Home>Whiteboard Worksheets>Equations, formulae and identities
 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 J: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 19 20 21 22 23 24 25 28 29 30 31 32 33 34 35 36
 Simplify expressions

Click under the expression
to reveal the answer

J28: Simplify algebraic expressions
Use the 1, 2, 3 and 4 buttons to generate the expressions. Four levels of difficulty, for example:
level 1: 2a + 3a
level 2: 2ab - 4ab level 3: 2a - 3b + 5a -6b, level 4: 2x³ - 4y + 2x³ - 7y.
Use these buttons to generate either one expression or ten expressions.

 Use these buttons to generate the expressions: 1: eg 2 x a x b 2: eg 2p x 3q 3: eg 3ab2 + 2ab 4: a mixture
 Use these buttons to generate the expressions: 1: eg 2(3b + 4c) 2: eg 2(3b + 4c) + 3(2b - 3c) 3: eg 2b(3b + 4c)

J33: Factorise
Option 1: 6b + 8c Option 2: 6b2 + 8bc (Options 1 and 3, see above)

J34: Rearrange formulas : change the subject of a formula
Five levels of difficulty (buttons 1 to 5). Button 6 generates a variety.

 Construct and solve linear equations

Balancing problems

J29: What is the weight of a gold bar?
Use the 1 ,2 and 3 buttons to generate the expressions. Three levels of difficulty, for example:
level 1: small whole number solutions

level 2: multiple of ten solutions

level 3:
gold bars on both sides
Use these buttons to generate either one problem or four problems.
J30:
What is the weight of a gold bar? : solver
Options as above. This resource solves balance problems step by step. Click on the forward and back buttons to go through the steps. Click underneath the scales to reveal the equation.

J36: What is the weight of a square and a hexagon?
Four scales are shown.

Work out the weight of a square and a hexagon. They weigh the same amount on each of the four scales.

Simultaneous equations with a difference

J1: Fishy Equations

Work out the weight of each fish. A fishy introduction to simultaneous equations!

J20: Shape people and simultaneous equations

Two or three rows of polygon people are shown (click the '2 rows' or '3 rows' buttons). Two numbers are hidden behind the shape people: one behind the triangle and one behind the circle. What are the hidden numbers? Click on the shape people to show or hide the numbers.

J21: Simultaneous equations generator

Click on the four option buttons to generate new simultaneous equations:
1.
Positive answers and coefficients of x and y
2.
Positive and negative answers and positive coefficients of x and y
3. Positive answers and positive and negative coefficients of x and y
4.
Positive and negative answers and coefficients of x and y

Arithmagons
In an arithmagon, the number in a square is the sum of the numbers in the two circles on either side of it. What could the letters be? Find relationships between the letters. There are many possible solutions for the arithmagons. The answer sheet will give one set of solutions.

J2: Sum puzzle

Solve simple equations

J3: Work out what number each shape represents (positive numbers)
J4: Work out what number each shape represents (positive and negative numbers)

J5: Work out the value of each letter (positive numbers)

Pyramid equations
In each pyramid each number is the sum of the two numbers immediately below. Find the value of n

J6: Pyramid 1 positive whole number solutions

J7: Pyramid 2 positive and negative whole number solutions

J8: Pyramid 3
positive whole number solutions.

J9: Pyramid 4
positive and negative whole number solutions

J10: Pyramid 5 positive whole number solutions

J11: Pyramid 6 positive and negative whole number solution

Square equations
Work out the value of a and b so that each row and column adds up to the required total.

J12: Square equations 1: positive whole number solutions.

J13: Square equations 2: positive and negative whole number solutions.

type 1

type 2

type 3(+), type 4( + and -)

type 5(+), type 6( + and -)

type 7

type 8

Linear equations

J14: Solve equations
Eight levels of difficulty
. Click on the 1 to 8 buttons to generate the equations.

J15: Solve inequations and equations
Seven levels of difficulty
. Click on the 1 to 7 buttons to generate the equations.

Use formulae

The train journey.
125 metres travelled in 5 seconds.

Substitute numbers into expressions.

J16: Substitute cards
Substitute positive numbers into expressions.
The questions appear on cards (see example on the left).

J18: Substitute positive numbers

J19: Substitute positive and negative numbers

J25: Use distance, time and speed formulae
 Explain the relationships between time, distance and speed. A train moves along a track: change the distance it travels, the time it takes or the speed it travels at. The formula can be revealed when the train stops moving. Select the two variables using these buttons. Use the sliders to change the distance, time or speed. From left: hide/show the train. Start the train. A new set of variables. Zoom in or out of the train journey.

 Simplify or transform algebraic expressions Click on the expressions to hide or show them: in the above example click on 3x or 7 or 28x etc. J22: Multiply out brackets (positive values only) eg (3x +2)(2x + 1) = 6x2 + 10x + 2 factorise the expression 6x2 + 10x + 2 J23: Multiply out brackets (positive and negative values) eg (3x -2)(2x + 1) = 6x2 - x - 2 factorise the expression 6x2 - x - 2 Use these buttons to generate a new expression. Click the '1' button to ensure the coefficient of the x terms is 1. Click the '2' button to have random coefficients of x. The diagram might not fit on the screen, click again if this happens. The diagrams are drawn to scale: can you say what the value of x is? Use these buttons to hide or show the expression or the factorised expression. J24: Solve quadratic equations eg: x2 + 3x - 10 = 0 Click twice under each equation to reveal the solutions. J35: Solve equations using trial and improvement Option 1 eg: x² + 3x = 35 Option 2: x³ - 4x = 35 Option 3: x³ - 4x² = 35

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