Home>Whiteboard Worksheets>Applying mathematics and solving problems
 Choose the topic: Please select ..... A: Applying mathematics and solving problems B: Place value, ordering and rounding C: Integers, powers and roots D: Fractions, decimals, percentages, ratio and proportion E: Number operations and the relationships between them F: Mental methods and rapid recall of number facts G: Calculations: written methods H: Calculations: calculator methods I: Calculations: checking results J: Equations, formulae and identities K: Sequences, functions and graphs L: Geometrical reasoning: lines, angles and shapes M: Transformations N: Coordinates O: Construction & loci P: Measures and mensuration Q: Statistics R: Probability A: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
 Problems involving numbers An example of a wall puzzle A1: Wall puzzles The number on a brick is either the sum, difference or product of the two numbers below. Drag the numbers on to the wall. When the numbers are in the right place the polygon characters will spin round. There are 6 levels of difficulty: level 1, five numbers have to be placed on the wall, level 6, all ten numbers have to be dragged to the wall. Use these buttons to decide how the numbers are worked out. The choices are: the sum, the difference or a mixture (product, sum, difference). Select the level with the slider. Click on 'go'. Click on the 'change' button to quickly generate a new wall puzzle. Word problems involving consecutive integers, prime and square numbers. Missing digit problems. A2: Word and missing digit problems Fibonacci's sequence investigation. A3: Interactive resource : change the first two numbers in the sequence, can you predict the 5th number? .. the 6th number. Reveal the 6th number and watch how it changes as the first number changes. What does it go up in? Change the second number, what happens to the 6th number? Click in the cells to hide or show the numbers. Fibonacci's sequence puzzles: the empty cells are filled by adding the two preceding numbers. A4: Number cell puzzles 1 (positive numbers only) A5: Number cell puzzles 2 (positive and negative numbers) A25: How many of each polygon? For example: A party of squares and pentagons has 37 sides altogether. How many squares and pentagons are at the party? There are two solutions. First the maximum number of polygons to be used and the maximum number of sides they can have. Click on the 'ok' button.

Problems involving algebra

An example of a two-function 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 two-team 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 one-player 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).

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