Lesson 1 - Basic Algebra

Lesson 1 - Basic Algebra

Barnsley College

Learning intentions - Develop your use of algebra

Bronze - To simplify expressions with one term

Silver - To simplify expressions with different terms

Gold - To simplify expressions by multiplying terms

Poll

How confident are you in using algebra?

• Very confident (5/5)

• Pretty confident (4/5)

• I'm OK at using it (3/5)

• I struggle understanding algebra (2/5)

• I really don't get algebra at all (1/5)

What is algebra?

For introduction, be sure to watch the video on the right. 

This will give you a brief introduction on what algebra is and how it can be used!

Simplifying expressions - collecting like terms​

In algebra, one of the things that we can do is collect 'like terms'. This is gathering some of the letters used together. An example of this would be:

f + f + f

When collecting this, we could add all the fs together to make 3f.

If we did the same for p + p - p + p...

We would get 2p. This is because we add the first p to the second, take away the third and add the fourth. Watch the video on the right to make sure you know how to do this before the quiz next!

Simplifying expressions - collecting like terms​

Check out this video to help you with collecting like terms before tying the quiz.

Multiple Choice

Simplify:

3x + 2x

• 5x

• x

• 6x

• 5

Simplify 3x + 2x

Because the terms are the same and the operation is a +, we can simply the numbers together, giving us 5x.

Multiple Choice

Combine like terms:

a + a + a + a

• a + 4

• 4a

• a⁴

• 4a + 4

Combine like terms:

• Because we are adding together like terms, we can simply add them one after another, so a+a+a+a becomes 4a.

• If this was a x a x a x a, that would be a⁴.

Combine like terms

Because we are adding together like terms, we can simply add them one after another, so a+a+a+a becomes 4a.

If this was a x a x a x a, that would be a⁴.

Multiple Choice

Combine like terms:

x+y+xy+x

• 3xy

• 2x+xy+y

• 2xy+x

• 3x+2y

Combine like terms

Here, you can only combine together the LIKE terms, so x, y and xy are all separate!

This should have left you with 2x+xy+y

Multiple Choice

Simplify:

2x + 1 + 7x

• 10x

• 10

• 9x + 1

• 9 + 1x

Simplify 2x + 1 + 7x

• Again, you can only add together LIKE terms, so the 2x and 7x can be combined, but the 1 must be on its own

• This should have given you 9x + 1

Multiple Choice

Collect like terms:

x²+y²+x+2y-3y²

• 2x²

• x²+y²+x-y

• x²-2y²+x+2y

• 3x+y

Collect like terms:

x²+y²+x+2y-3y²

• A crazy questions! But like the others, you can only add or subtract the LIKE terms. This should have left you with x²-2y²+x+2y

Simplifying expressions - multiplying​

When multiplying expressions, you are able to multiply terms as follows:

5 x a = 5a

3p x 7 = 21p

5a x 4w = 20aw

4y x 2y = 8y²

Simplifying expressions - multiplying​

Check out the video before moving on to the questions!

Multiple Choice

Simplify 2 x b

• 2b

• b²

• 2 x b

• b x b

Simplify 2 x b

• In this questions, you would show the answer as 2b

• Although 2 x b is correct, this is not SIMPLIFIED

Multiple Choice

Simplify 2b x 3

• 6b

• 5b

• 4b

• 3b

Simplify 2b x 3

• When multiplying, the terms do NOT have to be LIKE

• This means that 2b x 3 will be 6b!

Multiple Choice

Simplify 2b x 3b x 2t

• 12bbt

• 7b²t

• 12b²t

• 6b x 2t

Simplify 2b x 3b x 2t

• Much like the last question, you can multiply all of these terms together. If you first multiply 2b x 3b you get 6b². If you then multiply this by 2t, you get 12b²t.

Multiple Choice

Simplify 2b x 2c x 2t

• 8bct

• 6 x b x c x t

• 6bct

• b²c²t²

Simplify 2b x 2c x 2t

• Just like the last question, all terms can be multiplied together to give you 8bct.

• Remember, put your letters in alphabetical order when doing this. This questions was the correct order but it won't always be this way!

Multiple Choice

4b² x 3c

• b¹²c²

• 7b²c

• 12 x bc

• 12b²c

4b² x 3c

• Final question, multiplying the terms should have given you 12b²c.

Applying the skill

On the next slide you will see a quiz about applying algebra to situations.

Can you use the images and your knowledge of algebra to help calculate the perimeters of the shapes?

Multiple Choice

The distance around a shape is its _____________.

• area

• perimeter

Area and perimeter

• Area - the volume inside a shape - you get this by multiplying the length and the width and it will always be a ² number.

• Perimeter - this is the distance around a shape and you can get this by adding all the lengths of the sides of the shape.

Multiple Choice

The perimeter is 82 ft. What is the length of the longer side?

• 13

• 22

• 28

• 31

• 34

The perimeter is 82 ft. What is the length of the longer side?

• Woah! Difficult one. Knowing that the lengths and the widths have to be the same as it's a RECTANGLE, we can then add all of the like terms together.

• 4x + 8 + 2x + 3 + 4x + 8 + 2x + 3 = 12x + 22

• If we then minus 22 from the 82 for the perimeter, we should know that 12x is equal to 60.

• If we divide both sides by 12, we should be able to work out that x = 5.

• The length is 4x + 8 and we know that x = 5, so the equation should be 4 x 5 + 8 = ...

• This should give us the value of 28!

Poll

How confident are you in using algebra now you have come to the end of the session?

• Very confident (5/5)

• Pretty confident (4/5)

• I'm OK at using it (3/5)

• I struggle understanding algebra (2/5)

• I really don't get algebra at all (1/5)

Exit ticket!

Fantastic work! Be sure to head over to your Microsoft Teams page for Maths and find the Microsoft Forms quiz on the 'assignments' tab. 

If you complete this quiz, that will act as your register for this session. No completed quiz - no mark!