This week's fractions rubrics, ready for class.

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Standards alignment

What this fractions math content covers

Worksheets are mapped to the following published standards. Pick a standard to focus your worksheet on the matching skill.

• CCSS

  3.NF.A.1Grade 3

  Understand a fraction 1/b as one part of a whole partitioned into b equal parts.

• CCSS

  3.NF.A.2Grade 3

  Understand a fraction as a number on the number line.

• CCSS

  3.NF.A.3Grade 3

  Explain equivalence of fractions and compare fractions by reasoning about their size.

• CCSS

  4.NF.A.1Grade 4

  Explain why a/b = (n·a)/(n·b) and use this to recognize and generate equivalent fractions.

• CCSS

  4.NF.A.2Grade 4

  Compare two fractions with different numerators and denominators.

• CCSS

  4.NF.B.3Grade 4

  Decompose a fraction into a sum of fractions with the same denominator.

• CCSS

  5.NF.A.1Grade 5

  Add and subtract fractions with unlike denominators (including mixed numbers).

• CCSS

  5.NF.B.4Grade 5

  Multiply a fraction by a whole number or another fraction.

• CCSS

  5.NF.B.7Grade 5

  Divide unit fractions by whole numbers and whole numbers by unit fractions.

• CCSS

  6.NS.A.1Grade 6

  Divide fractions by fractions, including word problems.

Common mistakes

Misconceptions students bring to fractions

Specific errors to watch for when reviewing student work — pulled from classroom research and teacher reports.

1. 1

   Adding numerators and denominators directly.

   What to teach instead: Find a common denominator first; only the numerators add.

   1/2 + 1/3 ≠ 2/5. Convert to sixths: 3/6 + 2/6 = 5/6.

2. 2

   Believing a fraction with a larger denominator is always larger.

   What to teach instead: With the same numerator, a larger denominator means smaller pieces.

   1/4 < 1/2, even though 4 > 2.

3. 3

   Forgetting that mixed numbers and improper fractions are equal in value.

   What to teach instead: 1¾ and 7/4 are the same number written two ways.

4. 4

   Inverting only one fraction when dividing.

   What to teach instead: Keep the first fraction, flip the second, change division to multiplication.

   2/3 ÷ 1/4 = 2/3 × 4/1 = 8/3.

5. 5

   Multiplying always makes a number bigger.

   What to teach instead: Multiplying by a fraction less than 1 makes the result smaller.

   10 × 1/2 = 5, which is less than 10.

Key vocabulary

Fractions terms students should know

A short glossary of core vocabulary you can drop into any worksheet, quiz, or study guide.

Numerator

The top number of a fraction; tells you how many parts you have.

Denominator

The bottom number of a fraction; tells you how many equal parts the whole is split into.

Equivalent fractions

Fractions that name the same amount, like 1/2 and 2/4.

Mixed number

A whole number plus a fraction, like 2¾.

Improper fraction

A fraction whose numerator is larger than (or equal to) its denominator, like 9/4.

Common denominator

A shared denominator used to add or compare fractions.

Simplest form

A fraction where the numerator and denominator share no common factors other than 1.

Reciprocal

The fraction you get by flipping numerator and denominator. The reciprocal of 3/4 is 4/3.

Unit fraction

A fraction with 1 as its numerator, like 1/3.