Tag Archives: Nth term

321. Patterns and sequences

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Now what have a pair of roller skates got to do with number sequences? If you can guess before the reason, I’ll be surprised – it’ll mean there is more than one person as random as me!

Image Credit: No Fear adjustable quad skates/Amazon.co.uk

As you may have guessed from my earlier post 317. Pyramid Power I’m currently doing an Algebra unit on Number Sequences. I’ve changed the way I’ve taught this topic this year to incorporate a ‘Big Picture’ view as opposed to one lesson on drawing the next picture, the next on finding the Term to Term rule and finishing with a lesson on finding the Nth term. The beauty of mathematics lies in the connections we make, not the disparate skills.

After the investigative approach of the Pyramid Numbers lesson, we did some text book work on generating number sequences (eg Start with 5, add 3) expanding to look at the physical patterns each time, so the previous rule would have looked like N groups of 3 dots plus 2 dots. As with any class (mixed ability or not) there were varying levels of progression in these lessons. To pull everyone forward I wrote structured worksheets and allowed the students to choose which they did. I described them using the following comparisons with the roller disco at our local Sports Centre:

  • Sheet 1 – beginner on roller skates, need a bit of hand holding (I’ll own up to demonstrating our local instructor’s technique for teaching beginners in front of the class)
  • Sheet 2 – okay on skates, just a word of encouragement every now and then
  • Sheet 3 – speedskating, no fear of the next challenge
  • Extension – all the skills! Some tasty questions from a tough textbook exercise

After a student completes a sheet they just move to the next – there are no duplicate questions. I printed them A5 to stick neatly in their books but you might prefer A4. Solutions are provided.

Patterns and sequences A4 one per page

Patterns and sequences A4 two per page

Patterns and sequences solutions (docx)

Patterns and sequences solutions (pdf)

BTW I can tell you from personal experience that landing on your rear whilst speed skating really does hurt!

212. Crack the Code 1

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I love the worksheets produced by danwalker on TES resources. Basically a set of results are combined to make a numerical code. You could have a ‘Kilner’ stye jar with a changeable combination padlock and a prize locked inside as motivation.

Image credit: www.waragainstwork.com

Image credit: www.waragainstwork.com

I’ve started using this style of activity with sleepy sixth formers, unmotivated low ability Year 10 and excitable Year 9s. Dan Walker has released the following activites on TES resources:

Parametric Equations

Binomial Expansion

Percentages

I’ve now created a Code sheet for Number Patterns. It covers term to term rules, using an Nth term rule, finding an Nth term and finding a specified term.

Number Patterns Crack the Safe (pdf)

153. Sequences Starter 2

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So, you’ve got term to term sequences sussed. Time to tackle Nth term!

This idea just sort of appeared in my sequences lesson.

Equipment
Giant playing cards (or numbers on two different colours of A5 card)
Numbered headbands (I made crowns out of corrugated border card)

Set Up
1.Lay out one coloured set of cards on a table or the floor – these are the ones we needed in class. We started with all the cards in the suit.

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2. Issue headbands to four pupils.

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3. Pupils stand in number order.
4. Give each pupil a different. coloured card from a sequence to hold facing them.

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Task
1. Explain that each person represents a term in a sequence, given by the headband.
2. Pupil 1 turns around their card – Red 3.
Question: What is the next number?
Answer: Don’t know
3. Pupil 2 turns around their card – Red 5.
Question: What is the next number?
Answer: Might predict 7
4. Pupil 3 turns around their card – Red 7.
Question: What is the next number? Why?
Answer: 9, add 2.
5. Reveal the last number – Red 9.
6. What is the pattern? Add 2 Which multiplication table has the same pattern? Twos
7. Give each pupil in the sequence the appropriate number from the two times table.
Question: How do you turn the two times table into the sequence?
Answer: Add 1
8. How do you get from the headband to the sequence?
Headband x 2 + 1 = sequence

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9. What about a headband with 10 on it? Or 100? Or a mystery number?
10. Try this with other sequences and develop the idea of Nth term.

Outcome
I used this as a plenary for a term to term sequences lesson with a shared class. In the following lesson my colleague, D, used this idea to develop the concept of Nth term with another class. He wanted to make something for the pupils to have in their book to remember this. This is what he came up with: Handout for sequences intro (pptx) or How to for sequences(docx). I’m currently trying out hosting my own resources, rather than using TES resources – so we’ll see how effective this is.