Pure mathematics is, in its way, the poetry of logical ideas.
Albert Einstein
Albert Einstein
Grade 6 Math Unit Plans
Unit 1: Operations with Whole Numbers and Decimals
This unit reviews the concepts of place value and computation with whole numbers and decimals.
Topics
Place Value/Add and Subtract Whole Numbers and Decimals
Multiply Whole Numbers and Decimals
Divide Whole Numbers and Decimals
Objectives
To help students review place-value skills and computation with whole numbers and decimals.
To help students review multiplication of whole numbers and decimals.
To help students review and reinforce division of whole numbers and decimals, as well as work with metric measurements.
Content
Place Value
https://www.youtube.com/watch?v=x-Dqe5U1TXA
Compare and Order Numbers
Round Numbers
Place Value and Powers of Ten
Add and Subtract Whole Numbers and Decimals
Multiply Whole Numbers
Multiply Decimals by Whole Numbers
Multiply Decimals by Decimals
Divide Whole Numbers by One Digit Divisors
Divide Whole Numbers by Two Digit Divisors
Divide Decimals by Whole Numbers
Divide Decimals by Decimals
Mental Math with Powers of Ten
Decimals and the Metric System
Assessment
Monitoring Progress
Summative Assessment
Ongoing Review
Unit 2: Fractions and Number Theory
This unit reinforces number theory and fractions concepts and extends the relationship between fractions, mixed numbers and decimals.
Topics
Number Theory
Fraction Concepts
Fractions and Decimals
Objectives
To help students identify factors and multiples.
To help students reinforce skills in working with fractions.
To help students to extend their understanding of the relationships between fractions mixed numbers, and decimals.
Content
Factors and Prime Numbers
https://www.mathplayground.com/howto_primenumbers.html
Exponents
https://www.youtube.com/watch?v=WwHyPoqUQec
Prime Factorization
https://www.mathplayground.com/howto_primefactorization.html
Divisibility Rules
https://www.mathplayground.com/howto_divisibility.html
Greatest Common Factors
Least Common Multiple
https://www.mathplayground.com/howto_gcflcm.html
Write Equivalent Fractions
https://www.youtube.com/watch?v=04dKkEi3w0g
Simplest Form
https://www.mathplayground.com/howto_fractions_reduce.html
Compare and Order Fractions
https://www.mathplayground.com/howto_comparefractions.html
Fractions, Mixed Numbers, and Decimals
https://www.mathplayground.com/howto_fractions_decimals.html
Terminating and Repeating Decimals
Assessment
Monitoring Progress
Summative Assessment
Ongoing Review
Unit 3: Operations With Fractions
This unit reviews and reinforces computation with fractions and reviews customary units of measure.
Topics
Add and Subtract Fractions
Multiply and Divide Fractions
Fractions and Measurement
Objectives
To help students develop proficiency at adding and subtracting fractions
To help students develop proficiency in multiplying and dividing fractions and mixed numbers.
To help students review and apply Metric units as well as review computation with fractions when solving problems.
Content
Add fractions with like denominators
https://www.youtube.com/watch?v=EJjnEau6aeI
Subtract fractions with like denominators
https://www.youtube.com/watch?v=UbUdyE1_b9g
Add fractions with unlike denominators
https://www.youtube.com/watch?v=bcCLKACsYJ0
Subtract fractions with unlike denominators
https://www.youtube.com/watch?v=2DPivVFCdqA
Add mixed numbers with like denominators
https://www.youtube.com/watch?v=EGy1W24EPEI
Subtract mixed numbers with like denominators
https://www.youtube.com/watch?v=q19UnHEofOA
Add mixed numbers with unlike denominators
https://www.youtube.com/watch?v=CfBYGFm5gPA
Subtract mixed numbers with unlike denominators
https://www.youtube.com/watch?v=_btQus9HV_I
Multiply fractions
https://www.youtube.com/watch?time_continue=115&v=CTKMK1ZGLuk
Multiply mixed numbers
https://www.youtube.com/watch?v=RPhaidW0dmY
Divide Fractions
https://www.youtube.com/watch?v=tnkPY4UqJ44
Divide Mixed Numbers
https://www.youtube.com/watch?v=51-U-Jkq79A
Dividing whole numbers and fractions
https://www.youtube.com/watch?v=PQsgXNggV7Q
Find the Reciprocal of a Number
https://www.youtube.com/watch?v=6YYiiixYz9A
Metric Units of Measurement
https://www.youtube.com/watch?v=7RkRv_pQMxc
https://www.mathplayground.com/howto_Metric.html
Assessment
Monitoring Progress
Summative Assessment
Ongoing Review
Unit 4: Integers and Rational Numbers
This unit develops computation with integers and introduces the concept of rational numbers.
Topics
Integer Concepts
Operations and Integers
Rational Number Concepts
Objectives
To help students review integers and how to compare and order them
To help students learn to compute with integers.
To help students make the transition from fractions and integers to rational numbers.
Content
Integers and Compare and Order Integers
https://www.youtube.com/watch?v=KLPlvaXg1FM
Add, Subtract, Multiply, and Divide Integers
https://www.youtube.com/watch?v=vQtDCtjJhmA
What are Rational Numbers
https://www.youtube.com/watch?v=SQ4cB9yXkHM
Compare and Order Rational Numbers
https://www.youtube.com/watch?v=J-mrAZbOvQ8
https://www.youtube.com/watch?v=WynEmwOyMjE
https://www.youtube.com/watch?v=CbrfJPv2qP8
Assessment
Monitoring Progress
Summative Assessment
Ongoing Review
Unit 5: Expressions and Equations
This unit continues development of evaluating and writing expressions and of solving equations.
Topics
Evaluate Expressions
Write Expressions
Equations
Objectives
To help students apply various mathematical properties when evaluating numerical and algebraic expressions.
To help students make the transition from writing and evaluating expressions to using expressions to solve problems.
To help students reinforce skills in solving equations.
Content
Use Addition Properties to Evaluate Expression
Use Multiplication Properties to Evaluate Expression
Order of Operations
Use the Distributive Property to Evaluate Expression
Evaluate Expression with Fractions
Write Addition and Subtraction Expressions
Write Multiplication and Division Expressions
Write Expressions with Fractions
Equations with Addition and Subtraction
Equations with Multiplication and Division
Equations with Fractions
Assessment
Monitoring Progress
Summative Assessment
Ongoing Review
Unit 6: Ratio, Proportion and Percent
This unit presents the concepts of ratios, rates, proportions, and percents, and explores the relationships between fractions, decimals and percents.
Topics
Ratio, Rates, and Proportion
Using Ratio and Proportion
Relating Fractions, Decimals, and Percents
Objectives
To help students understand the concepts of Ratios, Rates, and Proportions
To help students apply the concepts of Ratios and Proportions to real world situations
To help students understand the relationships between fractions, decimals and percents
Content
Ratios
Rates
Equivalent Ratios
Solve Proportions
Distance, Speed, and Time
Scale Drawings
Decimals and Percents
Fractions and Percents
Fractions, Decimals, and Percents
Assessment
Monitoring Progress
Summative Assessment
Ongoing Review
Unit 7: Applications of Percent
This unit presents the applications and uses of percents in the real world.
Topics
The Three Cases of Percent
Content Focus
Objectives
To help students understand the three types of percent problems they will encounter
To help students apply their skills with percent to real-world problems
Content
Find a Percent of a Number
Find a Percent
Find a Number When a Percent is Known
Percent Relationships
Mental Math;
Estimate with Percents
Simple Interest
Problem-Solving Strategy: Find a Pattern
Sales Tax and Discounts
Assessment
Monitoring Progress
Summative Assessment
Ongoing Review
Unit 8: Geometry of Plane Figures
This unit reviews the geometry of plane figures.
Topics
The Three Cases of Percent
Content Focus
Objectives
To help students learn about plane figures, including pairs of angles and circles
To help students learn about polygons and congruent and similar figures
To help students explore and learn about how geometric figures can be moved to create new figures
Content
Plane Figures
Pairs of Angles
Measure Angles
Draw Angles
Circles and central Angles
Triangles and Angle Sums
Quadrilaterals and Angle Sums
Draw Triangles and Quadrilaterals
Congruence and Constructions
Similar Figures
Polygons
Transformations Corresponding Parts of Congruent Figures
Assessment
Monitoring Progress
Summative Assessment
Ongoing Review
Unit 9: Geometry and Measurement
This unit presents producers for finding perimeter, area, surface area, and volume.
Topics
Perimeter and Area of Polygons
Circumference and Area of Circles
Surface Area and Volume of Solid Figures
Objectives
To help students review how to find the perimeter and area of polygons
To help students review how to find the circumference of a circle and develop the formula for finding the area of a circle
To help students apply formulas for surface area and volume of solid figures
Content
Perimeter and Area
Area of a Parallelogram
Area of a Triangle
Circumference
Area of a circle
Solid Figures
Surface Area
Volume of Rectangular Prisms
Volume of Other Solids
Assessment
Monitoring Progress
Summative Assessment
Ongoing Review
Unit 10: Data Analysis and Statistics
This unit continues development of statistical concepts, such as measures of central tendency and different ways to display data.
Topics
Statistics and Graphing
Analyzing and Representing Data
Objectives
To help students identify the mean, median, mode, and range of a data set and interpret and make graphs and tables.
To help students analyze data by using measures of central tendency and various displays of data.
Content
Use Statistics
Read and Make Double Bar Graphs
Frequency Tables and Histograms
Read and Make Double Line Graphs
Choose the Most Useful Statistical Measure
Clusters, Gaps and Outliers
Stem-and-Leaf Plots
Box-and –Whisker Plots
Assessment
Monitoring Progress
Summative Assessment
Ongoing Review
Unit 11: Statistics and Probability
This unit presents the concepts of collecting and using data and of finding various types of probabilities.
Topics
Sampling
Bias in Statistics
Probability and Outcomes
Objectives
To help students recognize and use appropriate data samples to solve problems
To help students be aware that surveys and statistics can be misleading
To help students identify all possible outcomes and use that information to find probabilities
Content
Use Samples to Predict
Select a Sample
Misleading Statistics
Interpret Data Displays
Possible Outcomes
Theoretical Probability
Experimental Probability
Disjoint Events
Independent Events
Dependent Events
Assessment
Monitoring Progress
Summative Assessment
Ongoing Review
Unit 12: Coordinate Graphing, Equations, and Integers
This unit extends the concepts of the coordinate plane, graphing and solving equations, and working with integers.
Topics
The Coordinate Plane
Graphing Equations
Integers and Equations
Objectives
To help students graph ordered pairs and find distances and area on a coordinate grid
To help students learn to solve and graph equations with two variables
To help students work with expressions and equations that involve integers
Content
Graph points in the coordinate Plane
Geometric Figures and the Coordinate Plane
Graphs and Measurement
Functions
Graph Linear Equations
Order of Operations With Integers
Evaluate and Simplify Expressions With Integers
Write Expressions With Integers
Equations With Integers
Assessment
Monitoring Progress
Summative Assessment
Ongoing Review
This unit reviews the concepts of place value and computation with whole numbers and decimals.
Topics
Place Value/Add and Subtract Whole Numbers and Decimals
Multiply Whole Numbers and Decimals
Divide Whole Numbers and Decimals
Objectives
To help students review place-value skills and computation with whole numbers and decimals.
To help students review multiplication of whole numbers and decimals.
To help students review and reinforce division of whole numbers and decimals, as well as work with metric measurements.
Content
Place Value
https://www.youtube.com/watch?v=x-Dqe5U1TXA
Compare and Order Numbers
Round Numbers
Place Value and Powers of Ten
Add and Subtract Whole Numbers and Decimals
Multiply Whole Numbers
Multiply Decimals by Whole Numbers
Multiply Decimals by Decimals
Divide Whole Numbers by One Digit Divisors
Divide Whole Numbers by Two Digit Divisors
Divide Decimals by Whole Numbers
Divide Decimals by Decimals
Mental Math with Powers of Ten
Decimals and the Metric System
Assessment
Monitoring Progress
Summative Assessment
Ongoing Review
Unit 2: Fractions and Number Theory
This unit reinforces number theory and fractions concepts and extends the relationship between fractions, mixed numbers and decimals.
Topics
Number Theory
Fraction Concepts
Fractions and Decimals
Objectives
To help students identify factors and multiples.
To help students reinforce skills in working with fractions.
To help students to extend their understanding of the relationships between fractions mixed numbers, and decimals.
Content
Factors and Prime Numbers
https://www.mathplayground.com/howto_primenumbers.html
Exponents
https://www.youtube.com/watch?v=WwHyPoqUQec
Prime Factorization
https://www.mathplayground.com/howto_primefactorization.html
Divisibility Rules
https://www.mathplayground.com/howto_divisibility.html
Greatest Common Factors
Least Common Multiple
https://www.mathplayground.com/howto_gcflcm.html
Write Equivalent Fractions
https://www.youtube.com/watch?v=04dKkEi3w0g
Simplest Form
https://www.mathplayground.com/howto_fractions_reduce.html
Compare and Order Fractions
https://www.mathplayground.com/howto_comparefractions.html
Fractions, Mixed Numbers, and Decimals
https://www.mathplayground.com/howto_fractions_decimals.html
Terminating and Repeating Decimals
Assessment
Monitoring Progress
Summative Assessment
Ongoing Review
Unit 3: Operations With Fractions
This unit reviews and reinforces computation with fractions and reviews customary units of measure.
Topics
Add and Subtract Fractions
Multiply and Divide Fractions
Fractions and Measurement
Objectives
To help students develop proficiency at adding and subtracting fractions
To help students develop proficiency in multiplying and dividing fractions and mixed numbers.
To help students review and apply Metric units as well as review computation with fractions when solving problems.
Content
Add fractions with like denominators
https://www.youtube.com/watch?v=EJjnEau6aeI
Subtract fractions with like denominators
https://www.youtube.com/watch?v=UbUdyE1_b9g
Add fractions with unlike denominators
https://www.youtube.com/watch?v=bcCLKACsYJ0
Subtract fractions with unlike denominators
https://www.youtube.com/watch?v=2DPivVFCdqA
Add mixed numbers with like denominators
https://www.youtube.com/watch?v=EGy1W24EPEI
Subtract mixed numbers with like denominators
https://www.youtube.com/watch?v=q19UnHEofOA
Add mixed numbers with unlike denominators
https://www.youtube.com/watch?v=CfBYGFm5gPA
Subtract mixed numbers with unlike denominators
https://www.youtube.com/watch?v=_btQus9HV_I
Multiply fractions
https://www.youtube.com/watch?time_continue=115&v=CTKMK1ZGLuk
Multiply mixed numbers
https://www.youtube.com/watch?v=RPhaidW0dmY
Divide Fractions
https://www.youtube.com/watch?v=tnkPY4UqJ44
Divide Mixed Numbers
https://www.youtube.com/watch?v=51-U-Jkq79A
Dividing whole numbers and fractions
https://www.youtube.com/watch?v=PQsgXNggV7Q
Find the Reciprocal of a Number
https://www.youtube.com/watch?v=6YYiiixYz9A
Metric Units of Measurement
https://www.youtube.com/watch?v=7RkRv_pQMxc
https://www.mathplayground.com/howto_Metric.html
Assessment
Monitoring Progress
Summative Assessment
Ongoing Review
Unit 4: Integers and Rational Numbers
This unit develops computation with integers and introduces the concept of rational numbers.
Topics
Integer Concepts
Operations and Integers
Rational Number Concepts
Objectives
To help students review integers and how to compare and order them
To help students learn to compute with integers.
To help students make the transition from fractions and integers to rational numbers.
Content
Integers and Compare and Order Integers
https://www.youtube.com/watch?v=KLPlvaXg1FM
Add, Subtract, Multiply, and Divide Integers
https://www.youtube.com/watch?v=vQtDCtjJhmA
What are Rational Numbers
https://www.youtube.com/watch?v=SQ4cB9yXkHM
Compare and Order Rational Numbers
https://www.youtube.com/watch?v=J-mrAZbOvQ8
https://www.youtube.com/watch?v=WynEmwOyMjE
https://www.youtube.com/watch?v=CbrfJPv2qP8
Assessment
Monitoring Progress
Summative Assessment
Ongoing Review
Unit 5: Expressions and Equations
This unit continues development of evaluating and writing expressions and of solving equations.
Topics
Evaluate Expressions
Write Expressions
Equations
Objectives
To help students apply various mathematical properties when evaluating numerical and algebraic expressions.
To help students make the transition from writing and evaluating expressions to using expressions to solve problems.
To help students reinforce skills in solving equations.
Content
Use Addition Properties to Evaluate Expression
Use Multiplication Properties to Evaluate Expression
Order of Operations
Use the Distributive Property to Evaluate Expression
Evaluate Expression with Fractions
Write Addition and Subtraction Expressions
Write Multiplication and Division Expressions
Write Expressions with Fractions
Equations with Addition and Subtraction
Equations with Multiplication and Division
Equations with Fractions
Assessment
Monitoring Progress
Summative Assessment
Ongoing Review
Unit 6: Ratio, Proportion and Percent
This unit presents the concepts of ratios, rates, proportions, and percents, and explores the relationships between fractions, decimals and percents.
Topics
Ratio, Rates, and Proportion
Using Ratio and Proportion
Relating Fractions, Decimals, and Percents
Objectives
To help students understand the concepts of Ratios, Rates, and Proportions
To help students apply the concepts of Ratios and Proportions to real world situations
To help students understand the relationships between fractions, decimals and percents
Content
Ratios
Rates
Equivalent Ratios
Solve Proportions
Distance, Speed, and Time
Scale Drawings
Decimals and Percents
Fractions and Percents
Fractions, Decimals, and Percents
Assessment
Monitoring Progress
Summative Assessment
Ongoing Review
Unit 7: Applications of Percent
This unit presents the applications and uses of percents in the real world.
Topics
The Three Cases of Percent
Content Focus
Objectives
To help students understand the three types of percent problems they will encounter
To help students apply their skills with percent to real-world problems
Content
Find a Percent of a Number
Find a Percent
Find a Number When a Percent is Known
Percent Relationships
Mental Math;
Estimate with Percents
Simple Interest
Problem-Solving Strategy: Find a Pattern
Sales Tax and Discounts
Assessment
Monitoring Progress
Summative Assessment
Ongoing Review
Unit 8: Geometry of Plane Figures
This unit reviews the geometry of plane figures.
Topics
The Three Cases of Percent
Content Focus
Objectives
To help students learn about plane figures, including pairs of angles and circles
To help students learn about polygons and congruent and similar figures
To help students explore and learn about how geometric figures can be moved to create new figures
Content
Plane Figures
Pairs of Angles
Measure Angles
Draw Angles
Circles and central Angles
Triangles and Angle Sums
Quadrilaterals and Angle Sums
Draw Triangles and Quadrilaterals
Congruence and Constructions
Similar Figures
Polygons
Transformations Corresponding Parts of Congruent Figures
Assessment
Monitoring Progress
Summative Assessment
Ongoing Review
Unit 9: Geometry and Measurement
This unit presents producers for finding perimeter, area, surface area, and volume.
Topics
Perimeter and Area of Polygons
Circumference and Area of Circles
Surface Area and Volume of Solid Figures
Objectives
To help students review how to find the perimeter and area of polygons
To help students review how to find the circumference of a circle and develop the formula for finding the area of a circle
To help students apply formulas for surface area and volume of solid figures
Content
Perimeter and Area
Area of a Parallelogram
Area of a Triangle
Circumference
Area of a circle
Solid Figures
Surface Area
Volume of Rectangular Prisms
Volume of Other Solids
Assessment
Monitoring Progress
Summative Assessment
Ongoing Review
Unit 10: Data Analysis and Statistics
This unit continues development of statistical concepts, such as measures of central tendency and different ways to display data.
Topics
Statistics and Graphing
Analyzing and Representing Data
Objectives
To help students identify the mean, median, mode, and range of a data set and interpret and make graphs and tables.
To help students analyze data by using measures of central tendency and various displays of data.
Content
Use Statistics
Read and Make Double Bar Graphs
Frequency Tables and Histograms
Read and Make Double Line Graphs
Choose the Most Useful Statistical Measure
Clusters, Gaps and Outliers
Stem-and-Leaf Plots
Box-and –Whisker Plots
Assessment
Monitoring Progress
Summative Assessment
Ongoing Review
Unit 11: Statistics and Probability
This unit presents the concepts of collecting and using data and of finding various types of probabilities.
Topics
Sampling
Bias in Statistics
Probability and Outcomes
Objectives
To help students recognize and use appropriate data samples to solve problems
To help students be aware that surveys and statistics can be misleading
To help students identify all possible outcomes and use that information to find probabilities
Content
Use Samples to Predict
Select a Sample
Misleading Statistics
Interpret Data Displays
Possible Outcomes
Theoretical Probability
Experimental Probability
Disjoint Events
Independent Events
Dependent Events
Assessment
Monitoring Progress
Summative Assessment
Ongoing Review
Unit 12: Coordinate Graphing, Equations, and Integers
This unit extends the concepts of the coordinate plane, graphing and solving equations, and working with integers.
Topics
The Coordinate Plane
Graphing Equations
Integers and Equations
Objectives
To help students graph ordered pairs and find distances and area on a coordinate grid
To help students learn to solve and graph equations with two variables
To help students work with expressions and equations that involve integers
Content
Graph points in the coordinate Plane
Geometric Figures and the Coordinate Plane
Graphs and Measurement
Functions
Graph Linear Equations
Order of Operations With Integers
Evaluate and Simplify Expressions With Integers
Write Expressions With Integers
Equations With Integers
Assessment
Monitoring Progress
Summative Assessment
Ongoing Review