Download 7th GRADE - MATH - Tempe Elementary School District

7th GRADE - MATH
REQUIREMENT INFORMATION
ASSESSMENT INFORMATION
TD3 Textbook Resource
Glencoe Math: Course 2
NWEA/MAP Assessment
HOW TO READ THE CURRICULUM MAP
7th GRADE NWEA/MAP INFORMATION
• Standards are grouped into units in each quarter.
Spring National Norm (2011) 244
Example : Quarter 1: Unit 1
• Units build in understanding throughout the year and
AZMerit Assessment
should be followed in that order.
• Standards within each unit, however, may be taught in
AZMerit is a computer-based test that provides engaging
any order or in conjunction with each other.
questions and measures critical thinking skills for college
• Standards are labeled by grade level (6), domain (RP),
and career readiness. For schools that are not yet ready, a
cluster (A), and standard (3). Example: 6.RP.A.3
paper-based version is available.
• Knowledge for each standard appears directly adjacent to
AZMerit is aligned to Arizona’s state learning standards
the strand and standard identification.
which detail what students should be able to do at each
• When part of a standard is crossed out, that part of the
grade level.
standard will be addressed in a later unit.
The test is designed to measure student learning and
• “Also in”, in the AZCCRS column, shows where the
progress towards readiness for college and career.
standard appears throughout the map.
• “Big Ideas” are what students will understand by the end
of the unit.
• “Essential Questions” stimulate ongoing thinking of “Big
Ideas”.
• Key Terms come from the standard as well as additional
academic words to support instruction.
• The Big Ideas, Essential Questions, and Key Terms are
student friendly language.(They are also highlighted in
Revised 12/12/2016
Blue)
Tempe Elementary School District #3
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7th GRADE - MATH
Overview of Math Domains for 7th Grade
Ratios and Proportional Relationships (RP)
• Analyze proportional relationships and use them to solve real‐world and mathematical
problems.
The Number System (NS)
• Apply and extend previous understandings of operations with fractions to add, subtract,
multiply, and divide rational numbers.
Expressions and Equations (EE)
• Use properties of operations to generate equivalent expressions.
• Solve real‐life and mathematical problems using numerical and algebraic expressions and
equations.
Geometry (G)
• 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 (SP)
• 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.
Tempe Elementary School District #3
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7th GRADE - MATH
Standards for Mathematical Practices (MP)
Standards
Explanations and Examples
Students are
expected to:
7.MP.1. Make
sense of
problems and
persevere in
solving them.
7.MP.2.
Reason
abstractly and
quantitatively.
In Grade 7, students solve problems involving ratios and rates and discuss how they solved them.
Students solve real world problems through the application of algebraic and geometric concepts.
Students seek the meaning of a problem and look for efficient ways to represent and solve it. They may
check their thinking by asking themselves, “What is the most efficient way to solve the problem?”, “Does
this make sense?”, and “Can I solve the problem in a different way?”
7.MP.3.
Construct
viable
arguments and
critique the
reasoning of
others.
In Grade 7, students construct arguments using verbal or written explanations accompanied by
expressions, equations, inequalities, models, and graphs, tables, and other data displays (e.g., box plots,
dot plots, histograms). They further refine their mathematical communication skills through
mathematical discussions in which they critically evaluate their own thinking and the thinking of other
students. They pose questions like “How did you get that?”, “Why is that true?”, and “Does that always
work?” They explain their thinking to others and respond to others’ thinking.
7.MP.4.
Model with
mathematics.
In Grade 7, students model problem situations symbolically, graphically, tabularly, and contextually.
Students form expressions, equations, or inequalities from real world contexts and connect symbolic and
graphical representations. Students explore covariance and represent two quantities simultaneously.
They use measures of center and variability and data displays (e.g., box plots and histograms) to draw
inferences, make comparisons and formulate predictions. Students use experiments or simulations to
generate data sets and create probability models. Students need many opportunities to connect and
explain the connections between the different representations. They should be able to use all of these
representations as appropriate to a problem context.
In Grade 7, students represent a wide variety of real world contexts through the use of real numbers and
variables in mathematical expressions, equations, and inequalities. Students contextualize to understand
the meaning of the number or variable as related to the problem and decontextualize to manipulate
symbolic representations by applying properties of operations.
Tempe Elementary School District #3
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7th GRADE - MATH
Standards for Mathematical Practices (MP), continued
Standards
Explanations and Examples
Students are
expected to:
7.MP.5. Use
appropriate
tools
strategically.
Students consider available tools (including estimation and technology) when solving a mathematical
problem and decide when certain tools might be helpful. For instance, students in grade 7 may decide to
represent similar data sets using dot plots with the same scale to visually compare the center and
variability of the data. Students might use physical objects or applets to generate probability data and
use graphing calculators or spreadsheets to manage and represent data in different forms.
7.MP.6.
Attend to
precision.
In Grade 7, students continue to refine their mathematical communication skills by using clear and
precise language in their discussions with others and in their own reasoning. Students define variables,
specify units of measure, and label axes accurately. Students use appropriate terminology when referring
to rates, ratios, probability models, geometric figures, data displays, and components of expressions,
equations or inequalities.
7.MP.7. Look
for and make
use of
structure.
Students routinely seek patterns or structures to model and solve problems. For instance, students
recognize patterns that exist in ratio tables making connections between the constant of proportionality
in a table with the slope of a graph. Students apply properties to generate equivalent expressions (e.g., 6
+ 2x = 2 (3 + x ) by distributive property) and solve equations (e.g. 2c + 3 = 15, 2c = 12 by subtraction
property of equality; c=6
by division property of equality). Students compose and decompose two‐ and three‐ dimensional figures
to solve real world problems involving scale drawings, surface area, and volume. Students examine tree
diagrams or systematic lists to determine the sample space for compound events and verify that they
have listed all possibilities.
7.MP.8. Look
for and
express
regularity in
repeated
reasoning.
In Grade 7, students use repeated reasoning to understand algorithms and make generalizations about
patterns. During multiple opportunities to solve and model problems, they may notice that a/b ÷ c/d =
ad/bc and construct other examples and models that confirm their generalization. They extend their
thinking to include complex fractions and rational numbers. Students formally begin to make connections
between covariance, rates, and representations showing the relationships between quantities. They
create, explain, evaluate, and modify probability models to describe simple and compound events.
Tempe Elementary School District #3
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7th GRADE - MATH
7th Grade Key Terms
Absolute value
Absolute value symbol (|
|)
acute triangle
addition property of
equality
addition property of
inequality
additive identity property
additive inverse property
adjacent angle
algebra tiles
algebraic expression
associative property
average
bar notation symbol
circumference
coefficient
commission
commutative property
complementary angle
complex fraction
compound event
congruent
constant
constant of proportionality
cross section
dependent event
diameter
direct variation
discount
distribution
multiplicative inverse
distributive property
property
division property of
multiplicative property of
equality
zero
division property of
negative (-)
inequality
net
double box plot
non-proportional
double dot plot
obtuse triangle
experimental probability
per
fee
percent (%)
gratuity
percent error
histogram
pi (π)
independent event
plane
inequality
positive (+)
integer
principal
interquartile range
proportional
like terms
radius
lower quartile
random sample
markdown
range
markup
rate
mean
rate of change
mean absolute deviation
ratio
median
rational number
mode
relative frequency
multiplication property of
repeating decimal
equality
right triangle
multiplication property of
sample space
inequality
scale
multiplicative identity
scale drawing
property
ALL CAPS Term = second and final year of appearance
Tempe Elementary School District #3
scale factor
scale model
similar
simple event
simple interest
simplest form
solution set
statistics
stem-and-leaf plot
substitution
subtraction property of
equality
subtraction property of
inequality
supplementary angle
surface area
tax
term
terminating decimal
theoretical probability
tree diagram
uniform probability
unit rate
upper quartile
variability
variable
vertical angle
zero pair
5
7th GRADE - MATH
7The
first examples in each cell are examples of discrete things. These are easier for students and should be given before the measurement examples.
language in the array examples shows the easiest form of array problems. A harder form is to use the terms rows and columns: The apples in the grocery
window are in 3 rows and 6 columns. How many apples are in there? Both forms are valuable.
5Area involves arrays of squares that have been pushed together so that there are no gaps or overlaps, so array problems include these especially important
measurement situations.
4The
Tempe Elementary School District #3
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7th GRADE - MATH
Quarter 1 Unit 1
Suggested Number of Days: 10 Days
Big Ideas/Enduring Understandings:
Essential Questions:
Ratios and rates are multiplicative comparisons of two quantities or
measurements.
What are ratios and rates?
Standards for Mathematical Practice:
1.
2.
3.
4.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
5.
6.
7.
8.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Cluster
RP.A: Analyze proportional relationships and use them to solve real-world and mathematical problems.
G.A: Draw, construct, and describe geometrical figures and describe the relationships between them.
AZCCRS
Knowledge
Unit rate
7.RP.A.1
COMPUTE unit rates associated with ratios of fractions, including
ratios of lengths, areas and other quantities measured in like or
different units.
Note: For example, if a person walks ½ mile in each ¼ hour,
compute the unit rate as the complex fraction ½/¼ miles per hour,
equivalently 2 miles per hour.
Proportional relationships
7.RP.A.2
Skills
Equivalent ratios
RECOGNIZE and REPRESENT proportional relationships between
quantities.
a.
Also in Q1-Unit 2
b.
Key Terms
ratio
rate
unit rate
per
complex fraction
constant of
proportionality
proportional
non-proportional
scale
scale factor
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.
IDENTIFY the constant of proportionality (unit rate) in tables,
graphs, equations, diagrams, and verbal descriptions of
proportional relationships.
Tempe Elementary School District #3
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7th GRADE - MATH
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.
7.G.A.1
Also in Q4-Unit 13
Scale drawings
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.
SOLVE problems involving scale drawings of geometric figures,
such as computing actual lengths and areas from a scale drawing
and reproducing a scale drawing at a different scale.
Resources:
http://bit.ly/1Tfnk8f
Tempe Elementary School District #3
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7th GRADE - MATH
Quarter 1 Unit 2
Suggested Number of Days: 12 Days
Big Ideas/Enduring Understandings:
Essential Questions:
Proportional relationships are recognized or represented through tables,
graphs, equations, diagrams and verbal descriptions.
How are proportional relationships recognized or represented?
Standards for Mathematical Practice:
1.
2.
3.
4.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
5.
6.
7.
8.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Cluster
RP.A: Analyze proportional relationships and use them to solve real-world and mathematical problems.
AZCCRS
Knowledge
Proportional relationships
Equivalent ratios
Coordinate plane
7.RP.A.2
Constant of proportionality
Also in Q1-Unit 1
Skills
RECOGNIZE and REPRESENT proportional relationships between
quantities.
Key Terms
direct variation
rate of change
distributive property
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.
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.
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.
Tempe Elementary School District #3
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7th GRADE - MATH
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.
Variables
Simple equations
Word problems
Solutions
7.EE.B.4
Also in Q2-Unit 6,
Q2-Unit 7
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.
Note: 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.
Note: 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.
Note: Focus is limited to one-step proportional equations. Students
will solve multi-step equations in Units 6 & 7.
Resources:
http://bit.ly/1UZF9ul
Tempe Elementary School District #3
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7th GRADE - MATH
Quarter 1 Unit 3
Suggested Number of Days: 10 Days
Big Ideas/Enduring Understandings:
Essential Questions:
The whole and the proportional relationship are essential for solving a
ratio and percent problem.
What are essential components of a ratio and percent problem?
Standards for Mathematical Practice:
1.
2.
3.
4.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
5.
6.
7.
8.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Cluster
RP.A: Analyze proportional relationships and use them to solve real-world and mathematical problems.
EE.B: Solve real-life and mathematical problems using numerical and algebraic expressions and
equations.
AZCCRS
Knowledge
Skills
Multi step ratio and percent
problems
USE proportional relationships to SOLVE multistep ratio and percent
problems.
7.RP.A.3
Note: Examples: simple interest, tax, markups and markdowns,
gratuities and commissions, fees, percent increase and decrease,
percent error.
Positive and negative rational
numbers
Properties of operations
7.EE.B.3
Also in Q1-Unit 4,
Q2-Unit 5
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.
Key Terms
percent (%)
simple interest
principal
tax
markup
markdown
discount
gratuity
commission
fee
percent error
Note: 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,
Tempe Elementary School District #3
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7th GRADE - MATH
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.
Note: Focus on positive rational numbers.
Resources:
http://bit.ly/24QHE57
Tempe Elementary School District #3
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7th GRADE - MATH
Quarter 1 Unit 4
Suggested Number of Days: 12 Days
Big Ideas/Enduring Understandings:
Essential Questions:
The additive inverse property explains how to combine opposite
quantities.
What is important for understanding how to add and subtract integers?
Standards for Mathematical Practice:
1.Make sense of problems and persevere in solving them.
2.Reason abstractly and quantitatively.
3.Construct viable arguments and critique the reasoning of others.
4.Model with mathematics.
5.Use appropriate tools strategically.
6.Attend to precision.
7.Look for and make use of structure.
8.Look for and express regularity in repeated reasoning.
Cluster
NS.A: Apply and extend previous understandings of operations with fractions to add, subtract, multiply,
and divide rational numbers.
EE.B: Solve real-life and mathematical problems using numerical and algebraic expressions and
equations.
AZCCRS
Knowledge
Skills
Rational numbers
Number line
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.
Opposite quantities
a.Describe situations in which opposite quantities combine to
make 0.
Note: For example, a hydrogen atom has 0 charge because its two
constituents are oppositely charged.
7.NS.A.1
Distance
Additive inverse
Absolute value
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 real-world contexts.
c.Understand subtraction of rational numbers as adding the
additive inverse, p – q = p + (–q). Show that the
Tempe Elementary School District #3
Key Terms
rational number
integer
positive (+)
negative (-)
absolute value
absolute value
symbol (| |)
associative property
commutative
property
additive identity
property
additive inverse
property
zero pair
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7th GRADE - MATH
Properties of operations
d.
Real-world and mathematical
problems
7.NS.A.3
Rational numbers
distance between two rational numbers on the number line
is the absolute value of their difference, and APPLY this
principle in real-world contexts.
APPLY properties of operations as strategies to ADD and
SUBTRACT rational numbers.
SOLVE real-world and mathematical problems involving the four
operations with rational numbers. (Computations with rational
numbers extend the rules for manipulating fractions to complex
fractions.)
Also in Q2-Unit 5
Note: Focus on addition and subtraction of positive and negative
rational numbers.
Positive and negative rational
numbers
Properties of operations
7.EE.B.3
Also in Q1-Unit 3,
Q2-Unit 5
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.
Note: 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.
Note: Focus on problem situations involving addition and
subtraction of rational numbers.
Resources:
http://bit.ly/1R1nXh9
Tempe Elementary School District #3
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7th GRADE - MATH
Quarter 2 Unit 5
Suggested Number of Days: 8 Days
Big Ideas/Enduring Understandings:
Essential Questions:
Previous knowledge of multiplication, division, and properties of
operations support strategies used in understanding integers.
How can multiplying and dividing integers be understood?
Standards for Mathematical Practice:
1.Make sense of problems and persevere in solving them.
2.Reason abstractly and quantitatively.
3.Construct viable arguments and critique the reasoning of others.
4.Model with mathematics.
5.Use appropriate tools strategically.
6.Attend to precision.
7.Look for and make use of structure.
8.Look for and express regularity in repeated reasoning.
Cluster
NS.A: Apply and extend previous understandings of operations with fractions to add, subtract, multiply,
and divide rational numbers.
EE.B: Solve real-life and mathematical problems using numerical and algebraic expressions and
equations.
AZCCRS
Knowledge
Skills
Multiplication and division
Rational numbers
Apply and extend previous understandings of multiplication and
division and of fractions to multiply and divide rational numbers.
Products of rational numbers
7.NS.A.2
Integers
Quotients of 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.
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 realworld contexts.
c.Apply properties of operations as strategies to multiply and divide
rational numbers.
Key Terms
multiplicative
identity property
multiplicative
inverse property
multiplicative
property of zero
repeating decimal
terminating decimal
bar notation symbol
Properties of operations
Tempe Elementary School District #3
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7th GRADE - MATH
Long division
d.
Real-world and mathematical
problems
7.NS.A.3
Rational numbers
Also in Q1-Unit 4
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.
Solve real-world and mathematical problems involving the four
operations with rational numbers. (Computations with rational
numbers extend the rules for manipulating fractions to complex
fractions.)
Note: Focus on multiplication and division with positive and
negative rational numbers.
Positive and negative rational
numbers
Properties of operations
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.
7.EE.B.3
Also in Q1-Unit 3,
Q1-Unit 4
Note: 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.
Note: Focus on problem situations involving multiplication and
division with rational numbers.
Resources:
http://bit.ly/1TT9Fnj
Tempe Elementary School District #3
16
7th GRADE - MATH
Quarter 2 Unit 6
Suggested Number of Days: 14 Days
Big Ideas/Enduring Understandings:
Essential Questions:
Properties of operations support strategies used in evaluating expressions
and solving equations.
Real-world situations can be solved by creating, interpreting, and
evaluating expressions and equations.
Why are properties of operations important?
How can real-world situations be solved?
Standards for Mathematical Practice:
1.
2.
3.
4.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
5.
6.
7.
8.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Cluster
EE.A: Use properties of operations to generate equivalent expressions.
EE.B: Solve real-life and mathematical problems using numerical and algebraic expressions and
equations.
AZCCRS
Knowledge
Linear expressions
7.EE.A.1
Expressions
7.EE.A.2
7.EE.B.4
Also in Q1-Unit 2,
Q2-Unit 7
Skills
APPLY properties of operations as strategies to ADD, SUBTRACT,
FACTOR, and EXPAND linear expressions with rational coefficients.
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.
Note: For example, a + 0.05a = 1.05a means that “increase by 5%”
is the same as “multiply by 1.05.”
Variables
Simple equations
Word problems
Solutions
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
Tempe Elementary School District #3
Key Terms
substitution
variable
algebraic
expression
algebra tiles
coefficient
term
like terms
constant
simplest form
addition property of
equality
subtraction property
of equality
multiplication
property of
equality
division property of
equality
17
7th GRADE - MATH
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.
Note: 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.
Note: 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.
Note: Focus is on expressions and equations.
Resources:
http://bit.ly/1Op060j
Tempe Elementary School District #3
18
7th GRADE - MATH
Quarter 2 Unit 7
Suggested Number of Days: 8 Days
Big Ideas/Enduring Understandings:
Essential Questions:
An inequality is graphed to show all possible solutions.
Inequalities can be used to show disproportionate values in real-life
situations.
Why are inequalities graphed?
What situations can be shown using inequalities?
Standards for Mathematical Practice:
1.Make sense of problems and persevere in solving them.
2.Reason abstractly and quantitatively.
3.Construct viable arguments and critique the reasoning of others.
4.Model with mathematics.
5.Use appropriate tools strategically.
6.Attend to precision.
7.Look for and make use of structure.
8.Look for and express regularity in repeated reasoning.
Cluster
EE.B: Solve real-life and mathematical problems using numerical and algebraic expressions and
equations.
AZCCRS
Knowledge
Skills
Variables
Simple equations
Inequalities
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.
Word problems
Solutions
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.
7.EE.B.4
Key Terms
inequality
solution set
addition property of
inequality
subtraction property
of inequality
multiplication
property of
inequality
division property of
inequality
Note: For example, the perimeter of a rectangle is 54 cm. Its length
is 6 cm. What is its width?
Also in Q1-Unit 2,
Q2-Unit 6
Word problems
Solution set
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.
Tempe Elementary School District #3
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7th GRADE - MATH
Note: 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.
Resources:
http://bit.ly/1Op1U9G
Tempe Elementary School District #3
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7th GRADE - MATH
Quarter 2 Unit 8
Suggested Number of Days: 11 Days
Big Ideas/Enduring Understandings:
Essential Questions:
Probability is the likelihood of an event occurring.
Data can be collected to create an experimental probability to predict
future events.
What is probability?
How can the outcome of future events be predicted?
Standards for Mathematical Practice:
1.Make sense of problems and persevere in solving them.
2.Reason abstractly and quantitatively.
3.Construct viable arguments and critique the reasoning of others.
4.Model with mathematics.
5.Use appropriate tools strategically.
6.Attend to precision.
7.Look for and make use of structure.
8.Look for and express regularity in repeated reasoning.
Cluster
SP:C: Investigate chance processes and develop, use, and evaluate probability models.
AZCCRS
Knowledge
Skills
Probability
Likelihood
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 unlikely nor likely, and a probability near 1
indicates a likely event.
Probability
Data
Frequency
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.C.5
Key Terms
experimental
probability
theoretical
probability
uniform probability
relative frequency
sample space
simple event
tree diagram
7.SP.C.6
Note: For example, when rolling a number cube 600 times, predict
that a 3 or 6 would be rolled roughly 200 times, but probably not
exactly 200 times.
Tempe Elementary School District #3
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7th GRADE - MATH
Probability model
Uniform probability
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.
Note: For example, if a student is selected at random from a class,
find the probability that Jane will be selected and the probability
that a girl will be selected.
7.SP.C.7
Frequencies
b.
DEVELOP a probability model (which may not be uniform)
by OBSERVING frequencies in data generated from a
chance process.
Note: For example, find the approximate probability that a spinning
penny will land heads up or that a tossed paper cup will land openend down. Do the outcomes for the spinning penny appear to be
equally likely based on the observed frequencies?
Resources:
http://bit.ly/1OsmuRa
Tempe Elementary School District #3
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7th GRADE - MATH
Quarter 3 Unit 9
Suggested Number of Days: 11 Days
Big Ideas/Enduring Understandings:
Essential Questions:
Representations show the sample space and probability of the events.
What do representations of compound events show?
Standards for Mathematical Practice:
1.Make sense of problems and persevere in solving them.
2.Reason abstractly and quantitatively.
3.Construct viable arguments and critique the reasoning of others.
4.Model with mathematics.
5.Use appropriate tools strategically.
6.Attend to precision.
7.Look for and make use of structure.
8.Look for and express regularity in repeated reasoning.
Cluster
SP:C: Investigate chance processes and develop, use, and evaluate probability models.
AZCCRS
Knowledge
Compound events
Probability
7.SP.C.8
Sample space
Simulation
Skills
Key Terms
compound event
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.
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.
c.Design and use a simulation to generate frequencies for
compound events.
Tempe Elementary School District #3
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7th GRADE - MATH
Note: 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?
Resources:
http://bit.ly/225JWvp
Tempe Elementary School District #3
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7th GRADE - MATH
Quarter 3 Unit 10
Suggested Number of Days: 12 Days
Big Ideas/Enduring Understandings:
Essential Questions:
Random sampling increases the validity of the results and eliminates
biases which allow inferences to be made about the population.
Data distribution, variability, and the difference between centers give
information about the populations that lead to the inferences.
What benefit does random sampling provide when collecting data for a
survey?
What information from data can be used to make inferences?
Standards for Mathematical Practice:
1.Make sense of problems and persevere in solving them.
2.Reason abstractly and quantitatively.
3.Construct viable arguments and critique the reasoning of others.
4.Model with mathematics.
5.Use appropriate tools strategically.
6.Attend to precision.
7.Look for and make use of structure.
8.Look for and express regularity in repeated reasoning.
Cluster
SP:A: Use random sampling to draw inferences about a population.
SP.B: Draw informal comparative inferences about two populations.
AZCCRS
Knowledge
Statistics
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.
Random sample
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.A.1
7.SP.A.2
Skills
Note: For example, estimate the mean word length in a book by
randomly sampling words from the book; predict the winner of a
school election based on randomly sampled survey data. Gauge
how far off the estimate or prediction might be.
Tempe Elementary School District #3
Key Terms
statistics
random sample
distribution
variability
mean absolute
deviation
double box plot
double dot plot
histogram
stem-and-leaf plot
interquartile range
lower quartile
upper quartile
mean
average
median
mode
range
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7th GRADE - MATH
Data distribution
7.SP.B.3
Informally assess the degree of visual overlap of two numerical
data distributions with similar variabilities, measuring the difference
between the centers by expressing it as a multiple of a measure of
variability.
Note: For example, the mean height of players on the basketball
team is 10 cm greater than the mean height of players on the
soccer team, about twice the variability (mean absolute deviation)
on either team; on a dot plot, the separation between the two
distributions of heights is noticeable.
Measures of center
Measures of variability
Use measures of center and measures of variability for numerical
data from random samples to draw informal comparative
inferences about two populations.
7.SP.B.4
Note: For example, decide whether the words in a chapter of a
seventh-grade science book are generally longer than the words in
a chapter of a fourth-grade science book.
Resources:
http://bit.ly/1Osoxop
Tempe Elementary School District #3
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7th GRADE - MATH
Quarter 3 Unit 11
Suggested Number of Days: 12 Days
Big Ideas/Enduring Understandings:
Essential Questions:
There is a direct correlation between the circumference and the diameter
that maintains the constant ratio of pi.
The area of a circle is half the circumference multiplied by the radius.
What happens to the circumference of a circle when the diameter
changes?
What is the relationship between the area and circumference of a circle?
Standards for Mathematical Practice:
1.Make sense of problems and persevere in solving them.
2.Reason abstractly and quantitatively.
3.Construct viable arguments and critique the reasoning of others.
4.Model with mathematics.
5.Use appropriate tools strategically.
6.Attend to precision.
7.Look for and make use of structure.
8.Look for and express regularity in repeated reasoning.
Cluster
G.B: Solve real-life and mathematical problems involving angle measure, area, surface area, and
volume.
AZCCRS
7.G.B.4
Knowledge
Area and circumference of a
circle
Skills
Know the formulas for the area and circumference of a circle and
solve problems; give an informal derivation of the relationship
between the circumference and area of a circle.
Key Terms
radius
diameter
pi (π)
circumference
Resources:
http://bit.ly/1Ww11yt
Tempe Elementary School District #3
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7th GRADE - MATH
Quarter 4 Unit 12
Suggested Number of Days: 12 Days
Big Ideas/Enduring Understandings:
Essential Questions:
A two-dimensional figure is visualized when slicing through a threedimensional figure.
Surface area is the sum of the areas of the two-dimensional surfaces that
make up the three-dimensional figure.
What is visualized when a three-dimensional figure is sliced?
What is the relationship between area and surface area?
Standards for Mathematical Practice:
1.
2.
3.
4.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
5.
6.
7.
8.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Cluster
G.A: Draw, construct, and describe geometrical figures and describe the relationships between them.
G.B: Solve real-life and mathematical problems involving angle measure, area, surface area, and
volume.
AZCCRS
Knowledge
Skills
Cross section
DESCRIBE the two-dimensional figures that result from slicing threedimensional figures, as in plane sections of right rectangular
prisms and right rectangular pyramids.
Area
Volume
Surface area
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.A.3
7.G.B.6
Key Terms
plane
cross section
net
surface area
Resources:
http://bit.ly/1TbKQAJ
Tempe Elementary School District #3
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7th GRADE - MATH
Quarter 4 Unit 13
Suggested Number of Days: 12 Days
Big Ideas/Enduring Understandings:
Essential Questions:
Scale drawings are proportional to the actual object, and the ratio can be
used to find the actual measurements.
How can a scale drawing determine the actual measurements of an
object?
Standards for Mathematical Practice:
1.
2.
3.
4.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
5.
6.
7.
8.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Cluster
G.A: Draw, construct, and describe geometrical figures and describe the relationships between them.
AZCCRS
7.G.A.1
Knowledge
Skills
Scale drawings
SOLVE problems involving scale drawings of geometric figures,
such as computing actual lengths and areas from a scale drawing
and reproducing a scale drawing at a different scale.
Key Terms
scale drawing
scale model
similar
Also in Q1-Unit 1
Resources:
http://bit.ly/1TTaGfb
Tempe Elementary School District #3
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7th GRADE - MATH
Quarter 4 Unit 14
Suggested Number of Days: 12 Days
Big Ideas/Enduring Understandings:
Essential Questions:
The measurement of angles and length of sides determine the shape of a
geometric figure.
Special angle relationships determine how to write and solve equations for
angle measurements.
How is the shape of a geometric figure determined?
What determines how to write and solve equations for angle
measurements?
Standards for Mathematical Practice:
1.
2.
3.
4.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
5.
6.
7.
8.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Cluster
G.A: Draw, construct, and describe geometrical figures and describe the relationships between them.
G.B: Solve real-life and mathematical problems involving angle measure, area, surface area, and
volume.
AZCCRS
Knowledge
Geometric shapes
7.G.A.2
7.G.B.5
Skills
DRAW (freehand, with ruler and protractor, and with technology)
geometric shapes with given conditions.
Note: 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.
Supplementary angles
Complementary angles
Vertical angles
Adjacent angles
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.
Key Terms
congruent
acute triangle
obtuse triangle
right triangle
supplementary
angle
complementary
angle
vertical angle
adjacent angle
Resources:
http://bit.ly/1Ww1gK1
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