Core Math: Grade 8

Detailed Table of Contents

UNIT 1: WORKING WITH FRACTIONS

Lesson 1.1 - Performing Fraction Arithmetic Operations

  • Rules for mixed operations
  • Adding and subtracting operations are done from left to right
  • Multiplying and dividing operations are done from left to right
  • If mixing operations, do multiplication and division before addition and subtraction
  • If brackets are used, do the operations in brackets first

Lesson 1.2 - Solving Fraction Word Problems

  • Standard steps for solving word problems: plan, model, calculate, check, answer
  • Reading word problems carefully

UNIT 2: DECIMAL WORD PROBLEMS

Lesson 2.1 - Adding and Subtracting Decimals - Word Problems

  • Using addition in word problems to combine or increase quantities
  • Using subtraction in word problems to take away or find the difference in quantities
  • Carefully reading word problems
  • Using full statements and measurement units in answer to word problems

Lesson 2.2 - Multiplying Decimals - Word Problems

  • Calculating area using decimals
  • Working with unit prices

Lesson 2.3 - Dividing Decimals - Word Problems

  • Using division in word problems to find a number of equal parts

UNIT 3: MIXED OPERATIONS

Lesson 3.1 - Doing Mixed Operations with Decimals

  • Do calculations left to right if only addition and subtraction
  • Do calculations left to right if only multiplication and division
  • Do multiplication and division before addition or subtraction
  • Do operations in brackets first

Lesson 3.2 - Doing Mixed Operations with Decimals - Word Problems

  • Using standard problem solving steps: plan, model, calculate, check, answer
  • Solving word problems with unit prices or costs
  • Solving word problems with time and distance

UNIT 4: PERCENT BASICS

Lesson 4.1 - The Meaning of Percent

  • The meaning of percent
  • Percent as a fraction
  • Percentage and percent or percentage sign

Lesson 4.2 - Changing Between Percents and Decimals

  • Changing a percent to a decimal by moving the decimal point two places left
  • Changing a decimal to a percent by moving the decimal point two places left

Lesson 4.3 - Changing Between Percents and Fractions

  • Changing a percent to a fraction using a denominator of 100
  • Reducing fractions to lowest terms
  • Changing a fraction to a percent by first changing the fraction to a decimal number and then moving the decimal point two places right

Lesson 4.4 - Finding Percents - Word Problems

  • Creating percent answers to word problems by finding fractions and changing to decimals and then to percents

UNIT 5: PERCENT PROBLEMS

Lesson 5.1 - Finding a Percent of a Number

  • Finding the percent of a number by changing the percent to a decimal then multiplying the number by the decimal

Lesson 5.2 - Adding & Subtracting Percents

  • Adding percents
  • Subtracting percents

Lesson 5.3 - Finding Percent Increase

  • Find what an amount would be after a percent increase by changing the percent increase to a decimal and multiplying the original number by the decimal then add that amount to the original number
  • Find the percent increase by a change in numbers by using a fraction for the amount of increase and changing the fraction to a decimal and then to a percent

Lesson 5.4 - Finding Percent Decrease

  • Find what an amount would be after a percent decrease by changing the percent decrease to a decimal and multiplying the original number by the decimal then subtract that amount to the original number
  • Find the percent decrease by a change in numbers by using a fraction for the amount of decrease and changing the fraction to a decimal and then to a percent

Lesson 5.5 - Percent - Word Problems

  • Using percents to find the portion of something or the amount of increase or decrease in quantities
  • Use standard problem solving steps for percent problems: plan, model, calculate, check, answer

UNIT 6: RATIOS, PROPORTIONS, AND CONVERSION OF UNITS

Lesson 6.1 - Ratios

  • Using ratios to compare things
  • First term and second term in ratios

Lesson 6.2 - Calculating Proportions

  • Using proportions to compare things
  • Finding equivalent ratios by multiplying or dividing both terms by the same number
  • Finding equivalent ratios when the first or second terms are not 1

Lesson 6.3 - Converting Measurements

  • Units of measurement and measurement systems
  • Using conversion ratios to change measurements

Lesson 6.4 - Converting Money

  • Exchange rates and currency conversion ratios
  • Making currency conversions

UNIT 7: TEMPERATURE MEASUREMENT

Lesson 7.1 - Fahrenheit Scale

  • Measuring temperature by degrees
  • Fahrenheit temperature scale
  • Negative temperatures
  • Conditions at different Fahrenheit temperatures
  • The thermometer and how it measures temperature
  • The meaning of freezing point
  • The meaning of boiling point
  • Recording Fahrenheit temperatures with degree symbol and abbreviation for Fahrenheit

Lesson 7.2 - Celsius Scale

  • Celsius temperature scale
  • Conditions at different Celsius temperatures
  • Freezing point and boiling point on the Celsius scale
  • Recording Celsius temperatures with degree symbol and abbreviation for Celsius

Lesson 7.3 - Fahrenheit to Celsius Conversion

  • Formula for changing Fahrenheit degrees to Celsius degrees
  • Short cut approximate conversion from Fahrenheit degrees to Celsius degrees
  • Conversions with negative temperatures

Lesson 7.4 - Celsius to Fahrenheit Conversion

  • Formula for changing Celsius degrees to Fahrenheit degrees
  • Short cut approximate conversion from Celsius degrees to Fahrenheit degrees
  • Conversion with negative temperatures

UNIT 8: INTERSECTIONS AND PARALLELS

Lesson 8.1 - Intersecting Lines

  • Intersecting lines and opposite angles
  • The Opposite Angle Theorem
  • Perpendicular lines
  • Mathematical theorems and proof of a theorem

Lesson 8.2 - Equal Angles

  • Parallel lines
  • Transversals
  • Parallel lines and alternate angles
  • The Alternate Angle Theorem
  • Parallel lines and corresponding angles
  • The Corresponding Angle Theorem

Lesson 8.3 - Supplementary Angles

  • Parallel lines and supplementary angles
  • Parallel lines and interior angles
  • The Interior Angle Theorem

Lesson 8.4 - Angle Problem Solving

  • Solving for missing angles with intersecting lines
  • Solving for missing angles with parallel lines and transversals
  • Applying angle theorems to solve for missing angles

UNIT 9: TRIANGLES

Lesson 9.1 - Triangles

  • The properties of triangles
  • Vertices and interior angles in triangles
  • Acute triangles
  • Right triangles
  • Obtuse triangles
  • Use of a compass to draw arcs

Lesson 9.2 - Special Triangles

  • Equilateral triangles
  • Isosceles triangles
  • Scalene triangles
  • Size of interior angles vs. side of length
  • The Isosceles Triangle Theorem

Lesson 9.3 - Triangle Angle Sum Theorem

  • Proof of the Triangle Angle Sum Theorem
  • Interior angles of triangles

Lesson 9.4 - Exterior Angle Sum Theorem

  • Exterior Angle Sum Theorem
  • Proof of Exterior Angle Sum Theorem

Lesson 9.5 - Triangle Problem Solving

  • Learn how to solve for missing angles using
  • Triangle theorems and angle facts

Lesson 9.6 - Pythagorean Theorem

  • The hypotenuse of a right triangle
  • The Pythagorean Theorem

UNIT 10: POLYGONS

Lesson 10.2 - Polygons

  • Names of common polygons
  • Properties of polygons
  • Polygons, pentagons, hexagons, heptagons, octagons, nonagons, and decagons

Lesson 10.3 - Regular Polygons

  • Properties of regular polygons

UNIT 11: TRANSFORMATIONS OF SHAPES

Lesson 11.1 - Congruency

  • The properties of congruent shapes

Lesson 11.2 - Translations

  • Translations of shapes
  • Pre-image and translated image

Lesson 11.3 - Reflections

  • Properties of reflected shapes
  • Mirror and reflected image
  • Pre-image and reflected image

Lesson 11.4 - Rotations

  • Rotation of shapes
  • Pre-image and rotated image
  • Center of rotation

Lesson 11.5 - Magnifications

  • Magnification and dilation of shapes
  • Magnification factor; scaling shapes; image; pre-image

UNIT 12: USES OF TRANSFORMATIONS

Lesson 12.1 - Similarity

  • The properties of similar shapes

Lesson 12.2 - Reflective Symmetry

  • Reflective symmetry
  • Axis of symmetry and reflected shapes

Lesson 12.3 - Rotational Symmetry

  • Rotational symmetry
  • Center of rotational symmetry

Lesson 12.4 - Tessellations I

  • The tessellation or tiling of shapes
  • The properties of tessellated or tiled shapes
  • Interior angles of tessellated polygons

Lesson 12.5 - Tessellations Ii

  • The tessellation of parallelograms and distorted parallelograms
  • Tessellated polygons

UNIT 13: SOLID SHAPES

Lesson 13.1 - Cubes, Prisms, Pyramids

  • Polyhedra
  • The properties of cube shapes
  • The properties of prism shapes
  • The properties of pyramid shapes

Lesson 13.2 - Cylinders, Cones, Spheres

  • The properties of cylinder shapes
  • The properties of cone shapes
  • The construction of sphere shapes

Lesson 13.3 - Constructing Solid Shapes

  • The construction of solid shapes
  • Nets of solid shapes
  • Three dimensional shapes

UNIT 14: CONSTRUCTIONS

Lesson 14.1 - Angle Bisectors

  • Construct an angle bisector

Lesson 14.2 - Perpendiculars from a Line

  • Construct a perpendicular from a line

Lesson 14.3 - Perpendiculars to a Line

  • Construct a perpendicular to a line

Lesson 14.4 - Right Bisectors

  • Construct right bisectors

Lesson 14.5 - The Circumcircle

  • Circumcircles
  • Find a circumcenter
  • Construction of a circumcircle

Lesson 14.6 - The Incircle

  • Incircles
  • Incircle and inradius
  • Construction of an incircle

Lesson 14.7 - Parallel Lines

  • Construction of parallel lines
  • Using a compass

APPENDICES

  • Appendix A - Decimals and Percents Glossary
  • Appendix B - Rules for Working with Decimals
  • Appendix C - Geometry Glossary
  • Appendix D - Geometry Facts and Theorems