Algebra

Algebra is a part of mathematics that uses letters or symbols to represent an unknown value. For example **3x** means **3** lots of the value **x**.
 * __What is algebra?__**

An algebraic expression is when two or more algebraic terms are put together in an equation. For example: **3x + 2y**.

We can simplify an algebraic equation by adding or subtracting 'like terms'. Like terms are those represented by the same symbol in an expression.
 * __Simplifying Algebraic Equations__**


 * 3x + 2y + 5x + 3y - y**

In this equation, **3x** and **5x** are like terms and **2y**, **3y** and **y** are like terms.

To simplify this equation, we can first add the **x** terms together: **3x + 5x = 8x**

Our equation now looks like this: **8x + 2y + 3y - y**

We can then put together all of the **y** terms. The result is **2y + 3y - y = 4y**.

REMEMBER: the mathematical symbol that comes //before// the term is the one it belongs to. This will help you with more complicated equations.

Our simplified equation now reads: **8x + 4y**.

__**Algebra in primary schools.**__ Algebra is taught throughout primary schools, from as early as reception. Formal algebra doesn't begin until upper key stage 2, however the foundations need to be addressed at the start of the child's formal education - reception.

Algebra in reception and key stage one involves general sequencing of numbers, ordering them in specific ways and being able to recognise and write symbolic forms of numbers. Therefore it is important to use both written and symbolic number forms to ensure children are familiar with both and understand they mean the same thing; for example: fourteen add four equals eighteen, and introducing 14 + 4 = 18. This simple introductory activity introduces children to forming equations.

Children in reception and key stage one are also exposed to solving equations in most numeracy lessons. Children can be asked questions such as 4 + ▲ = 10 this is a simple way of introducing the idea of unknown values. Rather than introducing children immediately to equations involving 2y + 4y - y = 5y and so on, because children can become confused with a mix of numbers and letters whereas symbols such as ▲ are more accessible to children. Teachers can also ask children questions such as - "I double a number and add 2, the total is 12. What is the number?" This involves children noticing two unknown values can appear within the one equation and leads children to the idea that the unknown value isn't necessarily one fixed number but may be variable.

__**Introducing algebraic letters to children.**__ The concept of a letter representing a variable number (i.e. x = 4, x = 22...) can be quite challenging for children to grasp. A good way of introducing and building familiarity with this concept is through the game "What's My Rule?"

In this game, the teacher draws two columns on the board, **A** and **B**. In column **A**, the numbers 1-10 are written; a few corresponding numbers are then given for column **B**. By identifying the sequence emerging in column **B,** pupils are challenged to identify what number will be found in column **B** for a given number in column **A...**

This is best shown through an example__**:**__

In this example, we can see that the pattern is +2, as our sequence progresses by 2 each step. This is an easy way to introduce algebra as it builds on children's prior non-algebraic knowledge of number sequences. We can also expand the table to incorporate higher numbers (such as 100) in column **A** - in doing so, children are forced to develop a 'rule' for working out the number, as they cannot simply count up as they could do with the table above. Naturally, at higher levels, pupils can be introduced to the concept of the **nth term,** which can be placed at the bottom of column **A.** Pupils are then challenged to work out the rule rather than the numbers themselves in column **B.** This, however, is reasonably advanced for primary maths, and may only feature in higher level extension provision at Year 6, if at all.
 * **A** || **B** ||
 * 1 || 3 ||
 * 2 || 5 ||
 * 3 || 7 ||
 * 4 ||  ||
 * 5 ||  ||
 * 6 ||  ||
 * 7 ||  ||
 * 8 ||  ||
 * 9 ||  ||
 * 10 ||  ||

 Learning Algebra is achievable for all, children just need to take things one step at a time and learn the basic rules before moving on to more advanced topics. It can be seen as a daunting topic in maths because it can be relatively confusing, but once the basic rules and concepts are understood, it is much easier.  