Grade 6

2017-2018

M/J Grade 6 Mathematics
Curriculum Map
1205010

Volusia County Curriculum Maps are revised annually and updated throughout the year.
The success criteria are a work in progress and may be modified as needed.

Curriculum Map Committee & Reviewers

Name School Name School
Heidi Luby DeLand Middle School Cindy McNairy River Springs Middle School
Joyce Price Deltona Middle School Cassandra Reyes
Alena Rodgers Southwestern Middle School Abby Benito Campbell Middle School

DeLand Middle &
Southwestern Middle School

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Mathematics Florida Standards
Standards for Mathematical Practice

1. Make sense of problems and persevere in solving them. (MAFS.K12.MP.1)
Solving a mathematical problem involves making sense of what is known and applying a thoughtful and logical process
which sometimes requires perseverance, flexibility, and a bit of ingenuity.

2. Reason abstractly and quantitatively. (MAFS.K12.MP.2)
The concrete and the abstract can complement each other in the development of mathematical understanding:
representing a concrete situation with symbols can make the solution process more efficient, while reverting to a concrete
context can help make sense of abstract symbols.

3. Construct viable arguments and critique the reasoning of others. (MAFS.K12.MP.3)
A well-crafted argument/critique requires a thoughtful and logical progression of mathematically sound statements and
supporting evidence.

4. Model with mathematics. (MAFS.K12.MP.4)
Many everyday problems can be solved by modeling the situation with mathematics.

5. Use appropriate tools strategically. (MAFS.K12.MP.5)
Strategic choice and use of tools can increase reliability and precision of results, enhance arguments, and deepen
mathematical understanding.

6. Attend to precision. (MAFS.K12.MP.6)
Attending to precise detail increases reliability of mathematical results and minimizes miscommunication of mathematical
explanations.

7. Look for and make use of structure. (MAFS.K12.MP.7)
Recognizing a structure or pattern can be the key to solving a problem or making sense of a mathematical idea.

8. Look for and express regularity in repeated reasoning. (MAFS.K12.MP.8)
Recognizing repetition or regularity in the course of solving a problem (or series of similar problems) can lead to results
more quickly and efficiently.

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Grade 6 Mathematics: Mathematics Florida Standards

In M/J Mathematics 1, instructional time should focus on four critical areas: (1) connecting ratio and rate to whole number multiplication and division and
using concepts of ratio and rate to solve problems; (2) completing understanding of division of fractions and extending the notion of number to the system
of rational numbers, which includes negative numbers; (3) writing, interpreting, and using expressions and equations; and (4) developing understanding of
statistical thinking.

(1) Students use reasoning about multiplication and division to solve ratio and rate problems about quantities. By viewing equivalent ratios and rates as
deriving from, and extending, pairs of rows (or columns) in the multiplication table, and by analyzing simple drawings that indicate the relative size of
quantities, 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 solve a wide variety of problems involving ratios and
rates.
(2) Students use the meaning of fractions, the meanings of multiplication and division, and the relationship between multiplication and division to understand
and explain why the procedures for dividing fractions make sense. Students use these operations to solve problems. Students extend their previous
understandings of number and the ordering of numbers to the full system of rational numbers, which includes negative rational numbers, and in particular
negative integers. They reason about the order and absolute value of rational numbers and about the location of points in all four quadrants of the coordinate
plane.
(3) Students understand the use of variables in mathematical expressions. They write expressions and equations that correspond to given situations, evaluate
expressions, and use expressions and formulas to solve problems. Students understand that expressions in different forms can be equivalent, and they use the
properties of operations to rewrite expressions in equivalent forms. Students know that the solutions of an equation are the values of the variables that make
the equation true. Students use properties of operations and the idea of maintaining the equality of both sides of an equation to solve simple one-step
equations. Students construct and analyze tables, such as tables of quantities that are equivalent ratios, and they use equations (such as 3x = y) to describe
relationships between quantities.
(4) Building on and reinforcing their understanding of number, students begin to develop their ability to think statistically. Students recognize that a data
distribution may not have a definite center and that different ways to measure center yield different values. The median measures center in the sense that it is
roughly the middle value. The mean measures center in the sense that it is the value that each data point would take on if the total of the data values were
redistributed equally, and also in the sense that it is a balance point. Students recognize that a measure of variability (interquartile range or mean absolute
deviation) can also be useful for summarizing data because two very different set of data can have the same mean and median yet be distinguished by their
variability. Students learn to describe and summarize numerical data sets, identifying clusters, peaks, gaps, and symmetry, considering the context in which the
data were collected. Students in M/J Mathematics 1 also build on their work with area in elementary school by reasoning about relationships among shapes to
determine area, surface area, and volume.
They find areas of right triangles, other triangles, and special quadrilaterals by decomposing these shapes, rearranging or removing pieces, and relating the
shapes to rectangles. Using these methods, students discuss, develop, and justify formulas for areas of triangles and parallelograms. Students find areas of
polygons and surface areas of prisms and pyramids by decomposing them into pieces whose area they can determine. They reason about right rectangular
prisms with fractional side lengths to extend formulas for the volume of a right rectangular prism to fractional side lengths. They prepare for work on scale
drawings and constructions in Grade 7 by drawing polygons in the coordinate plane.

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Fluency Recommendations

MAFS.6.NS.2 Students fluently divide multi-digit numbers using the standard algorithm. This is the culminating
standard for several years’ worth of work with division of whole numbers.

MAFS.6.NS.3 Students fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm
for each operation. This is the culminating standard for several years’ worth of work relating to the

domains of Number and Operations in Base Ten, Operations and Algebraic Thinking, and Number and

Operations with Fractions.

MAFS.6.NS.1 Students interpret and compute quotients of fractions and solve word problems involving division of

fractions by fractions. This completes the extension of operations to fractions.

The following Mathematics and English Language Arts CCSS should be taught throughout the course:

LAFS.6.SL.1.1: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on

grade 6 topics, texts, and issues, building on others’ ideas and expressing their own clearly.

LAFS.6.SL.1.2: Interpret information presented in diverse media and formats (e.g., visually, quantitatively, orally) and explain how it

contributes to a topic, text, or issue under study.

LAFS.6.SL.1.3 : Delineate a speaker’s argument and specific claims, distinguishing claims that are supported by reasons and evidence from

claims that are not.

LAFS.6.SL.2.4: Present claims and findings, sequencing ideas logically and using pertinent descriptions, facts, and details to accentuate

main ideas or themes; use appropriate eye contact, adequate volume, and clear pronunciation.

LAFS.68.RST.1.3: Follow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical tasks.

LAFS.68.RST.2.4: Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific

scientific or technical context relevant to grades 6–8 texts and topics.

LAFS.68.RST.3.7 : Integrate quantitative or technical information expressed in words in a text with a version of that information expressed

visually (e.g., in a flowchart, diagram, model, graph, or table).

LAFS.68.WHST.1.1: Write arguments focused on discipline-specific content.

LAFS.68.WHST.2.4 : Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and

audience.

ELD.K12.ELL.MA.1 English language learners communicate information, ideas and concepts necessary for academic success in the

content area of Mathematics.

ELD.K12.ELL.SI.1 English language learners communicate for social and instructional purposes within the school setting.

RP: Ratios and Proportional Relationships Domain Abbreviations EE: Expressions and Equations
G: Geometry NS: Number System
SP: Statistics and Probability

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Grade 6 Mathematics Florida Standards At A Glance

Domains Ratios & The Number System Expressions and Equations Geometry Statistics and
Clusters Proportional Probability

 URnedleartisotannsdhirpastio  Apply and extend previous understandings  Apply and extend previous  Solve real-world  Develop

concepts and use of multiplication and division to divide understandings of arithmetic to and understanding

ratio reasoning to fractions by fractions algebraic expressions mathematical of statistical

solve problems  Compute fluently with multi-digit numbers  Reason about and solve one- problems variability

and find common factors and multiples variable equations and inequalities involving area,  Summarize and
surface area, describe
 Apply and extend previous understandings  Represent and analyze quantitative and volume distributions

of numbers to the system of rational relationships between dependent

numbers and independent variables

FSA Reporting Catagories and Percentage of Test:

Ratio and Proportional Relationships = 15% Expressions and Equations = 30% Geometry = 15%

Statistics and Probability = 19% The Number System = 21%

First Quarter Second Quarter Third Quarter Fourth Quarter

SMT 1 Focus 2: Measurement and Data Focus 4: Equivalent Expressions Focus 6: Relationships in

MAFS.6.SP.1.1 MAFS.6.EE.1.1 Geometry (continued)

Focus 1: Numbers and MAFS.6.SP.1.2 MAFS.6.EE.1.2 MAFS.6.G.1.2
Number Operations MAFS.6.SP.1.3 MAFS.6.EE.1.3 MAFS.6.G.1.4
MAFS.6.SP.2.4 MAFS.6.EE.1.4
MAFS.6.NS.2.4 MAFS.6.SP.2.5 MAFS.6.EE.2.6 DIA 4
MAFS.6.NS.2.2

MAFS.6.NS.1.1 DIA 2 Focus 5: Equations & Inequalities FSA
MAFS.6.NS.2.3
MAFS.6.NS 3.6a&c MAFS.6.EE.2.5

MAFS.6.NS.3.5 MAFS.6.EE.2.7 Required Standards for Advanced
MAFS.6.NS.3.7 MAFS.6.EE.2.8 and Preview for Regular

Focus 3: Proportionality – Ratios MAFS.6.EE.3.9

DIA 1 and Rates DIA 3 Operations with Integers

MAFS 6.RP.1.1 MAFS.7.NS.1.2

MAFS.6.RP.1.2 MAFS.7.NS.1.1

MAFS.6.RP.1.3 MAFS.7.NS.1.3

Focus 6: Relationships in

Geometry Simplifying Algebraic Expressions

MAFS.6.NS 3.6b&c MAFS.7.EE.1.1

MAFS.6.NS.3.8 MAFS.7.EE.1.2

MAFS.6.G.1.3

MAFS.6.G.1.1 Rates, Proportions and Percent

MAFS.7.RP.1.1

SMT 2 MAFS.7.RP.1.2
MAFS.7.RP.1.3

KEY: CONCEPTUAL UNDERSTANDING PROCEDURAL SKILLS & FLUENCY APPLICATION

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Grade 6 Mathematics Pacing Guide

Date Topic Focus Standard DIAs
Aug. 14 – Aug. 18 SMT 1/Procedures/ Factors and Multiples SMT 1
MAFS.6.NS.2.4

Aug. 21 – Aug. 24 Factors and Multiples MAFS.6.NS.2.4

Aug. 25 – Aug. 31 Bridging to Long Division MAFS.6.NS.2.2 DIA 1
Sept. 5 – Sept. 25 Operations with Fractions
1 MAFS.6.NS.1.1

Sept. 26 – Oct. 11 Operations with Decimals MAFS.6.NS.2.3

Oct. 12 – Oct. 25 Integers and Rational Numbers MAFS.6.NS.3.6 a & c,
MAFS.6.NS.3.5, MAFS.6.NS.3.7

TDD October 16 End of 1st Grading Period

Oct. 26 – Nov. 17 Displaying, Analyzing and Summarizing Data 2 MAFS.6.SP.1.1, MAFS.6.SP.1.2, DIA 2
MAFS.6.SP.1.3, MAFS.6.SP.2.4,

MAFS.6.SP.2.5

Nov. 20 – Nov. 29 Representing Ratios and Rates MAFS.6.RP.1.1, MAFS.6.RP.1.2

Nov. 30 – Dec. 8 Applying Ratios and Rates 3 MAFS.6.RP.1.3 a, b, d, e

Dec. 11 – Dec. 19 Percents/SMT 2 MAFS.6.RP.1.3c SMT 2
DIA 3
TDD December 21 End of 2nd Grading Period – Winter Break

Jan. 9 – Jan. 30 Generating Equivalent Expressions MAFS.6.EE.1.1, MAFS.6.EE.1.2,

Jan. 31 – Feb. 14 Equations and Relationships 4 MAFS.6.EE.1.3, MAFS.6.EE.1.4,
Feb. 15 – Feb. 22 Relationships in Two Variables
MAFS.6.EE.2.6

MAFS.6.EE.2.5, MAFS.6.EE.2.7,

5 MAFS.6.EE.2.8,

MAFS.6.EE.3.9

Feb. 23- Feb. 28 Distance and Area in Coordinate Plane 6 MAFS.6.NS.3.6 b & c, (DIA in Quarter 4)
Mar. 1 – Mar. 8 Area and Polygons MAFS.6.NS.3.8
MAFS.6.G.1.3

TDD March 9 End of 3rd Grading Period - Spring Break

Mar. 19 – Mar. 23 Area and Polygons 6 cont. MAFS.6.G.1.1 DIA 4
Mar. 26 – Apr. 6 Surface Area and Volume of Solids MAFS.6.G.1.2, MAFS.6.G.1.4

Apr. 10 – Apr. 21 Review and FSA Administration

Apr. 26 – May 9 Operations with Integers

May 10 – May 16 Simplifying Algebraic Expressions
May 17 - May 30 Rates, Proportions and Percents / End of 4th Quarter Period – Last Day for Students

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Key Shifts in Mathematics

The Mathematics Florida State Standards build on the best of existing standards and reflect the skills and knowledge students
will need to succeed in college, career, and life. Understanding how the standards differ from previous standards—and the
necessary shifts they call for—is essential to implementing them.

The following are the key shifts called for by the Standards:

1. Greater Focus on fewer topics
2. Coherence: Linking topics and thinking across grades
3. Rigor: Pursue conceptual understanding, procedural skills and fluency, and application with equal intensity

 Conceptual understanding: The Standards call for conceptual understanding of key concepts, such as place
value and ratios. Teachers support students ‘ability to access concepts from a number of perspectives so that
students are able to see math as more than a set of mnemonics or discrete procedures.

 Procedural skill and fluency: The Standards call for accuracy in calculation, number sense and deep
understanding of numerical principles, not blind memorization or fast recall (Boaler, 2009). Teachers structure
class time and/or homework time for students to practice core functions such as single; digit multiplication so
that students have access to more complex concepts and procedures.

 Application: The standards call for students to use math in situations that require mathematical
knowledge. Teachers provide opportunities for students to apply math in context. Correctly applying
mathematical knowledge depends on students having a solid conceptual understanding and procedural
fluency.

The rigor of each Mathematical Florida Standards on this curriculum map has an Icon to identify the component of rigor for
the purpose of lesson planning.

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Focus 1: Numbers and Number Operations

Standard Essential Question(s): Assessment Limits/Notes
How can rational numbers be represented in multiple ways?

How can you use integers to solve real-world problems?
Success Criteria

The students will: I know I am successful when I can:  Whole numbers less than or
MAFS.6.NS.2.4  apply odd and even numbers to understand factors and multiples.
 apply divisibility rules (review rules for 2, 4, 5, 8, and 10), equal to 100.
Find the greatest common factor
of two whole numbers less than or specifically for 3 and 9.  Least common multiple of two
equal to 100 and the least  find the least common multiple and greatest common factor and whole numbers less than or
common multiple of two whole equal to 12.
numbers less than or equal to 12. apply factors to the distributive property.
Use the distributive property to  Can be assessed in a real-
express a sum of two whole world context.
numbers 1-100 with a common
factor as a multiple of a sum of
two whole numbers with no
common factor.

MFAS: Least Common Multiples
Exile of Common Factors

SMP #7

MAFS.6.NS.2.2  connect estimation with place value to determine the standard  Items may only have 5-digit

algorithm for division. dividends divided by 2-digit

Fluently divide multi-digit numbers  use the standard algorithm to divide multi-digit numbers with and divisors or 4-digit dividends

using the standard algorithm. without remainders. divided by 2- or 3-digit

MFAS: Long Division Part B divisors.

SMP #6  Numbers in items are limited
to non-decimal rational
numbers.

 Answers may or may not
contain remainders.

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Focus 1: Numbers and Number Operations (continued)

Standard Essential Question(s): Assessment Limits/Notes
The students will: How can rational numbers be represented in multiple ways?
 At least the divisor or dividend
MAFS.6.NS.1.1 How can you use integers to solve real-world problems? needs to be a non-unit
Success Criteria fraction.
Interpret and compute quotients of
fractions, and solve word I know I am successful when I can:  Dividing a unit fraction by a
problems involving division of  understand how visual models such as fraction bars and area whole number or vice versa
fractions by fractions, e.g., by
using visual fraction models and models show the division of fractions by fractions with common 1 q q1
equations to represent the denominators. (e.g., a or a )
problem.  make connections to the multiplication of fractions.
 understand that the division of fractions requires students to ask, is below grade level.
MFAS: Juicing Fractions “How many groups of the divisor are in the dividend?” to get the
quotient.  Numbers in items must be
SMP #1 and 4  demonstrate further understanding of division of fractions when rational numbers.
creating word problems.
MAFS.6.NS.2.3  connect models of fractions to multiplication using multiplicative  Items may include values to
inverses as they are represented in models. the thousandths place.
Fluently add, subtract, multiply,  divide fractions by mixed numbers by first converting mixed
and divide multi-digit decimals numbers into a fraction with a value larger than one.  Items may be set up in
using the standard algorithm for  use equations to find quotients. standard algorithm form.
each operation. NOTE: Prior to division of decimals, students have had extensive
experience of decimal operations to the hundredths and thousandths  Remainders are possible with
MFAS: Adding Decimals Fluently (5.NBT.2.7) division.
 fluently add and subtract multi-digit decimals using the standard
SMP #6 algorithm.
 fluently multiply multi-digit decimals using the standard algorithm.
 fluently divide multi-digit decimals using the standard algorithm.
 “bring down” the next digit in the algorithm, and understand that I
am distributing, recording, and shifting to the next place value.

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Focus1: Numbers and Number Operations (continued)

Standard Essential Question(s): Assessment Limits/Notes
How can rational numbers be represented in multiple ways?

How can you use integers to solve real-world problems?
Success Criteria

The students will: I know I am successful when I can:  Numbers in items must be
MAFS.6.NS.3.6 (a and c only) rational numbers.
 extend understanding of the number line, which includes zero
Understand a rational number as a and numbers to the right, that are above zero, and numbers to the  Plotting of points in the
point on the number line. Extend left, that are below zero. coordinate plane should
number line diagrams and coordinate include some negative
axes familiar from previous grades to  use positive integers to locate negative integers, moving in the values (not just first
represent points on the line and in the opposite direction from zero. quadrant).
plane with negative number
coordinates.  understand that the set of integers includes the set of positive  Do not exceed a 10 × 10
a. Recognize opposite signs of whole numbers and their opposites, as well as zero. coordinate grid, though
scales can vary.
numbers as indicating locations on  understand that zero is its own opposite.
opposite sides of 0 on the number  understand that the opposite of -5 is denoted -(-5) and is equal to Other parts of this standard will
line; recognize that the opposite of be covered in Focus 6:
the opposite of a number is the 5; and know that the opposite of the opposite is the original
number itself, e.g., -(-3) = 3 and number; e.g., -(-a) = a. Relationships in Geometry
that 0 is its own opposite.  locate and position opposite numbers on a horizontal or vertical
c. Find and position integers and number line.
other rational numbers on a  compare and interpret rational numbers’ order on the number
horizontal or vertical number line line, making statements that relate the numbers’ location on the
diagram. number line to their order.

MFAS: What Is the Opposite?

SMP #7

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Focus 1: Numbers and Number Operations (continued)

Standard Essential Question(s): Assessment
How can rational numbers be represented in multiple ways? Limits/Notes

How can you use integers to solve real-world problems?  Numbers in
Success Criteria items must be
rational
The students will: I know I am successful when I can: numbers.
MAFS.6.NS.3.5
 use positive and negative numbers to indicate a change (gain or  Items should not
Understand that positive and negative numbers are loss) in elevation with a fixed reference point, temperature, and require the
used together to describe quantities having the balance in a bank account. student to
opposite directions or values (e.g., temperature perform an
above/below zero, elevation above/below sea  use appropriate vocabulary and manipulatives (number line and operation.
level, credits/debits, positive/negative electric 2-color counters) when describing and representing situations
charge); use positive and negative numbers to involving integers; e.g., an elevation of -10 feet is the same as
represent quantities in real-world contexts, 10 feet below the fixed reference point.
explaining the meaning of 0 in each situation.
 understand that negative numbers are always less than
positive numbers.

MFAS: Rainfall Change SMP #2

MAFS.6.NS.3.7  describe the relative position of two numbers on a number line  Numbers in

when given an inequality. items must be

Understand ordering and absolute value of rational  understand the absolute value of a number as its distance from positive or

numbers. zero on the number line. negative rational

a. Interpret statements of inequality as statements  understand that each nonzero integer, has an opposite and numbers.

about the relative position of two numbers on a integers are opposites if they are on opposite sides of zero and

number line diagram. are the same distance from zero on the number line (-4 and 4).

b. Write, interpret, and explain statements of  write, interpret, and explain statements of order for rational

order for rational numbers in real world- numbers in the real-world.

contexts.  recognize that if a < b, then -a > -b, because a number and its

c. Understand the absolute value of a rational opposite are equal distances from zero; recognize that moving

number as its distance from 0 on the number along the horizontal number line to the right means the numbers

line; interpret absolute value as magnitude for a are increasing.

positive or negative quantity in a real-world  describe the relative position of two numbers on a number line

situation. when given an inequality.

d. Distinguish comparisons of absolute value from  write, explain, and justify inequality statements.
statements about order.

MFAS: Positions of Numbers SMP #2

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Focus 2: Measurement and Data

Essential Question(s):

How do you account for variability in the data?

What effect does the distribution of data have on its center, spread, and overall shape?

How can you solve real-world problems by displaying, describing and summarizing data?

Standard Success Criteria Assessment

Limits/Notes

The students will: I know I am successful when I can:

MAFS.6.SP.1.1  distinguish between statistical questions and those that are not  N/A

statistical.

Recognize a statistical question as one  formulate a statistical question and explain what data could be

that anticipates variability in the data collected to answer the question.

related to the question and accounts for

it in the answers.

MFAS: TV Statistics

SMP #6

MAFS.6.SP.1.2  explain that there are three ways that the distribution of a set of  Numbers in items must
data can be described: by its center, spread, or overall shape. be rational numbers.
Understand that a set of data collected
to answer a statistical question has a  describe the center of a set of statistical data in terms of the  Dot/line plots,
distribution which can be described by mean, median, and the mode.
its center, spread, and overall shape. histograms, and box
 describe the spread of a set of statistical data in terms of
MFAS: Pet Frequency extremes, clusters, gaps, and outliers. plots are allowed.

SMP #4  describe the overall shape of the set of data in terms of its
symmetry or skewness.

 describe the distribution of the points on the dot plot in terms of
center and variability.

 define the center of a data distribution by a “fair share” value
called the mean.

 connect the “fair share” concept with a mathematical formula for
finding the mean.

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Focus 2: Measurement and Data

Essential Question(s):

How do you account for variability in the data?

What effect does the distribution of data have on its center, spread, and overall shape?

How can you solve real-world problems by displaying, describing and summarizing data?

Standard Success Criteria Assessment

Limits/Notes

The students will: I know I am successful when I can:

MAFS.6.SP.1.3  define a measure of center as a single value that  Numbers in items must

summarizes a data set. be rational numbers.

Recognize that a measure of center for a  determine measures of center by calculating the mean,  Data sets in items must

numerical data set summarizes all of its median, and mode of a set of numerical data. be numerical data sets.

values using a single number, while a  define a measure of variation as the range of the data,

measure of variation describes how its values relative to the measures of center.

vary using a single number.  determine measures of variation by calculating the

MFAS: Compare Measures of Center and interquartile range (IQR) of a set of numerical data.
Variability  determine the measures of variation by calculating the mean

absolute deviation (MAD) of a set of numerical data.

SMP #6

MAFS.6.SP.2.4  organize and display data as a line plot or dot plot,  Numbers in items must
histogram, and/or box plot. be rational numbers.
Display numerical data in plots on a number
line, including dot plots, histograms, and box  Given a box plot, students summarize the data by the 5-  Displays should include
plots. number summary (Min, Q1, Median, Q3, Max.) only dot/line plots, box
plots, or histograms.
MFAS: Shark Attack Data  describe a set of data using the 5-number summary and the
interquartile range.  Recommend intervals
SMP #4 given for creating a
 construct a box plot from a 5-number summary. histogram.
 identify the similarities and differences of representing the

same data in a line plot, a histogram, or a box plot.
 decide and explain which type of plot (dot plot, line plot,

histogram, or box plot) is the best way to display my data
depending on what I want to communicate about the data.

14

Focus 2: Measurement and Data

Essential Question(s):

How do you account for variability in the data?

What effect does the distribution of data have on its center, spread, and overall shape?

How can you solve real-world problems by displaying, describing and summarizing data?

Standard Success Criteria Assessment

Limits/Notes

The students will: I know I am successful when I can:

MAFS.6.SP.2.5  understand that the mean is a balance point by calculating the  Numbers in items must

distances of the data points from the mean and call the be rational numbers.

Summarize numerical data sets in distances, deviations.  Displays should include

relation to their context, such as by:  understand that the mean is the value such that the sum of the only dot/line plots, box
plots, or histograms.
a. reporting the number of deviations is equal to zero.

observations.  write a data collection summary (5 number summary) that includes

b. describing the nature of the attribute the number of observations, what is being investigated, how it is

under investigation, including how it measured, and the units of measurement.

was measured and its units of  justify the use of a particular measure of center or measure of

measurement. variability based on the shape of the data.

c. giving quantitative measures of  use a measure of center and a measure of variation to draw

center (median and/or mean) and inferences about the shape of the data distribution.

variability (interquartile range and/or  describe overall patterns and any deviations in the data and how
mean absolute deviation), as well as
they relate to the context of the problem.
describing any overall pattern and

any striking deviations from the

overall pattern with reference to the

context in which the data were

gathered.

d. relating the choice of measures of

center and variability to the shape of

the data distribution and the context

in which the data were gathered.

MFAS: Quiz Mean and Deviation

SMP#3

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Focus 3: Proportionality: Ratios and Rates

Essential Question(s):

How can ratios and proportional relationships be used to determine unknown quantities?

How can you use ratio and rates to solve real-world problems?

Standard Success Criteria Assessment Limits/Notes

The students will: I know I am successful when I can:

MAFS.6.RP.1.1  understand that a ratio is an ordered pair of non-negative numbers,  Whole numbers should be used

which are not both zero. for the quantities.

Understand the concept of a  explain the relationship that a ratio represents.  Ratios can be expressed as

ratio and use ratio language  create multiple ratios from a context in which more than two quantities fractions, with “:” or with words.
to describe a ratio are given and conceive of real-world contextual situations to match a Units may be the same or
relationship between two given ratio (equivalent ratio tables, tape diagrams, double number line 

quantities. diagram). different across the two

 write a ratio that describes a relationship between two quantities. quantities.

MFAS: Interpreting Ratios  Context itself does not

SMP #4 determine the order.

MAFS.6.RP.1.2  define the term “unit rate” and demonstrate my understanding by  Items using the comparison of a

giving various examples. ratio will use whole numbers.

Understand the concept of a  recognize a ratio written as a unit rate, explain a unit rate, and give an  Rates can be expressed as
example of a unit rate.  fractions, with “:” or with words.
unit rate a/b associated with  describe the ratio relationship represented by a unit rate.
 convert a given ratio to a unit rate. Units may be the same or
a ratio a:b with
b ≠ 0, and use rate language

in the context of a ratio  recognize that I can associate a ratio of two quantities, such as the different across the two

relationship. ratio of miles per hour is 5:2, to another quantity called the rate. quantities.

MFAS: Book Rates  given a ratio, identify the associated rate, and identify the unit rate  Context itself does not
and the rate unit. determine the order.

SMP #2  given a rate, find ratios associated with the rate, where the second  Name the amount of either
term is one and a ratio where both terms are whole numbers. quantity in terms of the other as
long as one of the values is one
 recognize that all ratios associated to a given rate are equivalent unit.
because they have the same value.

16

Focus 3: Proportionality: Ratios and Rates (continued)

Essential Question(s):

How can ratios and proportional relationships be used to determine unknown quantities?

How can you use ratio and rates to solve real-world problems?

Standard Success Criteria Assessment

Limits/Notes

The students will: I know I am successful when I can:

MAFS.6.RP.1.3  understand that if two ratios are equivalent, the ratios have the same value.  Rates can be

 identify both the additive and multiplicative structure of an equivalent ratio expressed as

Use ratio and rate reasoning to solve table and use the structure to make additional entries in the table. fractions, with “:”

real-world and mathematical problems,  determine whether two ratios are equivalent, based on the description of or with words.

e.g., by reasoning about tables of equivalent ratios, using tape diagrams, double number line diagrams, and/or  Units may be the

equivalent ratios, tape diagrams, double equivalent ratio tables. same or different

number line diagrams, or equations.  create and complete an equivalent ratio table, tape diagram, and/or double across the two

a. Make tables of equivalent ratios number line diagram to solve problems. quantities.

relating quantities with whole-number  use the value of a ratio to solve ratio problems in a real-world context.  Percent found

measurements, finding missing  compare different ratios using two or more equivalent ratio tables. as a rate per
values in the tables, and plot the  plot corresponding values from an equivalent ratio table on a coordinate 100.
pairs of values on the coordinate  Quadrant I only
plane.

plane. Use tables to compare ratios. for

b. Solve unit rate problems including  calculate the unit rate. MAFS.6.RP.1.3a

those involving unit pricing and  solve problems by analyzing different unit rates given in tables, equations, and

constant speed. graphs.

c. Find a percent of a quantity as a rate  model percents and write a percent as a fraction over 100 or a decimal to the

per 100 (e.g. 30% of a quantity hundredths place.

means 30/100 times the quantity);
solve problems involving finding the  calculate the percent of a given number by using visual representations (e.g.,
strip diagrams, percent bars, one-hundred grids)
whole, given a part and the percent.
 write a percent as a rate per one-hundred.
d. Use ratio reasoning to convert
measurement units; manipulate and  find the whole when given both the part and the percent using tape diagrams,
double number line diagrams, and tables of equivalent ratios.
transform units appropriately when

multiplying or dividing quantities.  use a ratio as a conversion factor when working with measurements of
e. Understand the concept of Pi as a different units.

ratio of the circumference of a circle  manipulate and transform units appropriately when multiplying or dividing
to its diameter. quantities.

MFAS: Party Punch - Compare Ratios  understand and explain that Pi is a ratio of the circumference of a circle to its
SMP #2 diameter.

17

Focus 4: Equivalent Expressions

Essential Question(s):

How can algebraic expressions and equations be used to model, analyze, and solve mathematical situations?

How can you generate equivalent numerical expressions and use them to solve real-world problems?

Standard Success Criteria Assessment

Limits/Notes

The students will: I know I am successful when I can:

MAFS.6.EE.1.1  explain the meaning of a number raised to a power.  Whole number

 write numerical expressions involving whole-number bases.
 Whole number
Write and evaluate numerical expressions involving operations.
exponents.
whole-number exponents.  understand that a base number can be represented with a

MFAS: Paul's Pennies positive whole number, positive fraction, or positive decimal
and that for any number a, we define am to be the product

SMP #6 of m factors of a. The number a is the base and m is called
the exponent or power of a.

 evaluate numerical expressions involving whole-number

exponents.

MAFS.6.EE.1.2  translate a relationship given in words into an algebraic  Numbers in

expression for all operations. items must be
rational
Write, read, and evaluate expressions in which letters  identify parts of an algebraic expression using mathematical numbers.

stand for numbers. terms for all operations.

a. Write expressions that record operations with  recognize an expression as both a single value and as two

numbers and with letters standing for numbers. or more terms on which an operation is performed.

b. Identify parts of an expression using  understand that a letter represents one number in an

mathematical terms (sum, term, product, factor, expression and when that number replaces the letter, the

quotient, coefficient); view one or more parts of expression can be evaluated to one number (link

an expression as a single entity. “unknown”—what they learned in elementary school—to

c. Evaluate expressions at specific values of their “variable”).

variables. Include expressions that arise from  apply the order of operations when evaluating both

formulas used in real-world problems. Perform arithmetic and algebraic expressions.

arithmetic operations, including those involving  substitute values in formulas to solve real-world problems.

whole-number exponents, in the conventional

order when there are no parentheses to specify a

particular order (Order of Operations).

MFAS: Substitution Resolution

SMP #6

18

Focus 4: Equivalent Expressions (continued)

Essential Question(s):

How can algebraic expressions and equations be used to model, analyze, and solve mathematical situations?

How can you generate equivalent numerical expressions and use them to solve real-world problems?

Standard Success Criteria Assessment Limits/Notes

The students will: I know I am successful when I can:

MAFS.6.EE.1.3  build and clarify the relationship of multiplication and division by  Positive rational numbers,

evaluating identities such as: ∙ = and ∙ = values may include exponents.

Apply the properties of operations   Variables must be included in
as strategies to generate equivalent  build and clarify the relationship of multiplication and addition by  the expression.
expressions. evaluating identities such as: 3g = g + g + g. Whole number coefficients

discover the commutative properties of addition and only.

MFAS: Generating Equivalent multiplication, the additive identity property of zero, and the

Expressions multiplicative identity property of one; and determine the

following = , = 1, and 1 ÷ = 1
1
SMP #8
 model [e.g., use algebra tiles to model that 3(2 + x) = 6 + 3x] and

write equivalent expressions using the distributive property and

move from an expanded form to a factored form of an

expression.

MAFS.6.EE.1.4  determine whether two expressions are equivalent by using the  Numbers in items must be

same value to evaluate both expressions. positive rational numbers.

Identify when two expressions are  understand that a letter in an expression or an equation can  Variables must be included in
equivalent (i.e., when the two represent a number and when that number is replaced with a the expression.

expressions name the same number letter, an expression or an equation is stated (ex: 3x = 6 is an
regardless of which value is equation and can also be seen as two equivalent expressions 3x
substituted into them). and 6).

For example, the expressions

+ + and 3 are equivalent

because they name the same number

regardless of which number stands

for.

MFAS: Property Combinations

SMP #8

19

Focus 4: Equivalent Expressions (continued)

Essential Question(s):

How can algebraic expressions and equations be used to model, analyze, and solve mathematical situations?

How can you generate equivalent numerical expressions and use them to solve real-world problems?

Standard Success Criteria Assessment

Limits/Notes

The students will: I know I am successful when I can:

MAFS.6.EE.2.6  use a variable to write an algebraic expression that represents a  Numbers in items must

real-world situation when a specific number is unknown. be nonnegative rational

Use variables to represent numbers and  explain and give examples of how a variable can represent a numbers.

write expressions when solving a real- single unknown number (ex: x = 9 or 5y = 10) or any number in a  Expressions must

world or mathematical problem; specified set (ex: m < 8 or n + 6 > 10). contain at least one

understand that a variable can  use a variable to write an expression that represents a consistent variable.
represent an unknown number, or, relationship in a particular pattern (e.g., use function tables to write
depending on the purpose at hand, any an expression that would represent the output for any input).
number in a specified set.
MFAS: Gavin's Pocket  develop expressions involving addition, subtraction, multiplication,
and division from real-world problems.

SMP #2

20

Focus 5: Equations & Inequalities

Essential Question(s):

How can algebraic equations and inequalities be used to model, analyze, and solve mathematical situations?

How can you use equations and relationships to solve real-world problems?

Standard Success Criteria Assessment Limits/Notes

The students will: I know I am successful when I can:

MAFS.6.EE.2.5  explain what the equality and inequality symbols mean  Numbers in items must be

and determine if a number sentence is true or false nonnegative rational

Understand solving an equation or inequality as based on the given symbol. numbers.

a process of answering a question: which values  understand solving an inequality is answering the  One-variable linear
equations and inequalities.
from a specified set, if any, make the equation question of which values from a specified set, if any,
 An equation or inequality
or inequality true? Use substitution to determine make the inequality true. should be given if a
context is included.
whether a given number in a specified set  understand that an inequality with numerical

makes an equation or inequality true. expressions is either true or false—it is true if the

MFAS: Finding Solutions of Inequalities numbers calculated on each side of the inequality sign

SMP #2 result in a correct statement and false otherwise.

MAFS.6.EE.2.7  solve one-step equations by relating an equation to a  Numbers and solutions

diagram. must be nonnegative

Solve real-world and mathematical problems by  calculate the solution of one-step equations by using rational numbers.
writing and solving equations of the form knowledge of order of operations and the properties of  One-variable linear
x + p = q and px = q for cases in which p, q and equality for addition, subtraction, multiplication, and
x are all nonnegative rational numbers. division and employ tape diagrams to determine their equations and inequalities
containing addition,

MFAS: University Parking answer. subtraction, multiplication,
SMP #2  check to determine if their solution makes the equation OR division.
 An equation or inequality
true.

 write and solve algebraic equations that represent real should be given if a

world problems. context is included.

MAFS.6.EE.2.8  write a simple inequality to represent the constraints or  Numbers in items must be

conditions of numerical values in a real-world or nonnegative rational

Write an inequality of the form x > c or x < c to mathematical problem. numbers.

represent a constraint or condition in a real-  explain what the solution set of an inequality represents.  Context in real-world items
world or mathematical problem. Recognize that
inequalities of the form x > c or x < c have  show the solution set of an inequality by graphing it on a should be continuous or
infinitely many solutions; represent solutions of
such inequalities on number line diagrams. number line. close to continuous.

 recognize that inequalities have infinitely many solutions  Limited to <, >, and =

when the values of x come from a set of rational  < and > introduced in 7th

MFAS: Transportation Number Lines numbers. grade

SMP #2

21

Focus 5: Equations & Inequalities (continued)

Essential Question(s):

How can algebraic equations and inequalities be used to model, analyze, and solve mathematical situations?

How can you use equations and relationships to solve real-world problems?

Standard Success Criteria Assessment Limits/Notes

The students will: I know I am successful when I can:  Items must involve relationships
MAFS.6.EE.3.9 and/or one-step equations
 create a table of two variables that represents a  containing addition, subtraction,
Use variables to represent two quantities in real-world situation in which one quantity will  multiplication, OR division.
a real-world problem from a variety of change in relation to the other.  Numbers in items must be positive
cultural contexts that change in relationship rational numbers (zero can be used
to one another; write an equation to express  explain the difference between the independent in the graph and table).
one quantity, thought of as the dependent variable and the dependent variable. Variables need to be defined.
variable, in terms of the other quantity, Relationships are to be continuous
thought of as the independent variable.  identify the independent and dependent variable
Analyze the relationship between the in a relationship.
dependent and independent variables using
graphs and tables, and relate these to the  write an algebraic equation that represents the
equation. relationship between the two variables.

For example, in a problem involving motion at  create a graph by plotting the independent variable
constant speed, list and graph ordered pairs of on the x-axis and the dependent variable on the y-
distances and times, and write the equation axis of a coordinate plane.
d = 65t to represent the relationship between
distance and time.  analyze the relationship between the dependent
and independent variables by comparing the table,
MFAS: Analyzing the Relationship graph, and equation.

SMP #2

22

Focus 6: Relationships in Geometry

Standard Essential Question(s): Assessment
How can you use geometric figures to solve real-world problems? Limits/Notes

Success Criteria  Numbers in items must
be rational numbers.
The students will: I know I am successful when I can:
MAFS.6.NS.3.6b&c  Plotting of points in the
 extend their understanding of the coordinate plane to coordinate plane should
Understand a rational number as a point on the include all four quadrants, and recognize that the axes include some negative
number line. Extend number line diagrams and (identified as the -axis and -axis) of the coordinate plane values (not just first
coordinate axes familiar from previous grades divide the plane into four regions called quadrants (that are quadrant).
to represent points on the line and in the plane labeled from first to fourth and are denoted by Roman
with negative number coordinates. Numerals).  Numbers in
b. Understand the signs of numbers in MAFS.6.NS.3.8 must be
 identify the origin, and locate points other than the origin, positive or negative
ordered pairs as indicating locations in which lie on an axis. rational numbers.
quadrants of the coordinate plane;
recognize that when two ordered pairs  locate points in the coordinate plane that correspond to  Do not use
differ only by sign, the locations of the given ordered pairs of integers and other rational numbers. polygons/vertices for
points are related by reflections across one MAFS.6.NS.3.8.
or both axes.  recognize that when two ordered pairs differ only by sign NOTE: this means that
c. Find and position integers and other of one or both coordinates, the locations of the points are figures should only
rational numbers on a horizontal or vertical related by reflections across one or both axes. contain horizontal or
number line diagram; find and position pairs vertical lines
of integers and other rational numbers on a  use the coordinate plane to graph points, line segments
coordinate plane. and geometric shapes in the various quadrants and then  Do not exceed a 10 × 10
use the absolute value to find the related distances.
coordinate grid, though
MAFS.6.NS.3.8
scales can vary.

Solve real-world and mathematical problems by
graphing points in all four quadrants of the
coordinate plane. Include use of coordinates
and absolute value to find distances between
points with the same first coordinate or the
same second coordinate.
MFAS: Graphing Points in the Plane

SMP #1

23

Focus 6: Relationships in Geometry (continued)

Essential Question(s):

How can you use geometric figures to solve real-world problems?

Standard Success Criteria Assessment
Limits/Notes
The students will: I know I am successful when I can:  Numbers in items

MAFS.6.G.1.3  use absolute value to determine distance between integers on must be rational
numbers.
the coordinate plane to find side lengths of polygons.  Items may use all four
quadrants.
Draw polygons in the coordinate plane given  draw polygons in the coordinate plane and find the area  When finding side
length, limit polygons
coordinates for the vertices; use coordinates enclosed by a polygon by composing or decomposing using to traditional
orientation (side
to find the length of a side joining points with polygons with known area formulas. lengths perpendicular
to axes).
the same first coordinate or the same  find the perimeter of irregular figures using coordinates to find
 Numbers in items
second coordinate. Apply these techniques the length of a side joining points with the same first coordinate must be positive
in the context of solving real-world and or the same second coordinate. rational numbers.
mathematical problems.  determine distance, perimeter, and area in real-world contexts.
 Limit shapes to those
MFAS: Fence Length  show the area formula for a parallelogram by composing it into that can be
SMP #5 rectangles.
MAFS.6.G.1.1 decomposed or
 justify the area formula for a right triangle by viewing the right
Find area of right triangles, other triangles, triangle as part of a rectangle composed of two right triangles. composed into
special quadrilaterals, and polygons by
composing into rectangles or decomposing  show the area formula for a triangular region by decomposing a rectangles and/or right
into triangles and other shapes; apply these triangle into right triangles. For a given triangle, the height of the
techniques in the context of solving real- triangle is the length of the altitude. The length of the base is triangles.
world and mathematical problems. either called the length base or, more commonly, the base.

MFAS: Area of Triangles  understand that the height of the triangle is the perpendicular
segment from a vertex of a triangle to the line containing the
SMP #2 opposite side. The opposite side is called the base.

 understand that any side of a triangle can be considered a base
and that the choice of base determines the height.

 deconstruct triangles to justify that the area of a triangle is
exactly one half the area of a parallelogram.

 find the area for a trapezoid by decomposing the region into two
triangles. I can decompose rectangles to determine the area of
other quadrilaterals.

 determine the area of composite figures in real-life contextual
situations using composition and decomposition of polygons.

 determine the area of a missing region using composition and
decomposition of polygons.

24

Focus 6: Relationships in Geometry (continued)

Standard Essential Question(s): Assessment
How can you use geometric figures to solve real-world problems? Limits/Notes

Success Criteria  Prisms in items must
be right rectangular
The students will: I know I am successful when I can: prisms.
MAFS.6.G.1.2
 calculate the volume of a right rectangular prism by reasoning about  Unit fractional edge
Find the volume of a right rectangular the number of unit cubes it takes to cover the first layer of the prism lengths for the unit
prism with fractional edge lengths by and the number of layers needed to fill the entire prism. cubes used for
packing it with unit cubes of the packing must have a
appropriate unit fraction edge lengths,  extend their understanding of the volume of a right rectangular prism numerator of 1.
and show that the volume is the same with integer side lengths to right rectangular prisms with fractional side
as would be found by multiplying the lengths.
edge lengths of the prism. Apply the
formulas V = l w h and V = b h to find  apply the formula V = lwh to find the volume of a right rectangular
volumes of right rectangular prisms with prism and use the correct volume units when writing the answer.
fractional edge lengths in the context of
solving real-world and mathematical  extend the volume formula for a right rectangular prism to the
problems. formula (V = Bh).
MFAS: Prism Packing
 develop, understand, and apply formulas for finding the volume of
right rectangular prisms and cubes.

 apply volume formulas to find missing volumes and missing
dimensions.

SMP#2  match a net to correct prism or pyramid.  Numbers in items
MAFS.6.G.1.4  draw a net for a given prism or pyramid. must be positive
 use a net to find the surface area of a given prism or pyramid. rational numbers.
Represent three-dimensional figures  solve real-world problems that involve finding the surface area of
using nets made up of rectangles and  Three-dimensional
triangles, and use the nets to find the prisms or pyramids figures are limited to
surface area of these figures. Apply  use nets to determine the surface area of three-dimensional figures. rectangular prisms,
these techniques in the context of  determine that a right rectangular prism has six faces: top and triangular prisms,
solving real-world and mathematical rectangular pyramids,
problems. bottom, front and back, and two sides. and triangular
 determine that surface area is obtained by adding the areas of all the pyramids.
MFAS: Windy Pyramid
faces.
SMP #4  apply the formulas for surface area and volume to determine missing

dimensions of aquariums and water level.

25

Focus 7: Operations with Integers

Standard Essential Question(s): Assessment
How can you use rational numbers to solve real-world problems? Limits/Notes

Success Criteria  Numbers in items must be
rational numbers.
The students will: I know I am successful when I can:
MAFS.7.NS.1.2  7.NS.1.2a, 2b, and 2c
 use patterns and properties to explore the require the incorporation
Apply and extend previous understandings of multiplication of integers. of a negative value.
multiplication and division and of fractions to multiply and
divide rational numbers.  use patterns and properties to develop procedures 
a. Understand that multiplication is extended from for multiplying integers.

fractions to rational numbers by requiring that  describe real-world situations represented by the
operations continue to satisfy the properties of multiplication of integers.
operations, particularly the distributive property,
leading to products such as (-1)(-1) = 1 and the rules  use the relationship between multiplication and
for multiplying signed numbers. Interpret products of division to develop procedures for dividing integers.
rational numbers by describing real world contexts.
b. Understand that integers can be divided, provided that  explain why the property of closure exists for the
the divisor is not zero, and every quotient of integers division of rational numbers, but not for whole
(with non-zero divisor) is a rational number, If p and q numbers.
are integers, then -(p/q) = (-p)/q = p/(-q). Interpret
quotients of rational numbers by describing real-world  describe real-world situation represented by the
contexts. Apply properties of operations as strategies division of integers.
to multiply and divide rational numbers.
c. Apply properties of operations as strategies to multiply  interpret the quotient in relation to the original
and divide rational numbers. problem.
d. Convert a rational number to a decimal using long
division; know that the decimal form of a rational  generalize the procedures for multiplying and
number terminates in 0’s or eventually repeats. dividing integers to all rational numbers.
MFAS: Negative Times
SMP #8  use long division to convert a rational number to a
decimal.

 verify that a number is rational based on its decimal
equivalent.

 identify rational numbers as numbers that can be
written in ratio form vs non-rational numbers that are
non-terminating decimals or undefined fractions.

26

Focus 7: Operations with Integers (continued)

Essential Question(s):

How can you use rational numbers to solve real-world problems?

Standard Success Criteria Assessment Limits/Notes

The students will: I know I am successful when I can:

MAFS.7.NS.1.1  use a number line or positive/negative chips to  Numbers in items must be

show that an integer and its opposite will rational numbers: use integers,

Apply and extend previous understandings of addition always have a sum of zero. decimals, and fractions.

and subtraction to add and subtract rational numbers;  use a number line to show addition as a  Limit decimals to those ending

represent addition and subtraction on a horizontal or specific distance from a particular number in in 0.25, 0.5, and 0.75.

vertical number line diagram. one direction or the other, depending on the  Limit fractions to halves and
fourths.
a. Describe situations in which opposite quantities sign of the value being added.

combine to make 0.  interpret the addition of integers by relating

b. Understand p + q as the number located a distance the values to real-world situations.

|q| from p, in the positive or negative direction  rewrite a subtraction problem as an addition

depending on whether q is positive or negative. problem by using the additive inverse.

Show that a number and its opposite have a sum  show the distance between two integers on a
of 0 (are additive inverses). Interpret sums of
number line is the absolute value of their
rational numbers by describing real-world contexts.
difference.
c. Understand subtraction of rational numbers as
adding the additive inverse, p – q = p + (–q). Show  describe real-world situations represented by
the subtraction of integers.
that the distance between two rational numbers on  use the properties of operations to add and
the number line is the absolute value of their
difference, and apply this principle in real-world subtract rational numbers.

contexts.

d. Apply properties of operations as strategies to add

and subtract rational numbers.

MFAS: Adding Integers

SMP #4

MAFS.7.NS.1.3  solve real-world problems that involve the  Must be rational numbers.

addition, subtraction, multiplication, and/or  Complex fractions may be used,

Solve real-world and mathematical problems involving division or rational numbers. but should contain fractions with
the four operations with rational numbers. single-digit numerators and
MFAS: Monitoring Water Temperatures denominators.

SMP #1

27

Focus 7: Simplifying Algebraic Expressions

Essential Question(s):

How can you use algebraic expressions to understand and explain real-world problems?

How can you determine if algebraic expressions are equivalent?

Standard Success Criteria Assessment Limits/Notes

The students will: I know I am successful when I can:
MAFS.7.EE.1.1
 use the commutative and associative  Numbers in items must be
Apply properties of operations as strategies to add,
subtract, factor, and expand linear expressions with properties to add linear expressions with rational numbers.
rational coefficients.
rational coefficients.  Expressions must be linear and
MFAS: Identify Equivalent Multistep Expressions
 Identify the different parts of an expression contain a variable.
SMP #7 including constants and variable terms, like

MAFS.7.EE.1.2 terms, and coefficients.

Understand that rewriting an expression in different  use the distributive property to add and/or
forms in a problem context can shed light on the
problem and how the quantities in it are related. subtract linear expressions with rational

MFAS: Explain Equivalent Expressions coefficients.

 use the distributive property to factor out

Greatest Common Factor of linear

expressions. (review if necessary).

 use equivalent expressions to understand the  Numbers in items must be

relationship between quantities. rational numbers, including

integers, fractions, and

decimals.

 Expressions must be linear.

SMP # 7

28

Focus 7: Rates, Proportions, and Percent

Essential Question(s):

How can you use rates and proportionality to solve real-world problems?

Standard Success Criteria Assessment Limits/Notes

The students will: I know I am successful when I can:

MAFS.7.RP.1.1  compute a unit rate by iterating (repeating)  Numbers in items must be

or partitioning given rate. rational numbers. Some items

Compute unit rates associated with ratios of fractions,  compute a unit rate by multiplying or dividing may include one rational
including ratios of lengths, areas, and other quantities
measured in like or different units. both quantities by the same factor. number and one whole number

MFAS: Computing Unit Rates  explain the relationship between using (other than 1), but the bulk of

SMP # 1 composed units and a multiplicative items from this standard should

comparison to express a unit rate. involve ratios expressed as

 use measures of lengths and areas to fractions.

calculate unit rates with the given context.  Ratios may be expressed as
fractions, with “:” or with words.

 Units may be the same or

different across the two

quantities.

MAFS.7.RP.1.2  determine whether two quantities are  Numbers in items must be
rational numbers.
proportional by examining the relationship
 Ratios should be expressed as
Recognize and represent proportional relationships given in a table, graph, equation, diagram or fractions, with “:” or with words.

between quantities. as a verbal description.  Units may be the same or

a. Decide whether two quantities are in a proportional  identify the constant of proportionality when different across the two

relationship, e.g., by testing for equivalent ratios in presented with a proportional relationship in quantities.

a table, or graphing on a coordinate plane and the form of a table, graph equation, diagram,

observing whether the graph is a straight line or verbal descriptions.

through the origin.  write an equation that represents a

b. Identify the constant of proportionality (unit rate) in proportional relationship.

tables, graphs, equations, diagrams, and verbal  identify proportional relationships and

descriptions of proportional relationships. identify the unit rate as the slope of the

c. Represent proportional relationships by equations. related linear function
d. Explain what a point (x, y) on the graph of a

proportional relationship means in terms of the

situation, with special attention to the points (0, 0)

and (1, r) where r is the unit rate.

MFAS: Teacher to Student Ratios

SMP # 4

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Focus 7: Rates, Proportions, and Percent (continued)

Essential Question(s):

How can you use rates and proportionality to solve real-world problems?

Standard Success Criteria Assessment Limits/Notes

The students will: I know I am successful when I can:  Numbers in items must be
MAFS.7.RP.1.3 rational numbers.
 use proportional reasoning to solve real-
Use proportional relationships to solve multi-step ratio world ratio problems, including those with  Units may be the same or
and percent problems. multiple steps.
different across the two
MFAS: Tiffany'sTax  use proportional reasoning to solve real-
world percent problems, including those with quantities.
SMP # 2 multiple steps.

 recall conversion of percent’s from ratio to
decimal to percent form.

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