### Number Sequences 1

What is the 7th:
a) Odd number; 13
b) Square number; 49
c) Prime number. 17

### Factors

Find all the factors of:

44

1, 2, 4, 11, 22, 44.

### Multiples

Subtract the 7th from the 10th multiples of:

11

33

### Polygons

What are the names of regular polygons with:
a) eight sides;
b) nine sides;
c) ten sides.

Octagon, Nonagon and Decagon (all regular)

### Rounding

Round the following numbers to three significant figures:
a) 48.02; 48.0
b) 794941; 795000
c) 0.003995; 0.00400

### Area of a Triangle

Find the area of a triangle that has a base of 6cm and a height of 11cm.

33cm2

### Area of a Trapezium

Find the area of a trapezium that has a base of 17cm, a height of 6cm and a top (parallel to base) of 7cm. 72cm2

Evaluate:

$$\frac{3}{6} + \frac{7}{9}$$ $$= 1\frac{5}{18}$$

### Fractions (Multiplying)

Evaluate:

$$\frac{2}{3} × \frac{5}{7}$$ $$= \frac{10}{21}$$

### Fractions (Dividing)

Evaluate:

$$\frac{2}{4} ÷ \frac{7}{6}$$ $$= \frac{3}{7}$$

### Circle (Vocabulary)

Name the red part.

### Venn Diagrams

Describe the red region.

### Shape Formulas

What is the formula?

What is it?

### Fraction to Percentage

Convert this fraction to a percentage to 3 significant figures.

$$\frac{1}{3}$$ $$= 33.3$$%

### Circle Area

Find the area of a circle that has a radius of 9cm. Give your answer to three significant figures.

254cm2

### Circle Circumference

Find the circumference of a circle that has a radius of 9cm. Give your answer to three significant figures.

56.5cm2

Calculate the value of:

8.6 + 7.8

= 16.4

### Decimals (Subtracting)

Calculate the value of:

7.3 − 4.8

= 2.5

### Decimals (Multiplying)

Calculate the value of:

2.3 × 6.2

= 14.26

### Decimals (Dividing)

Calculate the value of:

28.8 ÷ 12

= 2.4

### Indices (Simple)

What is the value of:

13

= 1

What is the value of:

1-3

= 1

Calculate the value of:

66 + 84

= 150

### Basic Subtraction

Calculate the value of:

94 − 27

= 67

### Basic Multiplication

Calculate the value of:

77 × 43

= 3311

### Basic Division 2

Calculate the value of:

1216 ÷ 16

= 76

### Percentage (Of)

Find the value of:

40% of 160

= 64

### Standard Form 1

Find the value of:

7.23 × 102

= 723

### Highest Common Factor

Find the highest common factor of thirty two and sixteen.

= 16

### Times Tables (2-5)

 3 × 3 = 9 4 × 3 = 12 6 × 5 = 30 8 × 3 = 24 7 × 5 = 35 5 × 2 = 10 9 × 4 = 36 2 × 4 = 8

### Times Tables (2-12)

 9 × 9 = 81 8 × 5 = 40 3 × 7 = 21 5 × 4 = 20 7 × 3 = 21 4 × 9 = 36 6 × 3 = 18 2 × 12 = 24

### Times Tables (2)

 9 × 2 = 18 8 × 2 = 16 3 × 2 = 6 4 × 2 = 8 5 × 2 = 10 7 × 2 = 14 6 × 2 = 12 2 × 2 = 4

### Times Tables (3)

 3 × 3 = 9 8 × 3 = 24 9 × 3 = 27 6 × 3 = 18 4 × 3 = 12 5 × 3 = 15 7 × 3 = 21 2 × 3 = 6

### Times Tables (4)

 4 × 4 = 16 7 × 4 = 28 3 × 4 = 12 5 × 4 = 20 6 × 4 = 24 9 × 4 = 36 8 × 4 = 32 2 × 4 = 8

### Times Tables (5)

 5 × 5 = 25 7 × 5 = 35 9 × 5 = 45 6 × 5 = 30 4 × 5 = 20 8 × 5 = 40 3 × 5 = 15 2 × 5 = 10

### Times Tables (6)

 5 × 6 = 30 4 × 6 = 24 7 × 6 = 42 6 × 6 = 36 3 × 6 = 18 8 × 6 = 48 9 × 6 = 54 2 × 6 = 12

### Times Tables (7)

 7 × 7 = 49 9 × 7 = 63 3 × 7 = 21 4 × 7 = 28 5 × 7 = 35 8 × 7 = 56 6 × 7 = 42 2 × 7 = 14

### Times Tables (8)

 8 × 8 = 64 5 × 8 = 40 4 × 8 = 32 9 × 8 = 72 7 × 8 = 56 3 × 8 = 24 6 × 8 = 48 2 × 8 = 16

### Times Tables (9)

 3 × 9 = 27 8 × 9 = 72 6 × 9 = 54 5 × 9 = 45 7 × 9 = 63 4 × 9 = 36 9 × 9 = 81 2 × 9 = 18

### Times Tables (12)

 6 × 12 = 72 5 × 12 = 60 8 × 12 = 96 4 × 12 = 48 9 × 12 = 108 7 × 12 = 84 3 × 12 = 36 2 × 12 = 24

### Fractions (Equivalent)

Write this fraction in its simplest form:

$$\frac{9}{27}$$ $$= \frac{1}{3}$$

### Fractions (Mixed)

Evaluate:

$$2\frac{4}{5} − \frac{6}{7}$$ $$= 1\frac{33}{35}$$

### Pythagoras

Find AB if AC = 5m and BC = 7m. 4.90m

### Trigonometry (Angle)

Find angle ABC if AC = 6m and AB = 7.1m. 40.2o

### Trigonometry (Side)

Find AC if angle ABC = 56o and AB = 5.3m. 7.86m

2

2

2

### Fraction to Decimal

Convert this fraction to a decimal to 3 significant figures.

$$\frac{4}{7}$$ $$= 0.571$$

### Decimal to Fraction

Convert this decimal to a fraction.

$$0.3$$ = $$\frac{3}{10}$$

### Percentage (Increase)

Increase £60 by 40%

£84

### Lowest Common Multiple

What is the lowest common multiple of four and fourteen.

= 28

### Sequence (Arithmetic)

7,21,35,49,63...

Find the:
a) next term; 77
b) nth term; 14n - 7
c) term number 49; 679

### Sequence (Geometric)

5,15,45,135,405...

Find the:
a) next term; 1215
b) nth term; 5 × 3n-1
c) term number 10; 98415

### Interest (Simple)

If £100 is invested for 5 years with a simple interest rate of 5%, find the amount of interest earned. £25.00

### Interest (Compound)

If £160 is invested with an interest rate of 4% compounded annually, find the value of the investment after 9 years. £227.73

### Currency Exchange

If £1 is worth $1.57, convert: a) £220 to dollars;$345.40

b) \$240 to pounds; £152.87

### Coordinates (Midpoint)

What are the coordinates of the midpoint of the line joining:

$$(6,8) \text{ and } (16,14)$$

(11,11)

What is the gradient of the line joining:

$$(-8,4) \text{ and } (-4,10)$$

$$\frac{3}{2}$$

### Coordinates (Square)

Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?

$$(3,2),(9,5),(0,8)$$

(6,11)

### Negative Numbers

a) 5 − 12 = -7
b) 5 × (-10) = -50
c) (10−16)(7−18) = 66
d) 50 ÷ (-10) = -5
e) (-6)2 = 36

### Substitution

If p = 6, q = 18 and
r = -8 evaluate:

a) 2q − p = 30
b) pq + r = 100
c) p2 − 5q - r = -46

### Equations (Type 1)

Solve:

$$2x = 4$$

$$x = 2$$

### Equations (Type 2)

Solve:

$$2x -9= 9$$

$$x = 9$$

### Equations (Type 3)

Solve:

$$5x -4= 3x + 12$$

$$x = 8$$

### Equations (Type 4)

Solve:

$$4(3x +4)+10= 98$$

$$x = 6$$

### Equations (Type 5)

Solve:

$$4(4x + 3)= 2(3x + 3)$$

$$x = -0.6$$

### Equations (Simultaneous 1)

Solve:

$$5x-3y = 0$$
$$3x+3y = 24$$

$$x = 3, y = 5$$

### Equations (Simultaneous 2)

Solve:

$$5x-4y = -8$$
$$5x-12y = -64$$

$$x = 4, y = 7$$

### Equations (Simultaneous 3)

Solve:

$$5x-6y = -31$$
$$3x+7y = -34.5$$

$$x = -8, y = -1.5$$

### Sets (Union)

Find the union of:

{5,6,7,8,9,10} and
{2,3,5,7,11,13}

{2,3,5,6,7,8,9,10,11,13}

### Sets (Intersection)

Find the intersection of:

{5,6,7,8,9,10} and
{3,4,5,6,7,8}

{5,6,7,8}

### Bearings

A plane flies from point A to point B on a bearing of 087o. What bearing would it return on from B to A? 267o

### Probability

A number is picked at random from the set

{1,2,3,4,5}

what is the probability it is even? $$\frac25$$

Evaluate:

30 ÷ 6 × 54 ÷ 6

45

### Simplify

Simplify the following by collecting like terms:

$$7d−3e−5d+7e$$

$$4e+2d$$

### Ratio

Divide 50 in the ratio

1:4

10 and 40

### Graph (Linear)

Draw a rough sketch of the graph of:

$$y=x$$

y intercept 0

### Prime Factors

Express the following number as the product of prime numbers:

72

2 x 2 x 2 x 3 x 3

### Percentage (Reverse)

In a sale an item costs £65 after a 35% reduction. What was the original price?

£100

### Averages

Find the mean, mode, median and range of the following:

1,3,1,10,5

Mean = 4, mode = 1,
median = 3 and range = 9

### Time (Analogue)

What time is this?

### Time (Digital)

Sketch a clock face:

### Decimals (Recurring)

Write the following recurring decimal as a fraction in its lowest terms.

0.232323... $$\frac{23}{99}$$

### Percentage (Decrease)

Decrease £80 by 40%

£48

### Brackets (Linear)

Expand:

$$2(6x-8)$$

$$12x-16$$

Expand:

$$(3x+4)(3x-2)$$

$$9x^2+6x-8$$

### Factorise (Linear)

Factorise:

$$9x-9$$

$$9(x-1)$$

Factorise:

$$x^2-1$$

$$(x+1)(x-1)$$

Factorise:

$$4x^2-1$$

$$(2x+1)(2x-1)$$

Which theorem?

### Standard Form 2

Find the value of:

4.66 × 10-2

= 0.0466

### Standard Form 3

Write in standard form:

2360000

= 2.36 × 106

### Standard Form 4

Write in standard form:

0.0000221

= 2.21 × 10-5

Find the nth term:

$$10, 15, 22, 31, 42,$$

$$n^2+2n+7$$

### Standard Form 5

Multiply 9 × 102
by 9 × 106 and give the answer in standard form.

= 8.1 × 109

Solve:

$$x^2-x-20= 0$$

$$x = 5$$ and $$-4$$

Solve this equation giving the solutions to 3 significant figures:

$$2x^2-2x-3 = 0$$

$$x = 1.82$$ and $$-0.823$$

### Polygon Angles

What is the size of each interior angle of a regular octagon?

135°

### Change The Subject

Make $$e$$ the subject of the formula
$$f=g(e+h)$$

$$e=\frac{f}{g}-h$$

### Basic Division 1

Calculate the value of:

1662 ÷ 2

= 831

### Number Sequences 2

What is the 12th:
a) Cube number; 1728
b) Triangular number; 78
c) Fibonacci number. 144

### Square Numbers

What are the three largest square numbers less than
81

64, 49, 36

### Prime Numbers

What is the 4th prime number?

7

### Last Lesson

Write down something you learnt in the previous mathematics lesson.

### Last Week

Write down something you learnt in one of the mathematics lessons last week.

## A Mathematics Lesson Starter Of The Day

Share
• Jan, South Canterbury
•
• Thank you for sharing such a great resource. I was about to try and get together a bank of starters but time is always required elsewhere, so thank you.
• Barbara Schindler, Newton Rigg College
•
• I use Refreshing Revision a lot but today all the brackets and fractions keep coming up 'jumbled' . There are curly brackets, part words / 's in odd places and it is impossible to make out the question. It is doing this on 2 computers I have tried. Can you help? thank you.

[Transum: Sorry to hear about this problem Barbara. I have tested it from here and it seems to be working OK. Please take a look at the MathJax FAQ. Many apologies for the inconvenience.]
• Lesley, UK
•
• Answers for the starter would be great so students can get immediate feedback and become independent learners.

[Thanks for your comments Lesley. The answers are only available to signed-in teachers and parents I'm afraid. I you are a subscriber and are projecting this Starter for the whole class to see you can scroll down the page and show the same questions with the answers included in red.]
• Mrs B, Stockport
•
• Refreshing Revision really useful resource, that I have actually used for Ks2 revision as some topics are appropriate. I'd love to see either ks2 version, with purely ks2 SATs level topics or adding them to the current version.

[Transum: Thanks so much for your feedback Mrs B. If you could send me a list of your top ten ideas for topic you would like to see added I will work on it]
• Mark Adams, St Peters RC School Solihull
•
• It would be great if these questions came with answers as well.

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Ben Orlin answers maths' three big questions: Why do I need to learn this? When am I ever going to use it? Why is it so hard? The answers come in various forms-cartoons, drawings, jokes, and the stories and insights of an empathetic teacher who believes that mathematics should belong to everyone.

## A Compendium Of Mathematical Methods

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A Compendium of Mathematical Methods brings together over one hundred different approaches from classrooms all over the world, giving curious mathematicians the opportunity to explore fascinating methods that they've never before encountered.

If you teach mathematics to any age group in any country, you are guaranteed to learn lots of new things from this delightful book. It will deepen your subject knowledge and enhance your teaching, whatever your existing level of expertise. It will inspire you to explore new approaches with your pupils and provide valuable guidance on explanations and misconceptions. more...

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