Number Starter

Shape Starter

Algebra Starter

Data Starter

Starter #1 a, b and c are integers. If abc = 204 and bc = 51 What value is a? What two values are the other letters?

a – 4 b (or c) = 17 c (or b) = 3 Starter #1

Starter #2 The sum of 5 different odd numbers is 51. What are the numbers?

Starter #

Starter #3 Find possible dimensions of the following shapes such that their perimeter is numerically equal to their area: A square A rectangle A circle

4cm for square 6cm x 3cm rectangle (for example) Circle with radius 2cm Starter #3

Starter #4 Which of these algebraic expressions accurately describes the following: “Take a number, subtract two, square it, add two, divide by p, square it.

Starter #4 A

Starter #1 Using only the numbers 1, 2 and 3, make the numbers 1-10 using the following available operations: +, -, x, /, ^ (“to the power of”) You must use all three numbers each time

Starter #1 Various answers eg (1+2)/3 (3-2)+1 3/(1^2) 2^(3-1) (3x2)-1 3x2x1 (3x2)+1 (2x1)^3 (3x1)^2 3^2 + 1

Starter #2 A sequence is generated by finding the unique prime factors of 2n. For example, the 10 th term would be the number of unique prime factors of 2x10 2x10 = 20 = 5 x 2 x 2 The unique prime factors of 20 are 5 and 2 So the 10 th term in the sequence is 2. Find the first 5 terms.

Starter #

Starter #3 A cube has volume 64cm 3 What is the length of AB? A B

Starter #3 4Sqrt3

Starter #4 Think of a value for each letter so that the following are true: 1/a = a 2b < b c 2 < c d 3 < d < d 2

Starter #4 a = 1 b is negative c is between zero and one d is less than -1 1/a = a 2b < b c 2 < c d 3 < d < d 2

Starter #1 Which set of 6 consecutive numbers follow these 6 properties? PrimeFactorialSquareEvenCubeTriangular

Starter #2 Cube the numbers 1-10 What is the curious pattern with the final digit of each answer?

Starter #2 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000 All last digits are unique (0-9)

Starter #3 What is the 200 th digit of the consecutive numbers ?

Starter #3 103 (1-99 is 189 (9+ 90x2) digits, 101, 102, 103.)

Starter #4 Write the numbers from 1 to 8 into the squares, so that the squares with consecutive numbers do not touch (neither edges nor corners).

Starter #4

Place a set of coordinates in all 4 parts of the Venn below y = 2x + 1y = x + 3

Answers various except as shown y = 2x + 1y = x + 3 (2, 5)

Place the operations +, -, x, / In the Venn below: Obeys Associative LawObeys Distributive Law Obeys Commutative Law

Place the operations +, -, x, / In the Venn below: Obeys Associative LawObeys Distributive Law Obeys Commutative Law X + / -

Place a number in all 4 parts of the Venn below Multiple of 3 Factor of 72

Place two numbers in all 4 parts of the Venn below In the 6 x tableIn the 4 x table

What is the value of “a+w+a+y”?

15

What is a+b+c+d+e+f ?

720 o

Which line cuts the shaded area in half?

XD

Below is a number line. Which point represents the product of P and Q?

B

In the diagram, XY is a straight line. What is the value of x?

140 o

In the diagram, a rectangle is placed on a grid of 1cm x 1cm squares. What is the area of the rectangle?

30

A 30cm x 40cm page of a book includes a 2cm margin on each side as shown. What percentage of the page is occupied by the margin?

22%

Prove that where n is an integer, the sequence 6n + 3 will always produce odd numbers.

6n + 3 = 3(2n+1) Algebraic definition of an odd number Algebraic definition of an odd number Odd x odd is always odd

The diagram shows an equilateral triangle with its corners at the midpoints of alternate sides of a regular hexagon. What fraction of the area of the hexagon is shaded?

3/8

In parallelogram PQRS the ratio of ∠ PSQ to ∠ PQS is 1:5. What is the size of ∠ QSR ?

75 o

At the Marldon Apple-Pie-Fayre bake-off prize money is awarded for 1sr 2nd and 3rd places in ratio 3:2:1. Last year Mrs Keat and Mr. Jewell shared third prize equally. What fraction of the total prize money did Mrs. Keat receive ?

1/4

The diagram shows an equilateral triangle inside a rectangle. What is the value of x+y ?

60

Each number in the middle of a row or column is the average of the numbers either side.

Each number in the middle of a row or column is the average of the numbers either side.

Results for multiplying the rows and columns are given. Complete the grid

Results for multiplying the rows and columns are given. Complete the grid

10 2 = ? 2 + ? = ? 2 + ? 2

10 2 = =

Cross out two numbers so that all rows and columns add to multiples of

160 as a product of its prime factors is 2 5 x 5 Use this information to show that 160 has 12 factors

1 2 2 x 2 2 x 2 x 2 2 x 2 x 2 x 2 2 x 2 x 2 x 2 x x 5 2 x 2 x 5 2 x 2 x 2 x 5 2 x 2 x 2 x 2 x 5 2 x 2 x 2 x 2 x 2 x 5

324 as a product of its prime factors is 2 2 x 3 4 Use this information to show that 324 has an integer square root. What is the square root of 324?

Sqrt (2 2 x 3 4 ) = 2 x 3 2 = 18

2800 as a product of its prime factors is 2 4 x 5 2 x 7 How many square numbers are factors of 2800?

6 square numbers are factors 2 4 x 5 2 x 7 1 is a factor 2 2 is a factor (2 x 2) x (2 x 2) is a factor 5 2 is a factor (5 x 2) x (5 x 2) is a factor (5 x 2 x 2) x (5 x 2 x 2) is a factor

216 as a product of its prime factors is 2 3 x 3 3 How many cube numbers are factors of 216?

216 as a product of its prime factors is 2 3 x x 1 x 1 2 x 2 x 2 3 x 3 x 3 (2 x 3) x (2 x 3) x (2 x 3)

Starter 1 If five people pack five boxes of flowers in five minutes, how many are needed to pack fifty boxes in fifty minutes?

Five people

Starter 2 A fish has a tail as long as its head plus a quarter the length of its body. Its body was three quarters of its total length. Its head was 4 inches long. How long was the fish?

128 inches

Starter 3 Find a quantity such that the sum of it and one seventh of it is equal to nineteen

16 and 5/8

Starter 4 A boy and a girl are to be chosen as class reps at school. If the class has twelve boys and ten girls, how many different combinations are there?

120

Starter 1 The length of the rectangle below is 4 times greater than the width. What is the greatest possible area of the shape? 3n 2 cm (4n+3) cm

(3n+2)(n-6) = 0 n = 6 is greatest value for n So greatest area = 36 x 3 x 27 = 2916cm 2

Starter 2 For A-D, explain what kind of simplification has been performed on this number: A 17.2 B C 20 D

Starter 2 For A-D, explain what kind of simplification has been performed on this number: A 17.2 (1dp) B (truncated to 3dp) C 20 (1 sf) D (5dp)

Starter 3 Waynetta is going to make a rectangle using 20cm of string. What are the dimensions of the rectangle with the largest area?

Square of side 5cm

Starter 4 Using the numbers 1-16, complete the magic square below such that each row / diagonal sums to 34:

Starter 1 Think of 5 different types of question that could produce this answer: 30cm 2

Starter 2 Think of 5 different types of question that could produce this answer: ab(c+d)

Starter 3 Think of 5 different types of question that could produce this answer:

Starter 4 Think of 5 different types of question that could produce this answer:

Starter 1 Find the surface area of this tube

14pi+48pi+36pi 98pi cm^2

Starter 2 How many integers under 100 have digit sums of < 10 ?

Starter 3 If the width and height of an open cylinder are equal to the diameter of a sphere, what is the relationship between their surface areas?

They are the same

Starter 4 Think of 5 different types of question that could produce this answer: 36π

Starter 1 A quadrilateral ABCD is inscribed within a circle. AD crosses the centre of the circle ∠ BAC = 26 o ∠ DBC = 50 o Find the internal angles of the quadrilateral

A = 76, B = 128, C = 104, D = 52

Starter 2 (a-b) 2 If the difference between a and b is 3, which will produce the biggest answer? a < b or b < a ?

neither

Starter 3 How many numbers between 100 and 200 (inclusive) are multiples of 6?

(200/6) – (100/6) 16

Starter 4 An isosceles triangle has internal angles 50 o, 65 o and 65 o Find, to 1 dp, any possible combination of side lengths that would make this shape geometrically possible.

Various answers. Choose a random side length Calculate other side(s)

Starter 1 Put these temperatures in ascending order (coldest first): -39 o C, -39 o F, -41 o C, -41 o F

-41 o C, -41 o F, -39 o F, -39 o C

Starter 2 For this regular octagon, Is the blue area equal to, greater than, or less than the yellow area?

They’re equal

Starter 3 How many odd numbers between are multiples of 7?

7

Starter 4 What is the date of the middle of the year?

366 / 2 = 183 rd day July 1st