Equivalent Fractions Worksheets: Visual Rectangle Model

About this resource

What's inside this resource

If two fractions are equivalent it means they are the same in terms of shape and size, but are expressed using different numbers

Equivalent fractions are best introduced using shape models before proceeding on to using the number line or any numerical method. If two fractions are equivalent it means they are the same in terms of shape and size, but are expressed using different numbers

In these resources fractions are compared using rectangles, where each rectangle represents the same area of a whole.

The 4 Sets of Worksheets form a progression as follows:

Worksheet Set 1:
Each pair of rectangles on the page has a fraction of it's space colored in. Students write down the (equivalent) fractions of each in numerical terms.

Worksheet Set 2:
For each pair of rectangles, equivalent fractions are shown . Students color in the areas on two rectangles that represent two given equivalent fractions.

Worksheet Set 3:
Pairs of coloured-in rectangles and the denominators of the equivalent fractions are shown. Students must determine the numerators (of each fraction) and the multiplier that connects the two fractions.

Worksheet Set 4:
Shown pairs of partially coloured-in rectangles pupils are asked to write down the fractions coloured-in and the multiplier connecting the two fractions.

How many worksheets are in each set ?

A lot. At the click of a button all numbers are randomised, so the questions change every time. This means you can create new worksheets for plenty of extra practice throughout the year or even give groups of pupils in your class different sets of questions.

Answers can be found on the second page of every worksheet, which are automatically generated when you create a new worksheet.

Note
These resources are PDF documents and work with the official Adobe Acrobat Reader on Windows or Mac computers with the randomising buttons also working via a touchscreen (on a PC or Mac) or on an Interactive Whiteboard.

Common Core Standards

CCSS3.NF.A.1
Understand a fraction 1/𝘣 as the quantity formed by 1 part when a whole is partitioned into 𝘣 equal parts; understand a fraction 𝘢/𝑏 as the quantity formed by 𝘢 printables/parts-of-and-anatomy-of">parts of size 1/𝘣.

CCSS3.NF.A.3
Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

CCSS3.NF.A.3a
Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

CCSS3.NF.A.3b
Recognize and generate simple equivalent fractions, (e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.

Teaching tips & learning objectives

Learning objectives

Identify the fraction represented by a colored-in rectangle and write it in numeral form.
Shade a rectangle to represent a given fraction, showing that equivalent fractions cover the same area.
Determine the multiplier that connects two equivalent fractions represented by rectangles.

Teaching tips

Click the randomize button before reusing a worksheet with a class or for extra practice, since it generates a fresh set of questions each time.
Start with Worksheets 1 and 2 (reading and shading a rectangle) before moving to Worksheets 3 and 4, which add the multiplier concept.
Use the automatically generated second answer page to check work quickly, since it matches whichever randomized set a student received.

Skills covered

Fraction identification from a visual model — reading a divided and shaded rectangle to write its fraction.
Equivalent fraction generation — recognizing when two shaded rectangles represent the same area.
Multiplicative reasoning — finding the multiplier that connects a fraction to an equivalent form.

Good to know

Questions teachers ask about this resource

Do the worksheets always give the same set of rectangle problems?

No — each worksheet has a randomize button that generates a new set of rectangle problems, along with a matching answer page, so the same worksheet can be reused for extra practice.

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Curriculum

Standards, concepts & topics

Standards

3. NF.A.1 — Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
3. NF.A.3 — Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. b. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model. c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.