Decimal & Percents: Step by Step

Table of Contents

UNIT 1: DECIMAL BASICS

Lesson 1.1 - Decimal Numbers

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

Lesson 1.2 - Changing Decimals to Fractions

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

Lesson 1.3 - Comparison Symbols

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

Lesson 1.4 - 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 1.5 - Rounding Decimals

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

Lesson 1.6 - 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 2: ADDITION & SUBTRACTION WITH DECIMALS

Lesson 2.1 - 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 2.2 - 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 2.3 - Adding & 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 3: MULTIPLICATION WITH DECIMALS

Lesson 3.1 - Multiplying Decimals by Tens

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

Lesson 3.2 - 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 3.3 - Multiplying Decimals

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

Lesson 3.4 - Multiplying Decimals - Word Problems

  • Calculating area using decimals
  • Working with unit prices

UNIT 4: DIVISION WITH DECIMALS

Lesson 4.1 - 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 4.2 - 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 4.3 - 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 4.4 - Dividing Decimals - Word Problems

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

UNIT 5: MIXED OPERATIONS

Lesson 5.1 - 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 5.2 - 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 6: PERCENT BASICS

Lesson 6.1 - The Meaning of Percent

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

Lesson 6.2 - 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 6.3 - 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 6.4 - Finding Percents - Word Problems

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

UNIT 7: PERCENT PROBLEMS

Lesson 7.1 - 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 7.2 - Adding & Subtracting Percents

  • Adding percents
  • Subtracting percents

Lesson 7.3 - 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 7.4 - 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 7.5 - Percents - 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 8: PRACTICAL PROBLEMS

Lesson 8.1 - Ratios

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

Lesson 8.2 - 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 8.3 - Converting Measurements

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

Lesson 8.4 - Converting Money

  • Exchange rates and currency conversion ratios
  • Making currency conversions

APPENDICIES

  • Appendix A - Finding Lowest Terms
  • Appendix B - Multiplication Table
  • Appendix C - Customary Units
  • Appendix D - Metric Units
  • Appendix E - Rules for Working with Decimals
  • Appendix F - Glossary