Number, Patterns & Algebra

When you are reading your favourite book the chances are you aren't having to sound out every word you read. Instead you are able to enjoy the story because your brain is instantly recognising and connecting the words to create a sense of meaning and a mental picture of what you have read.

"Mr. and Mrs. Dursley, of number four, Privet Drive, were proud to say that they were perfectly normal, thank you very much."
This is the very first sentence, in the very first book, of the world famous Harry Potter series by J.K. Rowling.

Imagine trying to read Harry Potter if you had to sound out and decode every word. With words like 'Mr.' and 'Mrs.' and 'four' in the very first sentence, words which don't sound like they look, you'd barely be started before the magic would disappear.

To really enjoy mathematics we just need to develop the same skills. We need to learn to read, think and speak in the language of mathematics.

The great news is that anyone can do it, and it's much, much easier than many people think. Your brain has already memorised hundreds, if not thousands of words, that it can recognise instantly as you read. To start thinking and speaking like a mathematician we just need to help our brain develop the same efficiency with a few basic number patterns. It's as easy as learning the alphabet. You'll see.

Let's start.

Addition & Subtraction

The most fundamental

Learning to add single digits with a total less than 10.

Why?

Learning the numbers that add to 10

1 + 9 = 10 2 + 8 = 10 3 + 7 = 10 4 + 6 = 10 5 + 5 = 10
and and and and
9 + 1 = 10 8 + 2 = 10 7 + 3 = 10 6 + 4 = 10

Why?

Learning which single digit numbers add to totals between 11 and 18.

2 + 9 = 11 3 + 8 = 11 4 + 7 = 11 5 + 6 = 11 and the reverse/commuted facts.

3 + 9 = 12 4 + 8 = 12 5 + 7 = 12 6 + 6 = 12 and the reverse/commuted facts.

4 + 9 = 13 5 + 8 = 13 6 + 7 = 13 and the reverse/commuted facts.

5 + 9 = 14 6 + 8 = 14 7 + 7 = 14   and the reverse/commuted facts.

6 + 9 = 15 7 + 8 = 15 and the reverse/commuted facts.

7 + 9 = 16 8 + 8 = 16 and the reverse/commuted facts.

8 + 9 = 17   and the reverse/commuted fact.

9 + 9 = 18

Why?

Learning

Multiplication & Division

Number, Pattern & Algebra Games

This is a great introductory version of the Countdown game.
For those who are new to the game the challenge is to arrange the numbers on any of the 6 coloured cards - using addition, subtraction, multiplication, or division - to achieve a total as close as possible to the given target number.
In this version, you can choose your level of difficulty and the target numbers are selected so that a solution is always possible.
Try starting with totals up to 20 or if you're feeling brave jump in and give the bigger numbers a go. It can be tricky but very rewarding.

Here's a slightly more challenging alternative.
This version has a solution button which will show you one possible way to get to the given target exactly. However, grouping symbols and the order of operations are used to show solutions, so until we look at these together in class you may need an adult or older sibling to help you make sense of the suggested solution.

This is the most advanced version of Countdown where it may not always be possible to reach the target exactly.
No answers are given in this version of the game so it is up to the players to check and confirm each other's solutions.
This might be a fun one to play with your family.
One way to score your game is to award ten points to any player who can achieve the target score exactly, 9 points to anyone who reaches a score 1 higher or lower than the target, 8 points for 2 away etc.
Try a few rounds. It's fun game to play with a group.

Fraction, Decimal and Percentage Games

The only possible winner in this game is you, but by practising your equivalent fractions in this way, you are establishing a great foundation for further explorations.