Functional Question Foundation and Higher

(Algebra 2) For the week beginning ….

Sequences Starter (Foundation/ Higher) Here are 12 cards numbered from 1 to 12.

1 2 3 6 1 0 5 7 4 1 2 9 11 8

Make as many sequences of numbers as you can.

·

You must use each card once only in a sequence · A sequence must have at least four terms

Possible questions ·

What is a sequence?

· What is a term?

· What is a rule?

· How can a sequence be described?

· Why do the numbers generated in a National Lottery draw not form a sequence?

· Why does the formula for the

n

th term give more information than the term-to-term rule?

· Give me an example of when knowing a sequence might be useful.

· Tell me …… sequences you know and their rules. (Term-to-term or

n

th, depending on level.)

Activity 1 (Foundation or “easy” Higher)

Mirrors

Sasha uses tiles to make borders for square mirrors.

The pictures show three different sized mirrors, each with a one centimetre border of tiles around.

She only uses 1 by 1 tiles.

1

Investigate the total number of 1 by 1 tiles that are needed to make borders for different sized square mirrors.

Draw some different sized mirrors and try to predict how many tiles will be needed for each mirror.

A “table of results” could be useful.

Try to be systematic.

Find a formula for

T

, the total number of tiles.

2 Why does your formula work for these mirrors?

3 Investigate square mirrors surrounded by wider borders and try to predict the number of tiles needed for each width of border.

4 Link all your formulas together.

5 Why does your formula work for all square mirrors?

Activity 1 (Higher)

Sasha uses tiles to make borders for square mirrors.

The pictures shows three different sized mirrors, each with a two centimetre border of tiles around.

1 She only uses 1 by 1 tiles.

Investigate the total number of 1 by 1 tiles that are needed to make borders for different sized square mirrors.

Draw some different sized mirrors and try to predict how many tiles will be needed for each mirror.

A “table of results” could be useful.

Try to be systematic.

Find a formula for

T

, the total number of tiles.

2 Why does your formula work for these mirrors?

3 Investigate square mirrors surrounded by wider borders and try to predict the number of tiles needed for each width of border.

4 Link all your formulas together.

5 Why does your formula work for all square mirrors?

AO3 question (Foundation/Higher) (a)

Here are the first four terms of a sequence and its

n

th term.

90 85 80 75 …… 5(19 –

n

) Show how Jayne can find the position in the sequence of the term that has a value of 0.

(b)

Jayne creates these patterns by shading squares.

[

2]

Show how Jayne can work out the number of squares in a pattern in

any

position in the sequence.

[

3]