New
New
Year 8

Securing understanding of sequences

I can begin to generalise a sequence.

New
New
Year 8

Securing understanding of sequences

I can begin to generalise a sequence.

Lesson details

Key learning points

1. Sequences can be continued using a rule.
2. This rule can be demonstrated with a diagram.
3. This rule can be described in words.

Common misconception

That sequences can only have constant additive or multiplicative patterns.

Give students two numbers and get them to carry the sequence on in different ways. Anything they come up with can be a sequence.

Keywords

• Sequence - A sequence is a succession of objects, diagrams or values usually formed according to a rule.

Students can build their own patterns with manipulatives. Challenge them to build patterns with the same rule or with different rules and same start value.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Starter quiz

6 Questions

Q1.
What do we call the expression in a fraction, written below the fraction line?
base
numerator
variable
Q2.
What is the next number in this sequence with a constant additive pattern? 5, 9, 13, , ...
Q3.
What is the missing number in this sequence with a constant multiplicative pattern? 2, 6, , 54, ...
Q4.
Match the calculation to the value it will find for the sequence ..., ?, 2,10, ...
Correct Answer:$$10\div 2$$,The multiplier for a constant multiplicative rule

The multiplier for a constant multiplicative rule

Correct Answer:$$10\times 5$$,The next value in a constant multiplicative sequence

The next value in a constant multiplicative sequence

Correct Answer:$$10 - 2$$,The value being added in a constant additive sequence

Correct Answer:$$10 + 8$$,The next value in a constant additive sequence

The next value in a constant additive sequence

Correct Answer:$$2\div 5$$,The previous value in a constant multiplicative sequence

The previous value in a constant multiplicative sequence

Correct Answer:$$2 - 8$$,The previous value in a constant additive sequence

The previous value in a constant additive sequence

Q5.
Match these directed number calculations to their answers.
Correct Answer:$$(-12) + (-6)$$,-18

-18

Correct Answer:$$(-12)\div (-6)$$,2

2

Correct Answer:$$(-12)-(-6)$$,-6

-6

Correct Answer:$$(-12)\times (-6)$$,72

72

Correct Answer:$$12\times (-6)$$,-72

-72

Correct Answer:$$12\div (-6)$$,-2

-2

Q6.
Match the answers to their corresponding fraction calculation.
Correct Answer:$$1\over 2$$,$${4\over 5}-{3\over 10}$$

$${4\over 5}-{3\over 10}$$

Correct Answer:$$11\over 10$$,$${4\over 5}+{3\over 10}$$

$${4\over 5}+{3\over 10}$$

Correct Answer:$$8\over 3$$,$${4\over 5}\div{3\over 10}$$

$${4\over 5}\div{3\over 10}$$

Correct Answer:$$6\over 25$$,$${4\over 5}\times{3\over 10}$$

$${4\over 5}\times{3\over 10}$$

Correct Answer:$$25\over 6$$,$$5\times{5\over 6}$$

$$5\times{5\over 6}$$

Correct Answer:$$6$$,$$5\div{5\over 6}$$

$$5\div{5\over 6}$$

Exit quiz

6 Questions

Q1.
Which of these best describes what a sequence is?
Numbers in the multiplication table for a specific number
Values which increase by the same amount each time
Events placed in chronological order
Correct answer: Values or patterns usually ordered according to a rule
Q2.
Which of these shows a sequence with a constant additive rule?
Correct Answer: An image in a quiz
Correct Answer: An image in a quiz
Q3.
Which representation is the same sequence as this?
Correct Answer: An image in a quiz
Q4.
What would the next number in this sequence be if it had a constant additive rule? 2, -4, ,...
Q5.
What would the next number in the sequence be if it had a constant multiplicative rule? 2, -4, , ...
Q6.
Match the next 2 numbers in the sequence which starts 5, 15, ... with the rule the sequence is following.

Correct Answer:..., 45, 135, ...,multiply by 3

multiply by 3