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GRADE 8 – CURRICULUM MAP – CCSS – 2012-13
UNIT 1 – NUMBER SENSE AND OPERATIONS REVIEW
Critical Area
Time Frame
Connections to prior
learning
Connections to future
learning
Additional Notes
Practice Standards
Essential Questions
-Number Sense & Operations
10 Days
-All units previously covered
-This unit will be taught in 2012 – 2013 and will be good review in future years
-Additional tasks and test items can be found at www.map.mathshell.org
-SMP1 – Problems
-SMP6 – Precision
What in the world are rational numbers and how and when do we use them?
Content Standards
6.NS.4a
7.NS.1b
Apply number theory concepts,
including prime factorization and
relatively prime number, to the
solution of problems.
Impact 2004
Impact 2009
Other
Greatest Common Factor
Lesson
Impact Course
2 2004 3.1.1
Vocab
Assessment
ESSENTIAL:
Integer, Absolute
Value, Rational
Numbers,
Expressions,
Equations
Understand p + q as the number
located a distance |q| from p, in the
positive to negative direction
depending on whether q is positive or
negative. Show that a number and its
opposite have a sum of o (additive
inverses). Interpret sums of rational
numbers by describing real-world
contexts.
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August 16, 2012
GRADE 8 – CURRICULUM MAP – CCSS – 2012-13
7.NS.1
7.EE.3
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.
NLVM
- Circle 3
- Circle 21
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 as strategies to calculate
with numbers in any form; convert
between forms as appropriate; and
assess the reasonableness of
answers using mental computation
and estimation strategies
Illustrative
Mathematics Tasks
- Discounted Books
- Shrinking
Illustrative
Mathematics Tasks
- Comparing Freezing
Points,
- Distances on the
Number Line 2,
- Operations on the
Number Line
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August 16, 2012
GRADE 8 – CURRICULUM MAP – CCSS – 2012-13
UNIT 2 – RADICALS AND EXPONENTS
Critical Area
Time Frame
Connections to prior
learning
Connections to future
learning
Additional Notes
Practice Standards
Essential Questions
- 8NS1 and 2 are supporting clusters while the rest are major clusters.
20 days
6th grade: whole numbers exponents, rational numbers, absolute value
7th grade: apply and extend understanding of rational numbers
Additional tasks and test items can be found at www.map.mathshell.org
SMP1 – Problems
SMP8 – Repeated Reasoning
8NS1 and 8NS2: How do we recognize and know value of rational numbers?
8EE1 and 8EE2: What effects do exponents and roots (radicals) have on numbers?
8EE3 and 8EE4: How can I make very large and very small numbers more manageable?
Content Standards
8.NS.1
Impact 2004
Understand informally that every
number has a decimal expansion; the
rational numbers are those with
decimal expansions that terminate in
0s or eventually repeat. Know that
other numbers are called irrational.
Course 2:
7.1 & 7.2
Impact 2009
Other
Illustrative Math
Task
-Converting Decimal
Representations of
Rational Numbers to
Fraction
Representations
-Identifying Rational
Numbers
Vocab
Assessment
ESSENTIAL:
Radicals, Irrational
Numbers
IMPORTANT:
Exponent, Base,
Power
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August 16, 2012
GRADE 8 – CURRICULUM MAP – CCSS – 2012-13
8.NS.2
8.EE.2
8.EE.1
8.EE.3
Illustrative Math
Task
-Estimating Square
Roots
Use rational approximations of
irrational numbers to compare the
size of irrational numbers, locate them
approximately on a number line
diagram, and estimate the value of
expressions (e.g., p2). For example,
by truncating the decimal expansion
of show that is between 1 and 2, then
between 1.4 and 1.5, and explain how
to continue on to get better
approximations.
Use square root and cube root
symbols to represent solutions to
equations of the form x2 = p and x3 =
p, where p is a positive rational
number. Evaluate square roots of
small perfect squares and cube roots
of small perfect cubes. Know that is
irrational.
Many Tasks on this
link:
Comparing rational
and irrational
numbers, Irrational
numbers on the
number line.
Course 3
4.3
Know and apply the properties of
integer exponents to generate
equivalent numerical expressions.
For example,
32 × 3–5 = 3–3 = 1/(3)3 = 1/27.
Course 3
4.1
Use numbers expressed in the form
of a single digit times an integer
power of 10 to estimate very large or
Course 3
4.1
Illustrative Math
Task
- The Ant and
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GRADE 8 – CURRICULUM MAP – CCSS – 2012-13
8.EE.4
very small quantities, and to express
how many times as much one is than
the other. For example, estimate the
population of the United States as 3 ×
108 and the population of the world as
7 × 109, and determine that the world
population is more than 20 times
larger.
Elephant
Perform operations with numbers
expressed in scientific notation,
including problems where both
decimal and scientific notation are
used. Use scientific notation and
choose units of appropriate size for
measurements of very large or very
small quantities (e.g., use millimeters
per year for seafloor spreading).
Interpret scientific notation that has
been generated by technology.
Powers Of Ten –
Outer Space to Atom
Course 3
4.1
Illustrative Math
Task
-Giant Burgers
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August 16, 2012
GRADE 8 – CURRICULUM MAP – CCSS – 2012-13
UNIT 3 – CONGRUENCE AND SIMILARITY USING TRANSFORMATIONS
Critical Area
Time Frame
Connections to prior
learning
Connections to future
learning
Additional Notes
Practice Standards
Essential Questions
Understand congruence and similarity using physical models, transparencies, or geometry software.
10 Days
Grade 7: Students develop understanding of the special relationships of angles and their measures (complimentary,
supplementary, adjacent, vertical)
-This is a major cluster.
-7G2 is a gap that needs to be taught in 2012-13 Course 1 Impact
-Additional tasks and test items can be found at http://map.mathshell.org
-8G5 is not being tested in 2012-13
-SMP3 – Arguments; SMP4 – Modeling; SMP5 - Tools
How can we use transformations to show similarity or congruence of two-dimensional figures?
Content Standards
8.G.1
8.G.1a
8.G.1b
8.G.1c
Verify experimentally the properties of
rotations, reflections and translation
Impact 2004
Impact 2009
Other
Course 3
6.1, 6.2, 6.3
NLVM: Triangles –
Build similar
triangles by
combining sides
and angles.
a. Lines are taken to lines and line
segments to line segments of the
same length
NLVM: Geoboard –
Coordinate –
Rectangular
geoboard with x
and y coordinates
b. Angles are taken to angles of the
same measure
c. Parallel lines are taken to Parallel
lines
Course 3
6.1, 6.2, 6.3
NLVM:
CompositionDilation
Reflection
Rotation
Translation
Vocab
Assessment Resources
ESSENTIAL:
Transformation,
Rotation, Dilation,
Translation, Similar,
Congruent,
Transversal
IMPORTANT:
Interior Angles, Exterior
Angles, Alternate
Interior Angles,
Alternate Exterior
Angles, Vertical Angles,
Corresponding Angles,
Complementary Angles
and Supplementary
Angles.
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GRADE 8 – CURRICULUM MAP – CCSS – 2012-13
8.G.2
8.G.3
Understand that a two-dimensional
figure is congruent to another if the
second can be obtained from the first
by a sequence of rotations,
reflections, and translations; given
two congruent figures, describe a
sequence that exhibits the
congruence between them.
Describe the effect of dilations,
translations, rotations and reflections
on two-dimensional figures using
coordinates.
8.G.4
Understand that a two-dimensional
figure is similar to another if the
second can be obtained from the first
by a sequence of rotations,
reflections, translations, and dilations;
given two similar two-dimensional
figures, describe a sequence that
exhibits the similarity between them.
8.G.5
Use informal arguments to establish
facts about the angle sum and
exterior angle of triangles, about the
angles created when parallel lines are
cut by a transversal, and the angleangle criterion for similarity of
triangles. For example, arrange three
copies of the same triangle so that the
three angles appear to form a line,
and give an argument in terms of
transversals why this is so.
Course 3 6.1,
6.2, 6.3
Course 3
6.1, 6.2, 6.3
6.3
Course 1 TE 1.2
Extension Problem
Course 3
2.2
Illustrative
Math Task:
-Find the missing
Angle
-Find the Angle
Page 7 of 18
August 16, 2012
GRADE 8 – CURRICULUM MAP – CCSS – 2012-13
UNIT 4 – LINEAR FUNCTIONS
Critical Area
Time Frame
Connections to prior
learning
Connections to future
learning
Additional Notes
Practice Standards
Essential Questions
-Grasp the concept of a function and use to describe quantitative relationships
- This is a MAJOR cluster
25 Days
Grade 5: Graphing and plotting points on a co-ordinate plane
Grade 6: Represent and analyze quantitative relationships between dependent and independent variables
Grade 7: Analyze and solve problems involving ratios and proportions including input and output tables and graphs
Grade 8: Solving systems of equations
Additional test and task items can be found at http://map.mathshell.org
S.MP.2 – Reasoning; S.MP.4 – Modeling; S.MP.7 – Structure
8F1, 2 and 4: What is a function and how can it be modeled?
8EE5 and 6: What mathematical ideas are represented by slope?
SP 1, 2, 3, 4: Why use a scatter plot?
Content Standards
8.F.1
Impact 2004
Understand that a function is a rule
that assigns to each input exactly one
output. The graph of a function is the
set of ordered pairs consisting of an
input and the corresponding output.
(Footnote: Function notation is not
required in Grade 8.)
Impact 2009
Other
NC - Develop an
understanding of
function.
NC – Matching Linear
Functions
n/a
Course 3
10.1
Vocab
Assessment Resources
ESSENTIAL:
Function, Linear,
Slope,
Y-Intercept
IMPORTANT:
Proportional
Relationships, Origin
Page 8 of 18
August 16, 2012
GRADE 8 – CURRICULUM MAP – CCSS – 2012-13
8.F.2
8.F.4
Compare properties of two functions
each represented in a different way
(algebraically, graphically, numerically
in tables, or by verbal descriptions).
For example, given a linear function
represented by a table of values and
a linear function represented by an
algebraic expression, determine
which function has the greater rate of
change.
Construct a function to model a linear
relationship between two quantities.
Determine the rate of change and
initial value of the function from a
description of a relationship or from
two (x, y) values, including reading
these from a table or from a graph.
Interpret the rate of change and initial
value of a linear function in terms of
the situation it models, and in terms of
its graph or a table of values.
Illustrative Math Task
F2 Battery Charging
Course 3
10.1, 10.2
EXPOSURE: Scatter
Plot, Cluster, Outlier,
Association,
Correlation, Line Of
Best Fit
Illustrative Math Task
F4: Baseball Cards
(good intro task)
Course 3
1.1, 1.2, 1.3
Chicken and Steak
Variations 1(good
instructional tool)
A Picture Tells a
Linear Story
Illustrative Math Task
F4: Video Streaming
8.EE.5
Graph proportional relationships,
interpreting the unit rate as the slope
of the graph. Compare two different
proportional relationships represented
in different ways. For example,
compare a distance-time graph to a
distance-time equation to determine
which of two moving objects has
greater speed.
Illustrative Math
Tasks
-Coffee by the Pound
(good intro),
-Comparing Speeds
in Graphs and
Equations,
Course 3
1.1
-Peaches and Plums,
-Sore Throats Var. 2,
-Who has the Best
Job?
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GRADE 8 – CURRICULUM MAP – CCSS – 2012-13
8.EE.6
8.SP.1
8.SP.2
8.SP.3
Use similar triangles to explain why
the slope m is the same between any
two distinct points on a non-vertical
line in the coordinate plane; derive the
equation y =mx for a line through the
origin and the equation y = mx + b for
a line intercepting the vertical axis at
b.
Construct and interpret scatter plots
for bivariate measurement data to
investigate patterns of association
between two quantities. Describe
patterns such as clustering, outliers,
positive or negative association, linear
association, and nonlinear
association.
Know that straight lines are widely
used to model relationships between
two quantitative variables. For scatter
plots that suggest a linear
association, informally fit a straight
line, and informally assess the model
fit by judging the closeness of the
data points to the line.
Use the equation of a linear model to
solve problems in the context of
bivariate measurement data,
interpreting the slope and intercept.
For example, in a linear model for a
biology experiment, interpret a slope
of 1.5 cm/hr as meaning that an
additional hour of sunlight each day is
associated with an additional 1.5 cm
in mature plant height.
Finding Slope of a
Line from Graphs,
Tables and Ordered
Pairs
Course 3
1.2
Similar triangles
Glued to the Tube or
Hooked on a Book
Course 3
2.1
Investigation
4
Impact of a Superstar
Exploring Linear Data
Scatter plots, cluster,
outlier,
association/correlatio
n (positive, negative,
none, linear, nonlinear),
Line of Best Fit
Video 26
Course 3
2.1 Inv. 4
Illustrative Math Task
-Birds' Eggs
Line of best fit
Course 3
2.1 Inv. 4
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GRADE 8 – CURRICULUM MAP – CCSS – 2012-13
8.SP.4
Understand that patterns of
association can also be seen in
bivariate categorical data by
displaying frequencies and relative
frequencies in a two-way table.
Construct and interpret a two-way
table summarizing data on two
categorical variables collected from
the same subjects. Use relative
frequencies calculated for rows or
columns to describe possible
association between the two
variables. For example, collect data
from students in your class on
whether or not they have a curfew on
school nights and whether or not they
have assigned chores at home. Is
there evidence that those who have a
curfew also tend to have chores?
Course 3
2.1 Inv. 4
Page 11 of 18
August 16, 2012
GRADE 8 – CURRICULUM MAP – CCSS – 2012-13
UNIT 5 – FUNCTIONAL RELATIONSHIPS
Critical Area
Time Frame
Connections to prior
learning
Connections to future
learning
Additional Notes
Practice Standards
Essential Questions
- Formulating and reasoning about expressions and equations
7 days
- * vertical alignment question
- 7EE4c. Extend analysis of patterns to include analyzing, extending, and determining an expression for simple arithmetic and
geometric sequences (e.g. compounding, increasing area), using tables, graphs, words, and expressions.
-This is a gap that needs to be addressed in 2012-13. Impact Course 2 2004 Inv. 5.1.
-Additional tests and tasks can be found at http://www.map.mathshell.org
SMP4 – Modeling; SMP7 – Structure
- 8F3: How is a non-linear function different from a linear function?
- 8F5: What is the story behind the graph?
Content Standards
8.F.3
8.F.5
Interpret the equation y = mx + b as
defining a linear function, whose
graph is a straight line; give examples
of functions that are not linear. For
example, the function
A = s2 giving the area of a square as
a function of its side length is not
linear because its graph contains the
points (1, 1), (2, 4) and (3, 9), which
are not on a straight line.
Describe qualitatively the functional
relationship between two quantities by
analyzing a graph (e.g., where the
function is increasing or decreasing,
linear or nonlinear). Sketch a graph
that exhibits the qualitative features of
a function that has been described
verbally.
Impact 2004
Impact 2009
Other
Illustrative Math
Task
-Introduction to
Linear Functions
Vocab
Assessment Resources
ESSENTIAL:
Non-Linear
Course 3
10.1
Course 3
10.1
Illustrative Math
Tasks
-Bike Race
-Riding By The
Library
-Tides
-Velocity vs. Distance
Page 12 of 18
August 16, 2012
GRADE 8 – CURRICULUM MAP – CCSS – 2012-13
UNIT 6 – SOLVING EQUATIONS WITH ONE VARIABLE
Critical Area
Time Frame
Connections to prior
learning
Connections to future
learning
Additional Notes
Practice Standards
Essential Questions
- Strategically choose and efficiently implement procedures to solve linear equations in one variable.
20 days
Grade 6: Reason about and solve one-variable equations and inequalities.
Grade 7: Solve real life and mathematical problems using numerical and algebraic expressions and equations.
- Acts as a stepping stone to solving simultaneous linear equations
- This is the culmination of linear equations. Fluency is expected.
- Additional tasks and test items can be found at http://www.map.mathshell.org
SMP1 – Problems; SMP2 – Reasoning; SMP6 - Precision
8EE7: How does solving one variable linear equation apply to real world problem?
Content Standards
8.EE.7
Solve linear equations in one
variable.
8.EE.7a
Give examples of linear equations
in one variable with one solution,
infinitely many solutions, or no
solutions.Show which of these
possibilities is the case by
successively transforming the given
equation into simpler forms, until an
equivalent equation of the form x =
a, a = a, or a = b results (where a
and b are different numbers).
Solve linear equations with rational
number coefficients, including
equations whose solutions require
expanding expressions using the
distributive property and collecting
like terms.
8.EE.7b
Impact 2004
Course 2,
Chapter 6
Impact 2009
Other
Course 3
7.1
Course 2
Chapter 6
Assessment Resources
ESSENTIAL:
Coefficient, Solution,
Like Terms
Illustrative Math Task
Solving Equations
Course 2
Chapter 6
Vocab
IMPORTANT:
Distributive Property
Course 3 7.1
Illustrative Math Task
-Coupon vs. Discount
Course 3 7.1
-The Sign of
Solutions
Page 13 of 18
August 16, 2012
GRADE 8 – CURRICULUM MAP – CCSS – 2012-13
UNIT 7 – PYTHAGOREAN THEOREM
Critical Area
Time Frame
Connections to prior
learning
Connections to future
learning
Additional Notes
Practice Standards
Essential Questions
-Understanding and applying the Pythagorean Theorem
-10 Days
-6th and 7th grade: Solve real life and mathematical problems involving area
-This unit supports grade level work with irrational numbers.
- Additional tasks and test items can be found at http://www.map.mathshell.org
-SMP3 – Arguments; SMP5 - Tools
-How can our understanding of the Pythagorean Theorem affect our understanding of the world around us?
Content Standards
8.G.6
Impact 2004
Explain a proof of the Pythagorean
Theorem and its converse.
Course 2 7.3
8.G.7
Apply the Pythagorean Theorem to
determine unknown side lengths in
right triangles in real world and
mathematical problems in two and
three dimensions.
Impact 2009
Other
Proofs of the
Pythagorean
Theorem
Vocab
Assessment Resources
ESSENTIAL:
Hypotenuse, Leg
IMPORTANT:
Right Triangle
Right Triangle Solver
– Practice finding
unknown sides
Course 2
7.3
NC – Applying the
Pythagorean
Theorem
NC – Real World
Pythagoras
Pythagorean
Theorem in a Math
Context (IT)
8.G.8
Apply the Pythagorean Theorem to
find the distance between two points
in a coordinate system.
Course 2
7.3
Page 14 of 18
August 16, 2012
GRADE 8 – CURRICULUM MAP – CCSS – 2012-13
UNIT 8 – SIMULTANEOUS LINEAR EQUATIONS
Critical Area
Time Frame
Connections to prior
learning
Connections to future
learning
Additional Notes
Practice Standards
Essential Questions
- Use systems of linear equations to represent, analyze and solve a variety of problems.
- 25 days
- Grade 8: Solving linear equations.
Additional tests and tasks can be found at http://www.map.mathshell.org
-SMP1 – Problems; SMP4 - Modeling; SMP6 - Precision
- 8EE8: How can two linear equations simultaneously solve one real world problem?
Content Standards
8.EE.8
Analyze and solve pairs of
simultaneous linear equations.
8.EE.8a
Understand that solutions to a
system of two linear equations in
two variables correspond to points
of intersection of their graphs,
because points of intersection
satisfy both equations
simultaneously.
8.EE.8b
Impact 2004
Impact 2009
Other
Supply and Demand
Tasks
Vocab
Assessment
ESSENTIAL:
Simultaneous,
System,
Point of Intersection
IMPORTANT:
Parallel
Course 3
7.3
Solve systems of two linear
equations in two variables
algebraically, and estimate
solutions by graphing the equations.
Solve simple cases by inspection.
For example, 3x + 2y = 5 and 3x +
2y = 6 have no solution because 3x
+ 2y cannot simultaneously be 5
and 6.
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August 16, 2012
GRADE 8 – CURRICULUM MAP – CCSS – 2012-13
8.EE.8c
Solve real-world and mathematical
problems leading to two linear
equations in two variables. For
example, given coordinates for two
pairs of points, determine whether
the line through the first pair of
points intersects the line through
the second pair.
Page 16 of 18
August 16, 2012
GRADE 8 – CURRICULUM MAP – CCSS – 2012-13
UNIT 9 – Volume Unit and Post MCAS Material
Critical Area
Time Frame
Connections to prior
learning
Connections to future
learning
Additional Notes
Practice Standards
Essential Questions
- Students complete volume work by solving problems involving cones, cylinders and spheres
- 9 days
- Grade 6: Area of a circle
- Grade 7: Surface area of a sphere, volume of a cube, and a right prism
-This is a culminating standard and fluency is expected.
-Additional tasks and test items can be found at www.map.mathshell.org
-6.SP.4 and 6.SP.4a to be done after MCAS in 2012-13 and 2013-14
-6.G.4 needs to be reviewed in 2012-13 and 2013-14
-7.SP.1 and 7.SP.8b need to be covered for 2012-13 after MCAS
SMP4 - Modeling
SMP5 - Tools
SMP6 - Precision
How can the volumes of cones, spheres and cylinders help us solve real world problems?
Content Standards
8.G.9
Know the formulas for the volume of
cones, cylinders, and spheres and
use them to solve real world and
mathematical problems.
Impact 2004
Impact 2009
Chapter 2.3
& The Soft
drink
Promotion
Course 2,
Chapter 5.1
Other
Finding Surface Area
and Volume
Blue Cube, 27 Little
Cubes (Stella
Stunner)
Vocab
Assessment Resources
ESSENTIAL:
Cone,
Sphere
IMPORTANT:
Volume,
Cylinder
Volume of Spheres
and Cones (Rich
Problem)
6.SP.4
Display numerical data in plots on a
number line, including dot plots,
histograms, and box plots.
Use supplementary
materials
Page 17 of 18
August 16, 2012
GRADE 8 – CURRICULUM MAP – CCSS – 2012-13
6.SP.4a
Read and interpret circle graphs
Use supplementary
materials
6.G.4
Represent three-dimensional
figures using nets made up of
rectangles and triangles, and use
the nets to find the surface areas of
these figures. Apply these
techniques in the context of solving
real-world and mathematical
problems.
Use supplementary
materials
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 produces representative
samples and support valid
inferences.
Use supplementary
materials
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.
Use supplementary
materials
Page 18 of 18
August 16, 2012