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PowerTeaching i3: Grade 7 Mathematics
Alignment to the
Common Core State Standards for Mathematics
Standards for Mathematical Practice
and
Standards for Mathematical Content for Grade 7
Section I: Alignment to the Standards for Mathematical Practice
Grade 7
Key Ideas and Details
Standard for Mathematical Practice 1: Make sense of problems and persevere in solving them.
The PowerTeaching curriculum consistently encourages students to ask questions, plan for solutions,
assess their reasoning and the reasonableness of their answers, and to check their work. The students
focus on these good habits as a part of the daily PowerTeaching lesson routine as well as specific
strategy lessons throughout the curriculum.
•
Team Huddle—During daily Team Huddle activities, students work with their teammates to
discuss, plan for, and solve math problems. Within the team, they must work through
disagreements, ensure that each teammate understands and can explain the solution, and
encourage each other when problems seem difficult.
•
Problem Solving Strategies—Students practice the various problem-solving strategies at
multiple points. Specific lessons introduce and have students practice the strategies: identify
extraneous data, make a model, find a pattern, guess and check, work backwards, and solve
a simpler problem.
•
Extended Response—Many PowerTeaching learning cycles culminate in an extended response
lesson. The math problems in these lessons are complex and combine multiple
math topics. The teacher modeling, teamwork activities, and individual practice are all centered
on solving these real-world problems in steps: understand the problem, find the parts,
make a plan, estimate the answer, find the solution, and assess the reasonableness and
correctness of the solution.
Standard for Mathematical Practice 2: Reason abstractedly and quantitatively.
Throughout PowerTeaching students will routinely approach math concepts using both concrete and
abstract tools and methods.
•
Problem Solving Strategies—The problem solving strategies that students learn help them break
apart word problems and real-world math scenarios into the important information, then represent
this information as numeric and algebraic models.
•
Problem Solving Practice—In each cycle, students will apply the problem solving strategies they
have learned. Many lessons include real-world math problems. The students learn to represent
the solutions to these problems concretely and abstractly. Students are also routinely asked to
design a math story for a numeric or algebraic model.
•
Project-Based Learning—The PowerTeaching curriculum includes quarterly project-based
learning opportunities. These activities will be multi-day cycles of learning that include planning,
research, modeling, reporting, and presenting. Students will be required to represent their project
topic mathematically, use the math to find a solution to the problem they researched or an answer
to the question they asked, and then explain how the mathematical model relates back to their
original problem or question.
Standard for Mathematical Practice 3: Construct viable arguments and critique the reasoning of others.
Students will support their arguments with sound reasoning as well as critique or support the reasoning of
others. They will construct their supports and critiques both in writing as well as verbally.
•
Get the Goof—Each lesson includes a Get the Goof activity. Students will discuss a completed
problem related to recently studied math topics. They will work with their teams to identify the
error in think that led to a mistake in the math work. The students will explain the error and correct
the math.
•
Random Reporter—A part of the daily PowerTeaching routine includes teamwork and team
discussion to solve problems. At various points during each lesson, the teacher will use Random
Reporter to have a student from each team share their answer and support that answer with their
team’s reasoning.
•
Extended Response—One type of extended response math problem will have students critique
the math reasoning presented in the problem, correctly solve the problem, and construct a viable
argument to support their reasoning. These types of extended response situations will represent
about one third of the PowerTeaching extended response experiences.
Standard for Mathematical Practice 4: Model with mathematics.
Students will use tables, graphs, charts and diagrams to represent mathematical information. They will
also use number sentences, expressions, and equations to describe a situation. Students will also use
the information they gather in tables, graphs, charts, and diagrams to identify patterns, determine
relationships, and draw conclusion.
•
Problem Solving Strategy: Modeling—Students will receive specific and targeted instruction on
modeling as a strategy to solve math problems.
•
Problem Solving Practice—The ongoing problem solving experiences, word problems,
real-world scenarios, and extended response, often require students to represent the
data as a model. Students must determine which model would best help them find the
solution or answer the question.
Standard for Mathematical Practice 5: Use appropriate tools strategically.
Throughout the PowerTeaching curriculum, students will be guided to use various tools to solve math
problems and answer math questions. They will also be faced with opportunities to choose which tool
would best help them solve more complex math problems or real-world scenarios. The students will more
often be faced with choices when completing extended response and project-based learning activities.
Standard for Mathematical Practice 6: Attend to precision.
Students will use symbols, math vocabulary, and clear explanations in their team discussions and written
and oral explanations. Students will also make choices to best represent their solution and reasoning
clearly and efficiently.
•
Rubrics—Students will use rubrics to assess the completeness and clarity of their oral and
written explanations. They will also use the rubrics to critique the explanations of their peers.
Complete explanations include the correct answer stated as a complete sentence that identifies
the question and a clear explanation in words, as a diagram, using symbols.
•
Vocabulary—PowerTeaching key vocabulary is highlighted in each lesson. The definition is built
into the lesson instead of only existing in a separate glossary. Students will see the vocabulary
used correctly within the teacher modeling and be expected to use key vocabulary to support
their mathematical thinking.
Standard for Mathematical Practice 7: Look for and make use of structure.
Specific targeted skills in the PowerTeaching curriculum address the topics of structure and patterns.
•
Problem Solving Strategy: Look for a Pattern—Students will learn to identify problems that can be
solved by finding and describing a pattern. They will learn how to represent the data to most
efficiently identify the pattern. In later lessons, students will apply this strategy to new and more
•
•
complex problem solving situations.
Expressions and Equations—Within the Expressions and Equations content area students will
consistently work to make sense of data by defining any patterns they notice and translating
those patterns into expressions, equations, and graphs.
Formulas and Mathematical Rules—In the PowerTeaching curriculum, students will be guided
through instruction, modeling, teamwork, and individual practice, to define rules and formulas
based on work with multiple examples. Instead of being given the rule, they will have to write the
rule, and then prove it by applying it to new situations.
Standard for Mathematical Practice 8: Look for and express regularity in repeated reasoning.
Specific targeted skills in the PowerTeaching curriculum address the topic of repeated reasoning to find
shortcuts, processes, and formulas.
• Expressions and equations—Within the Expressions and Equations content area, students will
prove expressions equivalent, prove or disprove solutions to equations and inequalities, and use
the properties of addition and multiplication.
• Geometry—Within the Geometry content area of PowerTeaching, students will apply their
knowledge of expressions and equations to geometry and derive formulas for area, volume, and
surface area.
Section II: Alignment to the Standards for Mathematical Content
Grade 7
Key Ideas and Details
Standard for Mathematical Content 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.
Unit 4 Cycle 1 Lesson 1—Basic Unit Rates
Objective: Find unit rates involving whole numbers and decimals
Unit 4 Cycle 1 Lesson 2—Unit Rates with Fractions
Objective: Find unit rates involving 1 of more fractions
Unit 4 Cycle 1 Lesson 3—Problem Solving with Unit Rates
Objective: Solve multiple-step, real-world problems dealing with unit rates
Standard for Mathematical Content 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.
Unit 4 Cycle 2 Lesson 4—Defining Proportional Relationships
Objective: Define and identify relationships that are proportional
Unit 4 Cycle 2 Lesson 5—Solving Proportions
Objective: Find values missing from proportional relationships
Unit 4 Cycle 2 Lesson 6—Proportions in Tables and Graphs
Objective: Use tables and graphs to continue to learn about, identify, and explore proportions
b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and
verbal descriptions of proportional relationships
Unit 4 Cycle 3 Lesson 8—Constant of Proportionality
Objective: Given a relationship, identify the constant of proportionality
c. Represent proportional relationships by equations.
Unit 4 Cycle 3 Lesson 9—Proportions as Equations
Objective: Write linear equations to represent proportional relationships
Unit 7 Cycle 1 Lesson 1—Writing Expressions with Percents
Objective: Write algebraic expressions to represent percent situations
d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the
situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
Unit 4 Cycle 2 Lesson 6—Proportions in Tables and Graphs
Objective: Use tables and graphs to continue to learn about, identify, and explore proportions
Standard for Mathematical Content 7.RP 3: Use proportional relationships to solve multistep ratio and
percent problems.
Unit 4 Cycle 2 Lesson 7—Problem Solving with Proportions
Objective: Solve multiple-step, real-world problems dealing with proportions
Unit 5 Cycle 1 Lesson 1—Basic Percents
Objective: Solve simple problems with percents
Unit 5 Cycle 1 Lesson 2—Word Problems with Percents
Objective: Solve multiple-step world problems involving percents
Unit 5 Cycle 1 Lesson 3—Percent Increase and Decrease
Objective: Calculate percent increase and decrease
Unit 5 Cycle 1 Lesson 4—Tax and Interest
Objective: Solve real-world problems related to simple tax, interest and compound interest
Standard for Mathematical Content 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. Describe situations in which opposite quantities combine to make 0.
Unit 2 Cycle 1 Lesson 1—Definition of Rational Numbers
Objective: Define, identify, and explore rational numbers
Unit 2 Cycle 1 Lesson 2—Adding Opposites
Objective: Add opposite numbers to a sum of zero
b. 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 realworld contexts.
Unit 2 Cycle 1 Lesson 2—Adding Opposites
Objective: Add opposite numbers to a sum of zero
c. 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.
Unit 2 Cycle 1 Lesson 3—Adding Rational Numbers I
Objective: Add integers using manipulatives and drawings
Unit 2 Cycle 2 Lesson 5—Subtracting Integers
Objective: Subtract integers using manipulatives and drawings
d. Apply properties of operations as strategies to add and subtract rational numbers
Unit 2 Cycle 1 Lesson 4—Adding Rational Numbers II
Objective: Add rational numbers using algorithms
Unit 2 Cycle 2 Lesson 6—Subtracting Rational Numbers
Objective: Subtract rational numbers using algorithms
Unit 2 Cycle 2 Lesson 7—Adding and Subtracting Rational Numbers
Objective: Add and subtract rational number to solve real-world problems
Unit 2 Cycle 2 Lesson 8—Order of Operations
Objective: Use the properties of operations and the Order of Operations to evaluate multiple-step
numeric expressions.
Unit 3 Cycle 2 Lesson 7—Order of Operations II
Objective: Use the properties of operations and the Oder of Operations to evaluate multiple-step
numeric expressions
Standard for Mathematical Content 7.NS 2: Apply and extend previous understandings of multiplication
and division and of fractions to multiply and divide rational numbers.
a. 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.
Unit 3 Cycle 1 Lesson 1—Multiplying Integers
Objective: Multiply integers using manipulatives and drawings
Unit 3 Cycle 1 Lesson 2—Properties of Multiplication
Objective: Use the Properties of Multiplication to multiply integers
Unit 3 Cycle 1 Lesson 3—Multiplying Rational Numbers
Objective: Multiply rational number using algorithms
b. 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-world contexts.
Unit 3 Cycle 2 Lesson 5—Dividing Integers
Objective: Divide integers using manipulatives and drawings
Unit 3 Cycle 2 Lesson 6—Dividing Rational Numbers
Objective: Divide rational numbers using algorithms
c. Apply properties of operations as strategies to multiply and divide rational numbers.
Unit 3 Cycle 1 Lesson 4—Multiplying Rational Numbers to Solve Real-Word Problems
Objective: Use problem solving strategies to solve problems involving multiplying rational numbers
Unit 3 Cycle 2 Lesson 6—Dividing Rational Numbers
Objective: Divide rational numbers using algorithms
Unit 3 Cycle 2 Lesson 7—Order of Operations II
Objective: Use the properties of operations and the Order of Operations to evaluate multiple-step
numeric expressions
d. 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.
Unit 3 Cycle 2 Lesson 6—Dividing Rational Numbers
Objective: Divide rational numbers using algorithms
Standard for Mathematical Content 7.NS 3: Solve real-world and mathematical problems involving the
four operations with rational numbers
Unit 3 Cycle 2 Lesson 8—Problem Solving with Multiplying and Dividing Fractions
Objective: Add, subtract, multiply, and divide rational number to solve real-world problems
Standard for Mathematical Content 7.EE 1: Apply properties of operations as strategies to add,
subtract, factor, and expand linear expressions with rational coefficients
Unit 6 Cycle 1 Lesson 1—Simplifying Expressions
Objective: Simplify expressions with rational coefficients
Unit 6 Cycle 1 Lesson 2—Evaluate Expressions
Objective: Given a value(s) for a variable(s), evaluate the expressions with rational coefficients
Unit 7 Cycle 1 Lesson 3—Write and Evaluate Expression to Answer Questions
Objective: Write numeric expressions to solve complex, real-world math situations.
Standard for Mathematical Content 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. For example,
a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.”
Unit 6 Cycle 1 Lesson 3—Rewrite and Evaluate Algebraic Expressions
Objective: Rewrite and evaluate expressions
Unit 7 Cycle 1 Lesson 2—Write Expressions Multiple Ways
Objective: Write expressions for contextual situations in different ways
Standard for Mathematical Content 7.EE 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.
Unit 7 Cycle 2 Lesson 6—Write and Solve Equations to Solve Problems
Objective: Write and solve multiple-step equations for given real-world situations
Standard for Mathematical Content 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. 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.
Unit 7 Cycle 2 Lesson 4—Solve Two-Step Equations
Objective: Solve equations with two steps that include addition, subtraction, multiplication, or division of
positive numbers
Unit 7 Cycle 2 Lesson 5—Solve Equations with Rational Numbers
Objective: Solve equations with multiple steps that include the four operations and rational numbers
b. 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.
Unit 7 Cycle 3 Lesson 7—Solve One-Step Inequalities
Objective: Solve simple inequalities with rational numbers and graph the solution
Unit 7 Cycle 3 Lesson 8—Solve Multiple-Step Inequalities
Objective: Solve multiple-step inequalities with rational numbers and graph the solution
Unit 7 Cycle 3 Lesson 9—Solve Inequalities to Solve Problems
Objective: Solve given inequalities to answer problems
Unit 7 Cycle 3 Lesson 10—Write and Solve an Inequality to Solve Problems
Objective: Write and solve inequalities for real-world situations
Standard for Mathematical Content 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.
Unit 8 Cycle 1 Lesson 1—Area and Perimeter
Objective: Find area and perimeter for various polygons
Unit 8 Cycle 1 Lesson 2—Find Measures Using Scale Drawings
Objective: Find missing lengths using scale drawings
Unit 8 Cycle 1 Lesson 3—Complete Scale Drawings
Objective: Complete scale drawings given various information
Unit 8 Cycle 1 Lesson 4—Scale Drawings and Area and Perimeter
Objective: Find area and perimeter given a scale drawing
Unit 8 Cycle 1 Lesson 5—Scale Drawings and Volume
Objective: Solve complex, real-world problems involving scale drawings and volume and surface area
Unit 8 Project Based Cycle—Geometry: Defining, Constructing, and Measuring Shapes
Objective: In a three-day cycle, use geometric knowledge to date to complete a long term activity in
teams and individually
Standard for Mathematical Content 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.
Unit 8 Cycle 2 Lesson 7—Construct Quadrilaterals
Objective: Given characteristics, construct quadrilaterals using protractors and rulers
Unit 8 Cycle 2 Lesson 8—Construct Triangles I
Objective: Given side measures, construct various triangles
Unit 8 Cycle 2 Lesson 9—Construct Triangles II
Objective: Given angle measures, construct various triangles
Unit 8 Project Based Cycle—Geometry: Defining, Constructing, and Measuring Shapes
Objective: In a three-day cycle, use geometric knowledge to date to complete a long term activity in
teams and individually
Standard for Mathematical Content 7.G 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.
Unit 8 Cycle 2 Lesson 6—Properties of Polygons
Objective: Identify and draw a polygon by sight or given characteristics
Unit 8 Project Based Cycle—Geometry: Defining, Constructing, and Measuring Shapes
Objective: In a three-day cycle, use geometric knowledge to date to complete a long term activity in
teams and individually
Standard for Mathematical Content 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.
Unit 9 Cycle 1 Lesson 1—Pi and the Parts of a Circle
Objective: Learn vocabulary associated with circles and understand pi
Unit 9 Cycle 1 Lesson 2—Circumference
Objective: Find the circumference of circles given an image and given measurements
Unit 9 Cycle 1 Lesson 3—Area of Circles
Objective: Find the area of circles as images and from given measures
Unit 9 Cycle 1 Lesson 4—Circles and Problem Solving
Objective: Solve complex, real-world problems related to finding area and circumference of a circle
Standard for Mathematical Content 7.G 5: Use facts about supplementary, complementary, vertical,
and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in
a figure
Unit 9 Cycle 2 Lesson 5—Identify Types of Angles
Objective: Identify types of angles by size and relation to other angles
Unit 9 Cycle 2 Lesson 6—Complementary and Supplementary Angles
Objective: Solve problems involving complementary and supplementary angles
Unit 9 Cycle 2 Lesson 7—Adjacent and Vertical Angles
Objective: Solve problems involving adjacent and vertical angles
Unit 9 Cycle 2 Lesson 8—Find Missing Angle Measures
Objective: Solve complex problems with one or more missing angle
Unit 10 Cycle 2 Lesson 5—Surface Area of Prisms
Objective: Find the surface area of various prisms given images and/or data
Unit 10 Cycle 2 Lesson 6—Surface Area of Pyramids
Objective: Find the surface area of various pyramids given images and/or data
Unit 10 Cycle 2 Lesson 7—Surface Area of Cones and Cylinders
Objective: Find the surface area of cones and cylinders given images and/or data
Unit 10 Cycle 2 Lesson 8—Surface Area and Problem Solving
Objective: Solve complex, real-world problems related to finding the surface area of simple and complex
3-d shapes.
Standard for Mathematical Content 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.
Unit 10 Cycle 1 Lesson 1—Volume of Prisms
Objective: Find the volume of various prisms given images and/or data
Unit 10 Cycle 1 Lesson 2—Volume of Pyramids
Objective: Find the volume of various pyramids and/or data
Unit 10 Cycle 1 Lesson 3—Volume of Cones and Cylinders
Objective: Find the volume of cones and cylinders given images and/or data
Unit 10 Cycle 1 Lesson 4—Volume and Problem Solving
Objective: Solve complex, real-world problems related to finding the volume of simple and complex
3-d shapes
Standard for Mathematical Content 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.
Unit 12 Cycle 1 Lesson 1—Understanding Random Sampling
Objective: Answer the question, “Why do we use random sampling?”
Unit 12 Cycle 1 Lesson 2—Characteristics of Random Sample
Objective: Identify the characteristics of random sample
Unit 12 Cycle 1 Lesson 3—Good vs. Bad Random Samples
Objective: Experiment in designing random sample and identify when samples are good or bad
Standard for Mathematical Content 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.
Unit 12 Cycle 2 Lesson 4—Answer Questions from a Random Sample
Objective: Given the results of a random sample, analyze them and draw conclusions
Unit 12 Cycle 2 Lesson 5—Create a Random Sample
Objective: Create a random sample for a given statistical question
Unit 12 Cycle 2 Lesson 6—Conduct a Random Sample
Objective: Conduct a random sample for given statistical questions and analyze the results
Standard for Mathematical Content 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.
Unit 12 Cycle 2 Lesson 7—Problem Solving with Data Distributions and Data Measures
Objective: Problem solve complex, real-world situations about numerical data displays, measures of
center, and measures of variability
Unit 13 Cycle 1 Lesson 1—Numerical Data Displays
Objective: Answer questions and make predictions given various numerical data displays
Unit 13 Cycle 1 Lesson 2—Comparing Number Data
Objective: Compare the number data from two related measures, answer questions and make predictions
Unit 13 Cycle 1 Lesson 3—Comparing Graphs
Objective: Compare graphs for the same or similar data sets and draw conclusions
Standard for Mathematical Content 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.
Unit 12 Cycle 2 Lesson 4—Finding Measures of Center and Variability
Objective: Given a data set, find the measures of center and variability
Unit 12 Cycle 2 Lesson 5—Comparing Measures of Center
Objective: Compute and compare the measures of center for two data sets or displays
Unit 12 Cycle 2 Lesson 6—Comparing Measures of Variability
Objective: Compute and compare the measures of variability for two data sets or displays
Unit 12 Cycle 2 Lesson 7—Problem Solving with Data Distributions and Data Measures
Objective: Problem solve complex, real-world situations about numerical data displays, measures of
center, and measures of variability.
Standard for Mathematical Content 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.
Unit 11 Cycle 1 Lesson 1—Understanding Probability
Objective: Write the probability of an event as a fraction and identify favorable and unfavorable events
Unit 11 Cycle 1 Lesson 2—Decimal and Percent Probability
Objective: Write the probability of a situation as a decimal and percent
Unit 11 Cycle 1 Lesson 3—Describing Probability
Objective: Describe the probability of an event in words
Standard for Mathematical Content 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.
Unit 11 Cycle 1 Lesson 1—Understanding Probability
Objective: Write the probability of an event as a fraction and identify favorable and unfavorable events
Unit 11 Cycle 1 Lesson 2—Decimal and Percent Probability
Objective: Write the probability of a situation as a decimal and percent
Unit 11 Cycle 1 Lesson 3—Describing Probability
Objective: Describe the probability of an event in words
Unit 11 Cycle 2 Lesson 5—Uniform Experimental Probability
Objective: Compare the experimental to the theoretical probability for uniform events
Unit 11 Cycle 2 Lesson 6—Non-Uniform Experimental Probability
Objective: Find the experimental probability for non-uniform events
Standard for Mathematical Content 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. Develop a uniform probability model by assigning equal probability to all outcomes, and use
the model to determine probabilities of events.
Unit 11 Cycle 2 Lesson 5—Uniform Experimental Probability
Objective: Compare the experimental to the theoretical probability for uniform events
b. Develop a probability model (which may not be uniform) by observing frequencies in data
generated from a chance process.
Unit 11 Cycle 2 Lesson 6—Non-Uniform Experimental Probability
Objective: Find the experimental probability for non-uniform events
Standard for Mathematical Content 7.SP 8: Find probabilities of compound events using organized
lists, tables, tree diagrams, and simulation.
a. 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.
Unit 11 Cycle 2 Lesson 4—Compound Probability
Objective: Find the probability of independent, compound events
Unit 11 Cycle 2 Lesson 7—Independent and Dependent Events
Objective: Identify independent and dependent events and find their probabilities
b. 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.
Unit 11 Cycle 2 Lesson 4—Compound Probability
Objective: Find the probability of independent, compound events
Unit 11 Cycle 2 Lesson 7—Independent and Dependent Events
Objective: Identify independent and dependent events and find their probabilities
c. Design and use a simulation to generate frequencies for compound events.
Unit 11 Project-Based Cycle—Probability Simulations
Objective: In a three-day cycle, design probability experiments, calculate theoretical probabilities, and find
experimental probabilities.