Fractions Eight Different Ways

Learning Intention: Students will understand that there are many different ways to express the concept of ‘part of a whole’.

Success criteria: Each student will produce a poster that demonstrates eight different ways to express a certain fraction, chosen by the distribution of individual fraction cards. We will use these cards and our ‘Fraction Walls’ to demonstrate adding, subtracting, multiplying and dividing fractions.

Each student will recieve a card with a fraction and create a poster that shows this fraction eight different ways (as above for one half). When you have finished, place your poster on the number line in the room.

Operations with Fractions

frac-multiply-2-5 copy frac2

You already know that when you multiply a whole number by another whole number, the answer is a larger number. But when you multiply a fraction by another fraction the answer is smaller! Look at the top picture – if you have 2/5 of a pizza left and you need to share it equally with your brother, how much of the original pizza do you get? How can you add 1/3 and 1/6 of a pizza?

Adding and Subtracting fractions – BBC Bitesize

Multiplying and dividing fractions – BBC Bitesize

How to Add and Multiply fractions – WikiHow

Equivalent fractions with a Fraction Wall

Screen Shot 2014-03-03 at 2.49.00 PM

Image Source

This week we will continue making our fraction wall and learning how to calculate equivalent fractions. Using your fraction wall, find equivalent fractions for the following: 1/2 (one half); 1/3 (one third); 1/4 (one quarter) 2/3 (two thirds) and 3/4 (three quarters). What are some other equivalent fractions that are “off the scale” – using fifteenths, sixteenths, twentieths or hundredths?

To add or subtract fractions we need to make sure they have the same denominator (bottom number). We can convert fractions so that they have the same denominator by multiplying both the numerator and the denominator by the same number. This interactive from NLVM helps to compare fractions and create fractions with the same denominator.

Here are some links to sites for learning more about fractions:

Fractions interactives from NLVM

Fractions as we know them today weren’t used in Europe until the 17th century. However, Egyptians have been using fractions since at least 1800BC, although they never wrote fractions with a numerator greater than one. These are called unit fractions. Fractions with a numerator greater than one were expressed as the sum of unit fractions. Find out more at the History of fractions and Egyptian fractions.

The National Library of Virtual Manipulatives has a range of interactive applets that you can access to learn about fractions:

Try at least three of these interactives and write a comment below about what you have learned.

Adding and subtracting fractions

Image is a screenshot from the Cool Math 4 Kids site.

When adding or subtracting fractions the first thing you need to do is make sure that the denominators (bottom numbers) are the same. If all the denominators are the same you can simply add or subtract the numerators (top numbers) and then simplify the answer if required. If the denominators are different, you need to find a common multiple and convert both fractions, so that the denominators are the same. Activities 4 and 5 below show how this is done:

1. Adding Fractions from Cool Maths 4 Kids.

2. Three simple steps to adding fractions from “Maths is Fun”.

3. BBC Bitesize – fractions activities – Choose the fractions activities from BBC Bitesize (Equivalent fractions and ordering and comparing fractions).

4. Adding fractions with different denominators from “Maths Playground”.

5. Adding fractions with different denominators from YouTube – Maths Made Simple Series.

Equivalent fractions

Learning intention: Students will be able to identify and name equivalent fractions (halves, thirds, quarters, fifths and sixths) and describe how they are calculated.

Success criteria: Students will successfully identify equivalent fractions on their fraction walls and name equivalent fractions on a number line.

Maths Playground – Visual fractions (the visuals are good, but the program doesn’t always allow the right answer?)

Maths is Fun – Equivalent fractions

Maths Games – Matching equivalent fractions

Fractions Apps on the iPad

Learning Intention: This lesson we will be using three different apps on the iPads to learn about the value of fractions, decimals and percentages.

Success Criteria: Students will understand the value of common fractions (1/2, 3/4, 1/3, 2/3 etc) and be able to order a list of common fractions, decimals and percentages.

1. Motion Math HD – Bounce the fraction ball at the corresponding point on the number line by moving the iPad (10 minutes).

2. Fraction Factory – Move the factory cog to the correct point on the number line (10 minutes).

3. Number Line – Order the fractions, decimals and percentages from smallest to largest (10 minutes).

Please leave a comment below about which app you liked best, why you liked it and what you learnt.

Why do we need to learn about fractions?


Still on the subject of fractions, why in the decimal, digital age do students still need to learn about fractions? Fractions are an important concept and very useful for discussions about measurement, probability and data. Although Australia and the U.K. , and almost all other countries in the world, have adopted the metric system, the United States still uses imperial measurements. One example is with drill bits, where there are conversion charts available to convert imperial sizes (increments of 1/64 of an inch) to millimetres.

Prior to learning operations with fractions, students should be able to order fractions, convert between mixed numbers and improper fractions and convert between decimals and fractions. BBC KS3 Bitesize has revision activities and a test about Fractions. If students can find ten fractions between 1/3 and 2/3 , they have a good understanding of the concept of fractions.

This article, “Teaching Fractions with Understanding: Part-whole concept” is based on research by Grace Lopez-Charles – “Assessment of Children’s Understanding of Rational Numbers” – PhD Thesis. It describes several different perspectives that students have and some ways of teaching fractions more effectively.