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Year 11
Higher

Making conjectures about patterns and relationships

I can make and test conjectures about the generalisations that underline patterns and relationships.

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Year 11
Higher

Making conjectures about patterns and relationships

I can make and test conjectures about the generalisations that underline patterns and relationships.

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Share activities with pupils
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Lesson details

Key learning points

  1. A conjecture can be made about underlying patterns.
  2. The conjecture can be tested to see if it holds.

Keywords

  • Prime number - A prime number is an integer greater than one with exactly 2 factors.

  • Triangular number - A triangular number is a number that can be represented by a pattern of dots arranged into an equilateral triangle. The term number is the number of dots in a side of the triangle.

  • Conjecture - A conjecture is a (mathematical) statement that is thought to be true but has not been proved yet.

Common misconception

Conjectures have to be correct so it's really hard to make a conjecture as you don't want to be wrong.

Conjectures are thought to be true but they may not be. This is why we test and see ways to prove whether a conjecture is true or not. It is perfectly acceptable for a conjecture to be proved wrong.

In Task B, pupils are asked to write their own conjectures. This is a great opportunity for pupils to peer mark and discuss results.
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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).

Lesson video

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Starter quiz

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6 Questions

Q1.
Which of these numbers are prime?
1
Correct answer: 2
Correct answer: 3
27
Correct answer: 41
Q2.
Which of these are square numbers?
Correct answer: 1
10
22
68
Correct answer: 100
Q3.
Which of these are triangular numbers?
5
9
Correct answer: 10
Correct answer: 15
20
Q4.
The number 100 has exactly factors.
Correct Answer: 9, nine
Q5.
Which of these expressions must represent a number 'one more than a multiple of 5' when $$n$$ is an integer?
$$n+1$$
$$2n+3$$
Correct answer: $$5n+1$$
Correct answer: $$5n-4$$
$$10n+2$$
Q6.
What is the value of $$3^n$$ when $$n=4$$?
Correct Answer: 81, eighty-one

Exit quiz

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6 Questions

Q1.
What sort of numbers always have an odd number of factors?
even numbers
odd numbers
prime numbers
Correct answer: square numbers
triangular numbers
Q2.
Give an example of a number less than 100 which is both square and triangular.
Correct Answer: 36, 1
Q3.
A conjecture is a (mathematical) statement which __________.
is always true.
cannot be proven.
is impossible.
Correct answer: is not yet proven true.
Q4.
Lucas writes the conjecture "All numbers of the form $$2^{n}-1$$ (where $$n$$ is an integer greater than 1) are prime". Which of the following are true?
This does not hold when $$n=2$$
This does not hold when $$n=3$$
Correct answer: This does not hold when $$n=4$$
This does not hold when $$n=7$$
Correct answer: This does not hold when $$n=9$$
Q5.
Which of these shows the first 4 numbers of the form $$7^n$$ where $$n$$ is a positive integer?
7, 14, 21, 28
1, 7, 49, 343
1, 128, 2187, 16384
Correct answer: 7, 49, 343, 2401
7, 77, 777, 7777
Q6.
Jacob has written out the first 4 numbers of the form $$7^n$$ where $$n$$ is a positive integer. Which of these conjectures hold true for these 4 values?
Numbers of this form always end in either 1, 3, or 9
Correct answer: Numbers of this form cannot be multiples of 10
Numbers of the form $$7^{2n}$$ where $$n$$ is a positive integer end in 9
Correct answer: Numbers of the form $$7^{4n}$$ where $$n$$ is a positive integer end in 1