriptive
https://www.khanacademy.org/math/arithmetic/fractions
- Interactive, tracks student points, objective descriptive videos, allows for hints
https://www.khanacademy.org/math/arithmetic/rates-and-ratios
- Interactive, tracks student points, objective descriptive videos, allows for hints
http://www.doe.k12.de.us/assessment/files/Math_Grade_6.pdf
- Common Core aligned assessment questions, including Next Generation Assessment Prototypes
https://www.georgiastandards.org/Common-Core/Pages/Math-6-8.aspx
- Common core assessments and tasks designed for students with special needs
http://www.parcconline.org/sites/parcc/files/PARCCMCFMathematicsGRADE8_Nov2012V3_FINAL.pdf
- PARCC Model Content Frameworks Grade 8
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