Core Math: Grade 7

Detailed Table of Contents

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

  • Adding 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