Equivalent Fractions – Visual Rectangle Approach

Four worksheets use shaded rectangles to teach equivalent fractions: Worksheet 1 asks pupils to write the fraction shown by a coloured-in rectangle, Worksheet 2 has pupils shade a rectangle to match a given fraction, and Worksheets 3 and 4 add the multiplier that connects two equivalent fractions. Every worksheet includes a button that randomizes the set of rectangle problems, generating a fresh page of questions along with a matching answer page each time it is clicked. A teacher's guide walks through the rectangle model and explains what each of the four worksheets asks pupils to do.

Year groups: Year 4
File type: PDF
Preparation: Print ready

Updated Oct 19, 2023

Subject: Fractions, Maths
Topic: Equivalent Fractions, Fractions
Resource types: Worksheets, Worksheets & Printables
Preparation: Print ready

From the author

About 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 coloured 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 colour 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.

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 coloured-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.