5th grade math test: a free 10-question quick check

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The same ten questions as a PDF, with a separate answer key.

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What the questions cover

The ten questions sample 5th grade: place value and powers of 10, adding mixed numbers and estimating with fractions, writing expressions and using parentheses, converting units, a line plot with fractions and the coordinate grid. Several ask your child to check someone else’s work, and two ask your child to type an answer.

The whole year covers these areas:

• Adding and subtracting fractions

  The first big fraction step of 5th grade. Your child adds and subtracts fractions with different denominators (the bottom numbers) by first rewriting them as pieces of the same size.

• Multiplying and dividing fractions

  Your child multiplies a fraction by a fraction, learns that a fraction is also a division (3/4 means 3 ÷ 4) and divides with unit fractions, the fractions with 1 on top.

• Place value and decimals

  Place value reaches thousandths. Your child learns that each place is worth 10 times the place to its right, and uses that to multiply and divide by 10, 100 and 1,000.

• Multi-digit and decimal arithmetic

  Long multiplication becomes a skill to do quickly, long division grows to two-digit divisors and all four operations now work on decimals to hundredths.

• Volume

  Volume is the space inside a solid shape. Your child measures it by counting unit cubes, then connects the count to length × width × height.

• Measurement conversions and line plots

  Converting between units of the same system, such as centimeters to meters, and line plots of measurements in halves, quarters and eighths.

• Expressions and patterns

  Writing and reading number expressions with parentheses, and comparing two number patterns side by side.

• The coordinate grid and shapes

  The coordinate grid appears for the first time, using only the part where both numbers are 0 or more. Shapes are sorted into families by their properties.

Every topic of the year, explained for parents, is on the 5th grade math page.

What you see at the end

The score, then every question with your child’s answer, the correct answer and a worked solution. A short message explains what a similar score usually means for 5th graders on our full assessment. Treat it as an indication: ten fixed questions cannot measure where a child stands.