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Equivalent fractions

How to work out Equivalent Fractions

July 15, 20243 min read

Fractions are something that a lot of people from primary through GCSE struggle with

I thought I will add the foundations of the explanation here (it goes on for a while which is why I haven’t bored you with all of it, but shout if you do want it (It will eventually all appear in the Clara James Approach and the 11+ resources).

 

Equivalent fractions

A fraction is a bit of something. I would suggest a piece of cake, but I was working with someone once and used that as my description, and he got locked onto the fact that the cake might crumble...

 

Actually, we’ll say we have a piece of cake regardless. It’s been cut into 8 equal parts. That 8, is the number that goes at the bottom of the fraction, the DENOMINATOR In effect, it tells us how many we have.

Imagine, 2 pieces of cake are eaten.

That means that 2/8 of the cake are eaten, or we have 6/8 of the cake left. (Because 8-2 leaves us with 6 pieces).

If all bar one of the pieces were eaten, we’d have 1/8 left and 7/8th eaten.

 

If you are asked to colour in ¼ of a repeating pattern, you would group four parts and just colour in 1 of them doing this repeatedly until all the parts are complete.

 

I hope that makes sense so far. Please do ask if not.

Next, we might be asked about equivalent fractions.

 

Imagine now that my cake is cut into 2 pieces. You can have a piece and I will also have a piece. We each get 1 piece out of 2 (1/2).

But 2 more friends turn up, so we cut it down into 4 equal pieces. However, they don’t want any, so instead of us having 1 big piece each, we get 2 pieces out of 4 each (2/4)

1         =  2

2             4

 

Because we doubled the 1 to get to two, we had to double the 2 as well.

If we multiply or divide the top and bottom numbers by the same amount, we will keep them equivalent. This is also how we simplify.

 

If we had the example:

 

6

12

 

Both can be divided by 6

6/6=1

12/6 =2

 

Giving us an equivalent fraction of ½

 

If the numbers are bigger, you may break it down into smaller steps. In this example you might have halved both numbers first, then divided them both by 3.

In other examples you might have divided by 5 or 10 first to keep it simple, then as the numbers got smaller and more manageable, you can start diving by the numbers you are less confident with.

 

I hope this makes sense.

The Clara James Approach

If you have a child who enjoys learning through games and being more creative, and you enjoy spending time with them, you might be interested in the Clara James Approach, the membership group we have put together to support you in supporting your primary school aged child with their maths and English.

Interested?

Click here to learn more: The Clara James Approach

 

 

 

 

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blog author image

Dawn Strachan

For the past 20+ years I have been a firm believer that learning should be an enjoyable experience. I appreciate that traditionally education has revolved around worksheets, textbooks, listening to teachers. But a grounding in early years and working with children who had a variety of learning styles from I learned that it is an individual activity that is personal to all of us. We don’t all learn in the same way. Our influences, our experiences, our capabilities all influence how we retain information. But through it all, I believe that if we can make it enjoyable and engaging, they will want to participate. With participation comes practice which in turn boosts skill and confidence. With an increase in skill and confidence comes a willingness to have a go. This in turn leads to more practice which leads to a positive spiral of success. The moral, we need to make learning fun, engaging, use a range of techniques.

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Happy New Year - Jan 2024

Happy new year!  

I hope you’ve had a brilliant break over Christmas.

I know some people have been on holiday, others have been enjoying family time at home. Either way, I hope it was fantastic.

Someone sent me a Christmas present just before the bog day, but I have no idea who it was from, so I can’t say thank you. I feel really guilty as it seems like bad manners, but it was just in a box from M&S with no message attached.

This year, I have committed to send out the notification when the monthly membership bundle goes live, but I am also going to send out an (initially) fortnightly newsletter with suggestions for revision / secondary school Math / English, then in the alternate week a newsletter with suggestions for the primary subjects.

If either of them isn’t relevant, please either let me know and I will ensure you just get the primary or secondary newsletter if you want it, or just click unsubscribe (but then you also won’t receive the email about when the bundle goes live).

My goal is to keep you more in the loop as to what is happening. For example, we occasionally put free courses on Udemy – we’ve just done one on angles – here’s the link if wanted. It was created to promote the topic book we have also created; we’ve also got revision planners for students that might be suitable for some GCSE parents.

At Christmas we also had some free times-tables colouring sheets which you may not have been aware of, so like I say, it may not be of interest to you, but if it is, at least you’ll be aware of it. I have 3 revision planners and 3 angles topic books to give away if you’re interested. Let me know and I’ll happily pop one in the post for you (or give it to you if I’m likely to see you…).

If you do have one, if you could give it feedback on Amazon (I’ll send you the link) that would be hugely appreciated.  

Happy new year for now and warm wishes,

Dawn

Times Tables - Jan 24

Hi,

 

Last week I sent out an email saying I was going to try and commit to sending out an email at the beginning of each week on ideas to support primary school children, then later in the week about supporting secondary school children.

As a result, I was asked if I could also send out some ideas to support the 11+.

(Again, if this doesn’t concern you let me know and I’ll try to ensure that you don’t receive them).

I’ll send the 11+ emails on an alternate Wednesday as I normally have Alfie, my grandson on a Tuesday and the odds of getting much done with a lively 2-year-old for company…  

There will be some cross over between primary school and secondary school subjects, but at any stage there is something you specifically want me to help with, please do shout.  

So, back on subject, sorry…  

Times tables have always been one of the key subjects that I work on with, specifically primary aged children, but also secondary school children, and often the parents say they’re awful at them as well…  

I don’t suggest learning them in chronological order.

If you do, you’ll hit some of the much harder ones before you get to some of the easier ones.

Instead, what I suggest (and you’ve probably heard me say this before) is that you start with the 10’s, 11’s, 2’s and 5’s as they do in school.

Then deviate across to the 9’s as there are so many tricks to help you to learn them.

Then the 6’s or 7’s. Crazy I know!   But they are quite simple if you split them so that 6x8 becomes: 5x8 + 1x8 = 50+8 Or 7x8 becomes 5x8 + 2x8 = 40 +16 = 56.

From there you can pretty much work in any order.

The 12’s is also straight forward as we can split it into 10x + 2x which would give us the same answer as 12x.  

There are more suggestions on the times tables over in the Clara James Approach, or I have a sequence of emails which sends out once a month with suggestions on how to learn each of the times tables with some resources. If it would help, the link is here: Support your child with their times tables - The fun way! (sendfox.com)

I hope that’s helpful and not just waffle.

Like I say if there is anything specific you would like us to focus on, please do give me a shout.  

Have a great week and warm wishes,  

Dawn

Hand Writing Support

Hi,

I hope you had a good weekend.

 

Something I am often asked about is supporting hand-writing skills.

At a young age this may relate to the hand muscles in the hands not yet being fully developed and I have a few suggestions that may help.

As the child gets older, you may want to find the support of an occupational therapist to provide some suggestions.

 

1.       Start big: I guess it’s a bit like parking a car. When you are first asked to park a car, you wouldn’t want to park in a narrow gap, you’d hopefully save that until you were more confident, more skilled. Handwriting practice is the same, using a big piece of paper is far better than trying to squeeze your imperfect shapes between two narrow lines. Even better, (if the weather is more forgiving) start by using water to paint on the side of the house, a patio or footpath). Use large movements and as these improve start to shrink it down to what is expected inside a school exercise book.  

2.       Jenga: I love this game and we’ve adapted it by writing numbers of the bricks so that we can practice number bonds or the times tables, we’ve also got grammatical terms on others so that we can also practice those. But the skill and care needed to remove the brick from the tower without it all tumbling is a great way to practice the fine motor skills which will in turn support handwriting.

 

3.       Colouring is another suggestion: keeping the colouring inside the lines is another skill that requires practice and patience. Again, the strokes used in colouring can further aid the shapes created when writing letters.  

4.       Sewing again requires the use of the fine motor skills needed for neat handwriting. You may just do a normal running stitch on a square of fabric, or you may decide to make something or use a more elaborate stitch. Either way I hope this helps.  

5.       Playdough and clay are other great early interventions to building up the muscles in the hands. The stronger and more developed the muscles are the more precise we can be with our writing.  

To be honest, anything that needs to be precise will help. Many crafts and building activities help.    

For some people, messy handwriting is always an issue.

There are a couple of members of my family whose handwriting I always struggle to read, yet they are so intelligent. It doesn't seem to add up. But my daughter says, if she doesn’t write quickly, she can’t remember everything her brain is throwing at her. Her brain works at such a speed.

I used to tutor a girl a couple of years back. I hadn’t realized her mum was an invigilator for the A’ levels at the school my youngest went to.

Not long after Hay sat her history the mum asked me if my daughter was doing her exams now.

Yes.

Does she do History?

Yes. Is she called Angel?

Yes.

She said, I thought it must be your daughter.

I have never seen anyone writing so quickly. I expected sparks to come off that page!  

There are many reasons why people have scruffy handwriting, sometimes it needs to be investigated and like I say, if you are worried about it, it might be worth while trying to get in touch with an occupational therapist.

Sometimes, practicing using the suggestions above will help.   Sometimes, like with Hay, it’s just one of those things that make them, them.  

I hope this has helped a bit.

Have a great week and warm wishes,

Dawn