Find out why teachers and school leaders love PlanBee

Find out why teachers and school leaders love PlanBee

Algebra is formally mentioned in the National Curriculum in Year 6. However, 'algebraic thinking' can be encouraged before this:

- Make sure children understand that the equals sign does not stand for a calcuating instruction, rather it means 'equivalent to'. This idea can be illustrated visually using a balance.
- Use pictures or symbols instead of letters in missing number problems. This familiarises children with the idea that a number can be represented by something else.

According to the National Curriculum, pupils in Year 6 should be taught to:

- use simple formulae
- generate and describe linear number sequences
- express missing number problems algebraically
- find pairs of missing numbers that satisfy an equation with 2 unknowns
- enumerate possibilities of combinations of 2 variables

The non-statutory notes and guidance suggest that pupils should be introduced to the use of symbols and letters to represent variables and unknowns in mathematical situations that they already understand, such as:

*missing numbers, lengths, coordinates and angles**formulae in mathematics and science**equivalent expressions (for example, a + b = b + a)**generalisations of number patterns**number puzzles (for example, what 2 numbers can add up to)*

These objectives are covered in our two ready-to-teach Year 6 lesson packs; **Algebra** and **More about Algebra**.

Algebra is a part of mathematics that helps represent a problem as a mathematical expression. It gives us rules about how **equations** should be made, and how they can be changed.

An equation is a mathematical sentence that has two **equal** sides separated by an equal sign, e.g.

3 + 5 **=** 8 3 + 5 **=** 4 + 4 8 **=** 2 + 6

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Take a look at **how to read and understand algebra equations**, then practise solving basic algebra addition and subtraction problems in this **ready-to-teach Year 6 Algebra lesson**. This plan pack includes detailed **teacher's notes** to help you explain how to understand and solve simple algebra equations. It also comes with a detailed **lesson plan**, a set of **slides** which explain, step by step, how to read and understand equations, plus a **choice of activities and printable resources** including solving equations worksheets.

**Scroll through the pictures for a preview of the lessons' resources:**

Algebra is used when we do not know the exact number in an equation. A **variable** (usually written as a letter, such as *a, b, x*) is used in place of an unknown number, e.g.

3 + 5 = ** a** 3 +

Algebra is used in many everyday life situations, such as working out the amount of each ingredient for a recipe, or daily budgeting with money. Many professions require the use of equations too, including air traffic controllers, architects, computer programmers and carpenters.

Algebra can be used to solve problems involving maths. Here is a simple example:

*Barney looks out of his window in the morning and counts 16 birds sitting in his apple tree. In the afternoon, he counts again - this time there are 27 birds in the tree. How many more birds are there in the afternoon than the morning?*

First, we need to write the problem as an equation, using a variable for the missing number:

16 + *x* = 27

The rules of algebra allow the equation to be changed until we can see what number the variable is representing. One of the rules of algebra is that whatever you do to one side of the equation, you must do to the other. This is called the **balance method**. So, we can subtract 16 from both sides, leaving x on its own, because 16-16 is zero:

16 - 16 + *x* = 27 - 16

*x* = **11**

There were 11 more birds in the apple tree in the afternoon than in the morning.

**£1.49**

This **ready-to-teach Year 6 Algebra lesson** will teach your class how to **express problems algebraically** - and how to solve them too! The included slides show clearly how to deconstruct a variety of number problems and use algebraic expressions and equations to solve them. After you've delivered the main teaching input, there's a choice of differentiated activities where children may apply their newly-learnt algebra skills by reading, understanding and solving problems by forming and solving equations.

**Scroll through the pictures for a preview of the lessons' resources:**

Here are some one-step equations and their solutions, using the **balance method**:

(Note: if a number is placed directly next to a letter, this means that the number and letter need to be multiplied together.)

*a* + 13 = 22

*a* + 13 - 13 = 22 - 13

*a* = **9**

*b* - 8 = 15

*b* - 8 + 8 = 15 + 8

*b* = **23**

3*c* = 24

3*c* = 24

3 3

* c* = **8**

* d* = 5

4

* d *x 4 = 5 x 4

4

*d* = **20**

Each answer can be checked by substituting it back into the equation in place of the letter.

Here are some two-step equations and their solutions, using the **balance method**:

2*e* + 8 = 14

2*e* + 8 - 8 = 14 - 8

2*e* = 6

2*e* = 6

2 2

*e* = **3**

5*f* - 6 = 19

5*f* - 6 + 6 = 19 + 6

5*f* = 25

5*f* = 25

5 5

*f* = **5**

*h* + 7 = 4

5

*h* + 7 x 5 = 4 x 5

5

*h* + 7 = 20

*h* + 7 - 7 = 20 - 7

*h* = **13**

*k* - 4 = 8

3

*k* - 4 + 4 = 8 + 4

3

*k* = 12

3

*k* x 3 = 12 x 3

3

*k = ***36**

If an equation has two variables, then it cannot have a single solution. For example:

*a* + *b* = 6

In this case, we know that the total of *a* and *b* cannot be higher than 6.

We also know that *a* and *b* must be different numbers.

We could begin by substituting *a* for 0. This means that *b* would be 6.

Next, we could substitute *a* for 1, meaning *b* would equal 5.

There are six possible solutions for this equation: *a* = 0, *b* = 6 *a* = 1, *b* = 5 *a* = 2, *b* = 4 *a* = 4, *b* = 2 *a* = 5, *1* = 6 *a* = 6, *b* = 0