Download MMS Math 8 Sequencing Map

Milwood Magnet School
Curriculum Sequencing Map
8th Grade Math
Timeline
Big Idea
(Overarching
Topic or Concept)
Enduring
Understandin
gs
Marking Period 1
Week 1-6
Technological
Innovations
“E3: Making life Easy,
Effective and Efficient”
Everything has a price
Essential
Questions
What is a good business
decision?
Scaffolding
Questions
What effect do fixed
and variable costs have
on profitability?
Which linear
representation is most
useful?
How do income and
expense affect
profitability?
GLCEs
MEAP Review - linear (2
weeks)
Solutions, Equations,
and Linear Inequalities
A.FO.08.10 Understand
that to solve the
equation f(x) = g(x)
means to find all values
of x for which the
equation is true, e.g.,
determine whether a
given value, or values
Marking Period 2
Week 7-12
Marking Period 3
Week 13-18
Marking Period 4
Week 19-24
Marking Period 5
Week 25-30
Global Food Chain
Alternative Energies
“Sustaining and improving
food production regionally
and globally”
“Sustainable power for
human benefit”
Medical
Biotechnology
Environmental
Biotechnology
“Improving our Quality of
Life”
“Preserving and Restoring
our environment”
“Adopting a sustainable
quality lifestyle for
ourselves and our
posterity”
Prior knowledge helps
to solve new problems
All choices have
consequences
How do our actions
effect the environment?
Does size matter?
Making choices always
involves compromise
What’s good for you
may not be good for
others
What factors need to be
considered when making
a business decision?
How do outside factors
impact business
operations?
How do you determine
profitability?
What do you need to
consider in managing
your resources?
How is profit represented
graphically?
Solve Problems
Under what
circumstances do you
need to consider
adjusting how you
operate?
How do you use a
graph to justify the
choices you make?
Non-Linear Functions
A.RP.08.01 Identify and
N.FL.08.11 Solve
problems involving ratio
units, such as miles per
hour, dollars per pound,
or persons per square
mile.*
Solutions, Equations, and
Linear Inequalities
A.FO.08.10 Understand
that to solve the equation
represent linear
functions, quadratic
functions, and other
simple functions
including inversely
proportional
relationships (y =
k/x); cubics (y = ax3);
roots (y = √x ); and
exponentials (y = ax ,
Examining current
patterns allows
discovery of future
applications
How do we analyze
relationships in a
system?
How does the pattern of
cell growth impact the
advances in medicine?
How does triangulation
of points help to
determine distances?
Marking Period 6
Week 30-36
Sustainable Systems
How can you use
knowledge about 3
dimensional shapes to
create a sustainable
“green” building?
Do all cells grow at the
same rate?
What is the relationship
between side lengths
and areas?
Numbers & Operations
Numbers & Operations
Volume & Surface Area
N.ME.08.02 Understand
N.ME.08.01 Understand
G.SR.08.06 Know the
meanings for zero and
negative integer
exponents.
the meaning of a square
root of a number and its
connection to the
square whose area is the
number; understand the
meaning of a cube root
and its connection to
the volume of a cube.
N.ME.08.03 Understand
that in decimal form,
rational numbers either
volume formulas for
generalized cylinders,
generalized cones and
pyramids, and apply
them to solve problems.
G.SR.08.07 Understand
the concept of surface
area, and find the
surface area of prisms,
cones, spheres,
pyramids, and
Solve Problems
N.MR.08.07
Understand percent
increase and percent
decrease in both sum
and product form, e.g.,
3% increase of a
quantity x is x + .03x =
What is the relationship
between surface area
and volume?
Milwood Magnet School
Curriculum Sequencing Map
8th Grade Math
from a given set, is a
solution of an equation
(0 is a solution of 3x2 +
2 = 4x + 2, but 1 is not
a solution).
A.FO.08.13 Set up and
solve applied problems
involving simultaneous
linear equations and
linear inequalities.
f(x) = g(x) means to find
all values of x for which
the equation is true, e.g.,
determine whether a
given value, or values
from a given set, is a
solution of an equation (0
is a solution of 3x2 + 2 =
4x + 2, but 1 is not a
solution).
Text: Say It With
Symbols
A.FO.08.11 Solve
simultaneous linear
equations in two variables
by graphing, by
substitution, and by linear
combination; estimate
solutions using graphs;
include examples with no
solutions and infinitely
many solutions.
A.FO.08.12 Solve linear
inequalities in one and
two variables, and graph
the solution sets.
Text: Shapes of Algebra
a > 0); using tables,
graphs, and
equations.*
A.PA.08.02 For basic
functions, e.g., simple
quadratics, direct and
indirect variation, and
population growth,
describe how changes
in one variable affect
the others.
A.RP.08.04 Use the
vertical line test to
determine if a graph
represents a function in
one variable.
Quadratic Functions
A.RP.08.05 Relate
quadratic functions in
factored form and
vertex form to their
graphs, and vice versa;
in particular, note that
solutions of a quadratic
equation are the xintercepts of the
corresponding quadratic
function.
A.RP.08.06 Graph
factorable quadratic
functions, finding
where the graph
intersects the x-axis and
the coordinates of the
vertex; use words
“parabola” and “roots”;
include functions in
vertex form and those
with leading coefficient
–1, e.g., y = x2 – 36, y =
(x – 2)2 – 9; y = – x2; y
1.03x.
N.FL.08.08 Solve
problems involving
percent increases and
decreases.
N.MR.08.09 Solve
problems involving
compounded interest or
multiple discounts.
Text: Growing,
Growing, Growing
terminate or eventually
repeat, and that
calculators truncate or
round repeating
decimals; locate
rational numbers on the
number line; know
fraction forms of
common repeating
decimals
N.ME.08.04 Understand
that irrational numbers
are those that cannot be
expressed as the
quotient of two
integers, and cannot be
represented by
terminating or repeating
decimals; approximate
the position of familiar
irrational numbers, e.g.,
√2, √3, π, on the
number line.
N.FL.08.05 Estimate and
solve problems with
square roots and cube
roots using calculators.
N.FL.08.06 Find square
roots of perfect squares
and approximate the
square roots of non-perfect squares by locating
between consecutive
integers, e.g., √130 is
between 11 and 12.
Pythagorean Theorem
G.GS.08.01 Understand
at least one proof of the
Pythagorean Theorem;
use the Pythagorean
cylinders.
Visualize Solids
G.SR.08.08 Sketch a
variety of twodimensional
representations of threedimensional solids
including orthogonal
views (top, front, and
side), picture views
(projective or
isometric), and nets; use
such two-dimensional
representations to help
solve problems.
Transformation &
Symmetry
G.TR.08.09 Understand
the definition of a
dilation from a point in
the plane, and relate it
to the definition of
similar polygons.
G.TR.08.10 Understand
and use reflective and
rotational symmetries
of two-dimensional
shapes and relate them
to transformations to
solve problems.
Text: Kaleidoscopes,
Hubcaps, and Mirrors,
Filling and Wrapping
Milwood Magnet School
Curriculum Sequencing Map
8th Grade Math
= – (x – 3)2.
Theorem and its
converse to solve
applied problems
including perimeter,
area, and volume
problems.
G.LO.08.02 Find the
distance between two
points on the coordinate
plane using the distance
formula; recognize that
the distance formula is
an application of the
Pythagorean Theorem.
Common Formulas
A.FO.08.07 Recognize
and apply the common
formulas:
(a + b) = a + 2 ab +
2
2
b
2
(a – b)2 = a2 – 2 ab +
b
2
(a + b) (a – b) = a2 – b2 ;
represent geometrically.
A.FO.08.08
Factor simple quadratic
expressions with
integer coefficients,
A.FO.08.09 Solve
applied problems
involving simple
quadratic equations.
Geometric Figures
G.SR.08.04 Find area
Text: Frogs, Fleas, and
Painted Cubes
Shapes of Algebra (9 weeks)
Math Hook
Your job is to measure,
improve and sustain
personal security of your
home, school, hang-out
spot, etc. Two security
companies have submitted
multiple proposals to have
the honor of your
business. You must
determine which company
meets your current need.
Investigation 3 (SIWS)
Determine what combination
of genetically modified and
non-genetically modified
crops will need to be grown
in order to maintain
profitability. Create a
graphical representation of
the solution and interpret its
meaning. (Shapes of
Algebra)
Investigation 2&3
Frog & Fleas (6 weeks)
Suppose your company
emits 200 metric tons
of carbon each year and
the following equation
models the cap 10x+ y
= 500. Determine when
your company will be
able to trade permits,
when will they have to
purchase or change the
way their company
G3 – 3 wks
Explore the relationships
between the number of
cell divisions and the
number of resulting cells.
Model this pattern using a
table, graph, and equation.
Interpret your models.
(Growing, growing,
growing – 3 weeks)
and perimeter of
complex figures by subdividing them into basic
shapes (quadrilaterals,
triangles, circles).
G.SR.08.05 Solve
applied problems
involving areas of
triangles, quadrilaterals,
and circles.
Text: Looking for
Pythagoras
Practical application of
Pythagorean Theorem to
find an unknown distance
(Pythagoras)
Investigation 1
Blueprint for green building
3D shapes represented 2
dimensionally
(Kaleidoscopes, hubcaps
& mirrors, FW)
Milwood Magnet School
Curriculum Sequencing Map
8th Grade Math
functions, when will
they meet the cap?
(Research & Review)
Investigation 4&5
Vocabulary
Distributive Property
Equivalent Expressions
Expanded Form
Exponential
Relationship
Factored Form
Function
Parabola
Patterns of Change
Quadratic Relationship
Roots
Algebraic Expression
Commutative Property
of Addition
Commutative Property
of Multiplication
Linear Relationship
Order of Operations
Surface Area
Term
X-intercept
Y-intercept
Solution(s)
Constant Term
Coefficient
Term
Variable
first/second differences
Combination method
Justify
Standard form of a linear
equation
Strategy
Substitution method
System of linear
equations
System of linear
inequalities
standard form
ax+by=c
symbolic reasoning
simultaneous
linear inequality
Estimate
Inequality
y = mx + b
slope-intercept form
slope
Coordinate
Cube Root
Cubic
Direct Variation
Expanded Form
Exponential
Relationship
Factored Form
Function
Indirect Variation
Intercept
Maximum Value
Minimum Value
Parabola
Quadratic Expressions
Quadratic Functions
Relationship
Root (zero)
equivalent
Triangular Numbers
Vertex
Vertex form
Vertical line test
Square Root
Line of Symmetry
Base - i.e. (2^5) where
2 is the “base”
Compound Growth
Compound Interest
Decay Factor
Decay Rate
Exponent
Exponential Decay
Exponential Growth
Exponential
Relationship
Growth Factor
Growth Rate
Rate of Decay
Standard Form
Vertical Line Test
Linear Growth
scientific notation
Complex Figure
Conjecture
Consecutive
Cube Root
Distance Formula
Hypotenuse
nonsquare rectangle
Legs
Perfect Squares
Pythagorean
Theorem
Quotient
theorem
Repeating Decimal
Sub-Dividing
Terminating
Decimal
Truncate
Area
Perimeter
Quadrilaterals
Rational Number
Real Number
Square Root
Volume
Irrational Number
Vertices
parallelogram
Angle of rotation
Center of rotation
Image
Line reflection
Mirror symmetry
Reflection
Reflection line
Reflection
symmetry
Rotation
Rotation symmetry
Transformation
Translation
Translation
symmetry
pi
radius
diameter
prism
cylinder
sphere
triangular prism
cone
pyramid
Congruent
Congruent figures
Line of symmetry
Symmetry
Tessellation
dimensions
base
Milwood Magnet School
Curriculum Sequencing Map
8th Grade Math
height
edge
volume
surface area
two-dimensional
three-dimensional
net
rectangular prism
faces
Formative
Assessments
Linear Sort
Linear Sort Reflection
Linear Functions
Reflection
Identifying Linear
Functions Graphic
Organizer
Unit
Summative
Assessment
Methods of Solving
Systems Graphic
Organizer
Graphing Quadratics
Mini Project Guidelines
and Rubric
Partner Activity - Solving
Systems by Equality
Linear vs
Exponential Brace
Map
Solving Systems
Assessment
Equation Comparison
Table
8th grade, Unit 1
authentic integrated
assessment
8th grade Authentic
Assessment
8th grade, Unit 2
authentic integrated
assessment
8th grade Authentic
Assessment
8th grade, Unit 3
authentic integrated
assessment
Performance Task:
Student Worksheet
Rubric
Performance
Task(Rubric
Included):
Student Worksheet
Student Graphic
Organizer
Performance Task:
Student Worksheet
Rubric
Example Paragraph
SOA Check Up 1
Comparing Linear and
Exponential Story
Problem
8th grade, Unit 4
authentic integrated
assessment
8th grade Authentic
Assessment
Performance Task:
Student Worksheet
Rubric
8th grade, Unit 5
authentic integrated
assessment
8th grade, Unit 6
authentic integrated
assessment
Milwood Magnet School
Curriculum Sequencing Map
8th Grade Math
Resources &
Materials
http://www.math.co
m/students/workshe
et/algebra_sp.htm
Table, Graph, and
Equation Graphic
Organizer
Curriculum Guide
(including
Authentic
Assessment)
Additional
Information
Curriculum Guide
(including SOA
Check Up 1)
Cyber Kids Videos
Revision 12, 4/16/10
http://www.math.com
/students/worksheet/a
lgebra_sp.htm
http://www.math.co
m/students/workshe
et/algebra_sp.htm
Table, Graph, and
Equation Graphic
Organizer
Table, Graph, and
Equation Graphic
Organizer
Asian Carp Fence
Article:
http://www.technov
elgy.com/ct/Science
-FictionNews.asp?NewsNu
m=312