Grade 8 Mathematics - Nexusnexuslearning.net/teachers/pacingguides/Danville/Grade 8/Grade 8... · Grade 8 Mathematics Standards of Learning Curriculum Guide Danville Public Schools,

Grade 8 Mathematics Standards of Learning Curriculum Guide

Danville Public Schools, 2002 (Revised 10/21/2003) 1 Math - Grade 8

Topic

SOL Essential Knowledge and Skills

Related

SOL

When Taught Instructional Strategies

Assessment Classroom Methods

Resources

Number and Number Sense Rational Numbers: Operations and Estimations *Include Whole Numbers, Fractions, and Decimals Order of Operations Number Sense and Number Theory

8.1 The student will: a) simplify

numerical expressions involving positive exponents, using rational numbers, order of operations and properties of operations with real numbers

b) recognize, represent, compare and order numbers expressed in scientific notation

c) compare and order decimals, fractions, percents and numbers written in scientific notation.

The student will be able to: Use problem solving, mathematical communication, mathematical reasoning, connections and representations to: Simplify numerical expressions

containing exponents where the base is a rational number and the exponent is a positive whole number, using the order of operations and properties of operations with real numbers.

Recognize, represent, compare and order rational numbers expressed in scientific notation using both positive and negative exponents.

Compare and order fractions, decimals, percents and numbers written in scientific notation.

Math 6.22 7.3

A.10

Math 8

1st – 4th 6 Weeks

1st & 2nd 9 Weeks

Pre- Algebra

1st – 4th 6 Weeks

1st & 2nd 9 Weeks

• Create a mnemonic device (i.e. Please

Excuse My Dear Aunt Sally) to remember the order of operation steps.

• Have students list the steps necessary to perform specific tasks (i.e. make sandwich). List steps on note cards and discuss the effect when the sequence is altered.

• Student

Demonstrat-ions

• Quizzes and Tests

• Mathematics SOL

Curriculum Framework, Grade 8, p. 2

• DOE Patterns, Functions, and Algebra Teacher Staff Development Guide

• http://www.pen.k12.va.us/VDOE/Instruction/math_resources.html

*Disclaimer: The teacher should review all sites prior to exposing them to the students.



Topic


Related

SOL



Resources

Number and Number Sense (con’t) Number Sense and Number Theory

8.2 The student will describe orally and in writing the relationship between the subsets of the real number system.

The student will be able to: Use problem solving, mathematical communication, mathematical reasoning, connections and representations to: Describe orally and in writing the

relationships among the sets of natural or counting numbers, whole numbers, integers, rational numbers, irrational numbers and real numbers.

Illustrate the relationships among the subsets of the real number system by using graphic organizers, such as Venn diagrams. Subsets include real numbers, rational numbers, irrational numbers, integers, whole numbers and natural numbers.

Identify the subsets of the real number system to which a given number belongs.

Determine whether a given number is a member of a particular subset of the real number system, and explain why.

Describe each subset of the set of real numbers.

Math 6.5

Math 8

1st, 3rd,

5th 6 Weeks

1st, 2nd,

4th 9 Weeks

Pre-

Algebra 8

1st, 2nd, 5th

6 Weeks

1st, 2nd, 4th

9 Weeks

• Construct a Venn diagram for the

subsets of the real number system (natural numbers, whole numbers, integers, rational numbers).

• Student

Demonstra-tions


• Graphic

Organizers • Mathematics SOL


• http://www.pen.k12.va.us/VDOE/Instruction/math_resource.html




Topic


Related

SOL



Resources

Computation and Estimation Rational Numbers: Operations and Estimations Proportional Reasoning

8.3 The student will solve practical problems involving rational numbers, percents, ratios and proportions. Problems will be of varying complexities and will involve real-life data, such as finding a discount and discount prices, and balancing a checkbook.

The student will be able to: Use problem solving, mathematical communication, mathematical reasoning, connections and representations to: Solve practical problems by using

computation procedures for whole numbers, integers, rational numbers, percents, ratios and proportions.

Maintain a checkbook and check registry for five or fewer transactions.

Compute a discount and the resulting (sale) price for one discount.

Math 6.6 7.4 7.6

Math 8

1st– 4th

6 Weeks

1st & 2nd 9 Weeks

Pre-

Algebra

2nd – 4th 6 Weeks

2nd & 3rd

9 Weeks

• Have students choose a sale ad from a

newspaper and explain the discounts and sale prices shown.

• Given the price of 5 to 10 items, students will round each price to the nearest dollar. Next, give an estimate for the entire list.

• Take the same items and calculate the item’s actual cost.

• Given the rate, find the sales tax using the estimate. Given the rate, find the sales tax using the actual cost.

• Student

Demonstra-tions


• Mathematics SOL


• Teachers’ Resource Book: Math On Call (Pp. 102, 104)

• Newspapers • http://www.pen.k1

2.va.us/VDOE/Instruction/math_resource.html




Topic


Related

SOL



Resources

Computation and Estimation (con’t) Rational Numbers: Order of Operations Algebra: Representations and Relationships *Include Whole Numbers, Fractions, and Decimals

8.4 The student will apply the order of operations to evaluate algebraic expressions for given replacement values of the variables. Problems will be limited to positive exponents.

The student will be able to: Use problem solving, mathematical communication, mathematical reasoning, connections and representations to: Substitute numbers for variables

in an algebraic expression and simplify the expression by using the order of operations. Exponents used are whole numbers less than 4.

Apply the order of operations to evaluate formulas.

Math 6.7 6.8 6.23 7.2 A.2

Math 8

1st

6 Weeks

1st 9 Weeks

Pre-

Algebra

1st & 2nd 6 Weeks

1st

9 Weeks

• Using single-digit numbers and two

operations chosen at random, determine how many different answers can be found by changing the operations. Do not change the order of the numbers.

• Using five single-digit numbers, four operations, and grouping symbols (i.e. Parentheses (); brackets {}; braces [ ]; and fraction Bars - ), determine how many different answers can be found by changing the grouping or operations.

• Student

Demonstra-tions


• Manipulatives • Mathematics SOL


• DOE Patterns, Functions, and Algebra Teacher Staff Development Guide

• Teacher Resource Book: Math On Call





Topic


Related

SOL



Resources

Computation and Estimation (con’t) Rational Numbers: Representations and Relationships

8.5 The student, given a whole number from 1 to 100, will identify it as a perfect square or find the two consecutive whole numbers between which the square root lies.

The student will be able to: Use problem solving, mathematical communication, mathematical reasoning, connections and representations to: Identify the perfect squares from 0

to 100. Identify the two consecutive

whole numbers between which the square root of a given whole number from 0 to 100 lies ( e.g., √57 lies between 7 and 8 since 7² = 49 and 8² = 64).

Math 6.22 A.10 A.13 6.7

Math 8

4th

6 Weeks

3rd 9 Weeks

Pre-

Algebra

5th 6 Weeks

4th

9 Weeks

• Interpolate to determine the value of

the square root. • Have students draw squares on graph

paper and count the blocks inside to illustrate perfect square numbers.

• Student

Demonstra-tions


• Manipulatives • Mathematics SOL


• Versi-Tiles, Booklet 4: Real Life Math Lab





Topic


Related

SOL



Resources

Measurement and Geometry Measurement: Actual and Estimate Geometry: Basic Ideas

8.6 The student will verify by measuring, and describe the relationships among vertical angles, supplementary angles and complementary angles, and will measure and draw angles of less than 360º

The student will be able to: Use problem solving, mathematical communication, mathematical reasoning, connections and representations to: Measure angles of less than 360º

to the nearest degree using appropriate tools.

Identify and describe the relationships among the angles formed by two intersecting lines.

Identify and describe pairs of angles that are vertical.

Identify and describe pairs of angles that supplementary.

Identify and describe pairs of angles that are complementary.

Math 6.13 7.7 G.3

Math 8

2nd

6 Weeks

2nd 9 Weeks

Pre-

Algebra

5th 6 Weeks

3rd

9 Weeks

• Given a sheet with intersecting lines,

measure each angle using a protractor and compare the angle measures of each picture to determine the relationships that exist.

• Student

Demonstra-tions


• Protractors • Mathematics SOL






Topic


Related

SOL



Resources

Measurement and Geometry (con’t) Rational Numbers: Operations and Estimations *Include Whole Numbers, Fractions, and Decimals Measurement: Actual and Estimate *Include Whole Numbers, Fractions, and Decimals *Use variables in formulas Geometry: Solid

8.7 The student will investigate and solve practical problems involving volume and surface area or rectangular solids (prisms), cylinders, cones and pyramids.

The student will be able to: Use problem solving, mathematical communication, mathematical reasoning, connections and representations to: Compute the surface area of a

pyramid by finding the sum of the areas of the triangular faces and the base.

Compute the surface area of a cone by calculating the sum of the areas of the side and the base using formulas.

Compute the volume and surface area of rectangular solids (prisms), cylinders, cones and square pyramids using formulas.

Investigate and solve problems involving volume and surface area of rectangular solids (prisms), cylinders, cones and pyramids.

Math 6.17 8.15 8.17 G.13

Math 8

5th

6 Weeks

3rd 6 Weeks

Pre-

Algebra

5th 6 Weeks

4th

9 Weeks

• Identify the plane figures that make up

the solid figures to help understand the formulas.

• Use real-life objects to explore the connection between solids and nets when studying surface area. Before cutting open their solids, make a rough sketch to predict how the flattened solid will look.

• Examine how changes in a dimension of the solid will affect the volume.

• Emphasize the difference between the height and slant height of a solid.

• Student

Demonstra-tions


• Mathematics SOL

Curriculum Guide, Grade 8, p. 10





Topic


Related

SOL



Resources

Measurement and Geometry (con’t) Geometry: Spatial Relationships

8.8 The student will apply transformations (rotate or turn, reflect or flip, translate or slide, and dilate or scale) to geometric figures represented on graph paper. The student will identify applications of transformations, such as tiling, fabric design, art and scaling.

The student will be able to: Use problem solving, mathematical communication, mathematical reasoning, connections and representations to: Identify the geometric

transformations (rotation, reflection, translation and dilation) by using a variety of real-life examples.

Demonstrate the reflection of a figure over a vertical or horizontal line on a coordinate grid.

Demonstrate 90º, 180º, 270º, and 360º rotations of a figure on a coordinate grid.

Demonstrate the dilation of a figure from a fixed point on a coordinate grid.

Math 6.15 6.21 7.11 G.2

Math 8

2nd & 4th 6 Weeks

2nd & 3rd 6 Weeks

Pre-

Algebra

5th 6 Weeks

3rd

9 Weeks

• Demonstrate rotations of 90º and 180º

by executing right face, left face and bout face.

• Using samples of linoleum, wallpaper, tile, carpet or fabric, identify different transformations.

• Student

Demonstra-tions


• Manipulatives • Patty paper • Grid paper • Mathematics SOL


• DOE Geometry for Middle Grades Teachers Staff Development Guide

• Teachers’ Resource Book: Math On Call

• Versi-Tile, Book 5: Intermediate Manipulative Lab





Topic


Related

SOL



Resources

Measurement and Geometry (con’t) Geometry: Solid Spatial Relationships

8.9 The student will construct a three-dimensional model, given the top, side and/or bottom views.

The student will be able to: Use problem solving, mathematical communication, mathematical reasoning, connections and representations to: Construct three-dimensional

models, given top, side and bottom views.

Math 6.15 7.11 G.2

Math 8

5th

6 Weeks

4th 9 Weeks

Pre-

Algebra

5th 6 Weeks

4th

9 Weeks

• Construct 3-dimensional figure using

cubes. Draw the top, bottom and side views on grid paper and figure the total surface area by adding all the areas together.

• Draw a 3 X 4 rectangle on the paper and place 12 cubes on the original layer. Have students arrive at the formula for the volume of a rectangular prism by multiplying the area of the base (number of cubes in each layer) times the number of layers (height).

• Student

Demonstra-tions


• Mathematics SOL


• Manipulatives • Grid paper • Isometric dot

paper • DOE Geometry

for Middle School Teachers Staff Development Guide





Topic


Related

SOL



Resources

Measurement and Geometry (con’t) Rational Numbers: Operations and Estimations *Include Whole Numbers, Fractions, and Decimals Measurement: Actual and Estimate Geometry: Basic Ideas Plane

8.10 The student will a) verify the

Pythagorean Theorem using diagrams, concrete materials and measurement

b) apply the Pythagorean Theorem to find the missing length of a side of a right triangle when given the lengths of the other two sides

The student will be able to: Use problem solving, mathematical communication, mathematical reasoning, connections and representations to: Identify the parts of a right

triangle (the hypotenuse and the legs).

Verify the Pythagorean Theorem using diagrams, concrete materials and measurement.

Find the measure of a side of a right triangle, given the measures of the other two sides. The measures of the sides of the triangle may be whole numbers no larger than 15 or decimals in tenths.

Solve real-life problems involving right triangles by using the Pythagorean Theorem.

Math 6.22 G.7

Math 8

4th

6 Weeks

3rd 9 Weeks

Pre-

Algebra

5th 6 Weeks

4th

9 Weeks

• Use calculators to solve problems

related to the Pythagorean Theorem, rounding answers to a given place value.

• Solve real-life problems using the Pythagorean Theorem.

• Student

Demonstra-tions


• Mathematics SOL


• DOE Geometry for Middle Grades Teachers Staff Development Guide

• Versi-Tile Book: Advance Math Lab, Book 6



Topic


Related

SOL



Resources

Probability and Statistics Probability

8.11 The student will analyze problem situations, including games of chance, board games or grading scales, and make predictions using knowledge of probability.

The student will be able to: Use problem solving, mathematical communication, mathematical reasoning, connections and representations to: Analyze a problem situation and

determine the likelihood of an event occurring using knowledge of probability.

Predict the outcome of an event by analyzing its probability.

Explain the consequences of making different choices using knowledge of probability.

Make predictions about the outcomes of games of chance, board games and grading scales by using knowledge of probability.

Math

6.1 6.2 6.3 6.18 6.20 7.14 7.17 7.18 8.11 8.12

Math 8

1st, 3rd,

5th 6 Weeks

1st, 2nd,

4th 9 Weeks

Pre-

Algebra

4th 6 Weeks

3rd

9 Weeks

• Calculate the probability of a student’s

name being randomly selected out of the names of all the class members.

• Study the chances of winning the Virginia State Lottery. Model the problem by using the spinners with 10 numbers and using computer programs to randomly generate three-digit numbers.

• Draw tree diagrams to determine the number of possible outcomes for a situation.

• Student

Demonstra-tions


• Mathematics SOL

Curriculum Framework Grade 8, p. 18

• DOE Probability and Statistics Staff Development Guide



• Spinners • Dice • Coins • Cards • Colored models *Disclaimer: The teacher should review all sites prior to exposing them to the students.



Topic


Related

SOL



Resources

Probability and Statistics (con’t) Data Analysis: Representations and Relationship *Include Whole Numbers, Fractions, and Decimals

8.12 The student will make comparisons, predictions and inferences using information displayed in frequency distributions; box-and-whisker plots, scattergrams; line, bar, circle and picture graphs; and histograms.

The student will be able to: Use problem solving, mathematical communication, mathematical reasoning, connections and representations to: Make comparisons, predictions

and inferences given data sets of no more than 20 items that are displayed in frequency distributions; box-and-whisker plots; scattergrams; line, bar, circle and picture graphs; and histograms.

Math 6.18 6.20 7.17 7.18 8.12

Math 8

2nd

6 Weeks

2nd 9 Weeks

Pre-

Algebra

1st & 4th 6 Weeks

1st & 3rd 9 Weeks

• Have students search newspapers or

magazines for tables or information that can be used to create a table or chart. Illustrate the same information through different graphs.

• Survey classmates and display the results of that survey using different graph forms.

• Student

Demonstra-tions


• Mathematics SOL



• Teachers’ Resource Book: Math On Call p. 70-80

• Tables, Charts and Graphs by Milliken Math





Topic


Related

SOL



Resources

Probability and Statistics (con’t) Data Analysis: Representations and Relationship *Include Whole Numbers, Fractions, and Decimals

8.13 The student will use a matrix to organize and describe data.

The student will be able to: Use problem solving, mathematical communication, mathematical reasoning, connections and representations to: Describe the characteristics of a

matrix, including designating labels for rows and columns.

Use a matrix of no more than 12 entries to organize and describe a data set.

Identify the position of an element by row and column.

Transfer data from a chart to a matrix.

Math A.4

Math 8

1st

6 Weeks

1st 9 Weeks

Pre-

Algebra

1st 6 Weeks

1st

9 Weeks

• Have students bring in newspaper or

magazine articles with information that can be organized into a matrix.

• Construct a 3 X 3 matrix in order to organize the following information: - Mr. Good came in before Mrs.

Grouch - Mrs. Grouch came in before Mrs.

Mean - Mr. Good came in after Mrs. Mean

• Student

Demonstra-tions


• Mathematics SOL





Topic


Related

SOL



Resources

Patterns, Functions, and Algebra Patterns and Functions: Representations and Relationships Algebra: Representations and Relationships *Include Whole Numbers, Fractions, and Decimals

8.14 The student will a) describe and

represent relations and functions using tables, graphs and rules

b) relate and compare tables, graphs and rules as different forms of representation for relationships

The student will be able to: Use problem solving, mathematical communication, mathematical reasoning, connections and representations to: Graph in a coordinate plane

ordered pairs that represent a relation.

Write a rule that represents a relation from a table of values.

Write a table of values from the rule that represents a relation.

Write a table of values from the graph of ordered pairs of a relation.

Describe and represent relations and functions using tables, graphs and rules.

Relate and compare different representations of the same relations.

Math 7.12 7.19 8.4 8.14 8.15 8.17 A.5

Math 8

4th & 5th 6 Weeks

3rd

9 Weeks

Pre- Algebra

3rd

6 Weeks

2nd 9 Weeks

• Use mapping and/or the vertical line

test to determine if a relation is a function.

• Student

Demonstra-tions


• Mathematics SOL


• DOE Patterns, Functions and Algebra Staff Development Guide



Topic


Related

SOL



Resources

Patterns, Functions, and Algebra (con’t) Data Analysis: Representations and Relationship *Include Whole Numbers, Fractions, and Decimals

8.15 The student will solve two-step equations and inequalities in one variable using concrete materials, pictorial representations and paper and pencil.

The student will be able to: Use problem solving, mathematical communication, mathematical reasoning, connections and representations to: Solve two-step linear equations by

showing the steps and using algebraic sentences.

Solve two-step inequalities by showing the steps and using algebraic sentences.

Math 6.8 6.23 7.4 7.22 8.1 8.3 8.4 8.17 A.1 A.3

Math 8

1st & 3rd 6 Weeks

1st & 2nd 9 Weeks

Pre-

Algebra

3rd 6 Weeks

2nd

9 Weeks

• Use the balance to symbolize

equations and describe the necessary steps to solve the equation.

• Remind students to reverse the order of operations when solving a multi-step equation.

• Student

Demonstra-tions


• Mathematics SOL



• Hands On Algebra



Topic


Related

SOL



Resources

Patterns, Functions, and Algebra (con’t) Patterns and Functions: Representations and Relationships Algebra: Representations and Relationships *Include Whole Numbers, Fractions, and Decimals Geometry: Spatial Relationships

8.16 The student will graph a linear equation in two variables, in the coordinate plane, using a table of ordered pairs.

The student will be able to: Use problem solving, mathematical communication, mathematical reasoning, connections and representations to: Construct a table of ordered pairs

by substituting values for x in a linear equation to find values of y.

Plot in the coordinate plane ordered pairs (x,y) from a table.

Connect the ordered pairs to form a straight line.

Math 7.12 8.14 A.6

Math 8

4th

6 Weeks

3rd 9 Weeks

Pre-

Algebra

3rd 6 Weeks

2nd

9 Weeks

• Put equations in y- form before

substituting values. • May use the graphing calculator (if

available) to check your results.

• Student

Demonstra-tions


• Mathematics SOL


• DOE Patterns, Functions and Algebra Staff Development Guide

• Graphing calculator (if possible)



Topic


Related

SOL



Resources

Patterns, Functions, and Algebra (con’t) Patterns and Functions: Representations and Relationships *Include Whole Numbers, Fractions, and Decimals *Include variables in formulas Algebra: Representations and Relationships *Include Whole Numbers, Fractions, and Decimals

8.17 The student will create and solve problems using proportions, formulas and functions.

The student will be able to: Use problem solving, mathematical communication, mathematical reasoning, connections and representations to: Write problems that require

establishing a relationship between ratios.

Solve problems by using proportions.

Create problems that require the use of a formula.

Substitute known values for values for variables in a formula.

Solve a formula by using algebraic procedures.

Create problems that involve a functional relationship.

Solve problems that involve functions.

Math 6.21 6.22 7.19 8.3 A.1

Math 8

2nd & 4th 6 Weeks

2nd & 3rd 9 Weeks

Pre-

Algebra

1st & 4th 6 Weeks

1st & 3rd 9 Weeks

• Using blueprints and scale models to

illustrate proportional relationships. • Make scale drawings using art work. • Illustrate solving for a variable by

using the formulas for perimeter, circumference, area, and volume.

• Student

Demonstra-tions


• Mathematics SOL





Topic


Related

SOL



Resources

Patterns, Functions, and Algebra (con’t) Algebra: Representations and Relationships *Include Whole Numbers, Fractions, and Decimals

8.18 The student will use the following algebraic terms appropriately: • domain • range • independent

variable • dependent

variable

The student will be able to: Use problem solving, mathematical communication, mathematical reasoning, connections and representations to: Apply the following algebraic

terms appropriately: domain, range, independent variable and dependent variable.

Identify examples of domain, range, independent variable and dependent variable.

Determine the domain function. Determine the range of a function. Determine the independent

variable of a relationship. Determine the dependent variable

of a relationship.

Math 5.21 A.5

Math 8

4th

6 Weeks

3rd 9 Weeks

Pre-

Algebra

3rd 6 Weeks

2nd

9 Weeks

• Student

Demonstra-tions


• Mathematics SOL




Documents

Grade 8 Mathematics - Nexusnexuslearning.net/teachers/pacingguides/Danville/Grade 8/Grade 8... · Grade 8 Mathematics Standards of Learning Curriculum Guide Danville Public Schools,