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Standards of Excellence

Curriculum Map

Mathematics

GSE Grade 7

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Georgia Department of Education

GSE Grade 7 Curriculum Map

1st Semester

Unit 1

(4 – 5 weeks)

2nd Semester

Click on the link in the table to view a video that shows instructional strategies for teaching each standard.

Unit 2

Unit 3

Unit 5

Unit 6

Unit 4

(4 – 5 weeks)

(4 – 5 weeks)

(4 – 5 weeks)

(3 – 4 weeks)

(4 – 5 weeks)

Unit 7

(3 – 4 weeks)

Operations with Rational

Numbers

Expressions and

Equations

Ratios and Proportional

Relationships

Geometry

Inferences

Probability

Show What We

Know

MGSE7.NS.1

MGSE7.NS.1a

MGSE7.NS.1b

MGSE7.NS.1c

MGSE7.NS.1d

MGSE7.NS.2

MGSE7.NS.2a

MGSE7.NS.2b

MGSE7.NS.2c

MGSE7.NS.2d

MGSE7.NS.3

MGSE7.EE.1

MGSE7.EE.2

MGSE7.EE.3

MGSE7.EE.4

MGSE7.EE.4a

MGSE7.EE.4b

MGSE7.EE.4c

MGSE7.RP.1

MGSE7.RP.2

MGSE7.RP.2a

MGSE7.RP.2b

MGSE7.RP.2c

MGSE7.RP.2d

MGSE7.RP.3

MGSE7.G.1

MGSE7.G.2

MGSE7.G.3

MGSE7.G.4

MGSE7.G.5

MGSE7.G.6

MGSE7.SP.1

MGSE7.SP.2

MGSE7.SP.3

MGSE7.SP.4

MGSE7.SP.5

MGSE7.SP.6

MGSE7.SP7

MGSE7.SP.7a

MGSE7.SP.7b

MGSE7.SP.8

MGSE7.SP.8a

MGSE7.SP.8a

MGSE7.SP.8b

MGSE7.SP.8c

ALL

These units were written to build upon concepts from prior units, so later units contain tasks that depend upon the concepts addressed in earlier units.

All units will include the Mathematical Practices and indicate skills to maintain.

NOTE: Mathematical standards are interwoven and should be addressed throughout the year in as many different units and tasks as possible in order to stress the natural connections that exist among mathematical topics.

Grades 6-8 Key:

NS = The Number System

RP = Ratios and Proportional Relationships

EE = Expressions and Equations

G = Geometry

SP = Statistics and Probability.

July 2019 ● Page 2 of 7

Georgia Department of Education

Georgia Standards of Excellence Grade 7 Mathematics

Curriculum Map Rationale

Unit 1: Building upon the understanding of rational numbers developed in 6th grade, this unit moves to exploring and ultimately formalizing rules for

operations (addition, subtraction, multiplication and division) with integers. Using both contextual and numerical problems, students explore what

happens when negative numbers and positive numbers are combined. Repeated opportunities over time will allow students to compare the results of

adding, subtracting, multiplying and dividing pairs of numbers, leading to the generalization of rules. Fractional rational numbers and whole numbers

should be used in computations and explorations.

Unit 2: Students build on what was learned in previous grades regarding mathematical properties such as commutative, associative, and distributive

properties, and conventions, such as order of operations. Students use these conventions and properties of operations to rewrite equivalent numerical

expressions. Students continue to use properties used with whole numbers, extending their use to integers, rational, and real numbers. Students write

expressions and equations in more than one format, demonstrating that they are still equal. Variables are used to represent quantities in real-world

problems.

Unit 3: This unit builds on student knowledge and understanding of rate and unit concepts, including the need to develop proportional relationships

through the analysis of graphs, tables, equations, and diagrams. Grade 7 pushes the student to develop a deep understanding of the characteristics of a

proportional relationship. Mathematics should be represented in as many ways as possible in this unit by using graphs, tables, pictures, symbols and

words.

Unit 4: Students learn to draw geometric figures using rulers and protractors with an emphasis on triangles. Students explore two-dimensional crosssections of cylinders, cones, pyramids, and prisms. Students write and solve equations involving angle relationships and solve problems that require

determining the area, volume, and surface area of solid figures. This unit also introduces students to the formula for the circumference and area of a

circle.

Unit 5: Building on the knowledge of statistics from sixth grade, students use random samples to make predictions about an entire population and

judge the possible discrepancies of the predictions. Students use real-life situations from science and social studies to show the purpose for using

random sampling to make inferences about a population. Note- Units 5 and 6 were combined in the revised curriculum map providing an uninterrupted

exploration of statistics.

Unit 6: Students begin to understand the probability of chance (simple and compound). They develop models to find the probability of simple events,

and make predictions using information from simulations.

July 2019 ● Page 3 of 7

Georgia Department of Education

GSE Grade 7 Expanded Curriculum Map – 1st Semester

1 Make sense of problems and persevere in solving them.

2 Reason abstractly and quantitatively.

3 Construct viable arguments and critique the reasoning of others.

4 Model with mathematics.

Unit 1

Operations with Rational Numbers

Apply and extend previous understandings of operations

with fractions to add, subtract, multiply, and divide

rational numbers.

MGSE7.NS.1 Apply and extend previous understandings of

addition and subtraction to add and subtract rational numbers;

represent addition and subtraction on a horizontal or vertical

number line diagram.

MGSE7.NS.1a Show that a number and its opposite have a

sum of 0 (are additive inverses). Describe situations in

which opposite quantities combine to make 0. For example,

your bank account balance is -$25.00. You deposit $25.00

into your account. The net balance is $0.00.

MGSE7.NS.1b Understand p + q as the number located a

distance from p, in the positive or negative direction

depending on whether q is positive or negative. Interpret

sums of rational numbers by describing real world contexts.

MGSE7.NS.1c Understand subtraction of rational numbers

as adding the additive inverse, p – q = p + (– q). Show that

the distance between two rational numbers on the number

line is the absolute value of their difference, and apply this

principle in real‐world contexts.

MGSE7.NS.1d Apply properties of operations as strategies to

add and subtract rational numbers.

MGSE7.NS.2 Apply and extend previous understandings of

multiplication and division and of fractions to multiply and

divide rational numbers.

MGSE7.NS.2a Understand that multiplication is extended

from fractions to rational numbers by requiring that operations

continue to satisfy the properties of operations, particularly the

distributive property, leading to products such as (-1)(-1) = 1 and

the rules for multiplying signed numbers. Interpret products of

rational numbers by describing real-world contexts

MGSE7.NS.2b Understand that integers can be divided,

provided that the divisor is not zero, and every quotient of

integers (with non‐zero divisor) is a rational number. If p

and q are integers then – (p/q) = (– p)/q = p/(–q). Interpret

Standards for Mathematical Practice

5 Use appropriate tools strategically.

6 Attend to precision.

7 Look for and make use of structure.

8 Look for and express regularity in repeated reasoning.

Unit 2

Expressions & Equations

Use properties of operations to generate equivalent

expressions.

MGSE7.EE.1 Apply properties of operations as strategies to

add, subtract, factor, and expand linear expressions with

rational coefficients.

MGSE7.EE.2 Understand that rewriting an expression in

different forms in a problem context can clarify the problem

and how the quantities in it are related. For example a +

0.05a = 1.05a means that adding a 5% tax to a total is the

same as multiplying the total by 1.05.

Solve real-life and mathematical problems using numerical

and algebraic expressions and equations.

MGSE7.EE.3 Solve multistep real-life and mathematical

problems posed with positive and negative rational numbers

in any form (whole numbers, fractions, and decimals) by

applying properties of operations as strategies to calculate

with numbers, converting between forms as appropriate, and

assessing the reasonableness of answers using mental

computation and estimation strategies.

For example:

• If a woman making $25 an hour gets a 10% raise,

she will make an additional 1/10 of her salary an

hour, or $2.50, for a new salary of $27.50.

• If you want to place a towel bar 9 3/4 inches long in

the center of a door that is 27 1/2 inches wide, you

will need to place the bar about 9 inches from each

edge; this estimate can be used as a check on the

exact computation.

MGSE7.EE.4 Use variables to represent quantities in a realworld or mathematical problem, and construct simple

equations and inequalities to solve problems by reasoning

about the quantities.

MGSE7.EE.4a Solve word problems leading to equations of

the form px + q = r and p(x + q) = r, where p, q, and r are

specific rational numbers. Solve equations of these forms

fluently. Compare an algebraic solution to an arithmetic

July 2019 ● Page 4 of 7

Unit 3

Ratios and Proportional Relationships

Analyze proportional relationships and use them to solve

real-world and mathematical problems.

MGSE7.RP.1 Compute unit rates associated with ratios of

fractions, including ratios of lengths, areas and other quantities

measured in like or different units. For example, if a person

walks 1/2 mile in each 1/4 hour, compute the unit rate as the

complex fraction (1/2)/(1/4) miles per hour, equivalently 2

miles per hour.

MGSE7.RP.2 Recognize and represent proportional

relationships between quantities.

MGSE7.RP.2a Decide whether two quantities are in a

proportional relationship, e.g., by testing for equivalent ratios

in a table or graphing on a coordinate plane and observing

whether the graph is a straight line through the origin.

MGSE7.RP.2b Identify the constant of proportionality (unit

rate) in tables, graphs, equations, diagrams, and verbal

descriptions of proportional relationships.

MGSE7.RP.2c Represent proportional relationships by

equations.

MGSE7.RP.2d.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.

MGSE7.RP.3 Use proportional relationships to solve

multistep ratio and percent problems. Examples: simple

interest, tax, markups and markdowns, gratuities and

commissions, and fees.

Draw, construct, and describe geometrical figures and

describe the relationships between them.

MGSE7.G.1 Solve problems involving scale drawings of

geometric figures, including computing actual lengths and

areas from a scale drawing and reproducing a scale drawing at

a different scale.

Georgia Department of Education

quotients of rational numbers by describing real‐world

contexts.

MGSE7.NS.2c Apply properties of operations as strategies to

multiply and divide rational numbers.

MGSE7.NS.2d Convert a rational number to a decimal using

long division; know that the decimal form of a rational

number terminates in 0s or eventually repeats.

MGSE7.NS.3 Solve real-world and mathematical problems

involving the four operations with rational numbers.

solution, identifying the sequence of the operations used in

each approach. For example, the perimeter of a rectangle is

54 cm. Its length is 6 cm. What is its width?

MGSE7.EE.4b Solve word problems leading to inequalities

of the form px + q > r or px + q < r, where p, q, and r are
specific rational numbers. Graph the solution set of the
inequality and interpret it in the context of the problem. For
example, as a salesperson, you are paid $50 per week plus $3
per sale. This week you want your pay to be at least $100.
Write an inequality for the number of sales you need to make,
and describe the solutions.
MGSE7.EE.4c Solve real-world and mathematical problems
by writing and solving equations of the form x+p = q and px
= q in which p and q are rational numbers.
July 2019 ● Page 5 of 7
Georgia Department of Education
GSE Grade 7 Expanded Curriculum Map – 2nd Semester
Standards for Mathematical Practice
5 Use appropriate tools strategically.
6 Attend to precision.
7 Look for and make use of structure.
8 Look for and express regularity in repeated reasoning.
1 Make sense of problems and persevere in solving them.
2 Reason abstractly and quantitatively.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
Unit 4
Unit 5
Unit 6
Unit 7
Geometry
Inferences
Probability
Show What We Know
Draw, construct, and describe geometrical
figures and describe the relationships
between them.
MGSE7.G.2 Explore various geometric
shapes with given conditions. Focus on
creating triangles from three measures of
angles and/or sides, noticing when the
conditions determine a unique triangle, more
than one triangle, or no triangle.
MGSE7.G.3 Describe the two-dimensional
figures (cross sections) that result from
slicing three-dimensional figures, as in plane
sections of right rectangular prisms, right
rectangular pyramids, cones, cylinders, and
spheres.
Solve real-life and mathematical problems
involving angle measure, area, surface area,
and volume.
MGSE7.G.4 Given the formulas for the area
and circumference of a circle, use them to
solve problems; give an informal derivation
of the relationship between the
circumference and area of a circle.
MGSE7.G.5 Use facts about supplementary,
complementary, vertical, and adjacent angles
in a multi-step problem to write and solve
simple equations for an unknown angle in a
figure.
MGSE7.G.6 Solve real-world and
mathematical problems involving area, volume
and surface area of two- and three dimensional
objects composed of triangles, quadrilaterals,
polygons, cubes, and right prisms.-
Use random sampling to draw inferences
about a population.
MGSE7.SP.1 Understand that statistics can be
used to gain information about a population by
examining a sample of the population;
generalizations about a population from a
sample are valid only if the sample is
representative of that population. Understand
that random sampling tends to produce
representative samples and support valid
inferences.
MGSE7.SP.2 Use data from a random sample
to draw inferences about a population with an
unknown characteristic of interest. Generate
multiple samples (or simulated samples) of the
same size to gauge the variation in estimates or
predictions
Draw informal comparative inferences
about two populations.
MGSE7.SP.3 Informally assess the degree of
visual overlap of two numerical data
distributions with similar variabilities,
measuring the difference between the medians
by expressing it as a multiple of the interquartile
range.
MGSE7.SP.4 Use measures of center and
measures of variability for numerical data from
random samples to draw informal comparative
inferences about two populations.
Investigate chance processes and develop,
use, and evaluate probability models.
MGSE7.SP.5 Understand that the probability
of a chance event is a number between 0 and 1
that expresses the likelihood of the event
occurring. Larger numbers indicate greater
likelihood. A probability near 0 indicates an
unlikely event, a probability around 1/2
indicates an event that is neither unlikely nor
likely, and a probability near 1 indicates a
likely event.
MGSE7.SP.6 Approximate the probability
of a chance event by collecting data on the
chance process that produces it and
observing its long-run relative frequency.
Predict the approximate relative frequency
given the probability. For example, when
rolling a number cube 600 times, predict that
a 3 or 6 would be rolled roughly 200 times,
but probably not exactly 200 times.
MGSE7.SP.7 Develop a probability model
and use it to find probabilities of events.
Compare experimental and theoretical
probabilities of events. If the probabilities
are not close, explain possible sources of the
discrepancy.
MGSE7.SP.7a Develop a uniform probability
model by assigning equal probability to all
outcomes, and use the model to determine
probabilities of events
MGSE7.SP.7b Develop a probability model
(which may not be uniform) by observing
frequencies in data generated from a chance
process. For example, find the approximate
probability that a spinning penny will land
heads up or that a tossed paper cup will land
ALL
July 2019 ● Page 6 of 7
Georgia Department of Education
.
open‐end down. Do the outcomes for the
spinning penny appear to be equally likely
based on the observed frequencies?
MGSE7.SP.8 Find probabilities of compound
events using organized lists, tables, tree
diagrams, and simulation.
MGSE7.SP.8a Understand that, just as with
simple events, the probability of a compound
event is the fraction of outcomes in the sample
space for which the compound event occurs.
MGSE7.SP.8b Represent sample spaces for
compound events using methods such as
organized lists, tables and tree diagrams. For
an event described in everyday language (e.g.,
“rolling double sixes”), identify the outcomes
in the sample space which compose the event.
MGSE7.SP.8c Explain ways to set up a
simulation and use the simulation to generate
frequencies for compound events. For
example, if 40% of donors have type A blood,
create a simulation to predict the probability
that it will take at least 4 donors to find one
with type A blood.
July 2019 ● Page 7 of 7
GCU College of Education
LESSON PLAN TEMPLATE
Teacher
Candidate:
Grade Level:
Date:
Unit/Subject:
Instructional Plan
Title
Lesson
summary
and focus:
National /
State
Learning
Standards:
6th grade
Chapter 7 Rational Numbers as Decimals and Percent
Understanding Decimals and Percentages
I. PLANNING
Throughout this lesson students will begin to strengthen and have the ability to
calculate fractions from a set of objects and convert fractions to decimals and
percentages. Develop a graph to base the individuals information and growth to
compare and contrast with other students in a group setting.
The Common Core State Standards (CCSS) are a set of academic standards in
mathematics and English language arts/literacy (ELA) developed under the
direction of the Council of Chief State School Officers (CCSSO) and the National
Governors Association (NGA).
The math standards include both content standards and mathematical practices
(process standards) outlining what each student should know and be able to do at
the end of each grade. The standards collectively define the skills and knowledge
all students need to succeed in college, career, and life, regardless of where they
live.
Specific learning target(s) / objectives:
• Students at the end of this class, will
properly be able to execute math
problems that involve decimals and
percentages.
• They will be well versed enough to
even work these problems out
through word problems and everyday
life.
Agenda:
*Come to class, get organized and put things
away.
*make sure pencils are sharpened and the
supplies you need for the lesson are at your
disposable.
*teacher speaks to class of the overview of
the day.
*practice problem on the board to work, 5
minutes and we discuses it as a class.
Teaching notes:
We will review prior information learned in a
previous math class. We will make sure that
students are familiar with what a fraction, decimal
and percent actually is and how and why we use
them. Prior to this 6th grade math, students have
been exposed to these types of math skills and if
anything have it logged in their brain and be
familiar when it is brought up for this class.
Formative assessment:
Page 1 of 4
*lessons on decimals and percentages 9:3011
*lunch 11-12
*silent time 12-12:15
*Continue with the lesson incorporating the
fractions into the mix. 12:30-1:30
*Clean up the class, review what is for
homework and have students wait until pick
up or when their bus is called.
Academic
Key vocabulary:
Language:
Decimals
Rational numbers
Percentage...
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