eighth grade math curriculum map -...

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.


*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


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


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 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.


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


Ordered Pairs

Graphing In the

Coordinate Plane

addition and subtraction,

multiplication and division,

squares and square roots,

and cubes and cube roots.


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.


solving problems by

selecting strategies and

using mental computation,

estimation, calculators or

computers, and paper and

pencil.




symbolically and

graphically.







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


Week 6:

Exponents

Ch. 2

Exponents

Properties of

Exponents

Patterns in

Exponents

Scientific Notation




solving problems by





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


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




solving problems by





pencil

3.01: Represent problem

situations with geometric

models




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


Finding Square

Roots

Real Number System








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,


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


Weeks 14-15:

Collecting, Displayin

g, and Analyzing

Data

Ch. 4

Misleading Graphs /

Statistics

Scatter Plots


solving problems by





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


Weeks 16-17:

Plane Geometry

Ch. 5

Ch. 5-7:

Transformations

(Reflections,

Rotations,

Translations)

Ch. 7-5: Dilations





models

3.03: Identify, predict, and

describe dilations in the

coordinate plane.







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


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


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.



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


and Cones

Scaling Three-

dimensional Figures

relationships of addition

and subtraction,





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


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)**




symbolically and

graphically.







Weeks 33 - 34:

Review EOG Review

eighth grade math curriculum map -...

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