Problems
involving algebra 
An example of a twofunction problem.

A6:
Target Numbers
The aim of this activity is to change the functions to match the target
number. Use the 'calculator' to input different numbers into the function
machines. The functions can be swapped over by dragging them from
side to side.
Two or three functions
can be selected using the purple buttons above. A new target number
is generated.
The inverse functions can be shown or hidden using the yellow button.
The inverses cannot be dragged.

Example of Shape Puzzle 1

Shape
Puzzles
Work
out the value of each shape. The total for each row and column is shown.
Use the sliders to input your answers. Click on the 'check' button to
see how many are correct.
The shapes will be watching you!
A7:
Shape Puzzle 1
Three of the same shape can appear in a row (see the example on the
left, three hexagons are in the top row).
A8:
Shape Puzzle 2
Three of the same shape will not appear in a row.
A9:
Shape Puzzle 3
The solutions can be negative numbers.

Example of dotty pattern (level 1)

Number
sequences

A10:
Dotty Patterns 1
Use Dotty Patterns to investigate number sequences and nth
terms.
A small piece of the pattern is shown (see example), the aim is
to decide what colour the dot is at selected coordinates. Use
the sliders (see left) to determine the coordinates.
Click on the colour of your choice then the 'final answer' button.
A much larger chunk of the pattern is revealed showing the dot
in question.
There
are 9 levels of difficulty. Experts can start at a higher level.
A11:
Dotty Patterns 2
Same activity as Dotty patterns 1, but the coordinates are
generated at random and therefore cannot be selected.


What do
the mystery buttons do?

Functions
A24:
Mystery
calculator : what functions do the 9 mystery buttons
carry out?
The
buttons showing polygon people carry out different functions. Click
on a button to see what it does. The results are saved in the table.
There are six 'levels':
1. Fixed add and subtract (the same operations everytime)
2. Random add and subtract
3. Fixed multiply and divide
4. Fixed multiply and add or subtract eg x 2 + 1
5. Random multiply and add or subtract
6. A variety of operations, eg rounding


Functions
I think of a number, add 3.7, then multiply by 5. The answer is 22.5.
What is the number?
A12:
Using whole numbers
A13: Using numbers to one decimal place
A function
machine changes the number n to the number 3n + 1.
What does it do to these numbers? 2, 5, 9, 21, 0
What numbers must be input to get these numbers? 10, 37, 100
A14:
Function machine


Pyramid
equations
In each pyramid each number is the sum of the two numbers immediately
below. Find the value of n
A15:
Pyramid 1 positive
whole number solutions
A16:
Pyramid 2 positive and negative
whole number solutions
A17:
Pyramid 3
positive whole number solutions.
A18:
Pyramid 4
positive and negative whole number solutions
A19:
Pyramid 5 positive
whole number solutions
A20:
Pyramid 6 positive and negative
whole number solution


Football
Shirts sequences
A21:
Shirt sequences generator: interactive
resource
Randomly
generates sequences of different coloured football shirts. What number
is on the back of the 50th shirt..100th shirt?
Press the play button to move up the sequence, press the back button
to move down. Tip: keep your eye on one of the shirts. Press the buttons
quickly or keep your finger on the 'right' or 'left' arrow keys to
speed up the sequence. 99 is the lowest number on a shirt and 999
is the highest.
A22:
Shirt Sequences Millionaire twoteam
game: a whiteboard sequences game
What
colour is the shirt with 33 on the back? Choose from five colours.
Money is won in the same way as the TV programme "Who Wants to
be a Millionaire?".
Choose to have either one or two shirt sequences on the screen (click
the '1' and '2' buttons). The game could be played by two teams with
one person from each team being close to the whiteboard to select
the colour of shirt. Each shirt sequence panel can be dragged to the
left or right to make it easier for pupils to access the buttons from
either side of the whiteboard.
A23:
Shirt Sequences oneplayer game: interactive
resource
What
colour is the shirt with 100 on the back? Choose from four colours.
Answer 10 questions (the questions are the same each time).
