Download Algebra 2

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
1
3
2
6
0
1
7
5
4
2
11
9 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 nth 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 nth, 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.
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?
AO3 question (Foundation/Higher)
(a) Here are the first four terms of a sequence and its nth 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.
[2]
(b) Jayne creates these patterns by shading squares.
Show how Jayne can work out the number of squares in a pattern in any position in the sequence.
[3]