## UNIT 1: ADDITION AND SUBTRACTION OF FRACTIONS

Lesson 1.1 - Adding and Subtracting Like Fractions

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

Lesson 1.2 - 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 1.3 - 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 1.4 - 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 1.5 - 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 2: MULTIPLICATION WITH FRACTIONS

Lesson 2.1 - Multiplying Whole Numbers by Fractions

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

Lesson 2.2 - Multiplying Fractions by Fractions

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

Lesson 2.3 - 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 2.4 - Multiplying by Fractions – Word Problems

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

## UNIT 3: DIVISION WITH FRACTIONS

Lesson 3.1 - 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 3.2 - 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 3.3 - 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 3.4 - Dividing with Fractions

• Using division to separate something many times

## UNIT 4: WORKING WITH FRACTIONS

Lesson 4.1 - 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 4.2 - Solving Fraction Word Problems

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

## UNIT 5: DECIMAL BASICS

Lesson 5.1 - Decimal Numbers

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

Lesson 5.2 - Changing Decimals to Fractions

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

Lesson 5.3 - Comparison Symbols

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

Lesson 4.4 - 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 5.5 - Rounding Decimals

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

Lesson 5.6 - 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 6: ADDING AND SUBTRACTING DECIMALS

Lesson 6.1 - 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 6.2 - 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 6.3 - 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 7: MULTIPLICATION WITH DECIMALS

Lesson 7.1 - Multiplying Decimals by Tens

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

Lesson 7.2 - 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 7.3 - Multiplying Decimals

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

Lesson 7.4 - Multiplying Decimals - Word Problems

• Calculating area using decimals
• Working with unit prices

## UNIT 8: DIVISION WITH DECIMALS

Lesson 8.1 - 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 8.2 - 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 8.3 - 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 8.4 - Dividing Decimals - Word Problems

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

## UNIT 9: MIXED OPERATIONS

Lesson 9.1 - 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 9.2 - 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 10: PERCENT BASICS

Lesson 10.1 - The Meaning of Percent

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

Lesson 10.2 - 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 10.3 - 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 10.4 - Finding Percents - Word Problems

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

## UNIT 11: PERCENT PROBLEMS

Lesson 11.1 - 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 11.2 - Adding & Subtracting Percents

• Subtracting percents

Lesson 11.3 - 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 11.4 - 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 11.5 - 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 12: RATIOS, PROPORTIONS, AND CONVERSION OF UNITS

Lesson 12.1 - Ratios

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

Lesson 12.2 - 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 12.3 - Converting Measurements

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

Lesson 12.4 - Converting Money

• Exchange rates and currency conversion ratios
• Making currency conversions

## UNIT 13: TEMPERATURE MEASUREMENT

Lesson 13.1 - 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 13.2 - 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 13.3 - 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 13.4 - 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 14: INTERSECTIONS AND PARALLELS

Lesson 14.1 - Intersecting Lines

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

Lesson 14.2 - Equal Angles

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

Lesson 14.3 - Supplementary Angles

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

Lesson 14.4 - 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 15: TRANSFORMATION OF SHAPES

Lesson 15.1 - Congruency

• The properties of congruent shapes

Lesson 15.2 - Translations

• Translations of shapes
• Pre-image and translated image

Lesson 15.3 - Reflections

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

Lesson 15.4 - Rotations

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

Lesson 15.5 - Magnifications

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

## UNIT 16: SOLID SHAPES

Lesson 16.1 - Cubes, Prisms, Pyramids

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

Lesson 16.2 - Cylinders, Cones, Spheres

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

Lesson 16.3 - Constructing Solid Shapes

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

## APPENDICES

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