Download Math 7 - Grand County School District

Scope and Sequence Overview…………...…………………. 1
Scope and Sequence …………………………………….…... 2
Utah Core Standards Map………….………………………... 5
Utah Core Standards Map with Gizmos……………………...17
Appendices A – C
A – Pre-assessments
B – Benchmarks
C – Summative Assessments
Scope and Sequence Math 7
1st Trimester 2nd Trimester 3rd Trimester Algebraic Reasoning Graphs Geometric Measurement Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Analyze proportional relationships and use them to solve real‐
world and mathematical problems. Draw, construct, and describe geometrical figures and describe the relationships between them. 7NS1D, Use properties of operations to generate equivalent expressions 7EE1, 7EE2, 7EE3, 7EE4 Integers and Rational Numbers 7RP1, 7RP2, 7RP2A, 7RP2B, 7RP2C, 7RP2D Percents Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. 7NSD, 7NS2A, 7NS2B, 7NS2C, Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Use properties of operations to generate equivalent expressions 7NS1, 7NS1B, 7NS1C, 7NS2, 7NS2A, 7NS2B, 7NS2C, 7NS3 Applying Rational Numbers Solve real‐life and mathematical problems using numerical and algebraic expressions and equations. Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. 7NS1, N7S1B, 7NS1C, 7NS2, 7NS2A, 7NS2B, 7NS3, Solve real‐life and mathematical problems using numerical and algebraic expressions and equations 7EE4 7RP3 7EE3 Collecting, Displaying, and Analyzing Data Use random sampling to draw inferences about a population. 7SP1 Draw informal comparative inferences about two populations. 7SP2, 7SP3, 7SP4 Geometric Figures Draw, construct, and describe geometrical figures and describe the relationships between them. 7G2, Solve real‐life and mathematical problems involving angle measure, area, surface area, and volume 7G5 7G3, 7G4, 7G6 Probability Investigate chance processes and develop, use, and evaluate probability models 7SP5, 7SP6, 7SP7, 7SP7A, 7SP7B, 7SP8, 7SP8A, 7SP8B, 7SP8C Multistep Equations and Inequalities Use properties of operations to generate equivalent expressions 7EE1, 7EE4, 7EE4A, 7EE4B Math 7 Scope and Sequence
1st Trimester
Topic
Review
Algebraic
Expressions
Integers and
Rational
Numbers
Content
Operations and properties
Variables and expressions, simplyfing
expressions
Translate words into marth
Model Addition and subtraction
Model multiplication and division
Solving equations containg Integers
Equivalent fractions and decimals
Comparing and ordering rational numbers
Appling Rational Adding and Subtracting rational numbers and
Numbers
decimals
Multiplying and dividing rational numbers and
decimals
Solving equations containg fractions
Proportional
Reasoning
Rates and Proportions
Solving Proportions
Similar Figures
Scale
Skills
Standards
Order of operations, Properties of Numbers
Evaluate Algebraic Expressions.
7.NS-1
Writing expressions
Negative Numbers. Opposites, Additive
Inverse, Absolute Value
7.EE.2
Modeling multiplication and division
Use variables to represent quatinites, and
construct equations and inequalities to solve
Solve real world applications involving the four
operations with rational numbers
Number line and visual representations and
converting to decimals.
Properties of addition and subtraction and
properties of rational number and decimals
Properties of multiplications and division, and
properties of rational number, decimals and
mixed numbers.
Solve equations using properties of fractions,
mixed numbers and decimals.
Proportional relationships, equivalent ratios,
and identify proportions
Cross product
Prove similar figures using ratios, congruency,
and geomtric shapes
understand drawing to use and determine scale
7.EE.1
Time in
50
minute
Periods
3
3
2
3
7.NS.1
7.NS2
7.NS.4
7n.NS.2c
7.NS.3
3
3
3
3
6
7.NS.2
6
7.NS.2
7.EE.4
7.RP.2
7.RP.3
7.RP.2
7.G.1
5
4
3
3
3
Math 7 Scope and Sequence
2nd Trimester
Topic
Graphs
Percents
Content
Skills
The coordinate Plane, Interpeting graphs
Learn vocabulary, plot and identify ordered
pairs, identify increasing and decreasing lines
Proportioanl relationships and direct variation
Find rate of change on a graph, use and
understand direct variation
determine slope
Convert fractions to decimals
Use and understand estimation, develop
techniques for estimation, and write equivalent
expressions.
Solve problems with percent of change,
commission, sales tax, percent of earnings and
compute simple interest.
Review finding central tendencies and plotting
box and whiskers
Slope
Fractions, decimals and percents
Estimating and using poperteis of rational
numbers
Finding percent of change, simple interst, and
applications of percents
Collecting,
Mean, Median, Mode, and range. Box and
Displaying, and whisker plots
Analyzing Data
Explore samples, use random samples, and
population samples
Geometric
Explore and classify angles and lines
Figures
Angles in polygons
Triangles, congruent figures, and
transformations
Compare and analyze samples
Complimentary, supplimentary angles and
parallel and perpindicular lines. Classify angles.
Line and angle relationships and contruct angle
bisectiors and congruent angles.
Find the measure of angles in polygons.
Identify congurent figures, parallel and
perpendicular lines, and angles formed by a
transversal. Explore transforamtions
Standards
7.RP.2
7.RP.1
7.EE.2
Time in
50
minute
Periods
2
3
2
3
3
7.EE.3
4
7.RP.3
4
7.SP.4
7.SP.1
4
4
7.G.5
7.G.3
7.G.2
4
4
Math 7 Scope and Sequence
3rd Trimester
Topic
Measurement
and Geometry
Content
Perimeter, Circumference and Area
Volume and Surface Area
Probability
Introduction to Probability
Application of Probability
Multi-Step
Equations and
Inequalities
Skills
Explore Periemeter and Circumference, use
formulas appropriately and find area of Circle
Area of Irregular Figures
Introduction to Three-Dimensional Figures
Cross Sections
Volume and surface area of Prisms and
Cylinders
Probability
Experimental probablity and develop a
Probability model
Sample spaces, Simulations, and Experimental
vs Theoretical probability
Theoretical Probability and Making Predictions
Probability of Independent and Dependent
events, Combinations, Permutations, and
Probability of Compound Event.
Standards
CC.7.G.4
Time in
50
minute
Periods
3
CC.7.G.6
CC.7G.3
CC.7.G.6
1
1
1
4
CC.7.P.5
2
3
CC.7.P.6
CC.7.P.7
CC.7.P.8
4
4
8
CC.7.SP.8
1
Multi-Step Equations
Inequalities
Model Two-Step equations, Solving Two-Step
CC.7.EE1
equations
Solving Multi-Step equations, Solving equations
with variables on both sides, Examine Solution CC.7.EE.4
Methods
Inequalites, Solving inequalities by addition or
subtractions, Solving inequalites by
CC.7.EE.4
multiplication or division, Solving mulit-step
inequalities
3
8
Utah CORE Math 7 Curriculum Standards Map Math 7 Critical Areas Clusters Standard 7. The Number System Apply and extend
previous understandings
of operations with
fractions to add, subtract,
multiply, and divide
rational numbers. 3.
Activities Formative Assessments Summative Assessments 1. Apply and extend previous
2.
Areas of Concern understandings of addition
and subtraction to add and
subtract rational numbers;
represent addition and
subtraction on a horizontal
or vertical number line
diagram. Apply and extend previous
understandings of
multiplication and division
and of fractions to multiply
and divide rational numbers. Solve real-world and
mathematical problems
involving the four operations
with rational numbers. Fractions When to use common denominators and how to find them. Multiples vs. Factors Real meaning of dividing fractions. Negative numbers Decimals: add, subtraction, multiplication and division UTIPS Pre‐assessment Quiz 1 (collecting like terms) Quiz 2 (Negative number operations) Quiz 3 (Negative number operations) Vocabulary Quiz UTIPS Chapter 1 Assessment 7. R&P Ratios & Proportional Relationships 1. Compute unit rates
Analyze proportional
relationships and use
them to solve realworld and
mathematical
problems. associated with ratios
of fractions, including
ratios of lengths,
areas and other
quantities measured
in like or different
units. 7. R&P Ratios & Proportional Relationships Analyze proportional
relationships and use
them to solve realworld and
mathematical
problems. 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
Fractions, decimals, %’s Measurement in multiple units. Estimation, appropriate units, reasonable units. Relative size – “How big things are” Unit conversion. Appropriate units. Real meaning of cross multiplication in that it skips two steps of inverse operation. Equivalent fractions. Constant rate of change equals slope. REPRESENTED GRAPHICALLY. Explaining whether a relation(ship) is linear Chapter 2 Pre‐
assessment Chapter 3 Pretest Quiz Rational Numbers Pop Quiz( Using Proportional relationships to solve real world Problem) Chapter 2 Assessment Chapter 3 Test 7. R&P Ratios & Proportional Relationships Analyze proportional
relationships and use
them to solve realworld and
mathematical
problems. 2.
Recognize and
represent
proportional
relationships
between quantities.
a)
Identify the
constant of
proportionality
(unit rate) in
Gets and activity’s in Direct Variation 7:2 Correctly finding delta y and delta x and putting in a rate. Rate of change equals slope (introduce & prepare for Math 8) Writing proportions & solving for unknown. EDITH plan Real world applications needed Activity , measurement, rate of change Speed activity tables, graphs,
equations,
diagrams, and
verbal
descriptions of
proportional
relationships.
7. R&P Ratios & Proportional Relationships 7. R&P Ratios & Proportional Relationships Analyze proportional
relationships and use
them to solve realworld and
mathematical
problems. Analyze proportional
relationships and use
them to solve realworld and
mathematical
problems. 2. Recognize and
b)
2.
represent
proportional
relationships
between quantities. Represent
proportional
relationships by
equations.
Recognize and
represent
proportional
relationships
between quantities. 7.
Expressions
& Equations Use properties of
operations to
generate equivalent
expressions. 1) Apply properties of
operations as strategies to
add, subtract, factor, and
expand linear expressions with
rational coefficients. FRACTIONS Properties of Operations What does a variable mean? Like terms 7.
Expressions
& Equations Use properties of
operations to
generate equivalent
expressions. 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.” 7.
Expressions
& Equations Solve real-life and
mathematical
problems using
numerical and
algebraic
expressions and
equations. Different activities to reinforce the Distributive Property Develop a upside down triangle questioning process for *fractions, *decimals, *variables, *percents Estimation Reading directions, what is the question, what is the relevant/extra information? 3) Solve multi-step real-life and
mathematical problems posed
with positive and negative
rational numbers in any form
(whole numbers, fractions, and
decimals), using tools
strategically. Apply properties
of operations to calculate with
numbers in any form; convert
between forms as appropriate;
and assess the
reasonableness of answers
using mental computation and
estimation strategies. For
example: If a woman making
$25 an hour gets a 10% raise,
she will make an additional
1/10 of her salary an hour, or
$2.50, for a new salary of
$27.50. If you want to place a
towel bar 9 3/4 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.
Using blocks as manipulatives’ identifying like terms associating line, area, and volume Bags of balls activity (7 bags each with 2 tennis balls, 5 ping pong balls) create activity) Analyze data about movies and sequels Chapter 3 Pretest Chapter 3 Test Chapter 7 Pretest Chapter 7 Test Chapter 4 Pretest Chapter 4 Test Chapter 4 Test 2 7.
Expressions
& Equations Solve real-life and
mathematical
problems using
numerical and
algebraic
expressions and
equations. 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. For
example, the
perimeter of a
rectangle is 54 cm.
Its length is 6 cm.
What is its width?
Defining variables as independent or dependent Manipulating equations ½ of the class prepare a poster as a customer, and ½ of the class prepare a poster as a wait staff. Both are given a scenario of menu and budget and tip. Compare each group. 7.
Expressions
& Equations Solve real-life and
mathematical
problems using
numerical and
algebraic
expressions and
equations. 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.
Assigning variables, rate(slope), and y‐intercept or salary 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. Drawing the school lesson where students cannot calculate scale Estimating measurements Chapter 8 Pretest Geometer’s Sketchpad Art project with dilation, rotation, etc… Chapter 8 Test 2) Draw (freehand, with ruler and
Precursor to art project 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.
7. Geometry 7. Geometry Draw
construct, and
describe
geometrical
figures and
describe the
relationships
between them. Draw
construct, and
describe
geometrical
figures and
describe the
relationships
between them. protractor, and with technology)
geometric shapes with given
conditions. Focus on
constructing triangles from three
measures of angles or sides,
noticing when the conditions
determine a unique triangle,
more than one triangle, or no
triangle
7. Geometry Draw
construct,
and describe
geometrical
figures and
describe the
relationships
between
them. 3) Describe the two-dimensional
figures that result from slicing threedimensional figures, as in plane
sections of right rectangular prisms
and right rectangular pyramids. 7. Geometry Solve real-life
and
mathematical
problems
involving
angle
measure,
area, surface
area, and
volume. Solve real-life
and
mathematical
problems
involving
angle
measure,
area, surface
area, and
volume. Solve real-life
and
mathematical
problems
involving
angle
measure,
area, surface
area, and
volume. 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. Orange slice diagram Vocabulary Breaking into individual components 7. Geometry 7. Geometry 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. 6) Solve real-world and mathematical
problems involving area, volume and
surface area of two- and threedimensional objects composed of
triangles, quadrilaterals, polygons,
cubes, and right prisms. Chapter 9 Classroom set Pretest of clay. Groups of two build assigned shape and present “sliced” assigned figure and describe mathematically See above Chapter 9 Test Geometer’s Sketchpad Beginning introduction to use Geometry Sketchpad Outside activity, both measurement and estimation.
“cross curriculum activity” Utah History, Band, Art, Science 7. Statistics
Use random
& Probability sampling to
draw
inferences
about a
population. 1. Understand that statistics can
7. Statistics
Use random
& Probability sampling to
draw
inferences
about a
population. 2.
7. Statistics
Draw informal
& Probability comparative
inferences
about two
populations. 3.
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.
Use data from a random
sample to draw inferences
about a population with an
unknown characteristic of
interest. Generate multiple
samples (or simulated
samples) of the same size to
gauge the variation in
estimates or predictions. For
example, estimate the mean
word length in a book by
randomly sampling words
from the book; predict the
winner of a school election
based on randomly sampled
survey data. Gauge how far
off the estimate or prediction
might be.
Informally assess the degree
of visual overlap of two
numerical data distributions
with similar variabilities,
measuring the difference
between the centers by
expressing it as a multiple of
a measure of variability. For
example, the mean height of
players on the basketball
team is 10 cm greater than
the mean height of players on
the soccer team, about twice
the variability (mean absolute
deviation) on either team; on
a dot plot, the separation
between the two distributions
of heights is noticeable.
Bias, representative sample Mini survey in classroom using random sampling Chapter 7 Pretest Quiz 7.1 Chapter 7 Test Cross curriculum activity with English. Randomly select a page and find the mean. Compare with others. Find a way to get the mean of a book? Vocabulary Boy shoe size vs girl shoe size, compare variability, plot on dot chart two different colors, finally compare across all classes to discuss larger sample space etc Chapter 10 Pretest Chapter 10 Test 7. Statistics
Draw informal
& Probability comparative
inferences
about two
populations. 4. Use measures of center and
7. Statistics
Investigate
& Probability chance
processes
and develop,
use, and
evaluate
probability
models. 5.
7. Statistics
Investigate
& Probability chance
processes
and develop,
use, and
evaluate
probability
models. 6.
measures of variability for
numerical data from random
samples to draw informal
comparative inferences about
two populations.For example,
decide whether the words in a
chapter of a seventh-grade
science book are generally
longer than the words in a
chapter of a fourth-grade
science book.
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.
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. 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.
Build a boat and float blocks. Construct Box and Whisker plot from data. Number line with 0 ‐ 1 plot with 5 different scenarios. Ex: snow in Florida, Sun or rises tomorrow Game project Probability of drawing a red card, vs experiment of drawing a red card 7. Statistics
Investigate
& Probability chance
processes
and develop,
use, and
evaluate
probability
models. 7. Develop a probability model
7. Statistics
Investigate
& Probability chance
processes
and develop,
use, and
evaluate
probability
models. 7.
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. 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.
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. 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?
High level for 7th grade, goal is to introduce Probability of selecting a jack and a red card High level Observed frequencies compared to theoretical probability. 7. Statistics
Investigate
& Probability chance
processes
and develop,
use, and
evaluate
probability
models. 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.
7. Statistics
Investigate
& Probability chance
processes
and develop,
use, and
evaluate
probability
models. 8.
Find probabilities of compound
events using organized lists,
tables, tree diagrams, and
simulation.
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.
Die and coin finding probability of head and a 2 on the die Or dealt 4 cards P(heart) with 2 chances w/o replacement, and with replacement (2 activities) Rolling two die locating P(of sum of 8) 7. Statistics
Investigate
& Probability chance
processes
and develop,
use, and
evaluate
probability
models. 8
Find probabilities of compound
events using organized lists,
tables, tree diagrams, and
simulation.
c)
4 blood types A, B, AB, O (create a bag of 10 of each, randomly draw, simulate outcomes) 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?
Common Core State Standards – 7th Grade Mathematics
CCSS Mathematical Practices The purpose of the Common Core State Standards is to ensure all students have access to rich, rigorous mathematics that prepares them to be college and career ready. The way
the math is taught is as important as the skills that are taught. The CCSS mathematical practices are included at the end of this document. The intent is for these practices to be
viewed as integral to each lesson and incorporated as a natural part of instruction. Constant review of the practices and purposeful inclusion into each lesson will help ensure
development of students as mathematical thinkers rather than as students who only know how to do math. To that end, teachers’ professional judgment based on the type of
instruction and needs of the students should be used when incorporating these mathematical practices.
1. Make sense of problems and persevere in solving them.
4. Model with mathematics.
7. Look for and make use of structure.
2. Reason abstractly and quantitatively.
5. Use appropriate tools strategically.
8. Look for and express regularity in
3. Construct viable arguments and critique the reasoning of others.
6. Attend to precision
repeated reasoning.
Assessments
Formative assessments are used to evaluate instructional programs, reflect on instructional practices, and modify programs and practices as needed throughout the school year.
These assessments can be formal or informal and should be:

immediate – given frequently to check for understanding. (ex. thumbs up/down, fist to 5, exit slips)

interim – given at intervals throughout the school year. (ex. quizzes, project component checks, TLI assessments)
Summative assessments are used to evaluate students and analyze results. These assessments are usually formal and given at the end of a period of study. ex. unit tests,
benchmark exams
Resource References





Glencoe: McGraw Hill, Course 2, Copyright 2013 (Lesson 1-2 refers to Chapter 1 Lesson 2)
LTF: Laying the Foundation Modules, National Math and Science Initiative
ABC: American Book Company, Mastering the Common Core in Mathematics Grade 7
On Core: Houghton Mifflin Harcourt, On Core Mathematics Grade 7
Hands On: Jossey-Bass, Teaching the Common Core Math Standards with Hands-On Activities
Additional Instructional Resources
 Discovery Learning
 Gizmos – math and science simulations
 Kahn Academy – math, science and social studies videos
 Kuta – math software
 Odyssey – language arts and enrichment and reinforcement
 TLI Quiz Builder – tool for creating language arts and math multiple
choice and open response assessments
Instructional Strategies  Group discussions
 Independent/group projects
 Labs
 Marzano’s research based strategies
 Modeling
 More time, question, pass (and come back)
 Recitations
 Repetition
 Role playing
 Service-learning
 Studios
 Think-pair-share
RP: Ratios and Proportional Relationships
NS: The Number System
EE: Expressions and Equations
G: Geometry
SP: Statistics and Probability
1st Nine Weeks
Analyze proportional relationships and use them to solve real‐world and mathematical problems. CCSS 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. For example, if a person walks 1/2 mile in each 1/4 hour, 1/2
compute the unit rate as the complex fraction /1/4 miles per hour, equivalently 2 miles per hour. Vocabulary
Complex fraction Resources
Glencoe: Lesson 1.2 On Core: Lessons 2‐1 ABC: Chapter 6
Hands On: p. 80
Assessments (Calculator)
http://www.illustrativemathematics.org/illustrations/1176 http://www.illustrativemathematics.org/illustrations/114 http://www.illustrativemathematics.org/illustrations/470 http://www.illustrativemathematics.org/illustrations/82 CCSS 7.RP.2: Recognize and represent proportional relationships between quantities.
Mathematical Practices: 2, 4, 6
Vocabulary
Rate Unite rate Unit ratio Dimensional analysis Proportional Nonproportional Equivalent ratios
Origin Constant rate of change Slope
Cross product Constant of variation Constant of proportionality Percent equation Quadrants Coordinate plane
Ordered pair X‐coordinate Y‐coordinate
X‐axis Y‐axis Proportion
Rate of change Direct variation Resources
Glencoe: Lesson 1.1, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9 On Core: Lessons 2‐2, 2‐3 ABC: Chapter 7
Hands On: p. 84
Assessments http://www.illustrativemathematics.org/illustrations/1183 http://www.illustrativemathematics.org/illustrations/1186 http://www.illustrativemathematics.org/illustrations/181
http://www.illustrativemathematics.org/illustrations/100 http://www.illustrativemathematics.org/illustrations/104 http://www.illustrativemathematics.org/illustrations/1178 http://www.illustrativemathematics.org/illustrations/101 http://www.illustrativemathematics.org/illustrations/95 http://www.illustrativemathematics.org/illustrations/180 CCSS 7.RP.2a: Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. Vocabulary
Coordinate plane Quadrants Ordered Pair X‐coordinate Y‐coordinate
X‐axis Y‐axis
Origin Proportional
Nonproportional Equivalent ratios
Direct variation Constant of variation
Constant of proportionality Percent equation
Resources
Glencoe: Lesson 1.4, 1.5, 1.9, 2.4 ABC: Chapter 7 On Core: Lessons 2‐2, 2‐3
Hands On: p. 84
Gizmos: Direct Variation – Proportions and Common Multipliers Assessments (Calculator)
Mathematical Practices: 2, 5 CCSS 7.RP.2b: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
Vocabulary
Rate Unit rate Proportion Cross product Proportional
Nonproportional Equivalent ratios
Slope Rate of change
Constant rate of change Direct variation Constant of variation Constant of proportionality
Resources
Glencoe: Lesson 1.1, 1.4, 1.6, 1.7, 1.8, 1.9 LTF: Module 2 Average Rate of Change (a.k.a. Slope); Module 4 Interpreting Rate Graphs; Module 9 Metric and Customary Measurements ABC: Chapter 7
On Core: Lessons 2‐1, 2‐3 Assessments (No Calculator)
Mathematical Practices: 2, 5, 8 Hands On: p. 84
Gizmos: Beam to Moon (Ratios and Proportions)
Dilations – Perimeters and Areas of Similar Figures Similar Figures ‐ Activity B – Weight and Mass CCSS 7.RP.2c: Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. Vocabulary
Proportion Cross product
Percent equation
Resources
Glencoe: Lesson 1.6, 2.4 ABC: Chapter 7 On Core: Lessons 2‐1
Hands On: p. 84
Gizmos: Beam to Moon (Ratios and Proportions) – Determining a Spring Constant – Estimating Population Size
Geometric Probability ‐ Activity A – Theoretical and Experimental Probability Assessments (No Calculator)
Mathematical Practices: 2, 8 CCSS 7.RP.2d: Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
Vocabulary
Rate of change Constant rate of change Resources
Glencoe: Lesson 1.7 ABC: Chapter 7 On Core: Lessons 2‐3
Hands On: p. 84
Gizmos: Direct Variation
Assessments (No Calculator)
Mathematical Practices: 2, 4 CCSS 7.RP.3: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. Vocabulary
Unit ratio Proportion Cross product Dimension analysis Percent proportion
Percent equation Percent of change
Percent of increase Percent of decrease
Percent error Discount Principal Simple interest
Sales tax Tip
Gratuity markup Selling price
Resources
Glencoe: Lesson 1.3, 1.6, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.8, 4.7 ABC: Chapter 5, 6
On Core: Lessons 2‐2, 2‐3, 2‐4, 3‐2
Hands On: p. 86
Gizmos: Estimating Population Size – Percent of Change Percents and Proportions Assessments (Calculator)
http://www.illustrativemathematics.org/illustrations/997 http://www.illustrativemathematics.org/illustrations/148 http://www.illustrativemathematics.org/illustrations/130 http://www.illustrativemathematics.org/illustrations/121 http://www.illustrativemathematics.org/illustrations/132 http://www.illustrativemathematics.org/illustrations/117 http://www.illustrativemathematics.org/illustrations/102 http://www.illustrativemathematics.org/illustrations/105 http://www.illustrativemathematics.org/illustrations/106 http://www.illustrativemathematics.org/illustrations/1330 http://www.illustrativemathematics.org/illustrations/886
http://www.illustrativemathematics.org/illustrations/266 http://www.illustrativemathematics.org/illustrations/884 Math Practices: 1, 2, 5, 6 2nd Nine Weeks
Apply and extend previous understandings of operations with fractions. CCSS 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.
Vocabulary
Opposites Additive inverse
Like fractions
Unlike fractions
Resources
Glencoe: Lesson 3.2, 4.3, 4.4, 4.5 ABC: Chapter 1, 2, 3, 6
On Core: Lessons 1‐2, 1‐3 Hands On: p. 90
CCSS 7.NS.1a: Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.
Vocabulary
Opposites Additive inverse
Resources
Glencoe: Lesson 3.2 ABC: Chapter 1, 2, 3, 6 On Core: Lessons 1‐2
Hands On: p. 90 Gizmos: Element Builder – Real Number Line ‐ Activity A
Assessments (No Calculator)
http://www.illustrativemathematics.org/illustrations/314 http://www.illustrativemathematics.org/illustrations/46 Mathematical Practices: 5
http://www.illustrativemathematics.org/illustrations/591 http://www.illustrativemathematics.org/illustrations/998 http://www.illustrativemathematics.org/illustrations/310 http://www.illustrativemathematics.org/illustrations/1475 CCSS 7.NS.1b: Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real‐world contexts. Vocabulary
Opposites Additive inverse
Resources
Glencoe: Lesson 3.2, 3.3 On Core: Lessons 1‐2 ABC: Chapter 1, 2, 3, 6
Hands On: p. 90
Assessments (No Calculator)
Mathematical Practices: 2, 3, 5, 7 CCSS 7.NS.1c: Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real‐world contexts. Vocabulary
Like fractions Resources
Glencoe: Lesson 3.3, 4.3 ABC: Chapter 1, 2, 3, 6
On Core: Lessons 1‐3
Hands On: p. 90
Gizmos: Adding and Subtracting Integers
Assessments (No Calculator)
Mathematical Practices: 2, 5, 7 CCSS 7.NS.1d: Apply properties of operations as strategies to add and subtract rational numbers.
Vocabulary
Opposites Additive inverse
Like fractions
Unlike fractions
Resources
Glencoe: Lesson 3.3, 4.3, 4.4, 4.5 ABC: Chapter 1, 2, 3, 6
On Core: Lessons 1‐2, 1‐3
Hands On: p. 90
Gizmos: Adding and Subtracting Integers with Chips Assessments (No Calculator)
Mathematical Practices: 5, 7 CCSS 7.NS.2: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
Vocabulary
Repeating decimal Bar notation Terminating decimal
Rational number
Common denominator
Resources
Glencoe: Lesson 3.3, 3.5, 4.1, 4.2, 4.6, 4.7, 4.8 ABC: Chapter 1, 2, 4
On Core: Lessons 1‐4 Hands On: p. 92
Least common denominator
CCSS 7.NS.2a: Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real‐world contexts. Resources
Glencoe: Lesson 3.3, 4.6 On Core: Lessons 1‐2, ABC: Chapter 1, 2, 4
Hands On: p. 92
Assessments (No Calculator)
Mathematical Practices: 2, 4, 7 CCSS 7.NS.2b: Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non‐zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real‐world contexts. Vocabulary
Rational number Common denominator
Least common denominator
Resources
Glencoe: Lesson 3.5, 4.2 On Core: Lessons 1‐5 ABC: Chapter 1, 2, 4
Hands On: p. 92
Assessments (No Calculator)
Mathematical Practices: 2, 4, 7 CCSS 7.NS.2c: Apply properties of operations as strategies to multiply and divide rational numbers.
Resources
Glencoe: Lesson 3.4, 3.5, 4.6, 4.8 On Core: Lessons 1‐4, 1‐5 ABC: Chapter 1, 2, 4
Hands On: p. 92
Assessments (No Calculator)
Mathematical Practices: 7 CCSS 7.NS.2d: Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.
Vocabulary
Repeating decimal Bar notation
Termination decimal
Resources
Glencoe: Lesson 4.1 On Core: Lessons 1‐1 ABC: Chapter 1, 2, 4
Hands On: p. 92
Assessments (No Calculator)
http://www.illustrativemathematics.org/illustrations/604 http://www.illustrativemathematics.org/illustrations/593 CCSS 7.NS.3: Solve real‐world and mathematical problems involving the four operations with rational numbers.
Vocabulary
Complex fraction Opposites Additive inverse
Like fractions
Unlike fractions
Resources
Glencoe: Lesson 1.2, 3.2, 3.3, 3.5, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8 LTF: Module 16 Limits‐A Physical Approach
ABC: Chapter 3, 4, 5, 6
Assessments (No Calculator)
http://www.illustrativemathematics.org/illustrations/298 Mathematical Practices: 1, 4
On Core: Lessons 1‐6, 2‐1
Hands On: p. 98
3rd Nine Weeks
Use properties of operations to generate equivalent expressions. CCSS 7.EE.1: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
Vocabulary
Variable Algebraic expression Algebra Coefficient Sequence Term Arithmetic sequence
Commutative property Associative property Property
Additive identity property Multiplicative property of Zero Counter example
Distributive property Equivalent expressions Term
Like terms Constant Simplest form
Monomial Factor
Linear expression Resources
Glencoe: Lesson 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8 On Core: Lessons 3‐1 ABC: Chapter 9
Hands On: p. 104
Assessments (No Calculator)
http://www.illustrativemathematics.org/illustrations/543 http://www.illustrativemathematics.org/illustrations/541 Mathematical Practices: 7
http://www.illustrativemathematics.org/illustrations/433 CCSS 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.” Vocabulary
Sales tax Tip Gratuity Markup Selling price Variable Algebraic expression Algebra Coefficient Define a variable
Commutative property Associative property Property
Additive identity property Multiplicative property of zero Distributive property
Equivalent expressions Simplest form Linear expression
Monomial Factor Term
Like term Constant Resources
Glencoe: Lesson 2.6, 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8 On Core: Lessons 3‐2 ABC: Chapter 8
Hands On: p. 106
Assessments (No Calculator)
Mathematical Practices: 7 Solve real‐life mathematical problems using numerical and algebraic expressions and equations. CCSS 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. 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. Vocabulary
Percent equation Percent of change Percent of increase Percent of decrease Percent of error Sales tax Tip
Gratuity Markup
Selling price Opposites
Additive inverse Repeating decimal Bar notation Termination decimal
Rational number Common denominator
Least common denominator Like fractions
Unlike fractions Resources
Glencoe: Lesson 2.1, 2.2, 2.4, 2.5, 2.6, 2.7, 2.8, 3.2, 3.3 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.8, 5.5 ABC: Chapter 9
On Core: Lessons 3‐6
Hands On: p. 108 Gizmos: Air Track – Fan Cart Physics – Ray Tracing (Lenses) – Ray Tracing (Mirrors) Assessments (Calculator)
http://www.illustrativemathematics.org/illustrations/997 http://www.illustrativemathematics.org/illustrations/478 http://www.illustrativemathematics.org/illustrations/884
http://www.illustrativemathematics.org/illustrations/712 http://www.illustrativemathematics.org/illustrations/108 Mathematical Practices: 5 CCSS 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.
Vocabulary
Equation Coefficient Addition property of equality Solution Inequality Subtraction property of equality Glencoe: Lesson 6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7, 6.8 Division property of equality
Multiplication property of equality Two‐step equation
Equivalent equation Resources
ABC: Chapter 8, 9
Addition property of inequality
Subtraction property of inequality On Core: Lessons 3‐3, 3‐4, 3‐5
Multiplication property of inequality
Division property of inequality Two‐step inequality Hands On: p. 110
Assessments
http://www.illustrativemathematics.org/illustrations/884 http://www.illustrativemathematics.org/illustrations/643 http://www.illustrativemathematics.org/illustrations/1475 http://www.illustrativemathematics.org/illustrations/986
CCSS 7.EE.4a: Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Vocabulary
Equatio
n Solution Equivalent equation Glencoe: Lesson 6.1, 6.2, 6.3, 6.4, 6.5 Subtraction property of equality
ABC: Chapter 8, 9 Addition property of equality
On Core: Lessons 3‐3
Hands On: p. 110
Coefficient
Division property of equality
Multiplication property of equality
Two‐step equation Resources
Gizmos: Air Track – Atwood Machine – Ray Tracing (Lenses) – Ray Tracing (Mirrors) – Solving Two‐Step Equations Assessments (No Calculator)
Mathematical Practices: 1, 2, 6, 7 CCSS 7.EE.4b: Solve word problems leading to inequalities of the form px + q>r or px + q<r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. Vocabulary
Inequality Subtraction property of inequality Glencoe: Lesson 6.6, 6.7, 6.8 Addition property of inequality
ABC: Chapter 8, 9
On Core: Lessons 3‐3, 3‐5
Multiplication property of inequality
Division property of inequality
Two‐step inequality
Resources
Hands On: p. 110
Gizmos: Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division Assessments (No Calculator)
Mathematical Practices: 1, 2, 5, 6, 7 Draw, construct and describe geometrical figures and describe the relationship between them.. CCSS 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.
Vocabulary
Scale drawing Scale model
Scale
Scale factor
Resources
Glencoe: Lesson 7.4 ABC: Chapter 11 On Core: Lessons 4‐1
Hands On: p. 114
Gizmos: Dilations – Perimeters and Areas of Similar Figures – Similar Polygons Assessments (Calculator)
Mathematical Practices: 2, 5
http://www.illustrativemathematics.org/illustrations/107 CCSS 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. Vocabulary
Acute triangle Right triangle Obtuse triangle
Scalene triangle
Isosceles triangle
Equilateral triangle
Triangle
Congruent segments Resources
Glencoe: Lesson 7.2 ABC: Chapter 11
On Core: Lessons 4‐2
Hands On: p. 116
Assessments (Calculator)
Mathematical Practices: 3, 5, 6 CCSS 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.
Vocabulary
Prism Bases Pyramid Plan Coplanar
Parallel Polyhedron
Edge Face Vertex Diagonal
Cylinder Cone cross section
Resources
Glencoe: Lesson 7.6 ABC: Chapter 13
On Core: Lessons 4‐3
Assessments (Calculator)
Mathematical Practices: 5 Hands On: p. 119
4th Nine Weeks
Solve real‐life and mathematical problems involving angle measure, are, surface area and volume. CCSS 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.
Vocabulary
Circle Center Glencoe: Lesson 8.1, 8.2, 8.3 Circumference
Diameter
LTF: Module 2 Finding Pi; Module 11 Rectangles and Circles
Radios
Resources
ABC: Chapter 12
Pi
Semicircle
On Core: Lessons 5‐1, 5‐2
Hands On: p. 121
Composite figure
Gizmos: Circle: Circumference and Area Assessments (Calculator)
http://www.illustrativemathematics.org/illustrations/1512 http://www.illustrativemathematics.org/illustrations/1513 Mathematical Practices: 2, 4, 5
http://www.illustrativemathematics.org/illustrations/34 http://www.illustrativemathematics.org/illustrations/765 CCSS 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.
Vocabulary
Vertex Right angle Acute angle Obtuse angle
Straight angle
Complement angles Supplementary angles
Vertical angles Congruent
Adjacent angles Resources
Glencoe: Lesson 7.1, 7.2 ABC: Chapter 10
On Core: Lessons 4‐4
Hands On: p. 124
Gizmos: Investigating Angle Theorems ‐ Activity A Assessments (Calculator)
Mathematical Practices: 5, 6 CCSS 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. Vocabulary
Composite figure Volume Lateral face
Surface area
Lateral surface area
Slant height
Regular pyramid
Resources
Glencoe: Lesson 8.3, LTF: Module 1 Unit Dog; Module 5 Shoe Print, Trapezoids, and Area; 8.4, 8.5, Module 5 Are the Units for Area Always Square?; Module 5 There’s a Hole in 8.7, 8.8 the Bucket Dear Liza, Dear Liza; Module 10 Maximizing Area; Module 10 Triangle Area Activity; Module 11 Fill It Up, Please – Part I ABC: Chapter 11, 13
On Core: Lessons 5‐3, 5‐4, 5‐5 Hands On: p. 127
Gizmos: Area of Parallelograms ‐ Activity A Balancing Blocks (Volume) Prisms and Cylinders ‐ Activity A Rectangle: Perimeter and Area Assessments (Calculator)
http://www.illustrativemathematics.org/illustrations/266 Mathematical Practices: 1, 5
Use random sampling to draw inferences about a population. CCSS 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. Vocabulary
Statistics Survey Population Sample Unbiased sample
Simple random sample
Systematic random sample Biased sample
Convenience sample
Voluntary response sample
Resources
Glencoe: Chapter 10.1, 10.2, (Lessons 10.3 and 10.5 are extensions of 7.SP.1)
ABC: Chapter 14
On Core: Lessons 6‐1 Hands On: p. 129
Gizmos: Polling: City – Polling: Neighborhood Assessments (Calculator)
http://www.illustrativemathematics.org/illustrations/559 http://www.illustrativemathematics.org/illustrations/260 Mathematical Practices: 4
http://www.illustrativemathematics.org/illustrations/558 http://www.illustrativemathematics.org/illustrations/974 CCSS 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. 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. Vocabulary
Statistics Survey Population Sample Unbiased sample
Simple random sample
Systematic random sample Biased sample
Convenience sample
Voluntary response sample
Resources
Glencoe: Chapter 10.1, 10.2 ABC: Chapter 14 On Core: Lessons 6‐1, 6‐2
Hands On: p. 131 Assessments (Calculator)
http://www.illustrativemathematics.org/illustrations/1339 Mathematical Practices: 4
Gizmos: Polling: City – Polling: Neighborhood – Populations and Samples Draw informal comparative inferences about two populations. CCSS 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. 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. Resources
ABC: Chapter 14 On Core: Lessons 6‐3
Hands On: p. 133
Assessments (Calculator)
http://www.illustrativemathematics.org/illustrations/1340 http://www.illustrativemathematics.org/illustrations/1341 Mathematical Practices: 4
CCSS 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. 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. Vocabulary
Double box plot Double dot plot
Resources
Glencoe: Chapter 10.4 LTF: Module 3 Box‐and‐Whisker Plot
ABC: Chapter 14
On Core: Lessons 6‐3
Hands On: p. 136
Gizmos: Constructing Box‐and‐Whisker Plots – Sight vs. Sound Reactions Assessments (Calculator)
http://www.illustrativemathematics.org/illustrations/1340 http://www.illustrativemathematics.org/illustrations/1341 Mathematical Practices: 4
Investigate chance processes and develop, use and evaluate probability models. CCSS 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. Vocabulary
Probability Outcome Simple event
Random Complementary events
Fundamental counting principal Resources
Glencoe: Chapter 9.1, 9.5 LTF: Module 6 Bulls Eye ABC: Chapter 15
On Core: Lessons 7‐1
Hands On: p. 139 Gizmos: Geometric Probability ‐ Activity A – Probability Simulations
Theoretical and Experimental Probability Assessments (Calculator)
http://www.illustrativemathematics.org/illustrations/1216 http://www.illustrativemathematics.org/illustrations/1521 Mathematical Practices: 4
http://www.illustrativemathematics.org/illustrations/1047 CCSS 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. 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. Resources
LTF: Module 6 Using Area to Estimate Probability ABC: Chapter 15
On Core: Lessons 7‐2, 7‐3
Hands On: p. 143
Gizmos: Theoretical and Experimental Probability
Assessments (Calculator)
Mathematical Practices: 4 CCSS 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. Vocabulary
Probability Outcome Simple event Random
Complementary events
Uniform probability model
Theoretical probability
Experimental probability Resources
Glencoe: Chapter 9.1, 9.2 ABC: Chapter 15
Hands On: p. 145
Assessments (Calculator)
http://www.illustrativemathematics.org/illustrations/1216 http://www.illustrativemathematics.org/illustrations/1022 Mathematical Practices: 4
CCSS 7.SP.7a: Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. Vocabulary
Probability Outcome Simple event Random Complementary events
Uniform probability model
Theoretical probability
Experimental probability Resources
Glencoe: Chapter 9.1, 9.2 LTF: Module 6 Movie Probability
ABC: Chapter 15
On Core: Lessons 7‐2, 7‐3 Assessments (Calculator)
Mathematical Practices: 4 Hands On: p. 145
Gizmos: Probability Simulations
CCSS 7.SP.7b: Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open‐end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies? Vocabulary
Uniform probability model Theoretical probability
Experimental probability
Resources
Glencoe: Chapter 9.2 ABC: Chapter 15
On Core: Lessons 7‐3
Hands On: p. 145
Assessments (Calculator)
Mathematical Practices: 4 CCSS 7.SP.8: 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? Vocabulary
Sample space Tree diagram Compound event
Simulation
Fundamental counting principal Permutation
Independent events
Dependent events Resources
Glencoe: Chapter 9.3, 9.4, 9.5, 9.6, 9.7 ABC: Chapter 15
On Core: Lessons 7‐4, 7‐5
Hands On: p. 148
Assessments (Calculator)
http://www.illustrativemathematics.org/illustrations/890 http://www.illustrativemathematics.org/illustrations/343 Mathematical Practices: 4
CCSS 7.SP.8a: Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.
Vocabulary
Sample space Tree diagram Compound event
Fundamental counting principal
Permutation
Independent events
Dependent events Resources
Glencoe: Chapter 9.3, 9.5, 9.6, 9.7 ABC: Chapter 15
On Core: Lessons 7‐4
Hands On: p. 148
Gizmos: Compound Independent Events
Assessments (Calculator)
http://www.illustrativemathematics.org/illustrations/885 Mathematical Practices: 4
CCSS 7.SP.8b: Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event. Vocabulary
Sample space Tree diagram Compound event
Fundamental counting principal Independent events
Dependent events
Resources
Glencoe: Chapter 9.3, 9.5, 9.7 LTF: Module 6 Family Fun (Binomial Probability)
ABC: Chapter 15
On Core: Lessons 7‐4 Hands On: p. 148
Gizmos: Permutations – Permutations and Combinations Assessments (Calculator)
http://www.illustrativemathematics.org/illustrations/885 Mathematical Practices: 4, 5
CCSS 7.SP.8c: Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood? Vocabulary
Simulation Resources
Glencoe: Chapter 9.4 ABC: Chapter 15 On Core: Lessons 7‐5
Hands On: p. 148
Assessments (Calculator)
Mathematical Practices: 4, 5 Gizmos: Compound Independent Events – Compound Independent and Dependent Events *
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Grand County
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Mrs. Martin Pre test Unit2
Name________________________
Date_________________________
Class_________________________
1: Half a pound of flour is poured into a jar. If it occupies two fifths of the jar, what
quantity of flour could be stored in the jar?
0.5 pounds
0.75 pounds
1 pound
1.25 pounds
2: Three fourths of two thirds of a meter is:
one fourth of a meter
one third of a meter
half a meter
one meter and a half
3: Line v in the coordinate graph below represents the distance in time travelled by a
vehicle. What is the distance travelled after 75 minutes?
50 miles
60 miles
70 miles
75 miles
4 and 5: The revenue of an online store is proportional to the monthly marketing
budget of the store, as can be seen in the table below:
Month
Marketing Budget($) Online Revenue($)
January 105,000
262,500
February 140,000
350,000
March
70,000
175,000
April
140,000
350,000
The constant of proportionality between the online revenue and the marketing budget
is
. If the marketing budget for the month of May was $128,000, the online
revenue of the same month was $
.
6: If the average duration of a song on a CD is x, the number of songs on the CD is n,
and the total duration of the songs from the CD is q, then:
x = n/q
x = q/n
x = qn
n = xq
7: A school has 500 students and 30 English teachers and 20 math teachers. The ratio
between the number of math teachers and the number of students of the school
is
0
0
0
0.04
0.06
0.1
0
25
8: In the coordinate plane below, the equation of the line that passes through the
points O(0,0) and A(1,n) is:
n = x/y
x = ny
y = nx
y = n/x
Math7Martin Name______________
TestReviewChapter3(usethespacsbelowforexamples)
Fractions Addition and Subtraction o Must have common denominators o Order doesn’t matter in addition but does matter in subtraction o Use the number line to help you solve negative and positive integers Multiplication and Division o Multiply the numerator by the numerator and the denominator by the denominator o Simplify o Change mixed numbers to improper fractions o When dividing, use the reciprocal of the divisor and multiply the two fractions. Decimals Adding and Subtracting  Line up decimals  Remember the rules of integers when adding and subtracting negative and positive numbers Multiplying Decimals  You must have same number of decimals in your answer as your question. Dividing Decimals 

When dividing a number by a decimals change the divisor to an integer then change the dividend by the same amount (adding zeros if necessary). Line up the answer on the dividing bracket and make sure to put the zero where it should be on the bar. Collecting Like Terms Make sure that the terms have the same letter and the same power then add the coefficient (number in front of the variable). Solving one step equations Use inverse operations to isolate the variable. Do the same to both sides to keep the equation balanced Quiz1
Mrs.MartinMath7
Name __________________________ _ Date ________________ Evaluate each expression for the given values of the variables 1. 7(x + 4) for x = 5 2. 11 – n ÷ 3 for n = 6 3. p + 6r2 for p = 11 and r = 3 4. 8 – (6x/y) + 2x for x = 2 and y = 4 Translate words into Math 5. The quotient of a number and 15 6. 3 plus the product of a number and 8 Simplify 7. 2y + 5y2 – 2y2 8. 10 + 9b – 6a –b Extra Credit Write an expression for the perimeter of the given figure, then simplify the expression Mrs.Martin Math7 Name________________________________________ Quiz2
Period______________________
Solvetheequationandshowyourwork! Answer
1. 3 + ‐7 = ____________ 2. ‐14 – 23 = ____________ 3. ‐45 + 36 = ____________ 4. 17 – (‐3) = ____________ 5. 14 – 14 = ____________ IntegerQuiz
Name __________________________________ Period_________________________ Show all your work 1. Solve ‐9 + n = 15 2. John bought 25 trading cards of which 19 were sports cards. What portion of the cards were sports cards (percent). 3. Solve ¾ ‐ 2/3 = 4. Find the decimal and percent of 6/19. 5. Divide and answer in simplest form 12 1/3 ÷ 3 1/8= IntegerQuiz(2)
Name __________________________________ Period_________________________ Show all your work 1. Solve 14 + x = ‐37 2. John bought dinner at Milts and the bill for the food and drink was $6.75. If he paid tax of 7% and a tip of 15% what is the total amount he paid? 3. Solve 2/7 – 4 2/3 = 4. Solve and answer is simplest fraction form 14/15 ÷ 3/5 = 5. Solve ‐8.5 + 3.527 = Name _______________________________________ Period _______________
Quiz6.2
Name_______________________________________ Period______________________
Use 1% or 10% to estimate the percent of a number 1. 4% of 220 Write an equivalent equation that does not contain fractions. Then solve the equation. 2. 4/5x + 4 = ½ Solve 3. Joy earns $9.75 per hour. Joy works 3 hours one day, and then 7 hours the next day. Use the distributive property to write equivalent expressions showing two ways to calculate Joy’s total earnings. Then solve. Quiz7.1 Name______________________________
Period______________
Usingthe1stdatasheetdeterminetherange,mean,mode,andmedian,and
thencreateaboxandwhiskersplot.
Dothisforthe2ndsetofdata.
Answerthefollowingquestionsfromtheboxandwhiskerplots
1. Which set has a greater interquartile range? 2. Which set has a greater median? 3. What would you consider outliers? 4. Looking at the two plots what conclusion can you make about the 2nd try? Mrs. Martin Math 7
Unit1
Name________________________
Date_________________________
Class_________________________
Vocabulary
Division
Multiplication
Place value
Product
quotient
1. The operation that gives the quotient of two numbers is ______________.
2. The _________ of the digit 3 in 4,903,6725 is thousands.
3. The operation that gives the product of two numbers is _______________,
4. The equation 15 / 3 = 5, the _________ is 5.
Give place value of the digit 4 in each number
5. 4,092
ex: thousands
6. 608,241
_____________
7. 7,040,000
_____________
8. 34,506,123
_____________
Find each product
9.
2x2x2
_____________
10. 10 x 10 x 10 x 10
_____________
11. 3 x 3 x 5 x 5
_____________
Find each quotient
12. 49 ÷ 7
_____________
13. 54 ÷ 9
_____________
14. 88 ÷ 8
_____________
Add, subtract, multiply, or divide
15. 425 + 12=
_____________
16. 62 - 47=
_____________
17. 62 x 42 =
_____________
18. 624 ÷ 7 =
_____________