Algebra

Learning Objectives:

Level 1

Equations and expressions

• Communicate and explain counting, grouping, and equal-sharing strategies, using words, numbers, and pictures.

Patterns and relationships

• Generalise that the next counting number gives the result of adding one object to a set and that counting the number of objects in a set tells how many.
• Create and continue sequential patterns.

Level 2

Equations and expressions

• Communicate and interpret simple additive strategies, using words, diagrams (pictures), and symbols.

Patterns and relationships

• Generalise that whole numbers can be partitioned in many ways.
• Find rules for the next member in a sequential pattern.

Algebra

What is it??

The first stage of Algebra thinking is seeing, continuing and making patterns.

The big ideas we have to understand are:

• counting is a sequential pattern

For example:

You can count in 2s: 2, 4, 6, 8, 10, You can predict what will be next - 12.

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• repeating pattern has a consistent element of repetition

For example:

💠 💠 ⮍ 🚩 ⏺ 💠 💠 ⮍ 🚩 ⏺ 💠 You can guess what shape should come next - 💠

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• sequential pattern has a consistent element of growth.

For example:

5, 10, 15, 20, (the numbers are growing by 5) OR with shapes:

Algebra

Time for practise and revision: (Remember your answers go in the pale green squares)

• counting is a sequential pattern (For example: count in 2s: 2, 4, 6, 8, 10, you know 12 is next)

Continue the following counting patterns for 3 more numbers:

1. 101, 102, 103, 104, 105, 106, , , ,
2. 40, 50, 60, 70, , , ,
3. 22, 24, 26, 28, 30, , , ,

For these ones you have to work out which numbers are missing:

1. 130, 140, , 160, 170, ,190, , 210,
2. 6, 8, ,12, 14, ,18, ,22, 24,
3. 30, 35, ,45, 50, 55, 60, ,70, 75, , 90

Algebra

Time for revision and practise: (Remember your answers go in the pale green squares)

• a repeating pattern has a consistent element of repetition

For Example: 💠 🚩 ⏺ 💠 🚩 ⏺ 💠 🚩 ⏺ (this shape - 💠 should be the next ‘term’)

(The core of this pattern is : 💠 🚩 ⏺ )

Continue the following patterns for 3 more ‘terms’ (parts): (copy and paste the pictures)

1. 🐈 🐈 🐶 🐦 🐈 🐈 🐶 🐦 🐈 🐈 🐶 , , ,
2. ⭐ 🍎 🍎 🌴 ⭐ 🍎 🍎 🌴 ⭐ 🍎 , , ,

For these patterns work out which terms are missing:

• 🛥 🐠 ,🌴 🛥 🐠 🐠 🌴 🛥 🐠 🐠 ,🛥 🐠 🐠 🌴 ,
• 🍌 🍦 🍹 ,🍌 🍦 🍹 🍕 🍌 , 🍹 🍕🍌 🍦 ,🍕

Extra: highlight the core of each pattern, No.1 is done for you.

Algebra

Time for revision and practise: (Remember your answers go in the pale green squares)

• A sequential pattern has an element of growth that stays the same.

For example: 5, 10, 15, 20, (the numbers are growing by 5) OR with shapes:

Continue the following patterns for 3 more ‘terms’ (parts): (copy and paste the pictures)

• 20, 40, 60, , , ,
• 5, 10, 15, 20, , , ,
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NOTE: You only have to add one more shape to this growing pattern.

Use the fill tool(little bucket).

Algebra

What’s next?

The third stage of learning about Algebra is using your knowledge of numbers and number patterns to solve problems.

The big ideas we have to understand are:

• each side of the = sign have to balance (they have to be equal!)
• We use what we do know to find out what we don’t.

Watch this video carefully:

Algebra

Time for practise:

• each side of the = sign have to balance (they have to be equal!)

For example: a) 4 + 6 = 10 both sides of the = sign, are = to 10

b) 7 + 3 = 6 + 4 because 7 + 3 = 10, and 6 + 4 = 10

Your turn. Make both sides of the equal sign balance (equal):

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Algebra

Time for more practise:

• each side of the = sign have to balance (they have to be equal!)

Your turn. Make both sides of the equal sign balance (equal):

a. 10 = 8 +

b. 1 + 2 = 1 + + 1

c. 4 + 1 = + 3

d. 20 = 10 +

e. 9 + = 2 + 8

f. 8 = 4 +

Algebra

Time for practise:

• We use what we do know to find out what we don’t.

For example: We know 2 + 4 = 6, so if we see 4 + , = 6, we know the missing number is 2

Your turn. Firstly we are going to complete these family of facts(related facts:

1.

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2.

We know this

So we can find this

Remember: + is the opposite of -

and ÷ is the opposite of x

These operations ‘undo’ each other.

Algebra

Time for more practise:

• We use what we do know to find out what we don’t.

Your turn. You will be given on fact and have to finish the next.

Eg If 2 x 4 = 8, then 8 ÷ 2 =

1. If 4 + 6 = 10, then 6 + 4 =
2. If 1 + 4 = 5 then 5 - 1 =
3. If 2 x 5 = 10, then 10 ÷ 2 =
4. If 2 x 6 = 12 then 12 ÷ 2 =
5. If 2 x 10 = 20 then 10 x 2 =

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Remember: + is the opposite of -

and ÷ is the opposite of x

These operations ‘undo’ each other.

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Algebra Word Problems

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Most of the word problems we do in maths use thinking with Algebra.

For example:

Sam has an 🍎 for lunch every day. How many apples does he eat in 1 week of school?

We know a school week has 5 days, if he has one 🍎 every day, that is 5 🍎s. So...

Your turn: 1. How many in 2 weeks? apples

2. How many in 3 weeks? apples

Can you see a pattern starting?

3. Ms Lange takes 3 hours to make 1 workbook.

How long does it take her to make 2 workbooks?

4. How long does it take her to make 3 workbooks?

5. How long does it take her to make 4 workbooks?

Can you see a pattern starting? Can you describe the pattern or what is happening in words?

I think…. .

Algebra

How are you getting on?

Highlight the face that shows how you feel about algebra so far.

Hopefully you now get:

• each side of the = sign have to balance (they have to be equal!)
• We use what we do know to find out what we don’t know.

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Next up:

Rules:as in ‘What rule is making this pattern?’ OR ‘What rule is making this sequence?’

In the next few slides you are given the rule, but have to work out what number will pop out of the machine when you use that rule.

Function Machine

(Rule Machine)

• 10

24

So if 14 goes into the + 10 machine and 24 comes out

Your turn!

Work out the answers that would come out of the ‘+10 Machine’ and write them in the green boxes.

Function Machines

(Rule Machine)

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6

So 4 goes into the + 2 machine and 6 comes out

Your turn!

Work out the answers that would come out of the ‘+2 Machine’ and write them in the green boxes.

• 2

These get called Function Machines but they are really

Rule Machines, we take the number and change it by using the rule.

Function Machine

(Rule Machine)

- 1

22

So if 23 goes into the - 1 machine and 22 comes out

Your turn!

Work out the answers that would come out of the

‘- 1 Machine’ and write them in the green boxes.