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Hickory Public Schools 8th Grade Math Curriculum Map
Course Description: Eighth grade math continues the study of both sixth and seventh grade math concepts with the addition of new material and skill building. Students will continue to learn and understand computing with real numbers, the use of measurement concepts, the use of properties and relationships in geometry, and the use of graphs and data analysis. The introduction of and building of new skills includes the students’ demonstrating an understanding of linear relations and fundamental algebraic concepts. Appropriate technology from manipulatives to calculators and application software should be used regularly for instruction and assessment.
EOG
Teacher-made exam
Hickory Public Schools Eighth Grade Math Power Standards
Students taking eighth grade math in Hickory Public Schools will… Algebra: Solve algebraic equations/inequalities as well as recognize and graph linear equations (using slope) in the coordinate plane. Data Analysis: Analyze and graph data in a scatter plot and approximate a line of best fit for the data. Geometry: Effectively apply the Pythagorean Theorem in real world situations and dilate figures in the coordinate plane. Measurement: Calculate the effect of dimensional change (area, surface area, and volume) on two or three dimensional figures and apply the use of indirect measurement in real world problems. Real Numbers: Evaluate and identify real numbers (rational and irrational) by using a variety of strategies and methods. *Algebra makes up 35-40% of the content of the NC 8
th grade EOG.
*Data Analysis makes up 20-25% of the content of the NC 8th grade EOG.
*Geometry makes up 10-15% of the content of the NC 8th grade EOG.
Hickory Public Schools 8th Grade Math Curriculum Map
*Measurement makes up 10-15% of the content of the NC 8th grade EOG.
*Real Number makes up 10-15% of the content of the NC 8th grade EOG.
8th Grade Vocabulary and Key Terms with Definitions
Goal 1: Real Numbers
1. Real number – all numbers on the number line; numbers included are rational numbers, irrational numbers, integers, whole numbers, and natural numbers
2. Rational – all positive and negative real numbers that can be written as a whole
number, fraction, or a decimal (terminating or repeating) 3. Irrational – all positive and negative real numbers that CANNOT be written as whole
number, fraction, or a decimal (terminating or repeating); these numbers usually are decimals that are non-terminating or roots of numbers that are not perfect squares (ex.
7 )
4. Exponential form – writing a number using a base and an exponent
5. Exponent – indicates how many times to use the base as a factor
6. Integers – all positive and negative whole numbers
7. Order of Operations – the order in which to solve an expression (Parentheses,
Exponents, Multiply/Divide, Add/Subtract)
8. Pi – the ratio of the circumference of a circle to its diameter; 14.3=Π
9. Absolute Value – the distance a number is from zero; distance has a positive value
(ex. 88,44 =−= and )
Goal 2: Measurement 1. Dilation – transformation of a figure in which it changes size, getting larger or smaller
2. Surface Area – the total area of the exterior surface of a solid
3. Scale Factor – the ratio of the two corresponding coordinates in a dilated figure; the
amount by which a dilated figure has been enlarged or reduced
4. Radius – a line segment connecting the center of another point on the circle
5. Diameter – a line segment that connects one side of the circle to the other side of the circle while passing through the center
6. Circumference – the distance around the circle
7. Similar Figures - same shape but not necessarily the same size
8. Ratio/Proportion – a comparison of two numbers such that when their cross products
are compared, they are equal
Hickory Public Schools 8th Grade Math Curriculum Map
9. Area – the amount of space inside of a two-dimensional figure
10. Perimeter – the distance around a figure
11. Volume – the amount of space inside of a three-dimensional figure
Goal 3: Geometry
1. Hypotenuse – the side of a right triangle across from the right angle 2. Leg – the two sides of a right triangle that create the right angle
3. Pythagorean Theorem – the equation used to solve for a missing side in a right
triangle (a2 + b
2 = c
2)
4. Right Triangle – a triangle with one right angle
Goal 4: Data Analysis
1. Scatter plot – a graph of paired data (x,y) plotted on an x and y axis illustrating a relationship
2. Correlation – the degree at which 2 variables are related (positive, negative, or no)
3. Coordinate Plane – the plane formed by the horizontal axis (x-axis) and the vertical
axis (y-axis)
4. Independent Variable – the variable in an equation that can have its value freely chosen
5. Dependent Variable – the variable in an equation whose value depends on the values
chosen for the other variable(independent) in the equation
6. Origin – the point where the x-axis and the y-axis intersect (0,0)
Goal 5: Algebra
1. Intercept – the point where a line crosses the x – axis (X-intercept) or y-axis (Y-intercept)
2. Inverse Operation – using the opposite operation in an equation in order to get values
to cancel out
3. Linear – description of a graph or an equation that form a line
4. Nonlinear – description of a graph or an equation that does NOT form a line
5. Function – a relation, or group of points, in which none of the x-values repeat; vertical line test - a graph can be a function if a vertical line can be drawn through the picture and the vertical line only touches the graph one time
6. Equation – an expression with an equals sign
Hickory Public Schools 8th Grade Math Curriculum Map
7. Inequality – an expression using >, <, >, or <
8. Linear Equation – equations that can be written as y = mx+b
9. Standard Form – linear equations that can be written as Ax + By = C
10. Solution – any and all values for a variable that make an equation or an inequality true
11. Algebraic Expression – any mathematical sentence that includes numbers and/or variables using operational symbols such as add, subtract, multiply, divide, square roots, exponents, etc.
12. Evaluate – to solve
13. Equivalent – equal
14. X-axis – horizontal axis in the coordinate plane 15. Y-axis – vertical axis in the coordinate plane
16. Coefficient – a number that is being multiplied by a variable
17. Like Terms – terms that have the same variables raised to the same power
18. Ordered Pair – a point written (x,y)
19. Reciprocal – multiplicative inverse of a number; a fraction flipped over so that the
numerator and denominator switch places
20. Square Root/Radical – symbol = x is called a radical; a number that must be
multiplied by itself to equal the given number under the radical
21. Cube Root – symbol = 3
x ; a number that must be multiplied by itself three times in
order to equal the given number under the radical
22. Parallel lines – lines that never intersect
23. Perpendicular lines – lines that intersect to form 4 right angles
24. Slope – Rise / Run; indicates the steepness of a line and whether a line goes uphill or downhill
*Some definitions were taken from www.mathwords.com
Hickory Public Schools 8th Grade Math Curriculum Map
Hickory Public Schools Grades 6-12
Mathematics Shared Agreements
Teachers of Secondary Mathematics in Hickory Public Schools agree that all students will...
1. Connect mathematics to the real world weekly. 2. Utilize 21st century technology to model and/or solve
mathematical concepts weekly.
3. Interpret text and apply proper problem-solving techniques weekly.
4. Use writing to demonstrate understanding of mathematical
concepts at least once per unit.
Hickory Public Schools 8th Grade Math Curriculum Map
Timeline/Content Lesson NCSCoS Objectives Essential Questions Key Terms
Weeks 1-3:
Algebra Toolbox
Ch. 1
Variables &
Expressions
Write Algebraic
Expressions
Solving Equations
Using + / -
Solving Equations by
x and /
Solving Simple
Inequalities
Combining Like
Terms
1.01: Develop number sense
for the real numbers.
1.02: Develop flexibility in
solving problems by selecting
strategies and using mental
computation, estimation,
calculators or computers, and
paper and pencil.
5.01: Develop an
understanding of function.
5.03: Solve problems using
linear equations and
inequalities; justify
symbolically and graphically.
5.04: Solve equations using
the inverse relationships of
Why do we use variables?
What are the tools needed in order
to solve an equation and/or
inequality?
• What is the error with how
the following expression is
solved? Explain why?
4x + 8x = 12x^2
How do equations and inequalities
differ?
• What explanation can you
provide for how to solve an
inequality when dividing by a
negative number?
• variable
• equation
• expression
• inequality
• like terms
• evaluate
• coordinate plane
• solution
• ordered pair
Hickory Public Schools 8th Grade Math Curriculum Map
Ordered Pairs
Graphing In the
Coordinate Plane
addition and subtraction,
multiplication and division,
squares and square roots,
and cubes and cube roots.
Hickory Public Schools 8th Grade Math Curriculum Map
Weeks 4-5:
Integers
Ch. 2
Adding Integers
Subtracting Integers
Multiplying and
Dividing Integers
Solving Equations
with Integers
Solving Inequalities
with Integers
1.01: Develop number
sense for the real numbers.
1.02: Develop flexibility in
solving problems by
selecting strategies and
using mental computation,
estimation, calculators or
computers, and paper and
pencil.
5.03: Solve problems using
linear equations and
inequalities; justify
symbolically and
graphically.
5.04: Solve equations using
the inverse relationships of
addition and subtraction,
multiplication and division,
squares and square roots,
and cubes and cube roots.
How can you explain how to solve
the following number sentence
using order of operations?
-5(-12+8) - (15-7) / 4
Is the following inequality solved
correctly? Explain your reasoning.
-4x > 124
x > -31
• integer
• order of operations
• absolute value
• equation
• inequality
• solution
• expression
• evaluate
• equivalent
• coefficient
• like term
Hickory Public Schools 8th Grade Math Curriculum Map
Week 6:
Exponents
Ch. 2
Exponents
Properties of
Exponents
Patterns in
Exponents
Scientific Notation
1.01: Develop number
sense for the real numbers.
1.02: Develop flexibility in
solving problems by
selecting strategies and
using mental computation,
estimation, calculators or
computers, and paper and
pencil.
How would you distinguish the
difference between multiplying
exponents (with the same base) and
dividing exponents (with the same
base)?
How would you create a rule for
simplifying an expression with a
negative exponent?
• exponents
• exponential form
Hickory Public Schools 8th Grade Math Curriculum Map
Weeks 7-9:
Rational and Real
Numbers
Ch. 3
Rational Numbers
Adding and
Subtracting Rational
Numbers
Adding and
Subtracting with
Unlike Denominators
Multiplying Rational
Numbers
Dividing Rational
Numbers
Solving Equations
Solving Inequalities
Squares and Square
Roots
1.01: Develop number
sense for the real numbers.
1.02: Develop flexibility in
solving problems by
selecting strategies and
using mental computation,
estimation, calculators or
computers, and paper and
pencil
3.01: Represent problem
situations with geometric
models
5.03: Solve problems using
linear equations and
inequalities; justify
symbolically and
graphically.
How are the different categories of
the real number system related?
• What are the characteristics
of rational and irrational
numbers, and what makes
them different?
Why is the number 9 considered a
"perfect square?"
• rational number
• irrational number
• real number
• equation
• expression
• inequality
• solution
• evaluate
• equivalent
• coefficient
• inverse operation
• radical
• square root
Hickory Public Schools 8th Grade Math Curriculum Map
Finding Square
Roots
Real Number System
5.04: Solve equations using
the inverse relationships of
addition and subtraction,
multiplication and division,
squares and square roots,
and cubes and cube roots.
Hickory Public Schools 8th Grade Math Curriculum Map
Weeks 10-13:
More Equations
and Inequalities
Ch. 10
Solving Two Step
Equations
Solving Multi-step
Equations
Equations with
Variables on Both
Sides
Solving Multi-step
Inequalities
Systems of Equations
1.01: Develop number sense for
the real numbers.
1.02: Develop flexibility in solving
problems by selecting strategies
and using mental computation,
estimation, calculators or
computers, and paper and pencil.
5.03: Solve problems using linear
equations and inequalities; justify
symbolically and graphically.
5.04: Solve equations using the
inverse relationships of addition
and subtraction, multiplication and
division, squares and square
roots, and cubes and cube roots.
How are equations used in the real
world? Why are they helpful?
• How would you explain
how to solve the following
equation:
3x + 5 – 9x = - 22 + -9x
What does a solution to a system
of equations mean in relation to
the graph of the system and the
algebraic representation?
• Why is (-5,4) a solution to
the system:
2x + 5y = 10
3x - y = -19
• equation
• inequality
• expression
• solution
• evaluate
• inverse
operation
• coefficient
• like term
• variable
Hickory Public Schools 8th Grade Math Curriculum Map
Weeks 14-15:
Collecting, Displayin
g, and Analyzing
Data
Ch. 4
Misleading Graphs /
Statistics
Scatter Plots
1.02: Develop flexibility in
solving problems by
selecting strategies and
using mental computation,
estimation, calculators or
computers, and paper and
pencil.
4.02: Approximate a line of
best fit for a given scatter
plot; explain the meaning of
the line as it relates to the
problem and make
predictions.
4.03: Identify misuses of
statistical and numerical
data.
Why is it important to recognize
misleading graphs and statistics?
Why is it important to be able
to create and interpret scatter plots?
• scatter plots
• correlation
• coordinate plane
• independent
variable
• dependent variable
• line of best fit
Hickory Public Schools 8th Grade Math Curriculum Map
Weeks 16-17:
Plane Geometry
Ch. 5
Ch. 5-7:
Transformations
(Reflections,
Rotations,
Translations)
Ch. 7-5: Dilations
1.01: Develop number
sense for the real numbers.
3.01: Represent problem
situations with geometric
models
3.03: Identify, predict, and
describe dilations in the
coordinate plane.
5.04: Solve equations using
the inverse relationships of
addition and subtraction,
multiplication and division,
squares and square roots,
and cubes and cube roots.
What does it mean to dilate a figure,
and how does it differ from other
transformations?
• When given a dilated figure,
how do you determine the
original points? How can you
determine its scale factor?
• dilation
• scale factor
Hickory Public Schools 8th Grade Math Curriculum Map
Weeks 18-20:
Ratios and Similarity
Ch. 7
Ratios and
Proportions
Ratios, Rates, and
Unit Rates
Solving Proportions
Similar Figures
Scale Drawings
Scale Models
2.02: Apply and use
concepts of indirect
measurement.
3.02: Apply geometric
properties and
relationships, including the
Pythagorean theorem, to
solve problems.
How are proportions used to solve
similar figures and scale
drawings? Why are proportions the
appropriate method to use?
• What algebraic concepts can
be applied to solve the
following proportion:
2x -1 = 5x - 1
5 15
• proportion
• ratio
• similar figure
Hickory Public Schools 8th Grade Math Curriculum Map
Weeks 21-25:
Perimeter, Area,
Surface Area,
Volume, and
Pythagorean
Theorem
Ch. 6
Perimeter and Area
of Rectangles and
Parallelograms
Perimeter and Area
of Triangles and
Trapezoids
Circles
Pythagorean
Theorem
Surface Area of
Prisms and Cylinders
Volume of Prisms
and Cylinders
Volume of Pyramids
2.01: Determine the effect
on perimeter, area or
volume when one or more
dimensions of two- and
three-dimensional figures
are changed.
2.02: Apply and use
concepts of indirect
measurement.
3.01: Represent problem
situations with geometric
models
3.02: Apply geometric
properties and
relationships, including the
Pythagorean theorem, to
solve problems.
5.04: Solve equations
using the inverse
How is the Pythagorean Theorem
applied in the real world?
What types of word problems would
use surface area and what types of
word problems would use volume
(without explicitly asking for each)?
How would you solve for the
missing radius of a circle if you were
given the area?
If you tripled all of the dimensions of
a cube, how does that affect the
surface area differently than the
volume?
• area
• circumference
• diameter
• perimeter
• volume
• surface area
• hypotenuse
• leg
• Pythagorean
theorem
• right triangle
Hickory Public Schools 8th Grade Math Curriculum Map
and Cones
Scaling Three-
dimensional Figures
relationships of addition
and subtraction,
multiplication and division,
squares and square roots,
and cubes and cube roots.
Hickory Public Schools 8th Grade Math Curriculum Map
Weeks 26-32:
Linear Equations
Ch. 11
Graphing Linear
Equations (2
variables/tables)
Slope of a Line
(to include Ch. 5-2)
Graphing using X-
and Y-intercepts
Using Slope and Y
intercept (y = mx + b)
**Standard Form**
**Writing Equations
using slope and Y-
intercept, slope and 1
point, and 2 points**
4.01: Collect, organize,
analyze, and display data
(including scatter plots) to
solve problems.
4.02: Approximate a line of
best fit for a given scatter
plot; explain the meaning of
the line as it relates to the
problem and make
predictions.
5.01: Develop an
understanding of function.
5.02: Write an equation of a
linear relationship given:
two points, the slope and
one point on the line, or the
slope and y-intercept
What makes a relationship linear?
• How would you describe the
slope of all 4 types of lines to
a 6th grader?
• What is the difference
between the X intercept and
the Y intercept of a line?
How can linear equations be applied
in the real world?
• intercept
• linear
• nonlinear
• function
• equation
• inequality
• standard form
• x-axis
• y-axis
• ordered pair
• cube root
• square root
• parallel line
• perpendicular line
• slope
• scatter plot
• line of best fit
Hickory Public Schools 8th Grade Math Curriculum Map
Direct Variation
Graphing Inequalities
in 2 Variables
Lines of Best
Fit/Scatter Plots
Systems of Equations
**LAB - Explore
cubes and cube roots
(Ch. 3-10)**
5.03: Solve problems using
linear equations and
inequalities; justify
symbolically and
graphically.
5.04: Solve equations using
the inverse relationships of
addition and subtraction,
multiplication and division,
squares and square roots,
and cubes and cube roots.
Weeks 33 - 34:
Review EOG Review
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