Download 7th Grade - Moving To the Common Core

East Saint Louis District 189 Math Curriculum Grade 7
A Story of Ratios Curriculum Overview
Sequence of Grade 7 Modules Aligned with the Standards
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Module 1: The Real Number System
Module 2: Rational Number Operations
Module 3: Algebraic Expressions
Module 4: Algebraic Equations and Inequalities
Module 5: Direct and Inverse Proportion
Module 6: Angle Properties and Straight Lines
Module 11: Circumference and Area of a Circle
Module 7: Geometric Construction
Module 8: Volume and Surface Area of Solids
Module 9: Statistics
Module 10: Probability
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13 Days
24 Days
20 Days
14 Days
17 Days
15 Days
11 Days (from the Grade 6 Book B Math in Focus)
16 Days
16 Days
16 Days
16 Days
Summary of Year
Seventh grade mathematics is about (1) developing understanding of and applying proportional relationships; (2) developing understanding of
operations with rational numbers and working with expressions and linear equations; (3) solving problems involving scale drawings and informal
geometric constructions, and working with two‐ and three‐dimensional shapes to solve problems involving area, surface area, and volume;
and (4) drawing inferences about populations based on samples.
Key Areas of Focus for Grade 7: Ratios and proportional reasoning; arithmetic of rational numbers
CCSS Major Emphasis Clusters
Ratios and Proportional Relationships
 Analyze proportional relationships and use them to solve real‐world and mathematical problems.
The Number System
 Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
Expressions and Equations
 Use properties of operations to generate equivalent expressions.
 Solve real‐life and mathematical problems using numerical and algebraic expressions and equations.
Adapted from Math In Focus
Page 1
East Saint Louis District 189 Math Curriculum Grade 7
Rationale for Module Sequence in Grade 7
In Module 1, students will extend their knowledge of numbers (whole numbers, integers, fractions and decimals) to irrational numbers. They
will identify numbers that make up the sets of rational numbers and those in the set of real numbers. They will locate numbers from both sets
on a number line. Students will explore the Density Property for rational numbers and for real numbers and learn that fractions can always be
written as a decimal. They will learn methods to approximate irrational numbers and develop number sense surrounding squares and square
roots. Students will also learn about significant digits, precision and their importance in measurement.
Counters and number lines will be used extensively in Module 2 to model addition and subtraction of integers. Counters are typically used to
model the concepts of “zero pairs” and additive inverses. Number lines help students to see that subtracting a number is the same as adding it’s
opposite. Number lines can also be used to model operations with rational numbers. Students should use concrete and pictorial
representations, such as number lines or tables with repeated addition, to derive “rules” for multiplying and dividing integers. (Use the Common
Core Standard 7 NS.2 to help show students deductively how the product of 2 negative integers is found. ) Students will extend their operation
skills to rational numbers, including decimals and percents, and to solve real world problem. In Grade 6, students learned to add and subtract
two fractions by finding the LCD. In this module students extend that knowledge to operations with 3 or more fractions. Students will also
extend work from Grade 6 to include working with negative rates of change.
Module 3 will deepen students understanding by applying their skills to more complex algebraic expressions. Students will work with
expressions that have more than two terms and more than one variable. Students will recognize and group like terms to simplify expressions,
even those that have rational number coefficients. Students will use brackets to group parts of algebraic expressions as they work with the
order of operations. Students will also look at multiple ways of representing terms with fractional coefficients. Students will broaden their
work of the distributive and commutative properties to include negative coefficients. Students will also learn that an expression such as -2x-1
can be factored to: -(2x + 1). Bar models will be used to simplify algebraic expressions with integer, decimal and fractional expressions. They are
also used to simplify expressions with two variables and to expand or factor expressions. Students will create bar models and diagrams to help
them visualize algebraic real world situations.
Students learn to identify equivalent equations in Module 4 and solve multi-step equations with variables on both sides and parentheses.
Students build on their work with expressions in Module 3 to solving equations. Students must understand that equivalent equations are
created each time an operation occurs on both sides of the equation. Students must be familiar with the three basic properties of equality:
Reflexive Property, Symmetric Property and Transitive Property. Using a balanced scale will support the concept of equivalent equations.
Addition, subtraction, multiplication and division call all be modeled using a balance scale. Students will learn that they can perform inverse
operations in any order and the solution remains the same. Students must also realize that they can isolate the variable on either side of the
equation. Students should learn multiple ways of solving equations that have fractional coefficients or parentheses in the equation. Students
will then move to solving inequalities and graphing the solution set. Through modeling on a number line, students will learn the reason for
Adapted from Math In Focus
Page 2
East Saint Louis District 189 Math Curriculum Grade 7
reversing an inequality sign when they multiply or divide both sides of an inequality by a negative number. Students will use equations and
inequalities to solve real world problems.
In Grade 6, students learned about ratios and rates. Module 5 is used to extend those skills to the concepts of direct and inverse proportions.
Students will learn there are four ways to write a proportion and it is key that students understand both ratios in the proportion compare
quantities in the same order. Data tables can be used to help students set up a proportion to describe a situation. Students will learn a variety
of ways to describe and write proportional relationships. Students will use bar models to interpret and solve direct and inverse proportional
problems. Students will also learn that the graph of a direct proportion relationship is a straight line that passes through the origin but does not
lie on an axis. Inverse proportional relationships are graphed as curves that never cross the x- or y-axis.
Students will explore and apply the properties of complementary angles, supplementary angles, adjacent angles, angles on a line, angles at a
point, vertical angles, pairs of angles formed by parallel lines and a transversal, as well as exterior and interior angels of a triangle in Module 6.
Students will use algebra throughout this module to solve geometric problems involving angle measures. Students will solve equations in order
to apply the angle sum properties to find unknown angle measurements. Bar models will be used to solve problems when angle measures are
related by a given ratio. Many properties should be discovered by students through observation and hands-on activities. Students will learn the
sum of the measures of angles on a line and the sum of the measures of angles at a point. While the symbol for congruence is NOT introduced in
middle school, the distinction should be made in written statements. Students will make observations, generate tables, recognize patterns, and
make generalizations in order to “discover” angle properties. Students should understand that they cannot really “know” that a geometric
relationship always holds true based on inductive reasoning alone.
In Module 7, students will use a straightedge and compass to construct angle bisectors and perpendicular bisectors. Remind students the point
is to discover relationships that hold true and not “draw” the picture. Students will learn to contrast deductive and inductive reasoning in this
module. Students should construct triangle and quadrilaterals. Students will be able to determine, given a set of dimensions, whether a unique
triangle, two triangles or no triangles can be formed. The explorations preview postulates and theorems learned in later grades. Students will
construct a rhombus in order to unify the constructions they did in the first part of the module. Students will also study scale factors and solve
scale problems using proportional reasoning.
**Module 11, from the 6th grade book, will help students learn to identify parts of the circle and use formulas to find the area and circumference
of circles. This knowledge will extend to finding the distance around figures that involve circular parts. Students will define a circle by the fact
that every point on the circle is equidistant from the center point of the circle. Students will use manipulatives to investigate the relationship
between radii and diameters and determine that each circle has an infinite number of radii. They will also discover that the circumference is
about 3 times the diameter of every circle. Students will learn the ratio of the circumference to the diameter is pi and multiple ways to
Adapted from Math In Focus
Page 3
East Saint Louis District 189 Math Curriculum Grade 7
represent this amount. Students will derive the area formula by cutting and rearranging sectors of a circle to find a near rectangle. Students will
use the formulas for circumference and area to solve real-world problems.
Students will learn to identify cylinders, cones, and pyramids, both as solids and from their nets in Module 8. Students will also learn to identify
the shapes of cross sections of those solids. All work with solids will be limited to right solids that have a central axis perpendicular to the base.
Explorations of finding the cross sections formed when plans intersect prisms, cylinders, cones, pyramids and spheres are appealing to visual
learners and enable students to develop formulas for finding the volume of solids. The majority of the examples should be limited to cross
sections that are parallel or perpendicular to the base. Students will also investigate the properties associated with the cross section of a cone.
Students will develop the formulas for the volume and surface area of prisms, cylinders, pyramids, cones and spheres.
In Module 9, students will learn to identify measures of variation. The divide data sets into quartiles and identify the interquartile range.
Students draw and interpret stem-and-leaf plots and box-and-whisker plots. They learn to find the mean absolute deviation. Students will also
learn about populations and samples. They understand and apply different random sampling methods, use statistics from a sample to make
inferences about a population and use an inference to estimate a population mean. Students also make comparative inferences about two
populations using two sets of sample statistics.
Probability is the focus of Module 10. Students learn about chance processes, and measuring the likelihood of events. Students learn to
distinguish between theoretical and experimental probability. Students will recognize that as the number of trials increases in an experiment
with a chance process, the experimental probability measures tent to approach the values of the theoretical probability measures. Students will
use Venn Diagrams to represent sample spaces and events.
Adapted from Math In Focus
Page 4
East Saint Louis District 189 Math Curriculum Grade 7
Alignment Chart
Module and
Approximate
Number of
Instructional
Days
Module 1:
The Real
Number
System
(13 days)
MP. 4
MP. 6
MP. 7
Common Core Learning Standards Addressed in
Grade 7 Modules
(24 days including
2 days for
cumulative review)
MP. 1
Number
Performance-Based
Talks and
Tasks/Assessments
Instructional www.illustrativemathematics.org
Strategies
SEE APPENDIX FOR PRINTED COPY
Apply and extend previous understandings
of operations with fractions.
7.NS.A.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.
7.NS.A.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.
Module 2:
Rational
Number
Operations
Suggested
Text Book
Resources
Apply and extend previous understandings
of operations with fractions.
7.NS.A.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.
Adapted from Math In Focus
Vocabulary:
*Approximate
*Irrational
Number
*Negative
Integers
*Opposites
*Postitive
Integers
*Precise
*Rational
Number
*Real Number
*Real Number
Line
*Repeating
Decimal
*Set of Integers
*Significant Digit
*Terminating
Decimal
Vocabulary:
*Additive
Inverse
*Complex
Fraction
*Least Common
Denominator
*Zero Pair
Comparing Freezing Points
7.NS.A.1
Distances on the Number
Line 2
7.NS.A.1
Equivalent fractions
approach to non-repeating
decimals
7.NS.A.2.d
Operations on the number
line
7.NS.A.1
Repeating decimal as
approximation
7.NS.A.2.d
Comparing Freezing Points
7.NS.A.1
Distances on the Number
Line 2
7.NS.A.1
Operations on the number
line
7.NS.A.1
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East Saint Louis District 189 Math Curriculum Grade 7
MP. 4
MP. 7
MP.8
7.NS.A.1a Describe situations in which opposite
quantities combine to make 0. For example, a hydrogen
atom has 0 charge because its two constituents are
oppositely charged.
7.NS.A.1b Understand p + q as 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.
7.NS.A.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.
7.NS.A.1d Apply properties of operations as strategies to
add and subtract rational numbers.
7.NS.A.2 Apply and extend previous understandings of
multiplication and division and of fractions to multiply and
divide rational numbers.
7.NS.A.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.
7.NS.A.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 quotients of rational numbers by describing real-
Adapted from Math In Focus
Page 6
East Saint Louis District 189 Math Curriculum Grade 7
world contexts.
7.NS.A.2c Apply properties of operations as strategies to
multiply and divide rational numbers.
7.NS.A.3 Solve real-world and mathematical problems
involving the four operations with rational numbers.
Module 3:
Algebraic
Expressions
(20 days)
MP.1
MP. 2
MP. 3
MP.4
Use properties of operations to generate
equivalent expressions.
7.EE.A.1 Apply properties of operations as strategies to
add, subtract, factor, and expand linear expressions with
rational coefficients.
Vocabulary:
*Like Terms
*Simplify
*Commutative
Property of
Addition
*Factoring
*Expanded Form
Sharing Prize Money
7.NS.A.3
Equivalent Expressions?
7.EE.A
Miles to Kilometers
7.EE.A
Writing Expressions
7.EE.A.1
7.EE.A.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. For
example, a + 0.05a = 1.05a means that “increase by 5%”
is the same as “multiply by 1.05.”
Solve real-life and mathematical problems
using numerical and algebraic expressions
and equations.
7.EE.B.3 Solve multi-step 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. 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
Adapted from Math In Focus
Discounted Books
7.EE.B.3
Page 7
East Saint Louis District 189 Math Curriculum Grade 7
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.
Module 4:
Algebraic
Equations and
Inequalities
(14 days)
MP. 2
MP. 4
MP. 7
MP. 8
Solve real-life and mathematical problems
using numerical and algebraic expressions
and equations.
Vocabulary:
*Equivalent
Equations
*Solution Set
*Equivalent
Inequalities
7.EE.B.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.
Fishing Adventures 2
7.EE.B.4
7.EE.B.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
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?
7.EE.B.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.
Module 5:
Direct and
Inverse
Proportion
(17 days in
including 2 days for
cumulative review)
Analyze proportional relationships and use
them to solve real-world and mathematical
problems.
7.RP.A.1 Compute unit rates associated with ratios of
Adapted from Math In Focus
Sports Equipment Set
7.EE.B.4.b
Vocabulary:
*Constant of
Proportionality
*Cross Product
*Direct
Proportion
*Inverse
Cooking with the Whole Cup
7.RP.A.1
Molly's Run
7.RP.A.1
Page 8
East Saint Louis District 189 Math Curriculum Grade 7
MP. 1
MP. 3
MP. 4
MP. 5
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.
7.RP.A.2 Recognize and represent proportional
relationships between quantities.
7.RP.A.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.
7.RP.A.2b Identify the constant of proportionality (unit
rate) in tables, graphs, equations, diagrams, and verbal
descriptions of proportional relationships.
7.RP.A.2c Represent proportional relationships by
equations. For 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.
7.RP.A.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
7.RP.A.3 Use proportional relationships to solve
multistep ratio and percent problems. Examples: simple
interest, tax, markups and markdowns, gratuities and
commissions, fees, percent increase and decrease,
percent error
Adapted from Math In Focus
Proportion
*Proportion
Molly's Run, Assessment
Variation
7.RP.A.1
Sore Throats, Variation 1
7.RP.A.2
Robot Races
7.RP.A.2
Robot Races, Assessment
Variation
7.RP.A.2
Music Companies, Variation 1
7.RP.A.2
Art Class, Assessment Variation
7.RP.A.2
Art Class, Variation 1
7.RP.A.2
Art Class, Variation 2
7.RP.A.2
Buying Bananas, Assessment
Version
7.RP.A.2
Buying Coffee
7.RP.A.2
Sand Under the Swing Set
7.RP.A.3, 7.G.B.6
Buying Protein Bars and
Magazines
7.RP.A.3
Chess Club
7.RP.A.3
Comparing Years
7.RP.A.3
Gotham City Taxis
7.EE.B.3, 7.EE.B.4, 7.RP.A.3
Finding a 10% increase
7.RP.A.3
Friends Meeting on Bikes
7.RP.A.3
Selling Computers
Page 9
East Saint Louis District 189 Math Curriculum Grade 7
7.RP.A.3
Tax and Tip
7.RP.A.3
The Price of Bread
7.RP.A.3
Two-School Dance
7.RP.A.3
Module 6:
Angle
Properties and
Straight Lines
(15 days)
MP. 1
MP. 2
MP. 3
MP. 5
Draw construct, and describe geometrical
figures and describe the relationships
7.G.A.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.
7.G.A.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.
Solve real-life and mathematical problems
involving angle measure, area, surface area,
and volume.
Vocabulary:
*Adjacent Angles
*Alternate
Exterior Angles
*Alternate
Interior Angles
*Complementary
Angles
*Congruent
Angles
*Corresponding
Angles
*Exterior Angles
*Interior Angles
*Supplementary
Angles
*Transversal
*Vertical Angles
Floor Plan
7.G.A.1
7.G.B.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
Module 7:
Geometric
Construction
(16 days)
MP. 1
Draw construct, and describe geometrical
figures and describe the relationships
between them.
7.G.A.1 Solve problems involving scale drawings of
Adapted from Math In Focus
Vocabulary:
*Bisect
*Bisector
*Compass
*Equidistant
*Included Angle
Floor Plan
7.G.A.1
Page 10
East Saint Louis District 189 Math Curriculum Grade 7
MP. 4
MP. 5
geometric figures, including computing actual lengths
and areas from a scale drawing and reproducing a scale
drawing at a different scale.
7.G.A.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
Module 11
(Grade 6):
Circumference
and Area of a
Circle
(11 days)
MP.2
MP.4
MP.5
MP.7
Draw construct, and describe geometrical
figures and describe the relationships
between them.
7.G.A.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.
*Included Side
*Midpoint
*Perpendicular
Bisector
*Scale
*Scale Factor
*Straightedge
*Arc
*Center
*Circumference
*Diameter
*Quadrant
*Radii
*Radius
*Semicircle
Resources
include
Module 11
from Math In
Focus Grade 6
B Book.
Solve real-life and mathematical problems
involving angle measure, area, surface area,
and volume.
7.G.B.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.
Module 8:
Volume and
Surface Area
of Solids
(16 days including
2 days for
cumulative review)
MP.1
MP. 4
Draw construct, and describe geometrical
figures and describe the relationships
between them.
7.G.A.3 Describe the two-dimensional figures that result
from slicing three-dimensional figures, as in plane
sections of right rectangular prisms and right rectangular
pyramids.
Adapted from Math In Focus
Vocabulary:
*Cylinder
*Cone
*Cross Section
*Hemishpere
*Lateral Surface
*Plane
*Slant Height of
a Cone
*Slant Height of
a Pyramid
Page 11
East Saint Louis District 189 Math Curriculum Grade 7
MP. 6
Solve real-life and mathematical problems
involving angle measure, area, surface area,
and volume.
*Sphere
*Surface Area
*Volume
Eight Circles
7.G.B.4
Measuring the area of a
circle
7.G.B.4, 7.RP.A.3
7.G.B.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.
7.G.B.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.
Module 9:
Statistics
(9.4 – 9.5
ONLY!)
(6 days)
MP. 1
MP.2
MP. 4
MP. 5
Use random sampling to draw inferences
about a population.
7.SP.A.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.
7.SP.A.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. For 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.
Adapted from Math In Focus
Vocabulary:
*Biased Sample
*Inference
*Population
*Random
Sample
*Sample
*Sample Size
*Simple Random
Sampling
*Stratified
Random
Sampling
*Systematic
Random
Sampling
*Unbiased
Sample
(9.4 – 9.5
ONLY!)
Mr. Brigg's Class Likes
Math
7.SP.A.1
Valentine Marbles
7.SP.A.2
Election Poll, Variation 1
7.SP.A
Election Poll, Variation 2
7.SP.A
Election Poll, Variation 3
7.SP.A
Estimating the Mean State
Area
7.SP.A
Page 12
East Saint Louis District 189 Math Curriculum Grade 7
Draw informal comparative inferences about
two populations.
7.SP.B.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. For 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.
Offensive Linemen
7.SP.B.3, 7.SP.B.4
College Athletes
7.SP.B.3, 7.SP.B.4
7.SP.B.4 Use measures of center and measures of
variability for numerical data from random samples to
draw informal comparative inferences about two
populations. For 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
Module 10:
Probability
(16 days including
two days for
cumulative review)
MP. 3
MP. 4
MP. 7
MP. 8
Investigate chance processes and develop,
use, and evaluate probability models.
7.SP.C.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.
7.SP.C.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.
Adapted from Math In Focus
Vocabulary:
*Biased
*Complementary
Event
*Event
*Experimental
Probability
*Fair
*Mutually
Exclusive
*Non-Uniform
Probability
Model
*Observed
Frequency
*Outcomes
Tossing Cylinders
7.SP.C.6
Rolling Dice
7.SP.C.6, 7.SP.C.7
How Many Buttons?
7.SP.C.7.a
Page 13
East Saint Louis District 189 Math Curriculum Grade 7
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.
7.SP.C.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.
7.SP.C.7a Develop a uniform probability model by
assigning equal probability to all outcomes, and use the
model to determine probabilities of events. For 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.
*Probability
*Probability
Distribution
*Probability
Model
*Relative
Frequency
*Sample Space
*Theoretical
Probability
*Uniform
Probability
Model
*Venn Diagram
7.SP.C.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 open-end
down. Do the outcomes for the spinning penny appear to
be equally likely based on the observed frequencies?
7.SP.C.8 Find probabilities of compound events using
organized lists, tables, tree diagrams, and simulation.
7.SP.C.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.
7.SP.C.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.
Adapted from Math In Focus
Rolling Twice
7.SP.C.8
Sitting across from Each
Other
7.SP.C.8.a, 7.SP.C.8.b
Waiting Times
7.SP.C.8
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East Saint Louis District 189 Math Curriculum Grade 7
7.SP.C.8c Design and use a simulation to generate
frequencies for compound events. For 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.
Key:
Major Clusters;
Supporting Clusters;
Additional Clusters
Examples of Linking Supporting Clusters to the Major Work of the Grade

Use random sampling to draw inferences about a population: The standards in this cluster represent opportunities to apply percentages and
proportional reasoning. To make inferences about a population, one needs to apply such reasoning to the sample and the entire population.

Investigate chance processes and develop, use, and evaluate probability models: Probability models draw on proportional reasoning and should be
connected to the major work in those standards.
Adapted from Math In Focus
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