Extending thinking about sequences
Lesson details
Learning outcome
I can appreciate that abstract sequences can have negative values.
Key learning points
- When you move away from physical representations of sequences, you can think abstractly.
- You can consider what happens if there was not a first term.
- The sequence could extend forward and backwards.
- You can generate previous terms using the inverse of the term-to-term rule.
Keywords
Arithmetic sequence - An arithmetic (or linear) sequence is a sequence where the difference between terms is a constant.
Geometric sequence - A geometric sequence is a sequence with a constant multiplicative relationship between successive terms.
Common misconception
All sequences can go on infinitely.
When we think abstractly and start a sequence such as 8, 10, 12, 14, 16, ... it is possible that it goes on infinitely. However, if we applied this sequence to a context such as pairs of pupils getting on a bus, then a physical limit will apply.
Teacher tip
Ask pupils to come up with their own examples of concrete sequences that we find in the real world and explain their physical limitations. Then ask them to think abstractly, and describe what would happen to the sequence if no physical limit existed.
Licence
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.An arithmetic (or linear) sequence is a sequence where the difference between successive terms is a __________.
Q2.Find the next term in the arithmetic sequence -25, -18, -11, -4, .
Q3.Find the missing term in the arithmetic sequence 27, , 55, 69, 83, ...
Q4.Find the common ratio of the geometric sequence 0.4, 1.6, 6.4, 25.6, ...
Q5.Find the next term in the geometric sequence 0.4, 1.6, 6.4, 25.6, , ... Give your answer as a decimal.
Q6.Which statements are true of the sequence 1920, 960, 480, 240, 120, ... ?
Assessment exit quiz
6 Questions
Q1.In mathematics, sequences can be described as concrete or __________.
Q2.In 1980, the world marathon record was 2 hrs 10 mins. In the year 2000, it was 2 hrs 5 mins. In the year 2020, it was 2 hrs 0 mins. This is an example of __________ sequence.
Q3.In 1980, the world marathon record was 2 hrs 10 mins. In the year 2000, it was 2 hrs 5 mins. In the year 2020, it was 2 hrs 0 mins. Why is this concrete sequence limited?
Q4.What value would come before this geometric sequence? 196, 1372, 9604, 67 228, ...
Q5.Scientists begin to study the population of a particular fish in the North Sea and find it forms a geometric sequence. Using the sequence to predict the population for year 5.
Q6.Scientists begin to study the population of a particular fish in the North Sea and find it forms a geometric sequence. Estimate the population of the fish the year before the study began.
To help you plan your 9 maths lesson on: Extending thinking about sequences, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your 9 maths lesson on: Extending thinking about sequences, 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 3 maths lessons from the Graphical representations unit, dive into the full secondary maths curriculum, or learn more about lesson planning.