Reporting Category: Numbers and Operations
Math: Grade 7
Unit: Accentuate The Negative: Positive and Negative Numbers
Enduring
Understanding and
Essential Questions
Big Idea:
Building an
understanding of
positive and negative
numbers (integers,
fractions, and decimals)
and how they are used in
a real world context.
Essential Question:
How do negative and
positive numbers help in
describing a situation?
Concepts & Eligible Content
Competencies
Use appropriate notation
to indicate positive
and negative numbers.
Compare and order
M7.A.1.2.1 Compare and/or
rational numbers.
order integers, mixed numbers,
fractions and decimals (fractions
and decimals may be mixed – no
more than 5 numbers in a set to
be ordered).
M7.A.1.2.2 Locate/identify
decimals, fractions, mixed
numbers and/or integers on a
number line (a mix of these
number forms may be on the
same number line).
Locate rational numbers
(positive and negative
fractions and decimals
and zero) on a number
line.
Understand the
relationship between a
positive or negative
number and its opposite
(additive inverse).
M7.A.2.1.1 Use the order of
operations to simplify numerical
expression (may use parenthesis,
brackets, +, -, x, ÷, squares up to
102 and cubes up to 43 whole,
numbers only.
Develop algorithms for
adding, subtracting,
multiplying, and dividing
positive and negative
numbers.
Suggested Length: 5-6 weeks
Key Vocabulary
absolute value
additive inverse
Associative
Property
Commutative
Property
Distributive
Property
expanding
factoring
integers
negative numbers
opposites
order of
operations
positive numbers
quadrant
rational numbers
Suggested
activities/labs and
assessments (formative
& summative)
Accentuate The
Negative textbook
Launch
-Discussion
-Pre-assessment
Explore
-Investigation
-Group Activity
Summarize
-Discussion
-Post-assessment
Quizzes
Check Ups
Self-Assessments
Unit Test
Unit Projects
Write mathematics
sentences to show
relationships.
M7.A.3.2.2 Solve problems
involving addition and
subtraction of integers.
Write and use related fact
families form
addition/subtraction and
multiplication/division
to solve simple equations
with missing facts.
Use parentheses and
order of operations to
make computational
sequences clear.
Understand and use the
Commutative Property
for addition and
multiplication of positive
and negative numbers.
Apply the Distributive
Property with positive
and negative numbers to
simplify expressions
and solve problems
M7.C.3.1.1 Plot and/or identify
ordered pairs on a coordinate
plane (all four quadrants).
Use positive and negative
numbers to graph in
four quadrants and to
model and answer
questions about applied
settings.
Reporting Category: Measurement; Geometry
Math: Grade 7
Unit: Filling and Wrapping: Three-Dimensional Measurement
Enduring
Understanding and
Essential Questions
Big Ideas:
Interpreting volume as
the number of unit cubes
that fill a 3-dimensional
figure and surface area
as the number of square
units that cover or wrap
the exterior of a 3dimensional figure.
Developing strategies
and algorithms for
finding and comparing
volumes and surface
areas of different 3dimensional figures.
Essential Question:
How are finding and
comparing volumes and
surface are of different
3-dimensional figures
useful in the world?
Concepts & Eligible Content
M7.B.2.1. Develop, use and/or
describe strategies to find the
measure of length, perimeter,
circumference, area or volume.
M7.B.2.1.1 Develop and/or use
strategies to find the perimeter
and/or area of compound figures
(compound figures should only
include quadrilaterals and
triangles). Area formulas
provided on the reference sheet.
Suggested Length: 5-6 weeks
Competencies
Key Vocabulary
Understand volume as a
measure of filling an
object and surface area as
a measure of
wrapping an object
area
base
circumference
cone
congruent
cylinder
dimensions
edge
face
height
length
net
perimeter
pi
prism
pyramid
radius
rectangular prism
sphere
surface area
unit cube
volume
width
Design and use nets to
visualize and calculate
surface areas of prisms
and cylinders
Explore patterns among
the volumes of cylinders,
cones, and spheres
M7.B.2.1.2 Find the
Develop strategies for
circumference and/or area of
circles (formulas provided on the finding the volumes of
square pyramids, prisms,
reference sheet).
cylinders, cones, and
spheres directly and by
comparison with known
M7.B.2.1.3 Find the area of
volumes
triangles and/or all types of
parallelograms (formulas
provided on the reference sheet). Understand that threedimensional figures may
have the same volume
but quite different
surface areas
Understand how changes
in one or more
Suggested
activities/labs and
assessments (formative
& summative)
Filling and Wrapping
textbook
Launch
-Discussion
-Pre-assessment
Explore
-Investigation
-Group Activity
Summarize
-Discussion
-Post-assessment
Quizzes
Check Ups
Self-Assessments
Unit Test
Unit Projects
M7.A.2.2.5 Select and/or use
ratios or proportions to solve
problems.
M7.A.2.2.6 Use proportions to
find the missing length of side in
similar figures.
M7.C.1.1 Define and/or apply
basic properties of two- and
three-dimensional geometric
shapes.
M7.C.1.2 Identify congruence
and/or similarity in polygons.
dimensions of a
rectangular prism or
cylinder
affects the prism’s
volume and surface area
Extend students’
understanding of
similarity and scale
factors to threedimensional figures
Use surface area and
volume to solve a variety
of real-world problems
Reporting Category: Probability
Math : Grade 7
Unit: What Do You Expect? Probability and Expected Value
Enduring
Understanding and
Essential Questions
Big Ideas:
Deepen and expand
understanding on basic
probability concepts by
gathering data,
understanding,
determining, and
reasoning with
theoretical, experimental
probabilities, and
expected value.
Essential Questions:
How can I use
theoretical, experimental
probabilities, and
expected value to help
me make decisions?
Suggested Length: 4-5 weeks
Concepts & Eligible Content
Competencies
Key Vocabulary
M7.E.3.1.1 Find the theoretical
probability of a simple and/or
compound event) answer written
as a fraction in lowest terms –
any compound events should be
independent)
Interpret
experimental and
theoretical
probabilities and the
relationship between
them.
M7.E.3.1.2 Find the theoretical
probability of an event not
occurring (e.g., what is
probability of not rolling a 1 on a
number cube)
Distinguish between
equally likely and
non-equally likely
outcomes.
area model
binomial probability
equally likely
expected value
experimental
probability
fair game
Law of Large
Numbers
outcome
payoff
probability
random
sample space
theoretical
probability
tree diagram
M7.E.3.1.3 Use data displayed
in charts, graphs or tallies to find
experimental probability
Review strategies for
identifying possible
outcomes and
analyzing
probabilities, such as
using lists or tree
diagrams.
Determine if a game
is fair or unfair.
M7.E.4.1.1 Formulate
predictions and/or draw
conclusions based on data
displays or probability
Analyze situations
that involve two
stages (or two
actions).
Use area models to
analyze situations
Suggested
activities/labs and
assessments
(formative &
summative)
What Do You Expect
textbook
Launch
-Discussion
-Pre-assessment
Explore
-Investigation
-Group Activity
Summarize
-Discussion
-Post-assessment
Quizzes
Check Ups
Self-Assessments
Unit Test
Unit Projects
that involve two
stages.
Determine the
expected value of a
probability
situation.
Analyze situations
that involve binomial
outcomes.
Use probability and
expected value to
make decision.
Reporting Category: Data Analysis
Math: Grade 7
Unit: Data Distributions: Describing Variability and Comparing Groups
Enduring
Understanding and
Essential Questions
Concepts & Eligible Content
Competencies
Suggested Length: 5-6 weeks
Key Vocabulary
attribute
bar graph
circle graph
counts
distribution
line plot
mean
Apply the process of median
measures
M7.E.2.1.1 Identify/calculate the statistical
measures of center
investigation
Essential Questions:
mean (average), median, mode
mode
How is data collected,
to pose questions, to
or range of a set of data.
analyzed, and displayed
identify ways data are numerical data
ordered value
to be useful for informed
collected, and to
outlier
decision-making?
determine strategies
for analyzing data in percents
M7.E.2.1.2 Decide/choose
range
order to answer the
which measure of central
relative frequencies
questions
posed.
tendency (mean, median, mode
repeated measures
or range) would be the most
scales
Determine
whether
to
appropriate for a given situation.
stem-and-leaf plot
use the mean or
median to describe a scatter plot
value bar graph
distribution.
variability of a set
Recognize that
variability occurs
whenever data
are collected.
Big Idea :
Collecting, organizing,
displaying and analyzing
data helps us make
informed decisions
about people and the
world around us.
M7.E.1.1.1 Analyze data and/or
answer questions pertaining to
data represented in histograms,
double bar graphs, multiple line
graphs or stem-and-leaf plots.
Use a variety of
representations,
including tables,
bar graphs, and line
plots, to display
distributions.
Describe the
variability in the
distribution of a
Suggested
activities/labs and
assessments (formative
& summative)
Data Distributions
textbook
Launch
-Discussion
-Pre-assessment
Explore
-Investigation
-Group Activity
Summarize
-Discussion
-Post-assessment
Quizzes
Check Ups
Self-assessments
Unit Test
Project: Create your
own design/picture
given data set.
Identify sources of
variability, including
natural variability and
variability that results
from errors in
measurement.
Use the shape of a
distribution to
estimate the location
of the mean and the
median.
Understand and use
counts or percents to
report frequencies of
occurrence of data.
Compare the
distributions of data
sets using their
centers (mean,
median, and mode),
variability (outliers
and range), and shape
(clusters and gaps).
Decide if a difference
among data values or
summary measures
matters.
Develop and use
strategies to compare
data sets to solve
problems.