Download Grade 7 - Morris School District

MORRIS SCHOOL DISTRICT
MORRISTOWN, NJ
2011-2012
GRADE 7 MATHEMATICS
C URRICULUM M AP
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Grade 7, focus on: (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.
Grade 7 Overview
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.
Geometry
◦ Draw, construct and describe geometrical figures and describe the relationships between them.
◦ Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
Statistics and Probability
◦ Use random sampling to draw inferences about a population.
◦ Draw informal comparative inferences about two populations.
◦ Investigate chance processes and develop, use, and evaluate probability models.
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Curriculum Map
Content/Objective
Essential Questions/
Enduring Understandings
Chapter 1 – Operations with Integers –
Essential Questions:
The learner will:
 How is an integer and its
 Solve multi-step real life and mathematical
absolute value related?
problems posed with positive and negative
rational numbers. Apply properties of
 Is the sum of 2 integers,
operations to calculate with numbers in any
positive, negative or zero?
form (7.EE.3)
How can you tell?
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Understand p + q as the number located a
distance lal 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 (7.NS.1b)
Apply properties of operations as strategies to
add and subtract rational numbers (7.NS.1d)
Solve real world and mathematical problems
involving the four operations with rational
numbers (7.NS.3)
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How are adding integers and
subtracting integers related?
Is the product of two
integers positive, negative,
or zero? How can you tell?
Understand subtraction of rational numbers
as adding the additive inverse, p-q = p + (-  Is the quotient of tow
integers positive, negative,
q). Show that the distance between two
or zero? How can you tell?
rational numbers on the number line is the
absolute value of their difference, and
apply this principle in real-world
 How can you use ordered
contexts(7.NS.1c)
pairs to locate points in a
Understand that multiplication is extended
coordinate plane?
from fractions to rational numbers by
requiring that operations continue to satisfy
the properties of operations, particularly
Enduring Understandings:
the distributive property. Interpret
products of rational numbers by describing
By applying the properties of
real-world contexts (7.NS.2a)
Apply properties of operations as strategies rational numbers and by viewing
negative numbers in terms of
to multiply and divide rational numbers
everyday contexts, students
(7.NS.2c)
explain and interpret the rules
Understand that integers can be divided,
for adding, subtracting,
provided that the divisor is not zero, and
multiplying and dividing with
every quotient of integers is a rational
Suggested Activity/
Appropriate Materials-Equipment
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Define Absolute Value
Find Absolute Value of integers
Comparing Values – Integers and
Absolute Value
Real Life Application – Comparing
freezing points of various substances
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Adding Integers with the Same Sign
Adding Integers with Different Signs
Adding More that Two Integers
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Subtracting Integers – 4 types 1.
Positive – Positive, 2. Positive –
Negative, 3. Negative – Positive, 4.
Negative – Negative.
Subtracting More than Two Integers
Real Life Application – Comparing
Ranges in Elevation
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Evaluation/Assessment
Pre-Assessment, Practice
and Problem Solving,
DoNows, oral questioning,
closure, alternative
assessment, quizzes, tests,
technology-based
assessments
*Note: Infuse Standardized
Test Practice
At the end of the following:
Chapters 3,6,9 Cumulative/Benchmark
Assessment
Multiplying Integers with the Same
Sign
Multiplying Integers with Different
Signs
Evaluating Positive and Negative
Exponents
Real Life Application – Negative
temperature change over x hours
Dividing Integers with the Same Sign
Dividing Integers with Different Signs
Evaluation Expression – Using
Substitution for x and y
Real Life Application – Calculating
means of ocean tides
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Content/Objective
number. If p and q are integers, the –(p/q)
=
(-p)/q = p/(-q). Interpret quotients of
rational numbers by describing real world
contexts(7.NS.2b)
Chapter 2 – Rational Numbers & Equations
The learner will:
 Understand that integers can be divided,
provided the divisor is not zero, and every
quotient of integers (with non-zero divisors) is
a rational number. If p and q are integers, then
–(p/q)=(-p)/q=p/(-q). Interpret quotients of
rational number by describing real-world
contexts. (7.NS.2b)
 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.2d)
 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 operation to
calculate with numbers in any form; covert
between forms as appropriate; and assess the
reasonableness of answers using mental
computation and estimation strategies. (7.EE.3)
 Understand p+q as the number located a
distance |q| from p, in the positive or negative
direction depending on whether q is a positive
or negative. Show that a number and its
opposite have a sum of 0 (are additive inverse).
Interpret sums of rational numbers by
describing real-world contexts. (7.NS.1b)
 Understand subtraction of rational numbers as
adding the additive inverse, p - q = p + (-q).
Show the distance between two rational
numbers on the number line is the absolute
Essential Questions/
Enduring Understandings
Suggested Activity/
Appropriate Materials-Equipment
negative numbers.
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Essential Questions:
 How can you use a number
line to order rational
numbers?
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How does adding and
subtracting rational numbers
compare with adding and
subtracting integers?
How does multiplying and
dividing rational numbers
compare with adding and
subtracting integers?
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How can you use inverse
operations to solve an
equation?
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How can you tell if 2 terms
are “like or unlike”?
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In a two-step equation,
which step should you do
first?
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Compare solving an
inequality with solving an
equation.
Enduring Understandings:
Students develop a unified
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Plotting Coordinate Pairs
Describing Location of Points
Real Life Application – Using Maps at
the Zoo to describe the location of
various exhibits
Define Rational/Irrational Numbers
Order Rational numbers on a number
line
The Game of Math Card War
Writing rational numbers as decimals
Writing a decimal as a fraction
Ordering the elevations of sea creatures
Use a number line to find the sum or
difference of rational numbers.
Financial Literacy – Balance a
checkbook
“In your own words” – Compare adding
and subtracting rational number with
adding and subtracting integers.
Adding/Subtracting positive/negative
fractions
Adding/Subtracting positive/negative
rational decimals
Real-life applications – Can the boat
and trailer pass under the bridge?
Evaluation/Assessment
Pre-Assessment, Practice
and Problem Solving,
DoNows, oral questioning,
closure, alternative
assessment, quizzes, tests,
technology-based
assessments
*Note: Infuse Standardized
Test Practice
At the end of the following:
Chapters 3,6,9 Cumulative/Benchmark
Assessment
Given a set of rational numbers, write a
story that uses addition, subtraction,
multiplication and division.
Repeat with a partner
Dividing fractions & rational decimals
Real Life Application – Find the mean
change in value of the given set of
stocks.
Using Commutative and Associative
Properties
4
Content/Objective
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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.1d)
Solve real world and mathematical problems
involving the four operations with rational
numbers. (7.NS.3)
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.2a)
Apply properties of operations as strategies to
multiply and divide rational numbers. (7.NS.3)
Describe situations in which opposite quantities
combine to make 0. (7.NS.1A)
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. (7.EE.4a)
Apply properties of operations as strategies to
add, subtract, factor and expand linear
expressions with rational coefficients. (7.EE.1)
Understanding 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. (7.EE.2)
Solve word problems leading to equations of
the form px = q > r, where p, q, and r are
specific rational numbers. Graph the solutions
set of the inequality and interpret it in the
Essential Questions/
Enduring Understandings
understand of number,
recognizing fractions, decimals
(that have a finite or a repeating
decimal representations), and
percents as different
representations of rational
numbers, maintaining the
properties of operations and the
relationships between addition
and subtraction, and
multiplication and division. They
use the arithmetic of rational
numbers as they formulate
expressions and equations to
solve problems.
Suggested Activity/
Appropriate Materials-Equipment
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Real Life Application – Finding the
charge of an atom
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Use algebra tiles or algebra balance
scales to model solving 1-step equations
using addition or subtraction
Define equivalent equations
Solve 1-step equations
Write an algebraic equation from a
word problem
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Use algebra tiles or algebra balance
scales to model solving 1-step equations
using addition or subtraction
Define Multiplication Property of
Equality and Division Property of
Equality
Solve 1-step equations
Write an algebraic equation from a
word problem
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Define “like” terms
Combine like terms
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Review 1st step of a 1-step equation –
add/subtract first
Model 2-step equations with algebra
tiles or algebra balance scales
Write a 2-step algebraic equation from a
word problem and solve.
Real Life Application – Find the height
of the roller coaster hill
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Evaluation/Assessment
Solving 1-step inequalities by using
addition, subtraction, multiplication or
division
Solving 2 step inequalities
5
Content/Objective
context of the problem.
Essential Questions/
Enduring Understandings
Suggested Activity/
Appropriate Materials-Equipment
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Evaluation/Assessment
Graph inequalities on a number line.
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Chapter 3 – Proportions and Variation
The learner will:
 Compute unit rates associated with ratios of
fractions, including ratios of lengths, areas and other
quantities measured in like or different units
(7.RP.1)
 Identify the constant of proportionality (unit rate) in
tables, graphs, equations, diagrams, and verbal
descriptions of proportional relationships (7.RP.2b)
 Decide whether two quantities are in a proportional
relationship (7.RP.2a)
 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.2d)
 Use proportional relationships to solve multistep
ratio and percent problems (7.RP.3)
 Represent proportional relationships by equations
(7.RP.2c)
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How do rates help you describe
real-life problems?
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How can you compare two
rates graphically?
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How can proportions help you
decide when things are ‘fair’?
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How can you write a proportion
that solves a problem in real
life?
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How can you use ratio tables
and cross products to solve
proportions in science?
Essential Questions:
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How can you compare lengths
between the customary and
metric systems?
How can you use a graph to
show the relationship between
two variables that vary
directly? How can you use an
equation?
How can you recognize when
two variables are inversely
proportional?
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Enduring Understanding
Students graph proportional
relationships and understand the
unit rate informally as a measure of
the steepness of the related line,
called slope. They distinguish
proportional relationships from
other relationships.
Define Ratio and Rate
Finding Ratios and Rates given data
Finding a Rate from a Table
Finding a Rate from a Line Graph
Define Slope
Finding Slopes given two points using
formula Δy/Δx
Finding a slope in a given table using
formula
Define Proportion and proportional
Determining Whether Ratios form a
Proportion
Define Cross Products
Identify Proportional Relationships
Writing a Proportion given data in a table
format or word problem
Solving Proportions using Mental Math
Pre-Assessment, Practice
and Problem Solving,
DoNows, oral questioning,
closure, alternative
assessment, quizzes, tests,
technology-based
assessments
*Note: Infuse Standardized
Test Practice
At the end of the following:
Chapters 3,6,9 Cumulative/Benchmark
Assessment
Solve Proportions Using Multiplication
Solving Proportions Using the Cross
Products Property
Real Life Application – Are costs of Pizza
slices and Pizza Pies cost proportional?
Define Customary and Metric System and
rates of conversion
Using proportions to convert units
Comparing Units of measure between the
two systems
Converting Rates between systems
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Define direct variation
Identify Direct Variation in a table
Identify Direct Variation in an equation
Using a direct variation model to do
calculations and graph linear equations
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Define indirect variation
Identifying Direct and Inverse Variation
Real Life Application
7
Chapter 4 – Percents
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Use proportional relationships to solve
multistep ratio and percent problems. (7.RP3)
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 operation to
calculate with numbers in any form; covert
between forms as appropriate; and assess the
reasonableness of answers using mental
computation and estimation strategies. (7.EE.3)
Understanding 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. (7.EE.2)
Essential Questions:
 How can you use models to
estimate percent questions?
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What is a percent of decrease?
What is a percent of increase?
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How can you find discounts
and markups efficiently?
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How can you find the amount
of simple interest earned on a
savings account? How can you
find the amount of interest
owed on a loan?
Enduring Understanding
Students extend their understanding
ratios and proportionality to solve a
wide variety of percent problems,
including those involving discount,
interest, taxes, tips.
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Estimate locations of percent on a
continuum
Use visual models to solve % of a
number problems
Working backwards - x is y% of what
number?
Real Life Application – Tax/Tip
Pre-Assessment, Practice
and Problem Solving,
DoNows, oral questioning,
closure, alternative
assessment, quizzes, tests,
technology-based
assessments
Finding the percent of increase/decrease
Percent decrease – Columbian River
Basin
Percent increase – Population of Florida
*Note: Infuse Standardized
Test Practice
Define Discount & Mark-up
Find the sale price given the original
price and percent discount
Find the original price given the sale
price and the percent discount
Find selling price given the wholesale
price and percent mark-up
At the end of the following:
Chapters 3,6,9 Cumulative/Benchmark
Assessment
Calculate simple interest
Financial Literacy – Calculating interest
on credit card debt
The National Debt – Calculate the
interest on the United States National
debt
Define Principal & Interest
Solve for each variable in the interest
formula
8
Chapter 5 – Similarity and Transformations
The learner will:
 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.1)
 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 (7.G.2)
Essential Questions:
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How can you use
proportions to help make
decisions in art, design, and
magazine layouts?
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How do changes in
dimensions of similar
geometric figures affect the
perimeters and areas of the
figures?
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What information do you
need to know to find the
dimensions of a figure that is
similar to another figure?
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How can you use a scale
drawing to estimate the cost
of painting a room?
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How can you use a scale
drawing and scale to
calculate the actual area?
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How can you use
translations to make a
tessellation?
Where do we see reflections
in everyday life? Create
your own example
What are the three basic
ways to move an object in a
plane?
Enduring Understanding:
Student solve problems about scale
drawings by relating corresponding
lengths within objects or by using
the fact that relationships of lengths
within an object are preserved in
similar objects. Students reason
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Define Similar figures and
corresponding sides and angles
Naming Corresponding Parts in two
similar figures
Identifying Similar Figures using ratios
of corresponding sides
Finding Ratios of Perimeters of Similar
Figures
Finding Ratios of Areas of Similar
Figures
Real Life Application – Compare
distances/areas of scale drawings to
actual dimensions (map of Utah)
Finding an Unknown Measure in a pair
of similar figures
Using Indirect Measurement
Using Proportions to Find Area a/b
vs. a2/b2
*Note: Infuse Standardized
Test Practice
At the end of the following:
Chapters 3,6,9 Cumulative/Benchmark
Assessment
Define Scale, Scale Drawing, and Scale
Model
Finding an Actual Distance using map
scales
Finding a Scale Factor given actual
height and scaled height
Define transformation and translation
Identify a Translation
Translating a Figure on a coordinate
plane using a given rule
Translating a Figure after graphing the
original
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Define reflection and line of reflection
Identify a Reflection
Reflecting a Figure in the x-axis
Reflecting a Figure in the y-axis
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Define Rotation, center of rotation, and
angle of rotation
Rotating a figure about the origin
Rotating a Figure about a point
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Pre-Assessment, Practice
and Problem Solving,
DoNows, oral questioning,
closure, alternative
assessment, quizzes, tests,
technology-based
assessments
9
Content/Objective
Chapter 6 – Surface Area of Solids
The learner will:
 Describe the two-dimensional figures that
result from slicing three-dimensional figures,
as in plane sections of right rectangular prisms
and right rectangular pyramids (7.G.3)
 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 (7.G.6)
 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.4)
Essential Questions/
Enduring Understandings
Suggested Activity/
Appropriate Materials-Equipment
Essential Questions:
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How can you draw threedimensional figures?
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How can you use a net to
find the surface area of a
prism?
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How can you find the
surface area of a cylinder?
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How can you find the
surface area of a pyramid?
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How can you find the
surface area of a cone?
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How can you find the
surface area of a composite
solid?
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Enduring Understanding
Students will understand problems
involving the area and
circumference of a circle and
surface area of 3 dimensional
objects. Students will work with 2dimensional figures by examining
cross-sections. They will solve realworld and mathematical problems
involving area, and surface area of
two and three-dimensional objects
composed of triangles,
quadrilaterals, polygons, cubes and
right prisms.
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Define three-dimensional figure,
polyhedron, and lateral faces
Drawing a Prism
Drawing a Pyramid
Drawing Views of a Solid (top, side and
front)
Finding the Surface Area of a
Rectangular Prism
Finding the Surface Area of a
Triangular Prism
Finding a Radius and Diameter
Finding the Circumference and Area of
a Circle given the radius or diameter
Calculate the Surface Area of a
Cylinder given height and radius or
diameter using formula
Finding lateral surface area of a
cylinder
Real life application – Food store –
Comparing label costs
Evaluation/Assessment
Pre-Assessment, Practice
and Problem Solving,
DoNows, oral questioning,
closure, alternative
assessment, quizzes, tests,
technology-based
assessments
*Note: Infuse Standardized
Test Practice
At the end of the following:
Chapters 3,6,9 Cumulative/Benchmark
Assessment
Define regular pyramid and slant height
Calculating the Surface Area of a
Square Pyramid given base edge and
slant height using formula
Calculating the Surface Area of a
Triangular Pyramid given base edge and
slant height using formula
Real life application – Roof and
shingles – How many bundles do you
need?
Finding the surface area of a cone given
radius and slant height using formula
Finding the slant height of a cone given
10
Content/Objective
Essential Questions/
Enduring Understandings
Suggested Activity/
Appropriate Materials-Equipment
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Unit 7: Volume of Solids
The learner will:
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Solve real world and mathematical problems
involving area, volume and the surface area of
two and three-dimensional objects composed of
triangles, quadrilaterals, polygons, cubes and
right prisms. (7.G.6)
Know the formulas for the area and
circumference of circles and use them to solve
problems; give an informal derivation of the
relationship between circumference and area
(7.G.4)
the surface area and radius
Real life application – surface area of
cones
Define composite solid
Identify the various solids that make up
different composite solids
Finding the surface area of a composite
solid – exposed faces only
Essential Questions:
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How can you find the volume
of a prism?
How can you find the volume
of cylinder?
How can you find the volume
of a pyramid?
How can you remember the
formulas for surface area and
volume?
How can you estimate the
volume of a composite solid?
When the dimensions of a solid
increase by k, how does the
surface area change? How does
the volume change?
Enduring Understandings
They will solve real-world and
mathematical problems involving
volume of two and threedimensional objects composed of
triangles, quadrilaterals, polygons,
cubes and right prisms
Evaluation/Assessment
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Activity: Pearl in Treasure Chest by
finding volume
Activity: Finding a formula for volume
of various prisms
Activity: Finding volume using a ream
of paper
Finding the volume of prism
Real-life Applications: Popcorn
Container Volume
Taking it Deeper: Aquarium problem
Activity: Finding the formula
experimentally using stacked coins
Activity: Making a business plan
selling cylindrical candles
Activity: Comparing Cylinders
Finding the volume of cylinders
Finding the height of cylinders
Real-life Applications: Finding the
missing volume of the salsa jar
Taking it Deeper: Hay Bales
Pre-Assessment, Practice
and Problem Solving,
DoNows, oral questioning,
closure, alternative
assessment, quizzes, tests,
technology-based
assessments
*Note: Infuse Standardized
Test Practice
At the end of the following:
Chapters 3,6,9 Cumulative/Benchmark
Assessment
Activity: Find the formula
experimentally using 2d nets
Activity: Comparing volumes of
pyramids
Activity: Breaking prisms into
11
Content/Objective
Essential Questions/
Enduring Understandings
Suggested Activity/
Appropriate Materials-Equipment
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Content/Objective:
Chapter 8 – Data Analysis and Samples
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Essential Questions:
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Understand that statistics can be used to
gain information about a population by
examining a sample of the population;
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generalizations about a population from a
sample are valid only if the sample is
representative of that population.
Understand that random sampling tends to
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produce representative samples and support
How can you use a stem-and
–leaf plot to organize a set of
numbers?
How do histograms show the
differences in distributions
of data?
How can you use a circle
graph to show the results of
pyramids
Finding the volume of pyramids
Real-life Application: Comparing
volume of sunscreen
Taking it Deeper: Finding the volume
of a teepee
Activity: Summarizing Volume
formulas of cones, pyramid, prisms,
and cylinders
Activity: Volumes of oblique solid
Finding the volume of cones
Finding the height of a cone
Real-life application: Sand timer rate
problem
Taking it Deeper: Lemonade Stand
Activity: Toy Company using a scale
measurement
Activity: Finding the volumes of
composite solids by finding the amount
of plastic needed for a lego car
Finding the volumes of composite
solids
Real-life Applications: Argentine peso
Taking it Deeper: Find the volume of a
group of solids to make a toy.
Suggested Activity /
Appropriate Materials-Equipment



Define Stem-and-Leaf plot
Making a Stem-and-Leaf Plot
Interpreting a Stem-and-Leaf Plot


Define Histogram
Making a Histogram given a frequency
table
Using a Histogram of real world data to
answer various questions

Evaluation/Assessment
Pre-Assessment, Practice
and Problem Solving,
DoNows, oral questioning,
closure, alternative
assessment, quizzes, tests,
technology-based
assessments
*Note: Infuse Standardized
Test Practice
12
Content/Objective



valid inferences (7.SP.1)
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
(7.SP.2)
Informally assess the degree of visual
overlap of two numerical data distributions
with similar variability’s, measuring the
difference between the centers by
expressing it as a multiple of a measure of
variability (7.SP.3)
Use measures of center and measures of
variability for numerical data from random
samples to draw informal comparative
inferences about two populations (7.SP.4)
Content/Objective:
Chapter 9 – Probability


Essential Questions/
Enduring Understandings
a survey?

How can you use a survey to
make conclusions about the
general population?
Suggested Activity/
Appropriate Materials-Equipment



Define Circle Graph
Making a Circle Graph given data in a
table, represent the data with percents,
totals, and degrees
Using Circle Graphs to answer various
questions
Evaluation/Assessment
At the end of the following:
Chapters 3,6,9 Cumulative/Benchmark
Assessment
Enduring Understanding:
Compare 2 data distributions and
address questions about differences
between populations. Students will
create and explain different types of
data representation. Students begin
informal work with random
sampling to generate data sets and
learn about the importance of
representative samples for drawing
inferences.



Essential Questions:

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 ½ indicates an event that is

neither likely nor unlikely, and a probability
near 1 indicates a likely event (7.SP.5)
Develop a uniform probability model by

assigning equal probability to all outcomes, and
use the model to determine probabilities of
How can you predict the
results of spinning a
spinner?
How can you find a
theoretical probability?
What is meant by
experimental probability?
What is the difference
between dependent and
independent events?
Define Population and Sample
Identify a Population and a Sample
Making Predictions based upon samples
Suggested Activity /
Appropriate Materials-Equipment








Define Experiment, Outcomes, and
Events
Identifying Outcomes
Counting Outcomes
Define Probability of an Event
Define Theoretical Probability
Finding Theoretical Probability
Using Theoretical Probability
Making a Prediction – Is the game fair?
How many spins will it take to win?
Pre-Assessment, Practice
and Problem Solving,
DoNows, oral questioning,
closure, alternative
assessment, quizzes, tests,
technology-based
assessments
*Note: Infuse Standardized
Test Practice
At the end of the following:
13
Content/Objective





events(7.SP.7a)
Develop a probability model (which may not
be uniform) by observing frequencies in data
generated from a chance process (7.SP.7b)
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 (7.SP.6)
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.8a)
Represent sample spaces for compound events
using methods such as organized lists, tables,
and tree diagrams. For an event described in
everyday language, identify the outcomes in
the sample space which compose the event
(7.SP.8b)
Design and use a simulation to generate
frequencies for compound events (7.SP.8c)
Content/Objective
Additional Topics
Topic 1 – Angles

Essential Questions/
Enduring Understandings
Enduring Understanding:
Student Investigate chance
processes and develop, use and
evaluate probability models.







Essential Questions
What is the difference between
complementary and
supplementary angles?
Use the facts about supplementary,
complementary, vertical, and adjacent angles in Can a triangle be created from 3
a multi-step problem to write and solve simple given side lengths or 3 given
equations for an unknown angle in a figure
angles?
(7.G.5)
Topic 2 – Geometry
 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,
Suggested Activity/
Appropriate Materials-Equipment
What happens to a solid when a
plane intersects it?
Define Experimental Probability
Making Predictions based on
Experimental Data
Comparing Experimental and
Theoretical Probabilities
Evaluation/Assessment
Chapters 3,6,9 Cumulative/Benchmark
Assessment
Define Independent and Dependent
Events
Identifying Independent and Dependent
Events
Finding the Probability of Independent
Events
Finding the Probability of Dependent
Events
Suggested Activity/
Appropriate Materials-Equipment
Topic 1 – Angles
 Define Key Vocabulary Terms
 Classify pairs of angles as
supplementary or complementary
 Finding missing angle measurements
using adjacent angles and vertical
angles
Topic 2 – Geometry
 Construct triangles with given side
lengths of straws
Student will gain familiarity with  Construct triangles with given angle
Pre-Assessment, Practice
and Problem Solving,
DoNows, oral questioning,
closure, alternative
assessment, quizzes, tests,
technology-based
assessments
*Note: Infuse Standardized
Test Practice
Enduring Understanding:
At the end of the following:
Chapters 3,6,9 14
Content/Objective

noticing when the conditions determine a
unique triangle, more than one triangle, or no
triangle (7.G.2)
Describe the two-dimensional figures that
result from slicing three-dimensional figures,
as in plane sections of right rectangular prisms
and right rectangular pyramids (7.G.3
Essential Questions/
Enduring Understandings
relationships between angles
formed by intersecting lines.
Students will notice the
conditions (angles/side lengths)
that create differing types
triangle or no triangles. Students
will understand how a solid is
affected by an intersecting plane
Suggested Activity/
Appropriate Materials-Equipment

measurements
Describe the intersection of a plane and
a solid
Evaluation/Assessment
Cumulative/Benchmark
Assessment
15