Transcript 30 Second Number Crunch 4

Number Starter
Number Starter
Shape Starter
Shape Starter
Algebra Starter
Algebra Starter
Data 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?
Starter #1
• a–4
• b (or c) = 17
• c (or b) = 3
Starter #2
The sum of 5 different odd numbers is 51.
What are the numbers?
Starter #2
17 + 11 + 13 + 7 +
3
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
Starter #3
• 4cm for square
• 6cm x 3cm rectangle (for example)
• Circle with radius 2cm
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 10th 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 10th term in the
sequence is 2.
• Find the first 5 terms.
Starter #2
• 1 1 2 1 2
Starter #3
• A cube has volume 64cm3
• 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
c2 < c
d3 < d < d2
Starter #4
•
•
•
•
a=1
b is negative
c is between zero and one
d is less than -1
1/a = a
2b < b
c2 < c
d3 < d < d2
Starter #1
• Which set of 6 consecutive numbers follow
these 6 properties?
Prime
Factorial
Square
Even
Cube
Triangular
23
24
25
26
27
28
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 200th digit of the consecutive
numbers 1-200 ?
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 + 1
y=x+3
Answers various except as
shown
y = 2x + 1
(2, 5)
y=x+3
Place the operations +, - , x, /
In the Venn below:
Obeys Associative Law
Obeys Distributive Law
Obeys Commutative Law
Place the operations +, - , x, /
In the Venn below:
Obeys Associative Law
Obeys Distributive Law
-
/
+
X
Obeys Commutative Law
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 table
In the 4 x table
What is the value of “a+w+a+y”?
15
What is a+b+c+d+e+f ?
720o
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?
o
140
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.
Odd x odd
is always
odd
6n + 3 = 3(2n+1)
Algebraic
definition
of an odd
number
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 ?
o
75
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
2
8
6
10
Each number
in the middle
of a row or
column is the
average of the
numbers
either side.
2
4
6
5
7
9
8
10
12
Each number
in the middle
of a row or
column is the
average of the
numbers
either side.
140
54
48
48
120 63
Results for
multiplying the
rows and
columns are
given.
Complete the
grid.
4
5
7
140
2
3
9
54
6
8
1
48
48
120 63
Results for
multiplying the
rows and
columns are
given.
Complete the
grid.
102 = ?2 + ?2
132 = ?2 + ?2
102 = 82 + 62
132 = 122 + 52
8
9
5
2
3
9
7
5
4
6
2
8
9
8
5
6
Cross out two
numbers so
that all rows
and columns
add to
multiples of 4
8
9
5
2
3
9
7
5
4
6
2
8
9
8
5
6
Cross out two
numbers so
that all rows
and columns
add to
multiples of 4
160 as a product of its prime factors is
25 x 5
Use this information to show that
160 has 12 factors
1
2
2x2
2x2x2
2x2x2x2
2x2x2x2x2
5
2x5
2x2x5
2x2x2x5
2x2x2x2x5
2x2x2x2x2x5
324 as a product of its prime factors is 22 x
34
Use this information to show that
324 has an integer square root.
What is the square root of 324?
• Sqrt (22 x 34) = 2 x 32 = 18
2800 as a product of its prime factors is
24 x 52 x 7
How many square numbers are factors of
2800?
6 square numbers are factors
24 x 52 x 7
1 is a factor
22 is a factor
(2 x 2) x (2 x 2) is a factor
52 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
23 x 33
How many cube numbers are factors of
216?
216 as a product of its prime factors is
23 x 33
1x1x1
2x2x2
3x3x3
(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?
3n2 cm
(4n+3) cm
(3n+2)(n-6) = 0
n = 6 is greatest value for n
So greatest area =
36 x 3 x 27 = 2916cm2
Starter 2
• For A-D, explain what kind of simplification
has been performed on this number:
17.192996
A
B
C
D
17.2
17.192
20
17.19300
Starter 2
• For A-D, explain what kind of simplification
has been performed on this number:
17.192996
A
B
C
D
17.2 (1dp)
17.192 (truncated to 3dp)
20 (1 sf)
17.19300 (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:
2
30cm
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:
0.0025
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 = 26o
• ∠DBC = 50o
• 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
50o, 65o and 65o
• 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):
• -39oC, -39oF, -41oC, -41oF
• -41oC, -41oF, -39oF, -39oC
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 1-100
are multiples of 7?
• 7
Starter 4
• What is the date of the middle of the year?
• 366 / 2 = 183rd day
• July 1st