math 8 curriculum

BCPS Curriculum Guide R07-2009

Math 8 Course Map

THIS COURSE: Math 8

Course Questions:

1. How are expressions, equations, and inequalities evaluated?2. What determines into which class a real number falls?3. How are various charts, graphs, and plots organized to understand collections of

data?4. What is the relationship between angles formed by lines and their

measurements?5. How are geometric figures in the coordinate plane transformed?6. How is the Pythagorean Theorem used?7. How are formulas used to find volume and surface area of 3-D figures?8. How are formulas and proportions used to solve practical problems?9. How are percents used in real life situations?10. How can probability be used to make predictions?11. How are tables, graphs, and rules used to graph linear equations?

Isabout

using mathematical concepts to introduce Algebraic skills and Geometric concepts as well as exploring statistical data.


Learned in theseUNITS

Critical Vocabulary

Exponents IntegersFractions FormulasDecimals InequalitiesPercents ExpressionsEquations TransformationsGraphs Number SystemsAngles Proportions3D Figures Properties

Algebra

Graphing

Proportions

Geometry

Real Numbers

Probability

Patterns Functions


Course: Math 8Unit 1: Algebra…is about…Pacing: 9 weeks

Key Unit Questions:

1. How are the properties of real numbers applied?

2. How are numeric and variable expressions simplified using order of operations?

3. How are 2 step equations and inequalities solved?

SOLs: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;

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.

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

Teacher Comments:**Teacher discretion - Multi-step equations and inequalities Holt 8 text 10-2, 10-3, 10-4

Expanding the knowledge of algebra by

Variable expressionsusing order

of operations

Equations and

inequalitiesNumeric

expressions using order

of operations

simplifying

simplifying

solving

applying applying

Properties of real

numbers


Essential Skills & Knowledge Suggested Activities & Assessments

Suggested Resources

8.1a The student will 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.

*** include negative exponents

8.4 The student will 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.

8.15 The student will 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.

-properties sort-order of operations mneumonic-FRAME with order of operation steps

-FRAME-Hands On Equations-Algeblocks

-Holt 8 text 2-6, 2-8

-http://janus.astro.umd.edu/astro/scinote-www.mathplayground.com/howto_pemdas.html

-Holt 8 text 1-1

-Holt 8 1-3, 1-4, 1-5, 2-4,2-5, 3-6, 3-7, 10-1-http://www.algebralab.org/lessons/lesson.aspx?filesAlgebra_Onevariableonestep.xml-http://www.learningwave.com/chapter/alpha/index.html


Required: Interactive Achievement Test

-mathnet:InteractiveAlgebra:Equationbuster-http://step.nn.k12va.us/math/middlemath/ppt/solve_one_step_inequalities.ppt--cached

-Holt 8 text 10-2 optional

Course: Math 8Unit 2: Graphing…is about…Pacing: 4 weeks

Key Unit Questions:

1. How is data organized with a variety of graphs and plots?

2. How is data compared, and predicted with a variety of graphs and plots?

3. How are inferences made from data?

4. How is data organized in a matrix (matrices)?

SOLs: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.

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

Organizing and analyzing

data

Bar, Line,

circle , and

picture graphs

Box & Whisker

Plots

Frequency Table & Histogra

ms

Patterns in Scattergrams

by examining

by identifying

by distinguishing

and formulating

To examine and create

by examining

Matrices



Suggested Resources

8.12 The student will 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.

8.13 The student will 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 real life source (newspaper) to analyze data-number line on floor and students become part of the graph

-convert various tables/charts to matrices-take survey and create matrix of data-M&M activity (CAMS)

-Holt 8 text 4-4, 4-5, 4-6, 4-7-www.mathteacher.com.au/year8/ch17_stat/03_freq/freq.htm-http://score.kings.k12.ca.us/lessons/mandm.html-http://quarknet.fnal.gov/toolkits/ati/histograms.html-http://www.wisc-online.com/objects.index_tj.asp?objid=TMH1101-http://teachhealthk-12.uthscsa.edu/curriculum/…-VDOE Box & Whisker

-Holt 8 text page 687-http://www.kidsnumber.com/math_magic.php

http://www.mathteacher.com.au/

BCPS Curriculum Guide R07-2009 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.

-Scope & Sequence pages 89-90

Required: Interactive Achievement Tests


Course: Math 8Unit 3: Proportions…is about…Pacing: 3 weeks

Key Unit Questions:

1. How are proportions used to solve practical problems?

2. How can problems be written that establish a relationship between ratios?

3. How are proportions used to identify and work with similar figures?

4. How are equivalent ratios determined?

SOLs:8.17 The student will create and solve problems, using proportions, formulas, and functions.8.3 The student will solve practical problems involving rational numbers, percents, ratios, and proportions.

Teacher Comments:

Using equivalent

ratios

Practical problem

s

To solve

Similar figures

To identify and apply

BCPS Curriculum Guide R07-2009Essential Skills & Knowledge Suggested

Activities & Assessments

Suggested Resources

8.17 The student will 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.

8.3 The student will 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.

-measure student heights and shadows to estimate height of tree or other tall object-construct an altimeter using a straw, string, ruler and a weight to create two similar triangles…find heights of different objects


-Holt 8 text 7-1, 7-2, 7-4-www.ehow.com/how_5011076_make-an-altimeter.html


Course: Math 8Unit 4: Geometry…is about…Pacing: 6 weeks

Key Unit Questions:

5. How is the Pythagorean Theorem applied?

6. How are square roots determined? (with the use of calculator)

7. How are angles identified and measured ?

8. What are the relationships of the angles between intersecting lines and how are they determined?

9. How are figures in the coordinate plane graphed and transformed ?

10. How are nets of 3D figures identified?

11. How are formulas used to calculate volume and surface areas?


a) verify the Pythagorean Theorem, using diagrams, concrete materials, and measurement; andb) 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.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 360°.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.

8.9 The student will construct a three-dimensional model, given the top, side, and/or bottom views.8.7 The student will investigate and solve practical problems involving volume and surface area of

rectangular solids (prisms), cylinders, cones, and pyramids.8.17 The student will create and solve problems, using proportions, formulas, and functions.

Teacher Comments:

Nets of 3D

figures

Exploring various

figures by Volume & Surface

Area

Pythagorean Theorem

finding

identifying

applying

Angles

analyzing

Coordinate Plane and

transformations

graphing



Suggested Resources

8.10 The student will 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

8.6 The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Measure angles of less than 360° 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

-use tiles to probe theorem-ask a carpenter how they determine right angles-Scope & Sequence pages 37-40,45

-protractor activities-FRAME-Scope & Sequence pages 47-51-use toothpicks and marshmallows to illustrate angles, vertices, and edges

-Intro to triangles Holt 8 text 5-3-Holt 8 text 6-3-http://www.mathisfun.com/pythagoras.htmlhttp://www.doe.virginia.gov/VDOE/EnhancedSandS/mgrade8.doc

-Holt 8 text 5-1, 5-2- www.kidsport.com/grade 7/math/measuregeo/measuringangles-www.mathleague.com/help/geometry/angles.htm-http://

BCPS Curriculum Guide R07-2009vertical.

Identify and describe pairs of angles that are supplementary.

Identify and describe pairs of angles that are complementary.

8.8 The student will 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 90° 180°, 270°, and 360° rotations of a figure on a coordinate grid.

Demonstrate the translation of a figure on a coordinate grid.

8.9 The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Construct three-dimensional models, given top,

side, and bottom views.

8.7 The student will 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.

-Dry erase coordinate plane boards-Scope & Sequence pages 60-67

-1997 AIM Activity Spacial Visualization (RMMS)-Scope & Sequence pages 68-69

-Cut a net of each figure to find total area -Scope & Sequence pages 56-58


mathworld.wolfram.com/Angle.html

-Holt 8 text 5-7

-Holt 8 text 6-5, 6-6, 6-7,6-8, 6-9

BCPS Curriculum Guide R07-2009 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.

8.17 The student will 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.


Course: Math 8Unit 5: Real Numbers…is about…Pacing: 4 weeks

Key Unit Questions:

12. How are fractions, decimals, percents, and scientific notation interchanged, compared, and ordered ?

13. How are percents used to solve consumer application problems?

14. How is percent of increase and decrease determined?

15. How do relationships between subsets of the real number system differ?

16. How are the values of square roots placed on a number line?


b) recognize, represent, compare, and order rational numbers expressed in scientific notationc) compare and order decimals, fractions, percents, and numbers written in scientific notation

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.

8.5 The student, given a whole number from 0 to 100, will identify it as a perfect square or find the two consecutive whole numbers between which the square root lies.

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

Teacher Comments:

Decimals, fractions, percents, scientific notation

Percent increase

& decrease

Consumer application problems

findingsolving

Comparing and ordering

Subsets of real

numbers

Classifying and identifing

Representing and

applying numbers by



Suggested Resources

8.1 The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to 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.

8.3 The student will 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.

8.5 The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Identify the perfect squares from 0 to 100.

-flash cards-sorts to order-Scope & Sequence pages 3-6

-Create advertising poster or sale flyer-Create a checkbook and go shopping -Scope & Sequence pages 103-106

-calculator exploration-Scope & Sequence pages 34-36

-Holt 8 text 2-9, 8-1-www.mathgoodies.com/lesson/volt/challenge_vol4htm-www.mathplayground.com/mathvideos/html-http://janus.astro.umd.edu/astro/scinote

-Holt 8 text 8-2, 8-3, 8-4, 8-6, 8-7-newspapers/flyers/catalogues

BCPS Curriculum Guide R07-2009 Identify the two consecutive whole numbers

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

8.2 The student will 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.

-FRAME-Flow Chart-Scope & Sequence pages 6-8-Concept Comparison or Concept Masteryof Rational and Irrational Numbers


-Holt 8 text 3-8, 3-9

-Holt 8 text 3-10


Course: Math 8Unit 7: Patterns and Functions…is about…Pacing: 3 weeks

Key Unit Questions:

17. How do functions and relations differ?

18. How are linear equations graphed?

19. How are domain, range, independent, and dependent variables identified?

20. How are rules determined from a table of values?

21. How are tables of values, graphs and rules related?

22. How are the domain, and range of a function determined? How are domain and range related to independent and dependent variables?


a) describe and represent relations and functions, using tables, graphs, and rules; andb) relate and compare tables, graphs, and rules as different forms of representation for relationships.

8.17 The student will create and solve problems, using proportions, formulas, and functions.8.18 The student will use the following algebraic terms appropriately: domain, range, independent variable, and

dependent variable.8.16 The student will graph linear equations in two variables, in the coordinate plane, using a table of ordered

pairs.Teacher Comments:

Functions and

relations

Identifying relationships

Linear equations

by comparing

by graphing Domain,

range, IV, DV

by identifying



Suggested Resources

8.14 The student will 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 relation.

8.17 The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Create problems that involve a functional

relationship.

-charts/tables from real life sources

-Scope & Sequence pages 107-120

-Holt 8 text 1-7, 1-8, 1-9

BCPS Curriculum Guide R07-2009 Solve problems that involve functions

8.18 The student will 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 of a function. Determine the range of a function. Determine the independent variable of a

relationship. Determine the dependent variable of a

relationship.

8.16The student will 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 for y.

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

Connect the ordered pairs to form a straight line.

-coordinate with science department experiments-point out alphabetical patterns


-Holt 8 text 12-4

-Holt 8 text 1-7, 1-8, 11-1

math 8 curriculum

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