Download 7th grade math curriculum pacing guide

COURSE CONTENT
MATHEMATICS
SEVENTH GRADE
CCRS
QUALITY
CORE
EVIDENCE OF STUDENT
ATTAINMENT
CONTENT STANDARDS
RESOURCES
FIRST SIX WEEKS
RVW
6th Grade Standards
10
[7.EE.4] Use variables to represent quantities in a real-world or mathematical
problem, and construct simple equations and inequalities to solve problems by
reasoning about the quantities.
a.
b.
Solve word problems leading to equations of the form px + q = r and p(x +
q) = r, where p, q, and rare specific rational numbers. Solve equations of
these forms fluently. Compare an algebraic solution to an arithmetic
solution, identifying the sequence of the operations used in each approach.
Example: The perimeter of a rectangle is 54 cm. Its length is 6 cm. What is
its width?
Solve word problems leading to inequalities of the
form px + q >r or px + q < r, where p, q, and rare specific rational numbers.
Graph the solution set of the inequality, and interpret it in the context of the
problem.
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.
Glencoe Ch. 1
Lessons 1-1A, 1-1B
Students:
Given a real world or mathematical
situation,








[7.EE.1] Apply properties of operations as strategies to add, subtract, factor, and
expand linear expressions with rational coefficients.
Define the variables and
constants in the situation,
Relate them to one another,
Write equations describing the
relationship,
Solve the equation (linear
situations) using properties of
the operations and equality.
Given a contextual situation involving a
linear inequality,

7
Lesson Page 33, 38 and 44
Model the situation with an
inequality,
Solve the inequality,
Graph the solution set of the
inequality,
Interpret and defend the
solution in the context of the
original problem.
Students:
Given contextual or mathematical
problems which may be modeled by
Lesson 1 – 1D
1
COURSE CONTENT
MATHEMATICS
SEVENTH GRADE
linear algebraic expressions with rational
coefficients,

8
RVW
[7.EE.2] Understand that rewriting an expression in different forms in a problem
context can shed light on the problem, and how the quantities in it are related.
Example: a + 0.05a = 1.05a means that "increase by 5%" is the same as "multiply by
1.05."
Review 6th Grade Standards
Use properties of the
operations (Table 3) to produce
combined and re-written forms
of the expressions that are
useful in resolving the
problem.
Students:

Explain how combining or
decomposing parts of algebraic
expressions can reveal
different aspects of the
expression and be useful in
interpreting a problem. (e.g.,
When determining the number
of tiles needed for a border
around a square pool of side n,
the expression 4n + 4 shows
counting 4 sides and then 4
corners. The expression 4(n+1)
shows counting four sides
which each include one corner.
The expression 4(n+2) - 4
shows counting the outer
border then subtracting the
corners as they have been
counted twice).
Glencoe Ch. 2
Lessons 2 – 1B, 2 – 1C
2
COURSE CONTENT
MATHEMATICS
SEVENTH GRADE
4
[7.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.
a.
b.
c.
d.
5
Describe situations in which opposite quantities combine to make 0.
Example: A hydrogen atom has 0 charge because its two constituents are
oppositely charged.
Understand p + qas the number located a distance |q| from p, in the positive
or negative direction depending on whether q is positive or negative. Show
that a number and its opposite have a sum of 0 (are additive inverses).
Interpret sums of rational numbers by describing real-world contexts.
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.
Apply properties of operations as strategies to add and subtract rational
numbers.
[7.NS.2] Apply and extend previous understandings of multiplication and division
and of fractions to multiply and divide rational numbers.
Students:

b.
c.
d.
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.
Understand that integers can be divided, provided that the divisor is not
zero, and every quotient of integers (with nonzero divisor) is a rational
number. If p and q are integers, then -(p/q) = (-p)/q =p/(-q). Interpret quotients of
rational numbers by describing real-world contexts.
Apply properties of operations as strategies to multiply and divide rational
numbers.
Convert a rational number to a decimal using long division; know that the
Describe situations that
illustrate the additive inverse
property as adding opposites to
equal zero.
Given contextual or mathematical
problems involving both positive and
negative rational numbers,

Find and justify sums and
differences of rational numbers
through connections to a
variety of representations
(including distance on a
number line) used for addition
and subtraction of whole
numbers and fractions.
Students:

a.
Glencoe Ch. 2

Glencoe Ch. 2-3 pg. 100-113
Find and justify products and
quotients of rational numbers
(positive and negative) through
connections to a variety of
representations and properties
of operations (including
multiplicative identity and
inverse) used for multiplication
and division of whole numbers
and fractions,
Use long division to convert a
rational number to a decimal
and explain why it must end in
3
COURSE CONTENT
MATHEMATICS
SEVENTH GRADE
decimal form of a rational number terminates in 0s or eventually repeats.
a zero or repeat.
SECOND SIX WEEKS
RVW
5
6th Grade Standards
[7.NS.2] Apply and extend previous understandings of multiplication and division and
of fractions to multiply and divide rational numbers.
Students:

a.
b.
c.
d.
6
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.
Understand that integers can be divided, provided that the divisor is not
zero, and every quotient of integers (with nonzero divisor) is a rational
number. If p and q are integers, then -(p/q) = (-p)/q =p/(-q). Interpret quotients of
rational numbers by describing real-world contexts.
Apply properties of operations as strategies to multiply and divide rational
numbers.
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.
[7.NS.3] Solve real-world and mathematical problems involving the four operations
with rational numbers. 1
(1computations with rational numbers extend the rules for manipulating fractions to
complex fractions.)
Glencoe Ch. 3
Lessons 3 – 1C
Page 127-173
Glencoe Ch. 3
Page 160-173

Find and justify products and
quotients of rational numbers
(positive and negative) through
connections to a variety of
representations and properties
of operations (including
multiplicative identity and
inverse) used for multiplication
and division of whole numbers
and fractions,
Use long division to convert a
rational number to a decimal
and explain why it must end in
a zero or repeat.
Students:
Given a variety of word problems
involving all four operations on rational
numbers, involving a variety of
complexities, (e.g.. mixed numbers,
complex fractions, location of the
unknown, etc.),

Glencoe Ch. 3
Explain and justify solutions
using a variety of
representations including
equations.
4
COURSE CONTENT
MATHEMATICS
SEVENTH GRADE
10
[7.EE.4] Use variables to represent quantities in a real-world or mathematical
problem, and construct simple equations and inequalities to solve problems by
reasoning about the quantities.
a.
b.
Solve word problems leading to equations of the form px + q = r and p(x +
q) = r, where p, q, and rare specific rational numbers. Solve equations of
these forms fluently. Compare an algebraic solution to an arithmetic
solution, identifying the sequence of the operations used in each approach.
Example: The perimeter of a rectangle is 54 cm. Its length is 6 cm. What is
its width?
Solve word problems leading to inequalities of the
form px + q >r or px + q < r, where p, q, and rare specific rational numbers.
Graph the solution set of the inequality, and interpret it in the context of the
problem.
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.
Students:
Given a real world or mathematical
situation,







[7.EE.3] Solve multistep real-life and mathematical problems posed with positive and
negative rational numbers in any form (whole numbers, fractions, and decimals), using
tools strategically. Apply properties of operations to calculate with numbers in any
form, convert between forms as appropriate, and assess the reasonableness of answers
using mental computation and estimation strategies.
Examples: 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 3/4inches long in the center of a door that is 27 1/2inches 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.
Define the variables and
constants in the situation,
Relate them to one another,
Write equations describing the
relationship,
Solve the equation (linear
situations) using properties of
the operations and equality.
Given a contextual situation involving a
linear inequality,

9
Glencoe Ch. 4
4.1-4.2
Pages 208-226
Model the situation with an
inequality,
Solve the inequality,
Graph the solution set of the
inequality,
Interpret and defend the
solution in the context of the
original problem.
Students:
Given contextual problems involving any
combination of numbers from the
rational numbers,


Pages 227-253
Model the problem with
mathematical symbols,
expressions, and equations that
aid in solving the problem,
Select strategies that are
useful, choose the appropriate
form of computation, reach a
5
COURSE CONTENT
MATHEMATICS
SEVENTH GRADE
solution, and defend the
solution in terms of the
original context (including
mental computation and
estimation strategies).
THIRD SIX WEEKS
1
[7.RP.1] Compute unit rates associated with ratios of fractions, including ratios of
lengths, areas and other quantities measured in like or different units.
Example: If a person walks 1/2 mile in each 1/4hour, compute the unit rate as the
complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.
Students:
Given ratios of fraction to fractions in
contextual situations,

11
[7.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.
Calculate the equivalent unit
rate and justify the unit rate
within the given context
Students:
Given contextual or mathematical
problems involving scale drawings of
geometric figures,

Glencoe Ch. 5
5.1, Pages 266-271
Data Games
Play.ccssgames.com
5.2
Pages 284-290
5.3
Pages 293-298
Solve, then communicate and
justify solution paths for
computing actual lengths and
areas.
Given a scale drawing,

2
[7.RP.2] Recognize and represent proportional relationships between quantities.
a.
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.
Students will reproduce the
drawing at a different scale.
Students:
Justify relationships as proportional and
identify the constant of proportionality
using graphs, tables, equivalent ratios,
and equations,
NCM Illuminations
Skin Weight
Whale Weight
6
COURSE CONTENT
MATHEMATICS
SEVENTH GRADE
b.
c.
d.
Identify the constant of proportionality (unit rate) in tables, graphs,
equations, diagrams, and verbal descriptions of proportional relationships.
Represent proportional relationships by equations.
Example: If total cost t is proportional to the number n of items purchased at
a constant price p, the relationship between the total cost and the number of
items can be expressed as t = pn.
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 ris the unit rate.

Explain the relationships
between representations of
proportions and extend that
relationship into a rule
(equation).
Given the graph of a proportional
relationship in a contextual situation, (i.e.
buying CDs of equal price),

Explain the association
between the unit rate and any
point on the line, (i.e. "If I paid
$3/CD, then point (5, 15)
means that I can buy 5 CDs for
$15").
FOURTH SIX WEEKS
RVW
3
Review 6th Grade Standards
[7.RP.3] Use proportional relationships to solve multistep ratio and percent problems.
Examples: Sample problems may involve simple interest, tax, markups and
markdowns, gratuities and commissions, fees, percent increase and decrease, percent
error.
Students:
Given multi-step problems involving
contexts with ratios and percents,

9
[7.EE.3] Solve multistep real-life and mathematical problems posed with positive and
negative rational numbers in any form (whole numbers, fractions, and decimals), using
tools strategically. Apply properties of operations to calculate with numbers in any
Glencoe Ch. 6
Pages 320-324
Glencoe Ch. 6
Pages 332
Dan Meyer's Which crayon should I
use?
Solve and justify solutions
using a variety of
representations and solution
paths
Students:
Given contextual problems involving any
combination of numbers from the
6-3
Pages 346-358
7
COURSE CONTENT
MATHEMATICS
SEVENTH GRADE
form, convert between forms as appropriate, and assess the reasonableness of answers
using mental computation and estimation strategies.
Examples: 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 3/4inches long in the center of a door that is 27 1/2inches 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.
RVW
21
rational numbers,


Review of 6th Grade Standards
[7.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.
Students:
Given a variety of chance events,


22
Model the problem with
mathematical symbols,
expressions, and equations that
aid in solving the problem,
Select strategies that are
useful, choose the appropriate
form of computation, reach a
solution, and defend the
solution in terms of the
original context (including
mental computation and
estimation strategies).
[7.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, and
predict the approximate relative frequency given the probability.
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.
Associate numbers close to
zero with unlikely events, and
numbers close to one with
likely events,
Compare likelihoods of given
events by associating larger
numbers with the more likely
events
Students:
Given the description of a chance event,
(e.g., rolling a certain number on a
number cube, getting heads when
flipping a coin, drawing a red card from
a deck of playing cards, etc.),

Ch. 7
7.1 Pages 377-400
7.3 Pages 405-409
Glencoe 8
8.1 Pages 429-447
8.2-8.3
Pages 449-463
Plan a data collection process,
8
COURSE CONTENT
MATHEMATICS
SEVENTH GRADE
collect and organize the
relevant data and use the longrun relative frequency to
justify an approximation of the
probability of the event.
Given the description of a chance event
and its probability,

23
[7.SP.7] Develop a probability model and use it to find probabilities of events.
Compare probabilities from a model to observed frequencies; if the agreement is not
good, explain possible sources of the discrepancy.
a.
b.
Develop a uniform probability model by assigning equal probability to all
outcomes, and use the model to determine probabilities of events.
Example: If a student is selected at random from a class, find the probability
that Jane will be selected and the probability that a girl will be selected.
Develop a probability model (which may not be uniform) by observing
frequencies in data generated from a chance process.
Example: Find the approximate probability that a spinning penny will land
heads up or that a tossed paper cup will land open-end down. Do the
outcomes for the spinning penny appear to be equally likely based on the
observed frequencies?
Predict and justify the
approximate relative frequency
for a given number of
occurrences, (e.g., if a number
cube is rolled 600 times,
predict that a 3 or a 6 would be
rolled roughly 200 times, but
probably not exactly 200
times).
Students:
Given the description of a chance event,
(e.g., rolling a certain number on a
number cube, getting heads when
flipping a coin, drawing a red card from
a deck of playing cards, etc.),


8.3 Continued
Pages 466-476
Find and describe the
probability of the event by
developing probability models
based on assigning equal
probabilities to each of the
possible outcomes (uniform
probability model) and test
whether or not this model may
or may not fit the observed
situation when the chance
event occurs,
Explain possible sources of
discrepancy between
9
COURSE CONTENT
MATHEMATICS
SEVENTH GRADE
developed probability models,
(e.g., uniform probability
model or other models) and
observed frequencies.
24
[7.SP.8] Find probabilities of compound events using organized lists, tables, tree
diagrams, and simulation.
a.
b.
c.
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.
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.
Design and use a simulation to generate frequencies for compound events.
Example: Use random digits as a simulation tool to approximate the answer
to the question: If 40% of donors have type A blood, what is the probability
that it will take at least 4 donors to find one with type A blood?
Students:
Given the description of a compound
event, (e.g., rolling a sum of seven with
two dice),

Chapter 8 continued
Use models, (e.g., organized
lists, tables, tree diagrams, and
simulations) to find and
explain the possible outcomes
in the event and find the
probability of each outcome.
Given a contextual or mathematical
situation involving probability related to
a compound event,

Develop a simulation and data
collection process, collect and
organize the relevant data, and
use the long-run relative
frequency to justify an
approximation of the
probability of the event and an
answer to the original question.
FIFTH SIX WEEKS
12
[7.G.2] Draw (freehand, with ruler and protractor, and with technology) geometric
shapes with given conditions. Focus on constructing triangles from three measures of
angles or sides, noticing when the conditions determine a unique triangle, more than
one triangle, or no triangle
Students:
Given sets of conditions for geometric
shapes,
Map
Possible Triangle Construction
GeoGebra
10
COURSE CONTENT
MATHEMATICS
SEVENTH GRADE

Draw (freehand, with a ruler
and protractor, and with
technology) the corresponding
shapes.
Given three measures (a combination of
side lengths and angle measures) of a
triangle,

13
[7.G.3] Describe the two-dimensional figures that result from slicing threedimensional figures, as in plane sections of right rectangular prisms and right
rectangular pyramids.
Students:
Given a 3-D figure, (e.g. right
rectangular prism, right rectangular
pyramid, cone, etc.),

14
[7.G.4] Know the formulas for the area and circumference of a circle, and use them to
solve problems; give an informal derivation of the relationship between the
circumference and area of a circle.
Use observations from the
drawing, reasoning, and
mathematical language, to
justify whether the conditions
determine a unique figure,
more than one figure, or no
figure.
Describe the plane (2-D)
section that results from slicing
the 3-D figure.
Students:

Glenco Pg. 795, Lesson 12
Illustrative Mathematic - Cube Ninjas
Glencoe Pg. 801, Lesson 13
Dan Meer's
Describe the relationship
between the formulas for area
and circumference of a circle
and derive an equation relating
the two formulas.
11
COURSE CONTENT
MATHEMATICS
SEVENTH GRADE
Given real world and mathematical
problems involving area and
circumference of circular regions,

15
[7.G.5] Use facts about supplementary, complementary, vertical, and adjacent angles
in a multistep problem to write and solve simple equations for an unknown angle in a
figure.
Students:
Given multi-step problems involving
angle measures,

16
[7.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 a variety of
representations including
models, drawings, and
equations based on area and
circumference formulas to find
and justify solutions and
solution paths.
Use knowledge of
supplementary,
complementary, vertical, and
adjacent angles to create and
solve equations for unknown
angles, and justify solutions
and solution paths.
Students:
Given real world and mathematical
problems involving area, volume, and
surface area (problems include figures
composed of triangles, quadrilaterals,
polygons, cubes, and right prisms),

Clencoe Ch. 12
Pages 674-679
Glencoe Ch. 10
Pages 557-597
Dan Myer's
Use a variety of strategies to
solve problems, and justify
solutions and solution paths.
12
COURSE CONTENT
MATHEMATICS
SEVENTH GRADE
SIXTH SIX WEEKS
17
[7.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.
Students:
Given data collected on a sample from a
population,

Make, explain and justify
inferences about the
population, if any, that could
be made from the sample data.
Given a statistical question about a
population,


18
[7.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.
Example: Estimate the mean word length in a book by randomly sampling words from
the book; predict the winner of a school election based on randomly sampled survey
data. Gauge how far off the estimate or prediction might be.
Describe and justify a data
collection process that would
result in representative data
from which inferences about
the population can be drawn,
Explain and justify their
reasoning concerning data
collection processes that do not
allow generalizations, (i.e.,
non-representative samples)
from the sample to the
population.
Students:
Given data from a random sample,

Dan Meyer's
Analyze the data and explain
inferences about the population
that can be drawn from the
sample data.
Given a population,
13
COURSE CONTENT
MATHEMATICS
SEVENTH GRADE

19
20
Ask statistical questions and
generate multiple samples (or
simulated samples) of the same
size to gauge the variation in
estimates or predictions.
[7.SP.3] Informally assess the degree of visual overlap of two numerical data
distributions with similar variabilities, measuring the difference between the centers
by expressing it as a multiple of a measure of variability.
Example: The mean height of players on the basketball team is 10 cm greater than the
mean height of players on the soccer team, about twice the variability (mean absolute
deviation) on either team; on a dot plot, the separation between the two distributions of
heights is noticeable.
Students:
Given two sets of data with similar
variabilities,
[7.SP.4] Use measures of center and measures of variability for numerical data from
random samples to draw informal comparative inferences about two populations.
Example: Decide whether the words in a chapter of a seventh-grade science book are
generally longer than the words in a chapter of a fourth-grade science book.
Students:





Glencoe Ch. 9
9.1-9.2
Pages 491-509
Informally assess and describe
the degree of visual overlap of
the distributions by comparing
visual representations of data
sets, (e.g., line plots,
coordinate plane graphs) and
statistical measures of center
and variability.
Generate statistical questions
that compare two populations,
Collect and organize data from
random samples to address the
questions,
Describe the sample
distributions using measures of
center and variability,
Justify answers to the
questions by drawing informal
comparative inferences about
the two populations from the
data sets and their descriptive
statistics.
Glencoe Ch. 9
9.3-9.4
Pages 513-545
Mathematic Assessment Project
14
COURSE CONTENT
MATHEMATICS
SEVENTH GRADE
15