Milwood Magnet School
Curriculum Sequencing Map
8th Grade Math
Timeline / Marking Period 1Week 1-6 / Marking Period 2
Week 7-12 / Marking Period 3
Week 13-18 / Marking Period 4
Week 19-24 / Marking Period 5
Week 25-30 / Marking Period 6
Week 30-36
Big Idea
(Overarching Topic or Concept) / Technological Innovations
“E3: Making life Easy, Effective and Efficient” / Global Food Chain
“Sustaining and improving food production regionally and globally” / Alternative Energies
“Sustainable power for human benefit” / Medical Biotechnology
“Improving our Quality of Life” / Environmental Biotechnology
“Preserving and Restoring our environment” / Sustainable Systems
“Adopting a sustainable quality lifestyle for ourselves and our posterity”
Enduring Understandings / Everything has a price / Making choices always involves compromise / What’s good for you may not be good for others. / Examining current patterns allows discovery of future applications / Prior knowledge helps to solve new problems / All choices have consequences
Essential Questions / What is a good business decision? / What factors need to be considered when making a decision? / How do outside factors impact decision making? / How do we analyze relationships in a system? / How do our actions effect the environment? / Does size matter?
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? / How do you determine profitability?
What do you need to consider in managing your resources?
How is profit represented graphically? / How do outside factors impact business operations?
How do you
make a good business decision?
Under what circumstances do you need to consider adjusting how you operate?
How are graphs, equations, and tables related and what information can be gathered from each?
What real world examples can be represented by quadratic functions?
What are the similarities and differences between linear and quadratic functions?
How do you use a graph to justify the choices you make? / How does the pattern of cell growth impact the advances in medicine?
Do all cells grow at the same rate? / How does area serve as a resource for all living things?
How does triangulation of points help to determine distances?
What is the relationship between side lengths and areas?
How do our actions impact the space available for living things? / How can you use knowledge about 3 dimensional shapes to create a sustainable “green” building?
What is the relationship between surface area and volume?
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 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.
Text: Say It With Symbols / Solve Problems
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 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).
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 / Non-Linear Functions
A.RP.08.01 Identify and 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 , 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 x-intercepts 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 = – (x – 3)2.
Common Formulas
A.FO.08.07 Recognize and apply the common formulas:
(a + b)2 = a2 + 2 ab + b2
(a – b)2 = a2 – 2 ab + b2
(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.
Text: Frogs, Fleas, and Painted Cubes
/ Numbers & Operations
N.ME.08.02 Understand meanings for zero and negative integer exponents.
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 = 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 / Numbers & Operations
N.ME.08.01 Understand 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 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 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.
Geometric Figures
G.SR.08.04 Find area and perimeter of complex figures by sub-dividing 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 / Volume & Surface Area
G.SR.08.06 Know the 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 cylinders.
Visualize Solids
G.SR.08.08 Sketch a variety of two-dimensional representations of three-dimensional 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
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 / 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 functions, when will they meet the cap?
(Research & Review)
Investigation 4&5 / 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) / 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)
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
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 / Methods of Solving Systems Graphic Organizer
Partner Activity - Solving Systems by Equality
Solving Systems Assessment
Equation Comparison Table / Graphing Quadratics Mini Project Guidelines and Rubric / Comparing Linear and Exponential Story Problem
Linear vs Exponential Brace Map
Unit Summative Assessment / 8th grade, Unit 1 authentic integrated assessment
8th grade Authentic Assessment
Performance Task:
Student Worksheet
Rubric
SOA Check Up 1 / 8th grade, Unit 2 authentic integrated assessment
8th grade Authentic Assessment
Performance Task(Rubric Included):
Student Worksheet
Student Graphic Organizer / 8th grade, Unit 3 authentic integrated assessment
Performance Task:
Student Worksheet
Rubric
Example Paragraph / 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
Resources & Materials / http://www.math.com/students/worksheet/algebra_sp.htm
Table, Graph, and Equation Graphic Organizer
Curriculum Guide (including Authentic Assessment)
Curriculum Guide (including SOA Check Up 1) / http://www.math.com/students/worksheet/algebra_sp.htm / http://www.math.com/students/worksheet/algebra_sp.htm
Table, Graph, and Equation Graphic Organizer / Table, Graph, and Equation Graphic Organizer / Asian Carp Fence Article:
http://www.technovelgy.com/ct/Science-Fiction-News.asp?NewsNum=312
Additional Information / Cyber Kids Videos
Revision 12, 4/16/10