Home>Whiteboard Worksheets>Sequences, functions and graphs
 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 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 An example of one of the number grids. Find the missing numbers in number grids. Click on the grid to hide or show the numbers. Click 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 to show different 'star' numbers and different multiples.

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

 Find the nth term of a sequence 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. An example of one of the number sequences Number sequences made from counters 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 pattern 1 pattern 2 Number sequences: formulas A 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).

 Use letter symbols Write algebraic expressions I think of a number n. Click on the 'Think of a number button': enter the number, press 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.

 Word problems involving functions 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

 Investigating sequences Example of investigation 1 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.

Graphs of linear functions: y = mx + c graphs

This example shows the red graph has been labelled. Drag the label about. The coordinates are shown.
K26: y = mx + c graph generator
 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. 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.

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.

K36: Two points on the line shown

K38: 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.

Inequalities and graphs

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.

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.

Graphs of linear functions arising from real-life situations

An example of a distance-time graph.

A section of a timetable.

Conversion graph

K28: 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 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:

 km-miles metres-feet and inches kg-pounds and ounces kg-stones and pounds Currency £ - € euros £ - \$ US £ - Japanese Yen £ - South Korean Won Use the slider to change the rate of exchange.

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

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