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