Demystifying Maths

What are number lines?

A number line is a line with numbers on! I like to think of them as zoomed in parts of a ruler, thermometer, or an axis of a graph.

A number line is a useful visual tool that helps to bridge the gap between using objects and just using numbers. They show the order and relationships between numbers as well as being great for calculations.

More on how they can be used next time!

Merry Christmas everyone!

Hoping you all have a wonderful day, even if your plans have had to change.

🍸🍺🍷🥂 Nope, not that kind of bar!

This kind of bar model is another visual representation that is great for problem solving.

Bar models are usually introduced in key stage one for part-whole problems, but they are useful for many types of problems all the way through to GCSE (and beyond!), such as:

⭐️ The four operations and understanding their inverses (+/-, x/➗)
⭐️ Fractions, decimals, and percentage questions
⭐️ Ratios
⭐️ Algebra

For me, they’re my favourite go to for ratio questions. Having such a versatile visual for a topic that so many people find tricky is invaluable.

Take a look at the diagram for the comparison bar model. Can you think of any other questions that require a similar diagram? Add them in the comments below.

A picture speaks a thousand words and having the right diagram really can make all the difference in understanding and solving a problem.

A whole group of objects can be broken down into two or more smaller groups. A part-whole model is a visual way of representing what ‘parts’ make up a particular ‘whole’.

Children are usually introduced to the cherry diagram part-whole model first, where the parts are draw as stems (the cherries) from the whole.

They can be drawn in different orientations, or have three or more parts, the parts themselves could even be decimals or fractions. Adding up all of the ‘parts’ in the model will give you the ‘whole’.

Why use them?

⭐️ Having a good understanding of how numbers are constructed and how we can manipulate them is a key skill for making many future problems simpler, particularly when solving mentally. These diagrams provide a visual way to stimulate thinking about this.

⭐️ They are a great way to highlight that it doesn’t matter what order we add numbers in (known as commutativity), e.g. 7 = 3 + 4 = 4 + 3

⭐️ Perfect for number bonds

⭐️ They highlight the relationship between addition and subtraction

Have your children worked with cherry diagrams yet?

Having trouble with the symbols < > ?

< is less than
> is greater than

⭐️ They’re always read from left to right
⭐️ The larger quantity is nearest to the open end of the symbol

So if you encounter the open end first when you’re reading, it’s a greater than symbol as you’ll already have said the larger amount.

Did you learn about the greedy crocodile? 🐊

This is a snappy (😂🙈) alternative way to help kids remember which symbol to use. The greedy crocodile is always going to eat the larger quantity. This method is still taught in schools, just be sure to make your crocodiles toothless! 🐊❌🦷

Why learn about number bonds?

🔹Develop a sense of number
🔹Show how a larger number is made up of smaller numbers
🔹Are a great starting point for addition and subtraction
🔹Help with mental maths

Number bonds are arguably an essential tool for solving problems mentally and can make light work of what appear to be tricky questions!

E.g.
🧠 297 + 49
= (297 + 3) + (49 – 3)
= 300 + 46
= 346

🧠 6 + 7 + 9 + 4 + 1 + 3
= (6 + 4) + (7 + 3) + (9 + 1)
= 10 + 10 + 10 = 30

And don’t be afraid to use fingers for number bonds to 10 🤚✋They’re a manipulative that we’re rarely without!

A new use for the place value table 🤩

I know that you’ll have seen a place value table before, but I thought that it would be worth highlighting a couple of useful things that it can show, other than the value of digits.

1) Each column is 10 x the column to the right of it. This is used when we multiply by ten – the digits move across a column and zeros are added to hold their new places.

2) Powers (indices). It’s great for introducing powers, but also for illustrating the rules of indices, 10^0 = 1, and that 10^-1 = 1/10

I showed this to my son last week, (he’s in year 11) as he always struggles to remember what negative indices are all about. This is a great way to combine following a pattern, knowing the place value table and realising that 1/10 = 10^-1.

The power of place value!
(Did you like what I did there? 🤪)

Not sure which numbers your young person will be introduced to this year, or which they should be familiar with already? This will sort that out! ✅

Of course these aren’t the only type of numbers, just the whole numbers (aka the integers). Fractions are introduced later in year 1, but relating them back to place value starts in year 3 with tenths. Looking at decimals more formally starts later in year 4. For now, whole numbers is what they’ll be focussing on! 🔍👀