2012 7th grade_math_curriculum_guide

7th Grade Math Curriculum Map
Introduction
This document contains all mandated 2010 Arizona Mathematical Standards for 7th grade mathematics. The standards have been organized into
units and clusters. The units represent the major domain under which the identified standards fall. The cluster represents the collection of similar
concepts within the larger domain. Within these units and clusters the performance objectives have been sequenced to represent a logical progression
of the content knowledge. It is expected that all teachers follow the sequence of units and clusters as described in the following document.

Organization
Approximate Time
Approximate times are based on a 60-minute instructional session for grades 6-8. All units and clusters must be taught prior to the 2013 AIMS
assessment.

Essential Questions
Essential Questions are to be posed to the students at the beginning of the cluster and revisited throughout the cluster. They are designed to facilitate
conceptual development of the content and can be used as a tool for making connections, higher order thinking and inquiry. The students should be
able to answer these on their own by the end of the cluster.

Big Ideas
Big Ideas are the essential understandings that are critical for students’ learning. These are the enduring understandings we want students to carry
with them from grade level to grade level. Answering the Essential Questions is indicative of a student mastering the Big Idea, however they are not
always synonymous. Thus, in cases that the answer to the Essential Question does not include all components of the Big Idea, the Big Idea (for teacher
use) has been provided in italics.

Common Misconceptions
These are common misunderstandings students bring to the learning process. Being aware of such misconceptions allows us to plan for them during
instruction.

Content Standards and Mathematical Practices
This document has been organized by content standards and mathematical practices. The content standards are those that represent knowledge
specific to the mathematical standard (The five domains). The mathematical practices describe varieties of expertise that mathematics educators at
all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in
mathematics education. The content standards and mathematical standards have been paired to represent possible combinations of content standards
with mathematical practices. As described in the Arizona state standards, the content standards are not intended to be taught in isolation; thus, the
pairing of these standards provides a possible context for teaching these standards. Each time, the performance objective should be taught to a
deeper level of understanding and/or should be connected to the other standards in the cluster.

9/10/2012 1 Isaac Elementary School District

Common Core/Cross Curricular
The standards in the Common Core/Cross Curricular column represent possible reading, writing, math and language standards that can be reinforced
or taught through the mathematical content standards with which they are paired.

Priority
With input from grade level teachers, standards have been prioritized in two ways. The content standards have been prioritized using a three-point
scale. Essential standards represent those that are heavily weighted on state/national exams, foundational, and/or applicable in multiple contexts.
Important standards are those that are applicable in many contexts and less heavily weighted on state/national exams. Useful standards are those
with the least weight on state/national exams and are likely only useful in a specific context. This is denoted in the priority column with the codes E
(essential), I (important) and U (useful). This label applies to the content standards only. The skill/process standards that are a priority for this
grade level are highlighted in blue and are expected to be mastered at this grade level.

Key Vocabulary
The key vocabulary that should be taught for each of the performance objectives is listed under key vocabulary. These vocabulary words are coded
as tier one (1), tier two (2) or tier three (3). Tier one words are those that are very common and should not be explicitly taught. Tier two words are
high utility words that can be used across content areas or contexts. Tier three words are content specific words.

Resources
The two types of resources listed are the Web Resources resources and the Core Resources. All are suggestions that teachers may use to support
instruction. They are aligned to the standards listed in the same row. The web resources are useful Internet links that can be used for the teacher’s
edification prior to instruction or as a tool during instruction. The core resources are suggested pages from the adopted texts.

Unit/Cluster Project
The Unit/Cluster Projects are possible projects that teachers can use to support students in making connections, critical thinking, higher order thinking,
and/or spiraling curriculum. Unit projects support standards from all clusters within a unit while cluster project support the standards in a particular
cluster. While it is not required that a teacher do a project with every unit or cluster these resources will support project-based instruction and
practice should the teacher choose to implement them.

Assessment
The assessment section of the map has been left blank for teachers to plan the dates that they will give a formative assessment for the cluster. It is
expected that each cluster be assessed using a common formative assessment.

Other
Standards may appear more than once. Each time they should be taught within the context of the cluster and/or revisited to a deeper level of
knowledge. Underlined segments of a standard indicate an additional piece of the standard that was likely not covered in previous clusters.
[Brackets] will occasionally appear though out the document and indicate clarification of the Standard. Bracketed information is not a part of the
standard itself.


Unit: Ratios of Proportional Relationships
Cluster: Rate of Change

Approximate Time: 3 weeks
Essential Questions Big Ideas

 Why is it important to know proportions?  Students will understand that proportional

relationships are used to solve real-world situation.

 How is rate of change and proportions related?  Students will understand that if two quantities are

proportional that one varies directly with another. As

the rate of one quantity changes, the other quantity

changes at an independent constant rate.

 What is a proportional relationship?

 Students will understand proportional relationship can

be displayed in tables, graphs, and real-life

contextual situations


Priority Standard Mathematical Common Core/Cross Key Vocabulary Resources
Practices Curricular Web Resources Core
*S1C1PO2. Find or use factors, multiples, Composite number Factor Tree MC: 4-1
or prime factorization within a set of GCF
numbers. Exponents
Factors
LCM
Multiples
Prime number
Prime factorization
7.RP.1. Compute unit rates associated with 7.MP.2. 6-8.RST.7 Complex fractions Proportion MC: 6-1, 6-2
ratios of fractions, including ratios of 7.MP.6. SC07-S1C2-04 Denominator
lengths, areas and other quantities ET07-S1C1-01 Equivalent Ratio and Proportion
measured in like or different units. For Numerator
example, if a person walks ½ mile in each Rate
¼ hour, compute the unit rate as the Ratio
complex fraction ½/¼ miles per hour, Reciprocal
equivalently 2 miles per hour.
7.RP.2. Recognize and represent 7.MP.1. 6-8.WHST.2c-f Constant Proportions (Rectangle) MC: 6-3
proportional relationships between 7.MP.2. 6-8.WHST.1c Coordinate pair
quantities. 7.MP.3. 6-8.RST.7 Coordinate plane Proportions (Cake)
7.MP.4. 6-8.RST.4 Equation
a. Decide whether two quantities are in a 7.MP.5. ET07-S6C2-03 Graph Proportions (What's
proportional relationship, e.g., by testing 7.MP.6. ET07-S1C1-01 Origin your rate?)
for equivalent ratios in a table or 7.MP.7. SC07-S1C4-01 Proportions
graphing on a coordinate plane and 7.MP.8. SC07-S2C2-03 Table Proportions (Walk the
observing whether the graph is a straight Unit rate plank)
line through the origin. Units

b. Identify the constant of proportionality
(unit rate) in tables, graphs, equations,
diagrams, and verbal descriptions of
proportional relationships.

c. 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.

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.

*S3C3PO4. Translate between graphs Function MC: 1-10, 3-7
and tables that represent a linear Linear
equation. Translate

Unit
Project:

Assessment:



Unit: Ratios of Proportional Relationships
Cluster: Ratio and Percent

Approximate Time: 2 week


 How is percent and proportions related?  Students will understand the relationship between

percents and proportions and how every percent is a

proportion.

 What is the difference between percent change and net change?  Students will understand that percents are used to

solve real-world problems that include: simple

interest, tax, percent change, percent error, fees and

commissions.

 Describe how proportional reasoning can be used to solve real-world  Students will utilize proportions to scale real-world

problems. figures. e.g. maps and building blueprints


*S1C3PO4. Estimate the measure of Approximate MC: 6-4
an object in one system of units given Conversion
the measure of that object in another Estimate
system and the approximate Measure
conversion factor. Ratio
7.G.1. Solve problems involving 7.MP.1. 6-8.RST.7 Area Scaling MC: 6-8
scale drawings of geometric figures, 7.MP.2. SC07-S1C2-04 Figures
such as computing actual lengths and 7.MP.3. SS07-S4C6-03 Length
areas from a scale drawing and 7.MP.4. SS07-S4C1-01 Model
reproducing a scale drawing at a 7.MP.5. SS07-S4C1-02 Scale
different scale. 7.MP.6. ET07-S1C1-01
7.MP.7.
7.MP.8.
7.RP.3. Use proportional 7.MP.1. 6-8.RST.3 Commisions Percent MC: 6-9, 7-1, 7-2,
relationships to solve multistep ratio 7.MP.2. SS07-S5C3-01 Decrease 7-3, 7-4, 7-5, 7-6,
and percent problems. Examples: 7.MP.3. SC07-S4C3-04 Error 7-7, 7-8, 7-9
simple interest, tax, markups and 7.MP.4. SC07-S4C3-05 Fees
markdowns, gratuities and 7.MP.5. Gratuities
commissions, fees, percent increase 7.MP.6. Increase
and decrease, percent error. 7.MP.7. Markdowns markups
7.MP.8. Percent
Ratio
Simple interest
Tax
Unit
Project:

Assessment:



Unit: The Number System
Cluster: The Number Line


 What is distance?  Students will understand that absolute value is the

distance between two units.

 What is a number?  Students will understand that all real numbers fit on

a number line i.e. rational and irrational

 How can the four arithematic operations can be representated on a number  Students will understand that arithematic operations

line? (addition, subtraction, multiplication, and division)

can be representated on a number line.

 How is subtraction and the additive inverse related?  Students will understand that subtracting a number

is the same as addings its additive inverse.

 How is division and the multiplicative inverse related?  Students will understant that dividing by a number

is the same as multiplying by its multiplicative

 Why can’t you divide by 0? inverse.

 Students will understand that you cannot divide by

0.


*S1C3PO1. Estimate and apply Benchmark
benchmarks for rational numbers and Estimate
common irrational numbers. Integers
Irrational numbers
Rational numbers
Terminating decimal
Whole number
*S1C3PO3. Estimate square roots of Consecutive MC: 1-3, 12-1
numbers less than 1000 by locating them Perfect square
between two consecutive whole numbers. Radical
Square roots
7.NS.1. Apply and extend previous 7.MP.2. 6-8.WHST.2f Absolute value MC: 2-1, 2-2, 2-4,
understandings of addition and subtraction 7.MP.4. 6-8.WHST.2b Addend 2-5
to add and subtract rational numbers; 7.MP.7. 6-8.RST.3 Additive inverse
represent addition and subtraction on a 6-8.RST.7 Difference
horizontal or vertical number line diagram. ET07-S1C1-01 Equation
SS07-S4C5-04 Equivalent expression
a. Describe situations in which opposite Horizontal
quantities combine to make 0. For example, Inverse properties
a hydrogen atom has 0 charge because its Multiplicative inverse
two constituents are oppositely charged. Minuend
Operations
b. Understand p + q as the number located Opposite
a distance |q| from p, in the positive or Subrahead
negative direction depending on whether q Sum
is positive or negative. Show that a number Variable
and its opposite have a sum of 0 (are Vertical
additive inverses). Interpret sums of
rational numbers by describing real-world
contexts.

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.

d. Apply properties of operations as
strategies to add and subtract rational
numbers.


*S1C1PO3. Compare and order rational Ascending order MC: 4-9
numbers using various models and Descending order
representations. Greater than
Greatest
Least
Less than
Rational number
7.NS.2. Apply and extend previous 7.MP.2. 6-8.RST.4 Convert MC: 2-6, 2-8
understandings of multiplication and 7.MP.4. 6-8.RST.5 Denominator
division and of fractions to multiply and 7.MP.7. SC07-S1C3-01 Dividend
divide rational numbers. SS07-S5C3-04 Divisor
Factor
a. Understand that multiplication is Fractions
extended from fractions to rational Numerator
numbers by requiring that operations Product
continue to satisfy the properties of Properties
operations, particularly the distributive -Communative
property, leading to products such as (– -Associative
1)(–1) = 1 and the rules for multiplying -Identity
signed numbers. Interpret products of -Distributive
rational numbers by describing real-world Quotient
contexts. Repatend
Terminates
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.

c. Apply properties of operations as
strategies to multiply and divide rational
numbers.

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
Project:

Assessment:


Unit: The Number System
Cluster: Order of Operation


 What are grouping symbols?  Grouping symbols include: Parentheses, absolute value,

 A base raised to the 0 power is what value? Why? square and cube roots, brackets, and braces

 Do we apply the rules of multiplication before division whilst using order of  Using the order of operations to evaluate expressions

operations to evaluate an expression? is essential.

 Do we apply the rules of addition before subtraction whilst using order of

operations to evaluate an expression?

 When would we express a number in scientific notation?  Scientific notation is used to express very large

quantities and very small quantities.

 Multiplying a number by an exponent with base 10

moves the decimal to the left or right.


*S1C2PO4. Represent and interpret Exponents MC: 1-2, p. LA2 –
numbers using scientific notation Scientific notation LA5
(positive exponents only). Standard form
Standard notation
7.NS.3. Solve real-world and 7.MP.1. 6-8.RST.3 Grouping MC: 1-4
mathematical problems involving the 7.MP.2. Order of operations
four operations with rational 7.MP.5. PEMDAS/GEMS
numbers. (Computations with rational 7.MP.6. Rational numbers
numbers extend the rules for 7.MP.7. Complex fractions
manipulating fractions to complex 7.MP.8.
fractions.)
Unit
Project:

Assessment:



Unit: Expressions and Equations
Cluster: Properties of Evaluating Expressions


 What is a variable?  Students will understand that a variable is just a

number that is replaced with a letter.

 What does it mean when one thing is equivalent to another thing?  Students will be able to use properties of operations

 What is a coefficient? to add, subtract, factor, and expand expressions with

rational coefficients.

 Students will look at a given problem and be able to

express it in a different context.


7.EE.1. Apply properties of 7.MP.2. 6-8.RST.5 Coefficients MC: 1-8
operations as strategies to add, 7.MP.6. Combine
subtract, factor, and expand linear 7.MP.7. Distributive property
expressions with rational coefficients. Expressions
Linear expressions
Terms
7.EE.2. Understand that rewriting an 7.MP.2. 6-8.WHST.1b-c Convert
expression in different forms in a 7.MP.6. 6-8.WHST.2b-c Expression
problem context can shed light on 7.MP.7. 6-8.RST.3
the problem and how the quantities 7.MP.8. 6-8.RST.7
in it are related. For example, a + SS07-S5C2-09
0.05a = 1.05a means that “increase SC07-S2C2-03
by 5%” is the same as “multiply by
1.05.”
Unit
Project:

Assessment:



Unit: Expressions and Equations
Cluster: Solving Equations


 How do we translate a written or verbal description into an algebraic  Students will be able to create an equation or

equation? inequality from a given text or real-world scenario.

 What is the difference between an expression and an equation?  Students will understand the difference between an

 What is an inequality? expression, equation, and inequality.

 Students will be able to solve for a missing piece of

information from a specific problem or text.

 Students will be able to check the reasonableness of

an answer.


*S3C3PO2. Evaluate an expression Evaluate MC: 1-6
containing one or two variables by Substitute
substituting numbers for the
variables.
7.EE.3. Solve multi-step real-life and 7.MP.1. 6-8.WHST.1b-c Estimate MC: 1-7
mathematical problems posed with 7.MP.2. 6-8.WHST2b Reasonable
positive and negative rational 7.MP.3. 6-8.RST.7 Solve
numbers in any form (whole numbers, 7.MP.4. ET07-S6C2-03
fractions, and decimals), using tools 7.MP.5.
strategically. Apply properties of 7.MP.6.
operations to calculate with numbers 7.MP.7.
in any form; convert between forms 7.MP.8.
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
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.
7.EE.4. Use variables to represent 7.MP.1. 6-8.SRT.3 Equation
quantities in a real-world or 7.MP.2. 6-8.RST.4 Inequality
mathematical problem, and construct 7.MP.3. Inverse operations
simple equations and inequalities to 7.MP.4.
solve problems by reasoning about 7.MP.5.
the quantities. 7.MP.6.
7.MP.7.
a. Solve word problems leading to 7.MP.8.
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?

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. 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.
*S5C2PO9. Solve logic problems Conditional statement
using multiple variables and multiple Logic
conditional statements using words,
pictures, and charts.
*S5C2PO10. Demonstrate and Deductive reasoning
explain that the process of solving
equations is a deductive proof.
Unit
Project:

Assessment:



Unit: Geometry
Cluster: Angles


 What is the difference between equal, approximate, and congruent?  Students will understand the difference between

equal, approximate, and congruent.

 Which angle relationships are congruent? Which are not?

 Students will utilize the properties of angles to solve

for the measure of an unknown angle.

*S4C1PO5. Identify corresponding Congruent
parts of congruent figures. Corresponding
Figures
7.G.5. Use facts about 7.MP.3. ET07-S1C4-01 Adjacent
supplementary, complementary, 7.MP.4. Angles
vertical, and adjacent angles in a 7.MP.5. Complemenatry
multi-step problem to write and 7.MP.6. Exterior
solve simple equations for an 7.MP.7. Interior
unknown angle in a figure. Same-Side
Straight
Supplementary
Transversal
Vertical angles
Unit
Project:

Assessment:



Unit: Geometry
Cluster: Geometric Properties


 What is a cross section?  Students will be able to determine what type of 2-D

 What is a 3D shape? figure is yeilded from a cross section of a 3-D figure.

 What is a 2D shape?

 Students will understand that the number of sides a

polygon directly translates to the sum of its interior

angles, regardless of shape.

 Students will know what the parts of a triangle are

and how they are related to each other.


*S4C1PO4. Describe the Interior angles
relationship between the number of Polygon
sides in a regular polygon and the Product
sum of its interior angles. Sides
Sum

7.G.2. Draw (freehand, with ruler 7.MP.4. 6-8.RST.4 Line segments
and protractor, and with technology) 7.MP.5. 6-8.RST.7 Parallelism
geometric shapes with given 7.MP.6. 6-8.WHST.2b-2f SC07- Perpendicularity
conditions. Focus on constructing 7.MP.7. S1C2-04 Points
triangles from three measures of 7.MP.8. ET07-S1C2-01 Protractor
angles or sides, noticing when the ET07-S6C1-03 Quadrilateral
conditions determine a unique Straight edge
triangle, more than one triangle, or Triangle
no triangle. Vertex
7.G.3. Describe the two-dimensional 7.MP.2. 6-8.WHST.1b 2-D
figures that result from slicing three- 7.MP.4. 6-8.WHST.2b 3-D
dimensional figures, as in plane 7.MP.5. Base
sections of right rectangular prisms 7.MP.7. Cross section
and right rectangular pyramids. Cube
Cylinder
Face
Right prism
Right pyramid
Vertex
Unit
Project:

Assessment:



Unit: Geometry
Cluster: Circumference and Area


 What is the difference between perimeter, area, surface area and  Students will be able to determine the parts of a
volume?
circle. I.e. circumference, area, arc, chord, diameter,

radius, and center point.
 Why is volume units cubed and surface area units squared?
 Students will understand that perimeter is the

measurement of length, having neither width nor

height.

 Students will understand that area is the measurement

of a surface space in a 2-D region, and that the

measuring tool used are squares that have a length

and width of one unit measure.

 Students will understand that volume is the

measurement of space that a 3-D object can occupy,

and that the measuring tool used are cubes that have

a length, width, and height of one unit measure.


7.G.4. Know the formulas for the 7.MP.1. 6-8.WHST.1d Area
area and circumference of a circle 7.MP.2. SC07-S2C2-03 Circumference
and solve problems; give an 7.MP.3. ET07-S6C2-03 Diameter
informal derivation of the 7.MP.4. ET07-S1C4-01 Pi
relationship between the 7.MP.5. Radius
circumference and area of a circle. 7.MP.6.
7.MP.7.
7.MP.8.
*S4C1PO1. Recognize the Arc
relationship between central angles Central angle
and intercepted arcs; identify arcs Chord
and chords of a circle.
*S4C4PO2. Identify polygons Perimeter
having the same perimeter or area. Polygons

*S5C1PO1. Create an algorithm to Algorithm
determine the area of a given Composite figure
composite figure.
7.G.6. Solve real-world and 7.MP.1. 6-8.WHST.2a Faces
mathematical problems involving 7.MP.2. ET07-S1C4-01 Net
area, volume and surface area of 7.MP.3. Surface area
two- and three-dimensional objects 7.MP.4. Volume
composed of triangles, 7.MP.5.
quadrilaterals, polygons, cubes, and 7.MP.6.
right prisms. 7.MP.7.
7.MP.8.
Unit
Project:

Assessment:



Unit: Statistics and Probability
Cluster: Stats and Data


 What is a random sample and why are they used to colelct data?  Students will understand that a random sample is

valid to making inferences and generalization about

 How can we design a random sample from a population? a population if there is an even representation.

 Students will understand that there is a margin of

error in making inferences with a random sample.


7.SP.1. Understand that statistics can 7.MP.3. SS07-S4C4-04 Generalizaitons
be used to gain information about a 7.MP.6. SS07-S4C4-05 Inferences
population by examining a sample SC07-S3C1-02 Population
of the population; generalizations SC07-S4C3-04 Random sample
about a population from a sample ET07-S4C2-01 Representative
are valid only if the sample is ET07-S4C2-02 Valid
representative of that population. ET07-S6C2-03
Understand that random sampling
tends to produce representative
samples and support valid
inferences.
*S2C1PO1. Solve problems by Data
selecting, constructing, and Dependent variable
interpreting displays of data Independent variable
including multi-line graphs and Multi-line graph
scatterplots. Scatterplot
*S2C1PO2. Interpret trends in a Data Set
data set, estimate values for missing Estimated value
data, and predict values for points Prediction
beyond the range of the data set. Range
Trends
7.SP.2. Use data from a random 7.MP.1. 6-8.WHST.1b Simulated
sample to draw inferences about a 7.MP.2. SC07-S1C3-04
population with an unknown 7.MP.3. SC07-S1C3-05
characteristic of interest. Generate 7.MP.5. SC07-S1C3-06
multiple samples (or simulated 7.MP.6. SC07-S1C4-05
samples) of the same size to gauge 7.MP.7. SC07-S2C2-03
the variation in estimates or ET07-S1C3-01
predictions. For example, estimate the ET07-S1C3-02
mean word length in a book by ET07-S4C2-02
randomly sampling words from the ET07-S6C2-03
book; predict the winner of a school
election based on randomly sampled
survey data. Gauge how far off the
estimate or prediction might be.
Unit
Project:

Assessment:



Cluster: Data Graph and Analysis


 Why is the average not a good measure of center to use when reporting  Students will understand that measures of center is a

data? good way to summarize a set of data, except if there

are outliers that skew the data.

 How do outliers affect a data set?

 Students will use measure of center to express a set of

data and correctly decide which measure of center

best fits a given set of data.


7.SP.4. Use measures of center and 7.MP.1. 6-8.WHST.1b Absolute deviation
measures of variability for numerical 7.MP.2. ET07-S1C3-01 Comparative -
data from random samples to draw 7.MP.3. ET07-S1C3-02 Inference
informal comparative inferences 7.MP.4. ET07-S4C2-01 Interquartile range
about two populations. For example, 7.MP.5. ET07-S4C2-02 Measure of center
decide whether the words in a chapter 7.MP.6. ET07-S6C2-03 - Mean
of a seventh-grade science book are 7.MP.7. SC07-S1C3-01 - Median
generally longer than the words in a SC07-S1C3-05 - Mode
chapter of a fourth-grade science SC07-S1C4-03 - Range
book. SC07-S2C2-03 Population
SC07-S4C3-04
SS07-S4C2-01
SS07-S4C4-06
SS07-S4C4-09
*S2C1PO3. Identify outliers and Mean
determine their effect on mean, Median
median, mode, and range. Mode
Range
Outlier
7.SP.3. Informally assess the degree 7.MP.1. 6-8.WHST.1b Data distribution
of visual overlap of two numerical 7.MP.2. SC07-S1C4-01 Measure of –
data distributions with similar 7.MP.3. SC07-S1C4-02 Variability
variabilities, measuring the 7.MP.4. SC07-S1C4-03
difference between the centers by 7.MP.5. SS07-S4C1-01
expressing it as a multiple of a 7.MP.6. SS07-S4C1-02
measure of variability. For example, 7.MP.7. SS07-S4C1-05
the mean height of players on the SS07-S4C4-06
basketball team is 10 cm greater than SS07-S4C6-03
the mean height of players on the ET07-S1C3-01
soccer team, about twice the ET07-S1C3-02
variability (mean absolute deviation) ET07-S4C2-01
on either team; on a dot plot, the ET07-S4C2-02
separation between the two ET07-S6C2-03
distributions of heights is noticeable.
Unit
Project:

Assessment:



Cluster: Simple and Compound Events


 How can probabilty be used to make informed predictions?  Students will understand that the probability of a

certain outcome is between 0, which is impossible to

 How does increasing the total number of possible outcomes affect the happen, and 1, which is certain to happen.

probability of a given situation?

 Students will understand that the probability that an

even will occur is equal to the number of favorable

outcome divided by the total number of outcomes.

 Students will understand that a sample space is a

diagram of all possible outcomes for a given

situation.


7.SP.5. Understand that the probability 7.MP.4. 6-8.WHST.1b Certain
of a chance event is a number between 7.MP.5. SS07-S5C1-04 Equally likely
0 and 1 that expresses the likelihood 7.MP.6. ET07-S1C3-01 Favorable outcome
of the event occurring. Larger numbers 7.MP.7. ET07-S1C3-02 Impossible
indicate greater likelihood. A Likely
probability near 0 indicates an unlikely Possible outcome
event, a probability around ½ Probability
indicates an event that is neither Simple event
unlikely nor likely, and a probability Unlikely
near 1 indicates a likely event.
7.SP.8. Find probabilities of compound 7.MP.1. 6-8.WHST.2d Compound event
events using organized lists, tables, 7.MP.2. ET07-S1C2-01 Sample space
tree diagrams, and simulation. 7.MP.4. ET07-S1C2-02 Simulation
7.MP.5. ET07-S1C2-03 Tree diagram
a. Understand that, just as with simple 7.MP.7. SC07-S1C4-03
events, the probability of a compound 7.MP.8. SC07-S1C4-05
event is the fraction of outcomes in the SC07-S1C2-02
sample space for which the compound SC07-S1C2-03
event occurs.

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 that compose the
event.

c. 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?
Unit
Project:

Assessment:


Cluster: Theoretical and Experimental Probabilities


 What are the similarities and differences between experimental and  Students will understand that probability is a theory

theoritical probability? and is the likelyhood that an event will happen, and

not concrete.

 Students will understand that the more trials used in

an experimental probability, the closer the

probability of an event occuring gets closer to its

theoretical probability.


7.SP.6. Approximate the probability of a 6-8.WHST.1a Conjecture
chance event by collecting data on the ET07-S1C2-01 Experimental
chance process that produces it and Frequency
observing its long-run relative frequency, ET07-S1C2-02 Predict
and predict the approximate relative ET07-S1C2-03 Relative
frequency given the probability. For ET07-S1C3-01 Theoretical
example, when rolling a number cube 600 ET07-S1C3-02
times, predict that a 3 or 6 would be rolled ET07-S4C2-01
roughly 200 times, but probably not exactly
ET07-S6C1-03
200 times.
ET07-S6C2-03
SC07-S1C2-03
SC07-S1C2-05
SC07-S1C3-05
SC07-S1C4-03
SC07-S1C4-05
SC07-S2C2-03
7.SP.7. Develop a probability model and 6-8.WHST.2d Discrepancy
use it to find probabilities of events. SC07-S1C2-02 Frequencies
Compare probabilities from a model to ET07-S1C2-01
observed frequencies; if the agreement is ET07-S1C2-02
not good, explain possible sources of the ET07-S1C2-03
discrepancy. ET07-S1C3-01
ET07-S1C3-02
a. Develop a uniform probability model by ET07-S4C2-01
assigning equal probability to all outcomes, ET07-S4C2-02
and use the model to determine ET07-S6C1-03
probabilities of events. For example, if a ET07-S6C2-03
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.

b. 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?


Unit
Project:

Assessment:



Unit: Displaying Data
Cluster: Data displays


 What is a vertex-edge graph?  Students will be able to read a vertex-edge

 How are vertex-edge graphs used in real life? diagram.

 What is the difference between a congurent transformation and a similar

transformation?  Students will be able to use a Venn Diagram to

represent algebraic problems.

 Students will be able to translate, rotate, and reflect

geometric figures in a coordinate plane.


*S2C3PO2. Solve counting Venn diagram
problems using Venn diagrams and
represent the answer algebraically.
*S2C4PO1. Use vertex-edge Circuits
graphs and algorithmic thinking to Euler/Hamilton
represent and find solutions to Paths
practical problems related to Vertex-Edge graphs
Euler/Hamilton paths and circuits.
*S4C2PO1. Model the result of a Coordinate plane
double transformation (translations Origin
or reflections) of a 2-dimensional Reflection
figure on a coordinate plane using Rotation
all four quadrants. Tranformation
Translation
X-Axis
Y-Axis
Unit
Project:

Assessment:


2012 7th grade_math_curriculum_guide

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