Detailed Table of Contents

UNIT 1: FRACTION CONCEPTS

Lesson 1.1 - Fractions and Mixed Numbers

• The concept of a fraction
• Numerator and denominator
• Fractions in measurement
• Fraction of a set
• Fractions larger than one
• Mixed numbers

Lesson 1.2 - Equivalent Fractions and Lowest Terms

• Equivalent fractions
• Using common multiples to create equivalent fractions
• Reducing fractions to lowest terms
• Using common factors to reduce fractions

Lesson 1.3 - Least Common Denominator

• Common denominator
• Making common denominators
• Least common denominator
• Using least common multiple to find equivalent fractions with common denominators

Lesson 1.4 - Comparison Symbols

• Less than symbol
• Greater than symbol

Lesson 1.5 - Comparing Fractions

• Comparing fractions with the same denominators
• Comparing fractions with different denominators by making equivalent fractions
  with common denominators

Lesson 1.6 - Mixed Numbers and Improper Fractions

• Mixed numbers and improper fractions
• Converting a mixed number to an improper fraction
• Converting an improper fraction to a mixed number

UNIT 2: ADDITION AND SUBTRACTION OF FRACTIONS

Lesson 2.1 - Adding and Subtracting Like Fractions

• Like fractions with common denominators
• Adding like fractions
• Subtracting like fractions
• Reducing to lowest terms in fractions calculations

Lesson 2.2 - Adding and Subtracting Unlike Fractions

• Adding unlike fractions by creating equivalent fractions with common denominators
• Subtracting unlike fractions by creating equivalent fractions with common
  denominators
• Using least common denominator in fractions calculations
• Reducing to lowest terms in fractions calculations
  

Lesson 2.3 - Adding Mixed Numbers

• Regrouping mixed numbers for addition
• Converting mixed numbers to improper fractions for addition
• Recording sum of mixed numbers as a mixed number

Lesson 2.4 - Subtracting Mixed Numbers

• Regrouping mixed numbers for subtraction
• Converting mixed numbers to improper fractions for subtraction
• Recording the remainder of subtraction mixed numbers as a mixed number

Lesson 2.5 - Adding and Subtracting Fractions – Word Problems

• Using addition where word problems combine or increase quantities
• Using subtraction where word problems reduce or remove quantities

UNIT 3: MULTIPLICATION WITH FRACTIONS

Lesson 3.1 - Multiplying Whole Numbers by Fractions

• Converting whole numbers to fractions to multiply by another fraction
• Multiplying numerators and denominators of fraction numbers

Lesson 3.2 - Multiplying Fractions by Fractions

• Multiplying numerators and denominators of fraction numbers
• Reducing the product of multiplied fractions to lowest terms

Lesson 3.3 - Multiplying Mixed Numbers by Fractions

• Converting mixed numbers to improper fractions for multiplication
• Recording the product of multiplied mixed numbers as a mixed number

Lesson 3.4 - Multiplying by Fractions – Word Problems

• Using multiplication where word problems combine or increase quantities many times

UNIT 4: DIVISION WITH FRACTIONS

Lesson 4.1 - Dividing Whole Numbers by Fractions

• Divide by a fraction by multiplying the reciprocal of the fraction divisor – flip and multiply
• Reducing the quotient in fraction form to lowest terms

Lesson 4.2 - Dividing Fractions by Fractions

• Divide a fraction by another fraction by multiplying the reciprocal of the fraction divisor
• Reducing the quotient in fraction form to lowest terms

Lesson 4.3 - Dividing Mixed Numbers

• Converting mixed numbers to improper fractions for arithmetic operations
• Divide an improper fraction by multiplying the reciprocal of the fraction divisor
• Reducing the quotient in fraction form to lowest terms

Lesson 4.4 - Dividing with Fractions

• Using division to separate something many times

UNIT 5: WORKING WITH FRACTIONS

Lesson 5.1 - 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 5.2 - Solving Fraction Word Problems

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

UNIT 6: DECIMAL BASICS

Lesson 6.1 - Decimal Numbers

• Whole numbers and fractions
• Mixed numbers
• Decimal numbers
• Decimal places
• How to say decimals
• Money and decimals

Lesson 6.2 - Changing Decimals to Fractions

• Parts of a fraction
• Changing decimals to fractions
• Reducing fractions to lowest terms

Lesson 6.3 - Comparison Symbols

• Greater than symbol
• Less than symbol
• Comparing whole numbers

Lesson 6.4 - Comparing Decimals

• Showing decimal values in grids and pictures
• Comparing decimal values in pictures
• Comparing decimal numbers from left to right
• Adding zeros to decimals to compare numbers of equal length

Lesson 6.5 - Rounding Decimals

• Rounding to nearest whole number
• Rounding to the nearest decimals for a selected decimal place value

Lesson 6.6 - Changing Fractions to Decimals

• Changing fractions to decimals with denominators in base ten
• Changing fractions to decimals by dividing the numerator by the denominator
• Common fractions and equivalent decimal numbers

UNIT 7: ADDITION AND SUBTRACTION OF DECIMALS

Lesson 7.1 - Adding Decimals

• Place value alignment in adding decimal numbers
• Make decimal numbers the same length by adding zeros
• Including decimal point after a whole number when adding to decimal numbers

Lesson 7.2 - Subtracting Decimals

• Place value alignment in subtracting decimal numbers
• Make decimal numbers the same length by adding zeros
• Checking answer by adding from bottom up

Lesson 7.3 - 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

UNIT 8: MULTIPLICATION WITH DECIMALS

Lesson 8.1 - Multiplying Decimals by Tens

• Moving decimal point to the right when multiplying decimals by base ten numbers

Lesson 8.2 - Multiplying Decimals by Tenths

• Moving decimal point to the left when multiplying decimals by base ten decimal numbers
• Adding a zero left of a decimal point if there is no whole number part

Lesson 8.3 - Multiplying Decimals

• Counting decimal places in the numbers multiplied to use in the product
• Multiplying dollars and rounding to two decimal places

Lesson 8.4 - Multiplying Decimals - Word Problems

• Calculating area using decimals
• Working with unit prices

UNIT 9: DIVISION WITH DECIMALS

Lesson 9.1 - Dividing by Tens or Tenths

• Moving decimal point to the left when dividing by base ten
• Moving decimal point to the left when dividing by decimal number in base ten

Lesson 9.2 - Dividing Decimals by Whole Numbers

• Long division of decimal numbers by decimal numbers
• Converting a decimal divisor to a whole number and changing the decimal place in the dividend and quotient
• Adding zeros to dividend if needed to complete division
• Repeating decimals
  

Lesson 9.3 - Dividing Decimals by Decimals

• Regrouping mixed numbers for addition
• Converting mixed numbers to improper fractions for addition
• Recording sum of mixed numbers as a mixed number

Lesson 9.4 - Dividing Decimals - Word Problems

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

UNIT 10: MIXED OPERATIONS

Lesson 10.1 - 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 10.2 - 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 11: RATIOS, PROPORTIONS, AND CONVERSION OF UNITS

Lesson 11.1 - Ratios

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

Lesson 11.2 - 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 11.3 - Converting Measurements

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

Lesson 11.4 - Converting Money

• Exchange rates and currency conversion ratios
• Making currency conversions

UNIT 12: LINES AND ANGLES

Lesson 12.1 - Lines

• Points and lines
• Rays and line segments
• Shapes made from points, lines, surfaces, and solids

Lesson 12.2 - Measuring Angles

• Angles
• How to measure angles
• Angle rotation and degrees
• Angle quarter turn; angle half turn; angle full turn
• Angle vertex
• Angle symbols
• Size of angles

Lesson 12.3 - Types of Angles

• Types of angles
• Straight and right angles
• Acute and obtuse angles
• Reflex angles
• Supplementary angles
• Complementary angles

UNIT 13: PLANE SHAPES

Lesson 13.1 - 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 13.2 - Quadrilaterals

• Plane shapes
• Squares, rhombi, parallelograms, and trapezoids

Lesson 13.3 - Polygons

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

Lesson 13.4 - Regular Polygons

• Properties of regular polygons

Lesson 13.5 - Circles

• The parts of a circle
• Using a compass to draw a circle or draw arcs

Lesson 13.6 - Ellipses

• Parts of an ellipse
• Elliptical shapes
• Lines of symmetry in ellipses

UNIT 14: SOLID SHAPES

Lesson 14.1 - Cubes, Prisms, Pyramids

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

Lesson 14.2 - Cylinders, Cones, Spheres

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

APPENDICIES

• Appendix A - Finding Lowest Terms
• Appendix B - Multiplication Table
• Appendix C - Customary Units
• Appendix D - Metric Units