Download Overview of Math Standards

Manhattan-Ogden USD 383 – Math Curriculum Design Map – Grade 7
Grade 7
Welcome to math curriculum design maps for ManhattanOgden USD 383, striving to produce learners who are:
•
•
•
•
•
•
Effective Communicators who clearly express ideas and effectively
communicate with diverse audiences,
Quality Producers who create intellectual, artistic and practical products
which reflect high standards
Complex Thinkers who identify, access, integrate, and use available
resources
Collaborative Workers who use effective leadership and group skills to
develop positive relationships within diverse settings.
Community Contributors who use time, energies and talents to improve
the welfare of others
Self-Directed Learners who create a positive vision for their future, set
priorities and assume responsibility for their actions. Click here for more.
Overview of Math Standards
Teams of teachers and administrators comprised the pK-12+ Vertical
Alignment Team to draft the maps below. The full set of Kansas College and
Career Standards (KCCRS) for Math, adopted in 2010, can be found here.
To reach these standards, teachers use Math in Focus curriculum, resources,
assessments and supplemented instructional interventions with additional
websites and app for specific skills.
1
Standards of 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. Click here for more.
Additionally, educators strive to provide math instruction centered on:
1: Focus - Teachers significantly narrow and deepen the scope of how time
and energy is spent in the math classroom. They do so in order to focus
deeply on only the concepts that are prioritized in the standards.
2: Coherence - Principals and teachers carefully connect the learning within
and across grades so that students can build new understanding onto
foundations.
3: Fluency - Students are expected to have speed and accuracy with simple
calculations; teachers structure class time and/or homework time for
students to memorize, through repetition, core functions.
4: Deep Understanding - Students deeply understand and can operate
easily within a math concept before moving on. They learn more than the
trick to get the answer right. They learn the math.
5: Application - Students are expected to use math concepts and choose the
appropriate strategy for application even when they are not prompted.
6: Dual Intensity - Students are practicing and understanding. There is
more than a balance between these two things in the classroom – both are
occurring with intensity. Click here for more.
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Grade 7
Essential
Questions
Unit/Chapter
KCCRS Standards
Vocabulary
1. The Real Number
System –
Representing
Rational Numbers on
the Number Line,
Writing Rational
Numbers as
Decimals, Introducing
Irrational Numbers,
Introducing the Real
Number System
OMIT 1.5
* Significant Digits
(this section is not
taught – not
emphasized in
standards)
2. Rational Number
Operations – Adding
Integers, Subtracting
Integers, Multiplying
and Dividing Integers,
Operations with
Integers, Operations
with Rational
Numbers, Operations
with Decimals
The Number System
7.NS.3 Apply and extend previous
understandings of operations with
fractions to add, subtract, multiply, and
divide rational numbers. Solve realworld and mathematical problems
involving the four operations with
rational numbers
opposites
set of integers
negative integers
positive integers
negative fractions
rational numbers
terminating decimal
repeating decimal
irrational numbers
approximate
real number
real number line
significant digits
precise
How can real numbers be
represented and used to
solve real-world
problems?
The Number System
7.NS.1a-d. 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.
7.NS.2a-c. Apply and extend previous
understandings of multiplication and
division and of fractions to multiply and
divide rational numbers.
7.NS.2d. Convert a rational number to a
decimal using long division.
additive inverse
zero pair
complex fraction
least common
denominator
How can operations of
addition, subtraction,
multiplication be applied
to rational numbers,
including negative
numbers?
1
Resources
I Can
Learning Targets
No calculator in
this chapter/
standard
7.NS.3
I can apply and extend
understandings of
operations with fractions
to add, subtract, multiply
and divide rational
numbers.
I can solve real world
problems involving the
four operations with
rational numbers.
Can you reverse the order
of rational numbers when
performing any operation
and still get the same
answer?
How do operations with
integers compare to
7.NS.1a-d
Green Textbook
A page 165
colored
counters No
calculator
Number lines
KCCRS flipbook
grade 7
additional
tools/resources
listed on page
26.
7.NS.2a-d
7.NS.1a-d
I can add and subtract
rational numbers.
I can represent addition
and subtraction on a
horizontal or vertical
number line diagram.
7.NS.2a-d
I can multiply and divide
rational numbers.
I can convert a rational
number to a decimal using
long division.
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Grade 7
Unit/Chapter
KCCRS Standards
Vocabulary
Essential
Questions
operations with rational
numbers?
3. Algebraic
Expressions – Adding
Algebraic Terms,
Subtracting Algebraic
Terms, Simplifying
Algebraic
Expressions,
Expanding Algebraic
Expressions,
Factoring Algebraic
Expressions, Writing
Algebraic
Expressions, RealWorld Problems:
Algebraic Reasoning
Expressions and Equations
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.
7.EE.3. Solve real-life and mathematical
problems using numerical and algebraic
expressions and equations. Solve multistep real-life and mathematical
problems posed with positive and
negative rational numbers in any form
4. Algebraic
Equations and
Inequalities –
Understanding
Equivalent Equations,
Solving Algebraic
Equations, Real-
Expressions and Equations
7.EE.1. Use properties of operations to
generate equivalent expressions. Apply
properties of operations as strategies to
add, subtract, factor, and expand linear
expressions with rational coefficients.
2
algebraic expression
How does the opposite of
n differ from the absolute
value of n? How are
properties useful in
solving a variety of
problems?
How can algebraic
expressions containing
rational numbers and
several variables be
simplified, expanded, or
factored to write
equivalent expressions?
How do operations on
rational numbers serve as
a foundation for creating
expressions?
*NOTE- equations are addressed in
Chapter 4
How many ways can
equivalent expressions be
written?
equivalent
equations
solution set
equivalent
inequalities
How can algebraic
equations and inequalities
be used to model
mathematical or realworld situations and to
find the values of
variables?
Resources
I Can
Learning Targets
KCCRS flipbook
grade 7
additional
tools/resources
listed on page
28.
7.EE.2
KCCRS flipbook
grade 7
additional tools
resources page
35.
7.EE.3
KCCRS flipbook
grade 7
additional tools
resources page
39.
7.EE.1
KCCRS flipbook
grade 7
tools/resources
page 33.
7.EE.4a-b
7.EE.2/7.EE.3
I can rewrite an
expression in different
forms.
I can identify equivalent
expressions.
I can use the distributive
property to simplify
algebraic expressions.
I can factor algebraic
expressions to show the
components of the
expression.
7.EE.1
I can solve real-life
problems using numerical
and algebraic expressions
in equations.
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Grade 7
Unit/Chapter
World Problems:
Algebraic Equations,
Solving Algebraic
Inequalities, RealWorld Problems:
Algebraic Inequalities
KCCRS Standards
Vocabulary
7.EE.4a-b. 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.
Essential
Questions
How do operations on
rational numbers serve as
a foundation for creating
numerical and algebraic
expressions, equations,
and inequalities?
Resources
I Can
Learning Targets
KCCRS flipbook
grade 7
tools/resources
page 42.
I can perform the
operations to add,
subtract, factor and
expand linear expressions
with rational coefficients.
7.EE.4a-b
I can use variables to
construct simple
equations and inequalities
to solve problems.
How many ways can
equivalent numerical and
algebraic expressions,
equations, and
inequalities be written?
5. Direct and Inverse
Proportion –
Understanding Direct
Proportion,
Representing Direct
Proportion
Graphically, Solving
Direct Proportion
Problems
* Understanding
Inverse Proportion
(this section is not
taught – not
3
Ratios and Proportional Relationships
7.RP.1. Analyze proportional
relationships and use them to solve realworld and mathematical problems.
Compute unit rates associated with
ratios of fractions, including ratios of
lengths, areas and other quantities
measured in like or different units.
7.RP.2a-d. Recognize and represent
proportional relationships between
quantities.
7.RP.3. Use proportional relationships to
solve multistep ratio and percent
problems
direct proportion
proportion
constant of
proportionality
cross products
inverse proportion
Can an expression,
equation, or inequality be
written to represent every
real-life and mathematical
problem?
What are the
types/varieties of
situations in life that
depend on or require the
application of ratios and
proportional reasoning?
How can two quantities
that are in a proportional
relationship be used to
solve real-world and
mathematical problems?
I can solve multi-step
equations.
7.RP.1
KCCRS flipbook
grade 7
additional
tools/resources
page 15.
7.RP.2a-d
KCCRS flipbook
grade 7
additional
tools/resources
page 19.
7.RP.1
I can use proportions to
solve real-world problems.
I can compute the unit
rates using measurements
in like or unlike units.
7.RP.2a-d
I can recognize
proportional relationships
between quantities.
7.RP.3
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Grade 7
Unit/Chapter
KCCRS Standards
Vocabulary
Essential
Questions
emphasized in
standards)
6. Angle Properties
and Straight Lines –
Complementary/Sup
plementary/and
Adjacent Angles,
Angles that Share a
Vertex, Alternate
Interior/Alternate
Exterior/and
Corresponding
Angles, Interior and
Exterior Angles
7. Geometric
Construction –
Constructing Angle
Bisectors,
Constructing
Perpendicular
Bisectors,
4
Geometry
7.G.1. 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.
7.G.5. Use facts about supplementary,
complementary, vertical, and adjacent
angles in a multi-step problem to write
and use them to solve simple equations
for an unknown angle in a figure.
Geometry
7.G.1. Draw, construct, and describe
geometrical figures and describe the
relationships between them.
7.G.2. Draw (freehand, with ruler and
protractor, and with technology)
geometric shapes with given conditions.
complementary
angles
supplementary
angles
adjacent angles
vertical angles
congruent angles
transversal
alternate interior
angles
alternate exterior
angles
corresponding
angles
interior angles
exterior angles
How do geometric
relationships and
measurements help us to
solve problems and make
sense of our world?
bisector
equidistant
bisect
straightedge
perpendicular
bisector
midpoint
How can triangles and
quadrilaterals be
constructed using a
compass, a protractor,
and a straightedge?
How can angles formed on
a line, or by parallel lines
and a transversal have
special properties that are
useful in solving realworld problems?
Resources
I Can
Learning Targets
7.RP.3
KCCRS flipbook
grade 7
additional
tools/resources
page 22.
I can solve multi-step ratio
and percent problems.
7.G.1
KCCRS flipbook
grade 7
additional
tools/resources
page 46.
7.G.1
I can solve problems with
scale drawings of
geometric figures by
computing the actual
lengths and areas.
7.G.5
KCCRS flipbook
grade 7
additional
tools/resources
page 57.
7.G.5
I can distinguish the
difference between
supplementary,
complementary, vertical
and adjacent angles.
7.G.1
KCCRS flipbook
grade 7
additional
tools/resources
page 46.
I can use the properties of
angles to solve simple
equations for an unknown
angle in a figure.
7.G.1
I can draw, construct and
describe geometric figures
and attributes’
7.G.2
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Grade 7
Unit/Chapter
KCCRS Standards
Constructing
Triangles,
Constructing
Quadrilaterals,
Understanding Scale
Drawings
Focus on constructing triangles given
three measures of angles and sides.
7.G.3. Describe the two-dimensional
figures that result from slicing threedimensional figures, as in plane sections
of right rectangular prisms and right
rectangular pyramids.
included side
included angle
scale
scale factor
Geometry
7.G.4 Solve real-life and mathematical
problems involving angle measure, area,
surface area, and volume. 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.
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.
cylinder
lateral surface
sphere
plane
cone
slant height
hemisphere
cross section
volume
surface area
Statistics and Probability
measure of
variation
8. Volume and
Surface Area of
Solids – Recognizing
Cylinders/Cones/Sph
eres/and Pyramids,
Finding Volume and
Surface Area of
Cylinders, Finding
Volume and Surface
Area of Pyramids and
Cones, Finding
Volume and Surface
Area of Spheres,
Real-World Problems:
Composite Solids
* (surface area and
volume – cubes and
right prism)
9. Statistics –
Interpreting Quartiles
5
Vocabulary
Essential
Questions
How are constructions of
triangles and
quadrilaterals used in the
real-world?
How do geometric
relationships and
measurements help us to
solve problems and make
sense of our world?
How are the measures of
attributes that
characterize two- and
three-dimensional
geometric figures, for
example angles, the same
and/or different?
How can measures of
central tendency and
Resources
I Can
Learning Targets
7.G.2
KCCRS flipbook
grade 7
additional
tools/resources
page 48.
I can construct geometric
shapes using a straightedge, protractor and
compass.
7.G.3
KCCTS flipbook
grade 7
additional
tools/resources
page 51.
7.G.4
KCCRS flipbook
grade 7
additional
tools/resources
page 55.
7.G.6
KCCRS flipbook
additional
tools/resources
page 60.
7.SP.1
7.G.3
I can describe the twodimensional figure that
results from slicing a three
dimensional figure.
7.G.4
I can recognize and use
the appropriate formula
to find surface area and
volume.
7.G.6
I know the formulas for
area and circumference of
a circle.
I know that surface area is
the sum of the area of the
faces of a threedimensional object.
7.SP.1
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Grade 7
Unit/Chapter
and Interquartile
Range, Stem-andLeaf Plots,
Understanding Box
Plots and Mean
Absolute Deviation,
Understanding
Random Sampling
Methods, Making
Inferences About
Populations
10. Probability –
Defining
Outcomes/Events/an
d Sample Space,
Finding Probability of
Events,
6
KCCRS Standards
Vocabulary
7.SP.1. Use random sampling to draw
inferences about a population.
Understand that statistics can be used
to gain information about a population
by examining a sample of the
population.
7.SP.2. Use data from a random sample
to draw inferences about a population
with an unknown characteristic of
interest.
7.SP.3. Draw informal comparative
inferences about two populations.
Informally assess the degree of visual
overlap of two numerical data
distributions with similar variability.
7.SP.4. Use measures of center and
measures of variability for numerical
data
first quartile
second quartile
upper quartile
range
lower quartile
third quartile
interquartile range
stem-and-leaf plot
box plot
box-and-whisker
plot
5-point summary
mean absolute
deviation
population
sample size
unbiased sample
simple random
sampling
systematic random
sampling
sample
random sample
biased sample
stratified random
sampling
inference
outcome
event
sample space
probability
biased
mutually exclusive
Statistics and Probability
7.SP.5. Investigate chance processes and
develop, use, and evaluate probability
models. Understand that the probability
of a chance event is a number between
Essential
Questions
measures of variations be
used to draw conclusions
about populations?
How can we use data from
random samples to make
important decisions, or to
accurately anticipate
future outcomes?
How can data be used to
inform, mislead, and/or
persuade people?
Resources
I Can
Learning Targets
KCCRS flipbook
grade 7
additional
tools/resources
page 63.
I can use random sampling
to draw inferences about
populations.
7.SP.2
KCCRS flipbook
grade 7
additional
tools/resources
page 65.
7.SP.3
KCCRS flipbook
grade 7
additional
tools/resources
page 69.
7.SP.2
I understand how to
analyze data to draw
inferences.
7.SP.3
I can compare two
populations and describe
with similar variability.
7.SP.4
I can use measures of
central tendency and
variability.
7.SP.4
KCCRS flipbook
grade 7
additional
tools/resources
page 69.
How can you use
probability to describe
how likely an event is to
occur?
7.SP.5
KCCRS flipbook
grade 7
additional
tools/resources
page 72.
7.SP.5
I can understand
probability as a number
between 0 and 1.
2016-17 Manhattan-Ogden USD 383 – Math Year at a Glance – Grade 7
Unit/Chapter
Approximating
Probability and
Relative Frequency,
Developing
Probability Models
KCCRS Standards
Vocabulary
0 and 1 that expresses the likelihood of
the event occurring.
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
7.SP.7a. Develop a probability model
and use it to find probabilities of events.
7.SP.8. Find probabilities of compound
events using organized lists, tables, tree
diagrams, and simulation
complement
fair
Venn diagram
complementary
events
relative frequency
experimental
probability
observed frequency
theoretical
probability
probability model
probability
distribution
uniform probability
model
non-uniform
probability model
Essential
Questions
Supplement KCCRS 7.SP.7b probability model and 8.SP.8c design and use simulation for compound events
7
Resources
7.SP.6
KCCRS flipbook
grade 7
additional
tools/resources
page 77.
7.SP.7a
KCCRS flipbook
grade 7
additional
tools/resources
page 79
7.SP.8
KCCRS grade 7
additional
tools/resources
page 82
I Can
Learning Targets
I can evaluate probability
models.
7.SP.6
I can approximate the
probability by collecting
data.
7.SP.7a
I can develop a probability
model.
7.SP.8
I can find the probabilities
of compound events.