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Course

5th Grade Math

Work with decimals to thousandths, add and multiply fractions, and find volume.

Work through the lessons in order, from powers of ten to independent problem-solving. By the end, you can read, compare, and round decimals to thousandths and use powers of ten. You can multiply multi-digit numbers and divide by two-digit numbers. You can add, subtract, multiply, and divide decimals to hundredths. You can use the order of operations and graph number patterns. You can add and subtract fractions with unlike denominators, multiply fractions, and divide unit fractions and whole numbers. You can convert units, find the volume of rectangular prisms, graph points on the coordinate plane, and sort shapes by their properties.

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.
  • A short turn is enough. If a lesson is hard, play the one before it again.
  • Estimate before you calculate, then check that the decimal point is in a sensible place. Use grid paper for decimals and the coordinate plane, and small cubes or a box for volume.

Each lesson has games, quizzes, and worksheets.

0 of 41

Place Value and Decimals

  1. 1Powers of TenMultiply and divide by powers of ten and use exponents.
    • Write 1,000 as 10³.
    • See how digits move when you multiply or divide by 10.
    • Find 3.6 × 100 and 52 ÷ 1,000.
  2. 2Decimals to ThousandthsRead and write decimals to thousandths.
    • Read 3.482 as three and four hundred eighty-two thousandths.
    • Write it in expanded form.
    • Explain the value of each digit.
  3. 3Compare and Order DecimalsCompare and order decimals to thousandths.
    • Line up the decimal points.
    • Compare 0.509 and 0.51.
    • Order decimals from least to greatest.
  4. 4Round DecimalsRound decimals to any place.
    • Round 4.367 to the nearest tenth.
    • Round to the nearest hundredth and whole number.
    • Use rounding to estimate.

Multiplying and Dividing Whole Numbers

  1. 5Multiply Multi-Digit NumbersMultiply multi-digit numbers with the standard method.
    • Multiply 324 × 46.
    • Connect the standard method to partial products.
    • Check with an estimate.
  2. 6Estimate QuotientsEstimate a quotient with compatible numbers.
    • Estimate 412 ÷ 21 as 400 ÷ 20.
    • Use the estimate to start division.
    • Check if an answer is reasonable.
  3. 7Divide by Two-Digit NumbersDivide up to four digits by a two-digit number.
    • Use partial quotients.
    • Use long division.
    • Adjust a quotient digit that is too big or too small.
  4. 8Multiplication and Division Word ProblemsSolve word problems with multi-digit multiplication and division.
    • Choose the operation.
    • Decide what to do with a remainder.
    • Explain the answer in a sentence.

Decimal Operations

  1. 9Add and Subtract DecimalsAdd and subtract decimals to hundredths.
    • Line up the decimal points.
    • Add zeros as placeholders, as in 5 − 2.36.
    • Check with an estimate.
  2. 10Multiply a Decimal by a Whole NumberMultiply a decimal by a whole number.
    • Find 4 × 0.3 with a model.
    • Find 6 × 2.45.
    • Place the decimal point using an estimate.
  3. 11Multiply DecimalsMultiply two decimals.
    • Find 0.4 × 0.6 on a hundred grid.
    • Count decimal places to place the point.
    • Find 1.5 × 2.3.
  4. 12Divide a Decimal by a Whole NumberDivide a decimal by a whole number.
    • Share 4.8 among 4.
    • Divide 7.25 ÷ 5.
    • Place the decimal point in the quotient.
  5. 13Divide by a DecimalDivide by a decimal to hundredths.
    • Find how many 0.5s are in 3.
    • Multiply both numbers by 10 or 100 first.
    • Divide 6.3 ÷ 0.7.
  6. 14Decimal Word ProblemsSolve word problems with money and other decimals.
    • Find the total cost of several items.
    • Find the price of one item.
    • Check that the answer is reasonable.

Expressions and Patterns

  1. 15Order of OperationsEvaluate expressions with parentheses, brackets, and braces.
    • Do the work inside grouping symbols first.
    • Multiply and divide before adding and subtracting.
    • Evaluate 2 × [5 + (6 − 2)].
  2. 16Write ExpressionsWrite and read expressions from words.
    • Write “add 8 and 7, then multiply by 2” as 2 × (8 + 7).
    • Explain that 3 × (18 + 932) is three times as large as 18 + 932.
    • Match expressions to words.
  3. 17Numerical PatternsMake two patterns from two rules and compare them.
    • Make a pattern that adds 3 and one that adds 6.
    • Line up the terms in a table.
    • Notice that each term in the second is twice the first.
  4. 18Graph Number PatternsGraph pairs from two patterns on a coordinate plane.
    • Make ordered pairs from the table.
    • Plot the pairs.
    • Describe the line they make.

Adding and Subtracting Fractions

  1. 19Common DenominatorsRewrite two fractions with a common denominator.
    • Find a common multiple of the denominators.
    • Rewrite 2/3 and 3/4 as twelfths.
    • Use the least common denominator.
  2. 20Add Fractions with Unlike DenominatorsAdd fractions with different denominators.
    • Find 2/3 + 5/4 = 8/12 + 15/12 = 23/12.
    • Simplify the answer.
    • Write it as a mixed number.
  3. 21Subtract Fractions with Unlike DenominatorsSubtract fractions with different denominators.
    • Find 5/6 − 1/4.
    • Use a model to check.
    • Simplify the answer.
  4. 22Add and Subtract Mixed NumbersAdd and subtract mixed numbers with unlike denominators.
    • Find 2 1/2 + 1 2/3.
    • Regroup to subtract, as in 4 1/4 − 1 2/3.
    • Check with an estimate.
  5. 23Fraction Word ProblemsSolve word problems that add and subtract fractions.
    • Draw a model for the story.
    • Use benchmark fractions to check, such as 2/5 + 1/2 = 3/7 is wrong because 3/7 < 1/2.
    • Write the answer in a sentence.

Multiplying and Dividing Fractions

  1. 24Fractions as DivisionSee a fraction as a division of the numerator by the denominator.
    • Share 3 pizzas among 4 people to get 3/4 each.
    • Write 3 ÷ 4 = 3/4.
    • Solve sharing word problems.
  2. 25Multiply FractionsMultiply a fraction by a fraction.
    • Find 2/3 of 4/5 with an area model.
    • Multiply numerators and denominators.
    • Multiply mixed numbers.
  3. 26Area with Fraction SidesFind the area of a rectangle with fraction side lengths.
    • Tile a rectangle with unit fraction squares.
    • Show that the area equals length × width.
    • Find the area of a 3/4 by 2/3 rectangle.
  4. 27Multiplying as ScalingPredict if a product will be bigger or smaller without multiplying.
    • See that times a fraction less than 1 makes a number smaller.
    • See that times a fraction greater than 1 makes it bigger.
    • Compare 3/4 × 12 to 12.
  5. 28Divide with Unit FractionsDivide a unit fraction by a whole number and a whole number by a unit fraction.
    • Find 1/3 ÷ 4 = 1/12 with a model.
    • Find 4 ÷ 1/5 = 20 with a model.
    • Check with multiplication.
  6. 29Multiply and Divide Fraction Word ProblemsSolve word problems that multiply or divide fractions.
    • Find how many 1/4-cup servings are in 3 cups.
    • Find 2/3 of a 3/4-mile trail.
    • Choose to multiply or divide.

Measurement and Data

  1. 30Convert Measurement UnitsConvert units within one measurement system.
    • Change 5 cm to 0.05 m.
    • Change 3.5 feet to inches.
    • Use powers of ten for metric units.
  2. 31Multi-Step Conversion ProblemsSolve word problems that need a unit conversion.
    • Convert before you compare.
    • Solve problems such as how many 250 mL cups fill 2 L.
    • Write the answer with the right unit.
  3. 32Line Plots with FractionsUse fraction operations to solve problems from a line plot.
    • Make a line plot of measurements in eighths.
    • Find the total of all the measurements.
    • Find the amount each would have if shared equally.

Volume

  1. 33Understand VolumeFind volume by counting unit cubes.
    • Say that volume is the space inside a solid.
    • Pack a box with unit cubes with no gaps.
    • Use cubic centimeters and cubic inches.
  2. 34Volume FormulasUse V = l × w × h and V = B × h.
    • Connect layers of cubes to multiplication.
    • Find the volume of a 4 × 3 × 5 prism.
    • Find a missing edge from the volume.
  3. 35Volume of Combined PrismsFind the volume of a solid made of two rectangular prisms.
    • Split the solid into two prisms.
    • Add the two volumes.
    • Solve real-world volume problems.

The Coordinate Plane and Shapes

  1. 36The Coordinate PlaneGraph and name points in the first quadrant.
    • Name the x-axis, y-axis, and origin.
    • Plot (3, 5): over 3, up 5.
    • Read the coordinates of a point.
  2. 37Solve Problems with GraphsGraph points to solve real-world problems.
    • Find the distance between points on a grid line.
    • Plot a map and find routes.
    • Read what a point means in the story.
  3. 38Classify Two-Dimensional FiguresSort shapes into a hierarchy by their properties.
    • Know that all squares are rectangles and rhombuses.
    • Draw a diagram of quadrilateral types.
    • Sort triangles by sides and by angles.

Review, Mixed Practice, and Challenges

  1. 39Whole Numbers and Decimals ReviewSolve mixed problems with whole numbers and decimals.
    • Multiply and divide multi-digit numbers.
    • Do all four operations with decimals.
    • Use the order of operations.
  2. 40Fractions and Volume ReviewSolve mixed problems with fractions, volume, and graphs.
    • Add, subtract, multiply, and divide fractions.
    • Find volume.
    • Graph points.
  3. 41Fifth Grade Math ChallengeComplete mixed questions covering the major units.
    • Choose the operation without being told.
    • Solve multi-step problems.
    • Find the areas that need more practice.