Paper Fractions

Introduction

As you have learnt in previous lessons, fractions are used to represent chances. The ability to apply basic mathematical operations to fractions is extremely important. In this lesson, you will be deepening your conceptual understanding of how fraction addition, subtraction, multiplication and division work by looking at paper fractions calculator!

Equivalent Fractions

Look at squares A to E, for each square (paper copies here - PRINT ME):

What fraction of the square is shaded?
Fold the square once, crossways.

How many parts is the paper divided into now?
What fraction is shaded?

Fold the square in half twice, crossways.

How many parts is the paper divided into now?
What fraction is shaded?

Fold the square in three equal parts, crossways.

How many parts is the paper divided into now?
What fraction is shaded?

Using squares A to E:

Are you able to find equivalent fractions for: ½, ⅓, ⅔, ¼ and ¾?
Can you find a rule of how you find equivalent fractions using the squares?
Show how you can you find equivalent fractions for the following questions using your rule.

Halves

Thirds

Fourths

Fraction operations

Now make your own paper fractions calculator by following the instructions on this sheet.

How would you use it to add, subtract, multiply and divide fractions?

Fractions paper folding calculator.pdf

Further questions

What if we have different denominators? How would you now fold your paper?

How would you multiply fractions? Take a look at this. Can you explain what is going on?

Further Practice

Take this opportunity to brush up on your skills of adding, subtracting, multiplying and dividing fractions. You may also want to look at improper fractions and mixed numbers. Do the relevant skills practice on DrFrostMaths, CorbettMaths, MyiMaths and Eedi. Watch any video and/or go through any online lesson as you see fit.

Transum

Fraction basics:

Fraction Dissect: Draw lines to dissect the rectangles to make the given fractions.
Express as a Fraction: Express one quantity as a fraction of another, where the fraction could be less than 1 or a mixed number.
Fraction of ...: Practise your ability to find a fraction of a given amount with this self marking exercise.

Ordering fractions:

Cheese and Onion Pies: Sort the fractions from smallest to largest.
Fraction Line: Arrange the fractions, shown in a variety of formats, in order from smallest to largest.
Fraction Order: Arrange the fractions and decimals in order from smallest to largest.
Fickle Fractions: Compare pairs of fractions to identify the largest or smallest in order to move through the maze.
Vinculum: A challenge to find fractions which are larger than the previous fraction but less than one.

Equivalent fractions:

Equivalent Fractions: Practise finding equivalent fractions numerically and in fraction diagrams.
Equivalent Fraction Pairs: The traditional pairs or Pelmanism game adapted to test knowledge of equivalent fractions.
Fraction Matcher: Match shapes and numbers in this fractions activity. Challenge yourself on many levels.
Overloaded Fraction: A set of ten puzzles requiring you to arrange the given digits to make an equivalent fraction.

Improper and mixed numbers:

Improper Fractions: A self-marking online exercise on converting improper fractions to mixed numbers and vice versa.
Mixed Numbers: A self marking quiz about the application of the four operations to mixed numbers.

Fraction arithmetics and puzzles:

Fractions: A series of self-marking exercises on adding, subtracting, multiplying and dividing fractions.
Fractionagons: Calculate the missing fractions in these partly completed arithmagon puzzles.
Fractions by Wholes: An exercise on multiplying and dividing proper fractions and mixed numbers by whole numbers.
Boxed In Fractions: The classic dots and boxes two-player game with the addition of some fractions which determine your score.
Circumfraction: Quite a challenging number placing puzzle involving fractions.

For more goodies on Fractions on Transum, click on the hyperlinks.

Here are some questions to get you started if you feel that you are pretty confident.

mathswatch clips 56, 7 fraction operations with answers.pdf

Extension

Have a go at the Fraction Challenge on Desmos where you will practice adding and subtracting fractions. You will create expressions to match given criteria (e.g. the greatest value, the least positive value, etc.). You will need to reason abstractly and structurally, arguing why your expressions are the greatest or least possible.

Take a look at the challenges underneath:

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