Myths about teaching can hold you back
- Year 11•
- Higher
Making conjectures about patterns and relationships
I can make and test conjectures about the generalisations that underline patterns and relationships.
- Year 11•
- Higher
Making conjectures about patterns and relationships
I can make and test conjectures about the generalisations that underline patterns and relationships.
Lesson details
Key learning points
- A conjecture can be made about underlying patterns.
- 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.
To help you plan your year 11 maths lesson on: Making conjectures about patterns and relationships, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 11 maths lesson on: Making conjectures about patterns and relationships, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
We use learning cycles to break down learning into key concepts or ideas linked to the learning outcome. Each learning cycle features explanations with checks for understanding and practice tasks with feedback. All of this is found in our slide decks, ready for you to download and edit. The practice tasks are also available as printable worksheets and some lessons have additional materials with extra material you might need for teaching the lesson.
The assessment exit quiz will test your pupils' understanding of the key learning points.
Our video is a tool for planning, showing how other teachers might teach the lesson, offering helpful tips, modelled explanations and inspiration for your own delivery in the classroom. Plus, you can set it as homework or revision for pupils and keep their learning on track by sharing an online pupil version of this lesson.
Explore more key stage 4 maths lessons from the Functions and proof unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
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Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.Which of these numbers are prime?
Q2.Which of these are square numbers?
Q3.Which of these are triangular numbers?
Q4.The number 100 has exactly factors.
Q5.Which of these expressions must represent a number 'one more than a multiple of 5' when $$n$$ is an integer?
Q6.What is the value of $$3^n$$ when $$n=4$$?
Assessment exit quiz
6 Questions
Q1.What sort of numbers always have an odd number of factors?
Q2.Give an example of a number less than 100 which is both square and triangular.
Q3.A conjecture is a (mathematical) statement which __________.
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?
Q5.Which of these shows the first 4 numbers of the form $$7^n$$ where $$n$$ is a positive integer?
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?