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K: 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 26 27 28 29
30 31 32 33 34 35 36 37 38 39
Generate and describe sequences
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An example of one of the number grids.
Use the resource

K33: Number grids

Find the missing numbers in number grids. Click on the grid to hide or show the numbers.
Hide or show all the numbersClick on this button to hide or show all the numbers in the grid

Option 1: part of a standard 1 to 100 number grid
Option 2:
the sequences go up or down in regular amounts from 1 to 10.

 

K37: Pascal's Christmas tree: Pascal's triangle on a Christmas tree. Use the sliders to change the number in the star and the multiples coloured. Use this button Play movie buttonto show different 'star' numbers and different multiples.

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Algebraic expressions, nth term and functions
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An example of one of the four algebra screens.

K34: Four algebra resources in one

Use the four buttons to select one of the four resources:
1. Algebraic expressions 2. Rules for input and
output numbers
3. Rules for sequences 4. Function machines

Solutions can be shown or hidden by clicking in the tables or alongside the questions.

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Find the nth term of a sequence

An example of a sequence

 

 

Link to Shirt Sequences
Link to football shirts sequences

An example of the colour sequences
The buttons used to select the colour


Link to Shape Sequences questions

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K1: Find a simple rule for the nth term of simple sequences.
K32: Fill in the missing terms of a sequence. Equal amounts are added or subtracted in each sequence.

K2: Use linear expressions to describe the nth term of arithmetic sequences.

K3: Find the nth term of any arithmetic sequence.

Football Shirts sequences

K4: 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.

K5: 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).

 

'Who wants to be a Millionaire?' two-team sequences games

K6: Shirt Sequences
What colour is the shirt with 33 on the back? Choose from five colours. Money is won 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.
K7: Play the Scottish teams version

K8: Play Shape Sequences same instructions as 'Shirt Sequences'.

K9: Shape sequences questions: what shape is the 33rd in a sequence of shapes? Click on the question mark to reveal the answer.

Link to number sequences
An example of one of the number sequences

Link to  Square Numbers

Number sequences made from counters
The buttons which determine the patterns
K10: Four different number sequences

The rule for each number sequence can be explained by look at how the counters are arranged. Click in the table to reveal hidden terms of the sequences.

K11: Square numbers

K12: Triangular numbers

Link to pattern 1
pattern 1
Link to pattern 2
pattern 2

Three bar fence

Number sequences: formulas

Use the slider to change the number of squaresA repeating pattern is made from squares and circles. How many squares will there be with 17 circles? How many circles with 20 squares?

Use the slider to determine the number of squares.

K13: Pattern 1
K14: Pattern 2

A fence is made from posts and bars. How many bars will there be with 20 posts?

K15: Fence 1 (two bars between each pair of posts).
K16: Fence 2 (three bars between each pair of posts).

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Use letter symbols
Example of writing algebraic expressions.

Write algebraic expressions

I think of a number n. Click on the 'Think of a number button': enter the number, press OK button
Click on the blue function buttons to perform operations on n. Click on the yellow and pink buttons to reveal the numbers and algebraic expressions.
K17: Algebraic expressions

K18: Algebraic expressions 2
Same idea as above but the functions are random. Hide or show the description of the function, the numbers or the expressions. Click on the 'change' button.

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Word problems involving functions
link to function machine

I think of a number, add 3.7, then multiply by 5. The answer is 22.5. What is the number?
K19: Using whole numbers
K20: 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
K21: Function machine

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Investigating sequences

Link to Fibonacci investigation
Example of investigation 1
Example of investigation 1

Example of investigation 2
Example of investigation 2

Fibonacci's sequence investigation.

K22: 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.

 

Number grid investigations

Work out what number will be at a particular place in a grid. For example which number is in column 20, row 8? Click on the cells to reveal the numbers.

K23: Investigation 1 : The numbers start from the bottom of each column. See example on left.
K24: Investigation 2 : The numbers zig-zag.

 

Number sequences

K25: Ten numbers are in a sequence, two of them are revealed. What are the missing numbers?
The same amount is added each time.

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Graphs of linear functions: y = mx + c graphs
Screenshot of a graph
This example shows the red graph has been labelled. Drag the label about. The coordinates are shown.
K26: y = mx + c graph generator
The buttons

If you are using Internet Explorer or Firefox press F11 to view the resource full-screen.

Select the type of graph to be generated:
Top left: lines with the same gradient.
Top right: lines which cut through the y-axis at the same point.
Second row: plot graphs with positive gradients.
Third row: plot graphs with negative gradients.

Fourth row: plot graphs of x = c and y = c.
Green buttons

Hide the blue or red graph.
Reveal or hide the coordinates
Reveal or hide the lines which touch the axes.

  Screenshot of a table
Click in the blue box above the table to reveal the equation of the line. This can then be dragged about.
Click on the x and y to reveal or hide the x and y values. Click in a cell of the table to reveal or hide individual values.

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An example of the quick y=mx+c graph generator

K31: More y = mx + c graphs

Drag the hands around to change the graphs. The equation labels can also be dragged.

Use these buttons to turn features on or off, from the left:
the hands, the coordinates, the equations, select one or two graphs.

Quick y=mx+c graph generators Just click on the change button. Click in the blue box to reveal the equation.

K35: Gradient shown
K36: Two points on the line shown

Use the activityK38: Which two points are on the line?

Ten points are shown, which two points lie on the line?
Click on the rectangle underneath the 'change' button to show the two points and the line.

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Inequalities and graphs

Use these buttons K30: y > mx + c or y < mx + c
Use the buttons to hide or show the regions.
Use the sliders to generate the graphs.

Click on the 1 button to hide one of the graphs. Click on the 2 button to show both graphs.

Link to the activity
Drag the points about

K27: The gradient of a straight line

Drag the two points about. The red triangle, coordinates and changes in x and y can be shown or hidden by clciking on the buttons.

Click in the other panel to show or hide the gradient.

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Graphs of linear functions arising from real-life situations

graph
An example of a distance-time graph.

timetable
A section of a timetable.

Link to the activity
Conversion graph

Link to distance-time graphK28: Distance-time graph and train timetable
If you are using Internet Explorer press F11 to view the resource full-screen.

A seaside train travels along the promenade from the tower to the lighthouse.
The train's timetable can be displayed and a distance-time graph is drawn as the train moves.
The timetable shows the 24 hour arrival and departure times of the train.
The graph shows the time and distance, in miles, from the tower. Click on the 'go' button to start the journey.

the buttonsThe buttons:
Click on the 'go' button to start the journey.
Top left: show or hide the timetable.
Top middle: Show or hide the times in the timetable: click in the timetable to show or hide individual times.
Top right: show or hide the graph.
Bottom left: replay the journey showing the graph generated.
Bottom middle: replay the journey showing the graph already generated.
Bottom right: zoom in or out of the graph ( the graph can be dragged left or right).

There are accompanying worksheets if you have subscribed to Active Worksheets.

K29: Conversion graphs (best viewed in full-screen mode, press F11)
This conversion graph resource will generate the following graphs:

The units which can be converted km-miles
metres-feet and inches
kg-pounds and ounces
kg-stones and pounds
The currency buttons

Currency
£ - € euros
£ - $ US
£ - Japanese Yen
£ - South Korean Won
Use the slider to change the rate of exchange.

Click on the lineClick on the line to show the values at that point.

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Quadratic graphs
use the resource

K39: y = x2 - x + 5
Generate quadratic graphs. Use the up and down buttons to change the equation.
Hide and show buttons
Hide and show the graph (left) and the table of values.


Click on the y  in the table of values.Click on the y at the top of the table to hide or show all the y values.
Click in individual cells in the table to hide or show each y value.

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