All lessons

Course

4th Grade Math

Multiply and divide multi-digit numbers, work with fractions and decimals, and measure angles.

Work through the lessons in order, from numbers to a million to independent problem-solving. By the end, you can read, compare, and round numbers to 1,000,000 and add and subtract them. You can multiply up to four digits by one digit and two digits by two digits, and divide with remainders. You can find factors, multiples, and prime numbers. You can make equivalent fractions, compare fractions, add and subtract mixed numbers, and multiply a fraction by a whole number. You can write tenths and hundredths as decimals, convert units, measure angles with a protractor, and sort shapes by their lines and angles.

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.
  • Keep practicing multiplication facts. Use grid paper for the area model and fraction strips for equivalent fractions. For angles, use a real protractor. Write each step so you can check your work.

Each lesson has games, quizzes, and worksheets.

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Place Value to 1,000,000

  1. 1Numbers to a MillionRead and write numbers to 1,000,000.
    • Read 352,408 as three hundred fifty-two thousand, four hundred eight.
    • Write numbers in standard, word, and expanded form.
    • Explain that each place is ten times the place to its right.
  2. 2Compare and Order Large NumbersCompare and order numbers to 1,000,000.
    • Compare from the greatest place.
    • Use >, <, and =.
    • Order four numbers from least to greatest.
  3. 3Round Large NumbersRound numbers to any place.
    • Round 46,382 to the nearest thousand.
    • Round to the nearest ten thousand.
    • Use rounding to estimate.
  4. 4Add and Subtract Large NumbersAdd and subtract multi-digit numbers with the standard method.
    • Line up the places.
    • Regroup across several places.
    • Check with an estimate.

Multi-Digit Multiplication

  1. 5Multiply by 10, 100, and 1,000Multiply by 10, 100, and 1,000 and by multiples of them.
    • See how digits shift one place for each 10.
    • Find 7 × 300 = 2,100.
    • Find 40 × 60 = 2,400.
  2. 6Multiply by a One-Digit NumberMultiply up to four digits by one digit.
    • Use an area model for 6 × 247.
    • Use partial products.
    • Connect partial products to the standard method.
  3. 7Multiply Two Two-Digit NumbersMultiply two two-digit numbers.
    • Use a four-box area model for 23 × 45.
    • Add the four partial products.
    • Check with an estimate.
  4. 8Times as ManySolve comparison problems with “times as many.”
    • Read 35 = 5 × 7 as 35 is 5 times as many as 7.
    • Draw a bar model for the comparison.
    • Tell “times as many” from “more than.”
  5. 9Multiplication Word ProblemsSolve word problems with multi-digit multiplication.
    • Choose the numbers to multiply.
    • Pick a strategy.
    • Check that the answer is reasonable.

Division with Remainders

  1. 10Divide with RemaindersDivide and find the remainder.
    • Share 23 into groups of 4 to get 5 R3.
    • Check by multiplying and adding the remainder.
    • Know the remainder is less than the divisor.
  2. 11What to Do with the RemainderDecide what the remainder means in a word problem.
    • Round up when every person needs a seat.
    • Drop the remainder when only full groups count.
    • Use the remainder as the answer when the question asks what is left.
  3. 12Divide with Partial QuotientsDivide up to four digits by one digit using partial quotients.
    • Take away easy multiples, such as 100 or 10 groups.
    • Add the partial quotients.
    • Use an area model for division.
  4. 13Long DivisionDivide up to four digits by one digit, place by place.
    • Divide, multiply, subtract, and bring down.
    • Place a 0 in the quotient when needed.
    • Check by multiplying.

Factors, Multiples, and Patterns

  1. 14Factors and Factor PairsFind all factor pairs of a number up to 100.
    • Find factor pairs with arrays.
    • List the factors of 36 in order.
    • Know when you have found them all.
  2. 15MultiplesTell if a number is a multiple of a one-digit number.
    • List multiples by skip-counting.
    • Use divisibility rules for 2, 3, 5, 9, and 10.
    • Connect factors and multiples.
  3. 16Prime and Composite NumbersTell if a number up to 100 is prime or composite.
    • Know a prime has exactly two factors.
    • Know 1 is neither prime nor composite.
    • Find the primes up to 50.
  4. 17Number and Shape PatternsMake a pattern from a rule and describe it.
    • Start at 1 and add 3 to make a pattern.
    • Notice that the numbers go odd, even, odd.
    • Extend a growing shape pattern.

Multi-Step Word Problems

  1. 18Multi-Step Word ProblemsSolve word problems that need several steps.
    • Plan the steps before you calculate.
    • Use all four operations.
    • Use estimation to check the answer.
  2. 19Write Equations for Word ProblemsWrite one equation with a letter for a multi-step problem.
    • Use a letter for the unknown.
    • Write 4 × 12 + 9 = n for a story.
    • Solve and explain the steps.

Equivalent Fractions

  1. 20Equivalent Fractions with ModelsUse models to show equivalent fractions.
    • Show 2/3 = 4/6 with area models.
    • See that the parts are smaller but there are more of them.
    • Use a number line.
  2. 21Make Equivalent FractionsMultiply or divide the top and bottom by the same number.
    • Write 3/4 = (3 × 2)/(4 × 2) = 6/8.
    • Write 8/12 in simplest form.
    • Explain why this keeps the value the same.
  3. 22Compare Fractions with Different DenominatorsCompare two fractions with different numerators and denominators.
    • Make a common denominator.
    • Make a common numerator.
    • Use >, <, and =.
  4. 23Benchmark FractionsCompare fractions to 0, 1/2, and 1.
    • Tell if a fraction is more or less than 1/2.
    • Compare 3/8 and 4/7 using 1/2.
    • Place fractions near 0, 1/2, or 1.

Adding, Subtracting, and Multiplying Fractions

  1. 24Add and Subtract FractionsAdd and subtract fractions with the same denominator.
    • Add 2/8 + 3/8 = 5/8.
    • Split a fraction into a sum, such as 3/8 = 1/8 + 2/8.
    • Subtract fractions with models.
  2. 25Mixed NumbersChange between mixed numbers and fractions greater than 1.
    • Write 2 1/3 as 7/3.
    • Write 11/4 as 2 3/4.
    • Place mixed numbers on a number line.
  3. 26Add and Subtract Mixed NumbersAdd and subtract mixed numbers with the same denominator.
    • Add the wholes and the parts.
    • Regroup when the parts make more than 1.
    • Borrow a whole to subtract.
  4. 27Multiply a Fraction by a Whole NumberMultiply a fraction by a whole number.
    • See 3 × 2/5 as 2/5 + 2/5 + 2/5 = 6/5.
    • See 5/4 as 5 × 1/4.
    • Solve word problems, such as 4 people each eat 3/8 of a pizza.
  5. 28Fraction Word ProblemsSolve word problems that add, subtract, or multiply fractions.
    • Draw a model for the story.
    • Choose the operation.
    • Write the answer as a mixed number when it makes sense.

Decimals

  1. 29Tenths and HundredthsWrite tenths and hundredths as decimals.
    • Write 3/10 as 0.3 and 47/100 as 0.47.
    • Shade a hundred grid.
    • Write 3/10 as 30/100.
  2. 30Decimals on a Number LinePlace decimals on a number line.
    • Split 0 to 1 into tenths.
    • Place 0.65 between 0.6 and 0.7.
    • Place decimals greater than 1.
  3. 31Compare DecimalsCompare two decimals to hundredths.
    • Compare 0.4 and 0.38 by writing 0.40.
    • Use >, <, and =.
    • Know that comparisons only work when both refer to the same whole.
  4. 32Add Tenths and HundredthsAdd a fraction in tenths to a fraction in hundredths.
    • Change 3/10 to 30/100.
    • Add 3/10 + 4/100 = 34/100.
    • Write the answer as a decimal.

Measurement and Conversions

  1. 33Convert Units of LengthChange larger units of length to smaller ones.
    • Use 1 foot = 12 inches and 1 yard = 3 feet.
    • Use 1 meter = 100 centimeters and 1 kilometer = 1,000 meters.
    • Make a conversion table.
  2. 34Convert Weight and CapacityChange pounds to ounces, liters to milliliters, and more.
    • Use 1 pound = 16 ounces.
    • Use 1 gallon = 4 quarts and 1 liter = 1,000 milliliters.
    • Use 1 kilogram = 1,000 grams.
  3. 35Convert TimeChange hours to minutes and minutes to seconds.
    • Use 1 hour = 60 minutes and 1 minute = 60 seconds.
    • Solve elapsed-time problems across the hour.
    • Solve problems with mixed units, such as 2 hours 15 minutes.
  4. 36Area and Perimeter FormulasUse formulas to find the area and perimeter of rectangles.
    • Use A = l × w.
    • Use P = 2 × l + 2 × w.
    • Find a missing side from the area or the perimeter.
  5. 37Line Plots with FractionsMake a line plot with halves, fourths, and eighths and use it to solve problems.
    • Measure to the nearest 1/8 inch.
    • Plot the measurements.
    • Find the difference between the longest and the shortest.

Lines, Angles, and Shapes

  1. 38Points, Lines, Rays, and AnglesDraw and name points, lines, segments, rays, and angles.
    • Tell a line from a segment and a ray.
    • Name right, acute, and obtuse angles.
    • Find each one in a drawing.
  2. 39Measure AnglesMeasure and draw angles with a protractor.
    • Know that a full turn is 360°.
    • Line up the protractor and read the right scale.
    • Draw an angle of a given size.
  3. 40Add and Subtract AnglesFind an unknown angle by adding or subtracting.
    • Split an angle into two parts.
    • Find the missing part, such as 90° − 35°.
    • Solve angle word problems.
  4. 41Parallel and Perpendicular LinesFind parallel and perpendicular lines.
    • Know parallel lines never meet.
    • Know perpendicular lines meet at a right angle.
    • Find them in shapes and letters.
  5. 42Classify Triangles and QuadrilateralsSort shapes by their lines and angles.
    • Find right triangles.
    • Sort quadrilaterals by parallel and perpendicular sides.
    • Name trapezoids, parallelograms, and rhombuses.
  6. 43Lines of SymmetryDraw the lines of symmetry of a shape.
    • Fold a shape to test a line of symmetry.
    • Find shapes with more than one line.
    • Complete a symmetric drawing.

Review, Mixed Practice, and Challenges

  1. 44Multiplication and Division ReviewMultiply and divide multi-digit numbers accurately.
    • Multiply and divide with your best strategy.
    • Interpret remainders.
    • Solve multi-step problems.
  2. 45Fractions and Decimals ReviewSolve mixed problems with fractions and decimals.
    • Compare fractions and decimals.
    • Add, subtract, and multiply fractions.
    • Change between fractions and decimals.
  3. 46Fourth Grade Math ChallengeComplete mixed questions covering the major units.
    • Choose the operation without being told.
    • Explain each strategy.
    • Find the areas that need more practice.