Core Math: Grade 5

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

APPENDICES

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