Articles

Rounding numbers up and down

Currently we don’t have a workbook covering rounding numbers up and down

We realise that it is an important capability that a child should master as part of their maths education, so we shall either write a new book covering this as part of Number & Place Value which will include Roman Numerals.

We have no release date for this workbook yet, but please subscribe and we’ll email updates including discount codes once the book is available.

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Working out one percent

Probably the most useful percentage to be able to work out is 1%, and then apply it to lots of problems

A question like “Work out 3% of 60” can look scary to a child who’s just getting to grips with percentages.

An easy way to work this out is to work out what one percent is.

1% = 60 / 100 = 0.6

From this it is easy to work out any percentage.

So 3% of 60 = 0.6 x 3 = 1.8

This is useful because once a child realises that it’s easy to work out what one percent of a number is, everything else becomes easy.

Once this realisation has been made and secured, it is worth working out a lot of examples so it becomes second nature to move fluently between fractions, decimals and percentages.

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National Curriculum on Recall

It is interesting that in the National Curriculum, most subjects for most years in KS2 refer to recall. For example;

recall and use equivalences between simple fractions, decimals and percentages, including in different contexts

National curriculum in England: mathematics programmes of study
https://www.gov.uk/government/publications/national-curriculum-in-england-mathematics-programmes-of-study/national-curriculum-in-england-mathematics-programmes-of-study

Switching between fractions, decimals and percentages

It’s very useful for children to learn and recall a few keystone numbers such as these, which helps to anchor their understanding;

FractionDecimalPercentage
1/20.550%
1/40.2525%
1/100.110%
2/12.0200%
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Focus on the least easy to remember maths

Is your child always hesitating at 7 x 8, or stumbling when it comes to dividing 1/4 by 1/3?

There’s a good case to focus on the really difficult maths which children have to deal with as part of their education.

On paper or whiteboard, ask a child to write down the most difficult calculations twice a day until it has not only been remembered, but understood.

This is what we mean by repetition and variation.

Repetition & variation with fractions

If a child is having problems with 1/4 of 1/6, then repeat the method over and over until they can copy you (that’s the repetition part).

Then, ask the child to work out 1/4 of 1/8 and 1/4 of 1/6.

Then, move on to 1/3 of 1/2 and 1/5 of 3/4.

Securing method and recall = numeracy

Repetition with variation will help secure not only the method, but also a wide range of examples which will help secure recall.

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Rolling a dice to get to ten

Here’s a really nice and simple game you can play with one dice

AIM: To get to ten in as few steps as you can

STEP 1: Throw the dice and note your number

STEP 2: Everyone else in the games rolls the dice and notes their number

STEP 3: You roll again and add it to your first number. If you’re lucky you may have rolled two fives, or a six and then a four – but probably not.

STEP 4: You keep rolling, either adding or subtracting the number each time until you get to ten.

For example 5 + 1 + 3 + 5 – 2 etc … until you hit ten.

VARIATION: It can be easier for each play to roll until they get ten, noting the number of rolls it has taken, then on to the next person – i.e. rather than rolling once before passing on the dice.

Scaling the dice game

This is a great game because you can scale it.

Try using two dice and make your target number 21.

You get the idea.

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Play to a child’s interests (then bring in the maths)

Too often, maths is an abstract subject for children, so it is very important to make it real. Then repeat.

Who likes football?

If a child likes football, you’re all set for at least a half-term.

How many payers on each side? Eleven.

So how many players are there on the field (assuming no one has been sent off)?

If there are five teams in a table, how many players is that?

How many matches must each team play to make sure they’ve played each team home and away?

You get the idea – and on top of the questions above there are loads of questions you could come up with to do with scores and points etc.

Make maths real

The point of the above questions is that an engaged child will understand your questions and most importantly, will be engaged.

Maths on the Motorway

Look at that truck, I can see twelve wheels on this side of the truck. How many wheels does it have in total?

Multiply the numbers of each cars numberplate you see. For example KD8 12L would be 8 x 1 x 2 = 16.

If we’re travelling at 60mph, how far will we go in twenty minutes?

I don’t like Maths, I like to Read

You can even bring on board children who don’t like maths (on the surface).

What are you reading right now?

About how many pages is that?

How many pages did you read yesterday?

About how long do you think it will take you to finish the book?

When you buy your next book, how much change will you get from £10?

Will there be enough change to also buy a hot chocolate?

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Two simple things a child should know about multiplication

To help secure multiplication (and to start the ball rolling with division) explain to a child that;

3 x 5 is the same as 5 x 3

Explain that 3 x 5 is the same as 5 + 5 + 5

… and that 5 x 3 is the same as 3 + 3 + 3 + 3 + 3

It works well to draw these up on a whiteboard and ask the child to replay this explanation with different and easier numbers, e.g. 2 x 3.

Why is this useful?

This is useful because a child might be able to remember a multiplication which rhymes – e.g. 6 x 8 = 48, so it makes sense to remember that 8 x 6 has the same answer even though it doesn’t rhyme.

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Practice, Practice, Practice (with variation)

Research on why repetition (with variation) increases probability of retention

There are many excellent papers with research supporting why repetition with variation has a high probability of increasing retention for children.

This research supports the view at KeyStageMaths.com that repetition with variation is an essential and often overlooked method to help children become fluent in numeracy.

Citations on education using repetition with variation

Here are a few citations:

Bruner (1961) stated that it is only through the exercise of problem solving and the effort of discovery that one learns the working heuristics of discovery. The more one has practice, the more likely is one to generalize what one has learned into a style of problem solving or inquiry that serves for any kind of task or almost any kind of task.

Marton, Wen and Wong (2005) pointed out that the likelihood of being able to recall something is higher if the learners hear or see something several times than if they do not. Furthermore, they commented that, unlike when you read the same presentation of something several times in the same way and thus repeat the same thing again and again, or read the same presentation in different ways, something is repeated and something is varied.

Noche & Yu (2015) found out from her study on supplemental self-paced instruction that focuses on the mastery of either concepts or procedures through repetition with variation, helps young adults improve their performance in tasks designed and proportional reasoning understanding and skills.

Buy & Download Now

You can buy and download it right away. Print and use as many times as you like.

A4, 21 pages, 164 Targeted Q&A for only £2.45 (approx $3.30)

You can buy and download it right away. Print and use as many times as you like.

A4, 21 pages, 188 Targeted Q&A for only £2.45 (approx $3.30)

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What Subjects are Taught in Key Stage Maths?

Key Stage Two Maths is broken into Lower (years 3 and 4) and Upper (years 5 and 6).

The table below shows the subjects taught and in which years:

SubjectY3Y4Y5Y6
Number – number and place value
Number – addition and subtraction
Number – multiplication and division
Number – fractions
Number – fractions (including decimals)
Number – fractions (including decimals and %’S)
Ratio and proportion
Algebra
Measurement
Geometry – properties of shapes
Geometry – position and direction
Statistics

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