Planning tool

Students:

• extend their knowledge of fractions to negative fractions
• calculate equivalent fractions from any starting denominator
• understand the terms ‘denominator’ and ‘numerator’
• express one quantity as a fraction of another
• express a fraction in simplest form using common divisors
• know that percentage means ‘out of one hundred’
• understand that fractions, decimals and percentages are three ways to represent numbers
• convert from one number type to another
• represent positive and negative fractions and mixed numerals on various intervals on a number line.

Some students may:

• confuse the numerator and denominator.
• believe that the larger denominator is the larger fraction when making comparisons.
• not realise that fractions, decimals and percentages are three ways of expressing the same value.
• find converting decimal percentage into a decimal difficult.
• believe a decimal can be written as a fraction using the same digits. For example, students write 2.9 as  29 .

The Learning from home activities are designed to be used flexibly by teachers, parents and carers, as well as the students themselves. They can be used in a number of ways including to consolidate and extend learning done at school or for home schooling.

Learning intention

We are learning to compare fractions, decimals and percentages by plotting them on a number line.

Why are we learning about this?

If you know about decimals, fractions and percentages, then you can solve many practical problems in your everyday life. For instance, imagine not being able to understand what your ATAR score means, or what the interest on your car loan amounts to for your monthly repayments. Imagine starting your career in hairdressing but being unable to mix colours because you do not understand the idea of proportions. Maths is useful. Trust us! 

What to do

How many sausage rolls can I make?

Warning: this activity could make you hungry.

Everyone enjoys a sausage roll for lunch or at a party! Let’s work out how many sausage rolls we can make from one packet of pastry.

A packet of pastry contains 10 sheets. We can make one really long sausage roll per sheet and then slice them to make two or three large sausage rolls, or we could make five or six cuts to make party-size sausage rolls.

Let’s think about this.

To make large sausage rolls, we could halve our long piece, or we could cut it into thirds. In this case, I have created a table to work out the total number of large sausage rolls that could be made relative to the number of cuts made. Record these in a table like the one below.

To make the party-size sausage rolls, we will need to cut our long piece into fourths, fifths, sixths or even sevenths.

1. How many party-sized sausage rolls can I make if I have 10 sheets of pastry?
2. Record these in a table like the one below.

Don’t cut yet!

Before slicing (that’s if you’re really making them, of course), let’s make sure the sausage rolls are approximately equal in length. We can practise where we would make our cuts using a number line and figure out how many divisions we would make per sheet. Then we could work out how many we would have altogether.

1. Below is a line to practise. You can draw one out yourself on a piece of paper.
2. Put an X where you want your cuts to be.
3. Above the X, write the fraction you were thinking of, say  1 2  or  1 3 .
4. Here’s an example. Do this for all sorts of fractions and see how many sausage rolls you can make with one packet of pastry. Remember: one packet contains 10 sheets of pastry.

How many people are coming?

Now, let’s do some backward thinking.

Say we decide to make 100 party-sized sausage rolls because we think that will be plenty for our party of friends coming over. (Of course, we can eat the leftovers later.) If we have ten sheets and we divide each sheet so that we have ten rolls per sheet, we will make 100. We know this because 10 × 10 = 100.

Once we know how many sausage rolls we have altogether, we can play with different proportions to see how many sausage rolls each person could have depending on how many friends turn up. 

Consider where on the number line below you would mark  1 2 ,  1 3 ,   1 4 ,  1 5  and 1 8 .

This line is a little different to the one above as it represents the total number of sausage rolls (100) on the bottom right-hand side.

1. How many sausage rolls would be equal to  1 2  of all the sausage rolls?

2. Mark with an X where half would be, then write the number of sausage rolls that amounts to directly below the line. Did you get 50? That means, if only one other person shows up including me, we would have 50 sausage rolls each! 

3. Your turn. What if there are four people altogether. Mark Xs on the line and figure out how many each person receives by writing the number directly below them.
4. What about five people?
5. What if there are nine people altogether?
6. How do you think caterers estimate how much food to make when they supply party-food for parties? 

Success criteria

• I can identify and explain the equivalence between a fraction, decimal and percentage.
• I can represent fractions and decimals on a number line.