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Conquering Negative Numbers

Nothing Nice About Negative Numbers!

September 02, 20244 min read

Nothing Nice About Negative Numbers

 

Yesterday I was working with a lad on negative numbers. I got the overall view that his opinion is that there is nothing nice at all about negative numbers!

I think this was worsened by the fact that his brain was still very much in holiday mode.

But I did wonder whether it would be worth just going over them again.

If we start with the question: 5-2:

You could probably answer this instinctively: Start with 5 and take 2 a way (move back 2 towards zero) to get the answer of 3.

0 0 0 0 0

     5

 

00 000

         3

 

However, if this was rearranged to have -2+5 it seems far more challenging!

What I suggest is that you draw or imagine a number line. The -2 gives you your starting point. Because we are adding move up the number line to the right →

Last night it was minus 2 degrees, and it got 5 degrees warmer. So, as we move up past the 0 and finish on the 3.

That’s our answer.

 

a negative plus a positive visual image

As our next example we could use the question, -2 -5.

Once again imagine (or draw) the number line. Your starting point is -2. This time it tells us to minus (or take) 5. So, we need to head left ← down the number line. In effect it’s getting colder.

Our answer would be -7.

 

Subtracting a negative from a negative visual image

Hopefully this is making sense.

Our next example might be 2-+5.

If you have a – and a + together, the minus always wins. It’s like an unfair arm wrestle with the – being the stronger contestant. You know the score before you’ve even started.

You can ignore the + and focus on the -, giving us the question 2-5.

Start at 2 on the number line and move left (because we are subtracting) down past zero to minus 3.

The next example could be 2- -5.

Here we have 2 negative signs together.

Please excuse my logic but it works for me…

When they are together, they feel positive, so it becomes an addition sum, giving us 2+5, which is the same as 7.

2 negatives TOGETHER make a positive / an addition question.

 

Next, we can move on to multiplying.

Multiplying negative numbers

If we are multiplying a positive by a negative the answer will be negative:

3x-5 = -15

-3x 5 = -15

1 negative in a multiplication question gives you a negative answer.

If we are multiplying 2 negatives together, we are again feeling more positive, giving us a positive answer:

-3 x -5 = 15

-5 x -3 = 15

 

multiplying 2 negatives or 2 positives

Finally, we can move on to division. This is like multiplication. If we have 1 negative number in the question, we will have a negative answer:

-15 ÷ 5 = -3

-15 ÷ 3 =-5

 

And again, 2 negatives in the question will give us a positive answer:

-15 ÷ -3 = 5

-15 ÷ =3 = 5

 

It works like this because if we worked the question backwards, we would in effect be doing the inverse (opposite) which is the same as multiplying.

 

I hope at least some of that made sense.

 

When you are practicing negative numbers, I would recommend drawing yourself a bright colourful number line that you can move up and down, also have fact sheets of the rules so that you can remind yourself of them when needed. That way you just need to focus on the actual maths and not the multiple different rules involved.

 

The games we would use would probably involve Ludo, snakes and ladders, and a board game. I might also be tempted with an older child to play chess, having a different number down the side and bottom of the board, then adding them together if you land on the square that links them. I hope that makes sense, a bit like you would read coordinates on a graph.

 

Each week we send out an email supporting some aspects of primary maths or English (Monday) or secondary (Thursday) maths or English. If you would like to receive either, please do let me know and I will make sure you get them: [email protected]

I hope it helps

 

negative numbersmaths supportparentinghome education
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