All lessons

Course

6th Grade Math

Use ratios and percents, work with negative numbers, solve one-step equations, and summarize data.

Work through the lessons in order, from ratios to independent problem-solving. By the end, you can use ratios, unit rates, and percents to solve problems. You can divide fractions, divide multi-digit numbers, and find the greatest common factor and least common multiple. You can place positive and negative numbers on a number line, find absolute value, and graph points in all four quadrants. You can write and evaluate expressions with exponents, solve one-step equations and inequalities, and find the area of triangles and polygons, the volume of prisms, and surface area from nets. You can find the mean, median, and spread of data and read dot plots, histograms, and box plots.

How to use these lessons

  • Start at the lesson marked Do this. Go on when you can do the line under the title by yourself.
  • Play the Games first. Then take the Quizzes. Eight of ten correct passes. The Worksheets are on paper. The answers are at the bottom.
  • Each lesson builds on the one before it. If a lesson is hard, go back one.
  • Show your steps on paper. Use ratio tables and double number lines for ratios, a number line for negative numbers, and grid paper for area and nets. Check each equation by putting your answer back in.

Each lesson has games, quizzes, and worksheets.

0 of 40

Ratios, Rates, and Percents

  1. 1RatiosWrite a ratio to compare two quantities.
    • Write 3 cats to 5 dogs as 3:5, 3 to 5, or 3/5.
    • Tell part-to-part ratios from part-to-whole ratios.
    • Describe a ratio in words.
  2. 2Equivalent Ratios and TablesMake equivalent ratios with a table or a double number line.
    • Fill in a ratio table.
    • Use a double number line.
    • Plot ratio pairs on a coordinate plane.
  3. 3Unit RatesFind a unit rate and use it to compare.
    • Find the price per ounce.
    • Find the speed in miles per hour.
    • Find the better buy.
  4. 4Understand PercentsWrite a percent as a rate per 100.
    • Shade 35% of a hundred grid.
    • Write 35% as 35/100 and 0.35.
    • Change fractions such as 3/4 to percents.
  5. 5Percent ProblemsFind a percent of a number and find the whole from a part.
    • Find 30% of 80.
    • Find the whole when 15 is 25% of it.
    • Use a percent bar model.
  6. 6Convert Units with RatiosUse ratios to convert measurement units.
    • Use 12 inches : 1 foot as a ratio.
    • Convert 5 feet to inches.
    • Convert rates, such as feet per second to feet per minute.

Dividing Fractions

  1. 7Divide Fractions with ModelsUse a model to divide a fraction by a fraction.
    • Find how many 1/6 are in 2/3.
    • Use a tape diagram.
    • Check with multiplication.
  2. 8Divide Fractions by MultiplyingDivide fractions by multiplying by the reciprocal.
    • Find the reciprocal of a fraction.
    • Find 3/4 ÷ 2/5 = 3/4 × 5/2.
    • Divide mixed numbers.
  3. 9Fraction Division Word ProblemsSolve word problems that divide fractions.
    • Find how many 3/4-cup servings are in 6 cups.
    • Find the width of a rectangle from its area and length.
    • Write an equation for the story.

Multi-Digit Numbers and Factors

  1. 10Divide Multi-Digit NumbersDivide multi-digit numbers with the standard method.
    • Divide 8,742 ÷ 31.
    • Continue past the decimal point instead of writing a remainder.
    • Check by multiplying.
  2. 11Decimal OperationsAdd, subtract, multiply, and divide decimals with the standard methods.
    • Add and subtract decimals of different lengths.
    • Multiply 3.42 × 1.5.
    • Divide 12.6 ÷ 0.35.
  3. 12Greatest Common FactorFind the greatest common factor of two numbers.
    • List factors and find the greatest shared one.
    • Use the GCF to write 36 + 8 as 4 × (9 + 2).
    • Solve problems about equal groups.
  4. 13Least Common MultipleFind the least common multiple of two numbers.
    • List multiples and find the smallest shared one.
    • Use prime factors.
    • Solve problems such as when two buses arrive together.

Integers and Rational Numbers

  1. 14Positive and Negative NumbersUse positive and negative numbers to describe real situations.
    • Describe temperatures below zero.
    • Describe height above and below sea level.
    • Describe money earned and spent.
  2. 15Opposites on a Number LinePlace a number and its opposite on a number line.
    • Know −3 and 3 are the same distance from 0.
    • Know the opposite of the opposite is the number itself.
    • Place fractions and decimals below 0.
  3. 16Absolute ValueFind the absolute value of a number.
    • Know |−7| = 7 is the distance from 0.
    • Use absolute value for a debt of $30.
    • Tell absolute value from order.
  4. 17Compare and Order Rational NumbersCompare and order positive and negative numbers.
    • Know −5 < −2 because it is farther left.
    • Order fractions, decimals, and integers.
    • Write a statement such as −3 °C > −7 °C.
  5. 18The Four-Quadrant Coordinate PlaneGraph points in all four quadrants.
    • Plot (−3, 4) and (2, −5).
    • Name the quadrant of a point.
    • Reflect a point across an axis.
  6. 19Distance on the Coordinate PlaneFind the distance between points that share an x or y coordinate.
    • Find the distance from (−2, 3) to (5, 3).
    • Use absolute value to find it.
    • Find the perimeter of a polygon on the grid.

Expressions

  1. 20ExponentsWrite and evaluate expressions with whole-number exponents.
    • Write 2 × 2 × 2 as 2³.
    • Evaluate 5² and (1/2)³.
    • Use exponents in the order of operations.
  2. 21Variables and ExpressionsWrite an expression with a variable from words.
    • Write “5 less than y” as y − 5.
    • Name terms, coefficients, and factors.
    • Write an expression for a real situation.
  3. 22Evaluate ExpressionsFind the value of an expression for a given variable.
    • Evaluate 3x² + 2 when x = 4.
    • Use formulas such as A = s².
    • Follow the order of operations.
  4. 23Equivalent ExpressionsWrite equivalent expressions with the distributive property and like terms.
    • Write 3(2 + x) as 6 + 3x.
    • Combine like terms, as in y + y + y = 3y.
    • Test two expressions with a value to see if they are equivalent.

Equations and Inequalities

  1. 24One-Step Equations with Addition and SubtractionSolve equations such as x + 7 = 15.
    • Do the same thing to both sides.
    • Use a balance model.
    • Check by substituting the answer.
  2. 25One-Step Equations with Multiplication and DivisionSolve equations such as 4x = 28 and x/3 = 6.
    • Divide both sides to undo multiplication.
    • Multiply both sides to undo division.
    • Write and solve an equation for a word problem.
  3. 26InequalitiesWrite an inequality and graph it on a number line.
    • Write “at least 12” as x ≥ 12.
    • Graph with open and closed circles.
    • Know an inequality has many solutions.
  4. 27Dependent and Independent VariablesWrite an equation that shows how one quantity depends on another.
    • Write d = 65t for distance and time.
    • Make a table and a graph.
    • Name the independent and dependent variables.

Area, Surface Area, and Volume

  1. 28Area of TrianglesFind the area of a triangle.
    • Show a triangle is half of a rectangle or parallelogram.
    • Use A = 1/2 × b × h.
    • Find the height of a triangle that leans.
  2. 29Area of Parallelograms and TrapezoidsFind the area of parallelograms and trapezoids.
    • Cut and move a parallelogram into a rectangle.
    • Use A = b × h.
    • Split a trapezoid into triangles and a rectangle.
  3. 30Area of PolygonsFind the area of a polygon by splitting it into simpler shapes.
    • Split a polygon into rectangles and triangles.
    • Find the area of a polygon on the coordinate plane.
    • Solve real-world area problems.
  4. 31Volume with Fraction EdgesFind the volume of a prism with fraction edge lengths.
    • Pack a prism with cubes of edge 1/2.
    • Show that V = l × w × h still works.
    • Solve real-world volume problems.
  5. 32Nets and Surface AreaUse a net to find the surface area of a solid.
    • Draw nets of prisms and pyramids.
    • Add the area of every face.
    • Tell surface area from volume.

Statistics

  1. 33Statistical QuestionsTell a statistical question from a question with one answer.
    • Know a statistical question expects varied answers.
    • Compare “How old am I?” and “How old are students in my school?”
    • Write your own statistical question.
  2. 34Mean, Median, and ModeFind the mean, median, and mode of a data set.
    • Find the mean as a fair share.
    • Find the median by ordering the data.
    • Choose the best center when there is an outlier.
  3. 35Range and Mean Absolute DeviationDescribe how spread out data is.
    • Find the range.
    • Find the mean absolute deviation.
    • Find the quartiles and the interquartile range.
  4. 36Dot Plots and HistogramsMake and read dot plots and histograms.
    • Make a dot plot of class data.
    • Group data into intervals for a histogram.
    • Describe the shape, center, and spread.
  5. 37Box PlotsMake and read a box plot.
    • Find the five-number summary.
    • Draw the box and whiskers.
    • Compare two groups with box plots.

Review, Mixed Practice, and Challenges

  1. 38Ratios and Numbers ReviewSolve mixed problems with ratios, percents, fractions, and integers.
    • Use unit rates and percents.
    • Divide fractions and decimals.
    • Compare positive and negative numbers.
  2. 39Expressions, Geometry, and Data ReviewSolve mixed problems with equations, area, volume, and data.
    • Solve one-step equations.
    • Find area, surface area, and volume.
    • Summarize a data set.
  3. 40Sixth Grade Math ChallengeComplete mixed questions covering the major units.
    • Choose a strategy without being told.
    • Solve multi-step problems.
    • Find the areas that need more practice.