What is Algebra?

Algebra. The mere mention of the word can cause even the bravest child to break out in a cold sweat. Yet despite what students may think, algebra exists to make their lives easier. To help alleviate any fears your child may be having, we’ve put together this ‘algebra for beginners’ blog that introduces this often misunderstood topic to them in a fun and accessible way.

Girl looking at algebraic equations.

What is algebra?

Contrary to popular belief, algebra is not simply the process of substituting the numbers and operations in mathematical equations with symbols. In fact, symbols didn’t appear in algebra until the introduction of the printing press in the fifteenth century – more than 2500 years after algebra was invented in ancient Babylon. Algebra is better thought of as a language for describing mathematical ideas. It is through algebra that we can model different phenomena and make sense of the world around us.

Where does the word algebra come from?

Still a bit puzzled as to what algebra is? Don’t worry, a lesson on its etymology should help. The word itself comes from the Arabic word al-jabr (‘the reunion of broken parts’), which features in the title of the book Ilm al-jabr wa’l-muḳābala (The Compendious Book on Calculation by Completion and Balancing) by the Persian mathematician and astronomer al-Khwarizmi. The word first entered the English language in the fifteenth century and was originally used to describe the surgical procedure used for placing broken or dislocated bones back in place – which is appropriate given that algebra helps us to piece together bits of information.

So, why do children need to know algebra then?

Aside from the fact that algebra is a prerequisite to secondary school math, algebra is also important for helping children develop their reasoning skills. It gives them a way of representing their ideas succinctly, and to work their way through math problems systematically. Algebra comes into its own for problems that involve unknown quantities. To see what this looks like in practice, read on!

How to do algebra

When helping your child understand how to do algebra, we find the real world is always a good setting, so let’s start with a trip to the store. Let’s say, a mother asks her two children to go down to the store and buy some groceries for her. She gives them a $50 note and says they can keep the change but it needs to be split evenly between the two of them. The children need to buy five loaves of bread priced at $2 each, three bottles of milk at $4 each and two boxes of eggs at $3 each. How much change are they each left with? It turns out we can use a simple algebraic equation to figure this problem out quickly and easily.

For this example, we are going to represent the change they are left with using the letter x (any letter will do – x just happens to be a popular choice). The total change will, therefore, be represented by 2x (because they need to divide it between themselves). For this example, we will also use to represent bread, m to represent milk and e to represent egg.

We can write the information given as:


50 – (5b + 3m+ 2e) = 2x


50 – ( 5 (2)+3 (4)+2 (3) ) =2x

 

By calculating the expression in the brackets, we can simplify this to:


50 – (10+12+6) =2x

Let’s keep going:


50-28 =2x


22 =2x

 

So the total change is $22, which means each sibling gets half of this, or $11.

student studying

Simple algebraic equations

No ‘introduction to algebra’ blog would be complete without a couple of short teasers – the following questions are ideal for students who are beginners when it comes to solving algebraic equations.

There are 26 cats in the pet shop. This is two more than three times the number of dogs. How many dogs are there in the pet shop?

Want something a bit more taxing?

Alice and Bob have some candy. If Alice gives Bob a piece of candy, Bob has twice as much candy as her. If Bob gives Alice a piece of candy, they have the same number. How many pieces of candy do they each have?

When getting your child to attempt these questions, always ask them to show their reasoning, as this is the essence of algebra (and indeed of all mathematics!). In the last example, they may solve the problem through trial and error. Algebra becomes really powerful when it gives us systematic methods that can be applied to a flexible range of problems.

 

Is your child still struggling with algebra?

Math-Whizz, the multi-award-winning online math tutor from Whizz Education, can help! After a no-pressure initial assessment, Math-Whizz can pinpoint gaps in your child’s core math knowledge (e.g. algebra) and provide them with individualized lessons that will close these gaps by catering to their unique level of ability and pace of learning. In fact, with just 45-60 minutes usage a week*, Math-Whizz can increase your child’s math ability by 18 months during their first year of use. To find out more, please visit our parents’ page.

*Research by Whizz Education – conducted with over 12,000 students and verified by independent experts – found that students who used Math-Whizz for 45-60 minutes a week increase their Math Age, on average, by 18 months in the first year of use

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