## Preparation- Print this two part investigation board.
- You need nine tiles numbered 1 to 9 that fit in the squares on this board.
You can fold and tear scrap paper to fit. Or you can print this grid and cut what you need. - Write the title of this challenge and today's date on a fresh page in your maths journal.
## Getting Started
Optional: - How do you know?
- Can you check it another way?
## Part A: Less Than FractionsIn the Getting Started, you could make any fraction you wanted. Now you can only make fractions worthless than 1.
- Open this Investigation Starter to read on screen or print.
- Just look at Part A.
The Starter tells you that there are 36 ways to make fractions < 1 using the tiles.How does a mathematician know that?
- If you want to try to find all of them, open your Learning to Work Like a Mathematician page and ask
*What might a mathematician do?*. - Are there any questions or strategies listed that might help?
Help from the Ancient Egyptians - What happens if you put 1 in the top box? Using the other tiles can you make any fractions that are less than one.
You are not an Ancient Egyptian. So you can try other numerators. ## Part B: Adding to make Less Than Fractions- Open this Investigation Starter again to read on screen or print.
- Just look at Part B.
...but of course a mathematician would want to know: - How many solutions are there?
- How do I know when I have found them all?
For example: Make the first fraction
That's the way it goes when you are working like a mathematician.You don't have to do all the remaining 35 - unless you really want to practise being a mathematician and feel the buzz when you find all the solutions. - If you do them all and send your work to us we will show it in the Gallery below.
< 1 fractions.
## Comparing FractionsIn Parts A and B you needed to compare fractions to find out which is bigger and which is smaller.For example, you might have to find out which is smaller ^{4}/_{7} or ^{3}/_{5}.This is actually a dumb question. For example, in one of these diagrams ^{4}/_{7} is greater than ^{3}/_{5} and in the other diagram ^{4}/_{7} is less than ^{3}/_{5}!- What is the different between the two diagrams?
It would be a LOT of work to do drawings for all the less than fractions in Part B.
- Draw a whole divided into fourths (quarters).
- Exactly underneath it, draw the same whole divide into thirds.
- Draw the same whole again (lined up with the first two) and divide it into new parts.
Mathematicians don't want to do a lot of work if they can find a better way by using something else they know.
Mathematicians thought they had this figured. ## Darren's Method for Comparing Fractions
Now you know which one is less and by how much. Therefore - Choose five pairs of fractions from the 36 in Part A.
- Write them in your journal one pair at a time.
- Use any of the methods to work out which is less and
work out the difference between the two. - Check your work using one of the other methods.
## Just Before You FinishFor this part you need your maths journal and your Working Like A Mathematician page.- Explain all the ways you have worked like a mathematician through this activity.
- The main skill in this activity is learning to compare fractions to see which is smaller or bigger.
Give yourself a score out of 10 to show how good you think you are at this. - Is there anything else you know now that you didn't know when you started Less Than Fractions?
## Answers & DiscussionThese notes were originally written for teachers. We have included them to support parents to help their child learn from Less Than Fractions.- Notes for Less Than Fractions.
Send any comments or photos about this activity and we can start a gallery here.
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