Fractions

Fractions

ICAS Questions 1-10

ICAS Questions 11-19

ICAS Questions 20-28

ICAS Questions 29-36

ICAS Questions 37-40

Super Darts

Jetta has just been given a dart game for her birthday. The board has an outer ring and an inner ring. The outer ring scores 3 points and the inner ring 7. Jetta was bored with only using three darts . She wondered if she used as many darts as she liked whether she could get 58 points.

Can she get 58? If so, in how many ways can she get 58?

(If she can’t get 58 find a number in the 50s that she can get and see how many times she can get that number.)

Calculator count to 1000

Select a number less than 20. Skip count

with it to 1000.

How many numbers can you find that will

hit no hundreds through to 1000.

My Dogs

I have three dogs of different ages. If I add their ages together I get 15. If I multiply their ages together I get 45. How old are my dogs?

The Fathers Day Card

Lee and Jamie have decided to buy their father a

card for Fathers Day. The card is going to cost

$5.95. Lee puts in 35c more than Jamie. How

much does each child contribute to the card?

At the Movies

John, Jo and Chris have got seats for the movies. In fact their seats are F5, F6, F7. In how many ways can they sit in those seats?

Tennis and Golf Players

In a class in the school down the road,

everyone plays tennis or golf or both.

In fact 80% play tennis and 70% play

golf. What percentage plays both

games?

The 500 Problem

Here’s a subtraction problem. The numbers a and b stand

for digits. If the two subtraction sums give the same

answer, what digits do a and b stand for?

500 - 5ab

5ab -500

Legs in the Barn

One third of the animals in the

barn are chickens. The rest are

pigs. There are 20 legs in all. How

many pigs are there

Pocket Money

Sally and David have agreed to work for their Mum over

the holidays. The pay they get will vary though. Sally will

get $10 for the first day she works and two more dollars

for every day she works after that.

David, on the other hand, will get $1

for the first day he works but for each

day he works from then on his pay will

be doubled. Who would you rather be

and why?

Competition

ANZAC Maths

1.During the first day of the Gallipoli campaign half of Australia’s 12

000 soldiers were killed. How many died?

2.700 out of 1500 New Zealanders were killed, write that as a

fraction and simplify it.

3.If the landing was on April 25, 1915, and the final retreat was on

December 21 of the same year how many days did the campaign

last?

4.2721 New Zealanders were killed, how many died per month on

average?

5.Only 9000 bodies of the 46 000 Allied troops that died were

identified, write that as a fraction, simplify it, write it as a

decimal and as a percentage.

6.In the whole of WW1 approximately 1 in 5 of New Zealand’s

soldiers were killed. Write that as a percentage. If 18 166 Kiwis

were killed approximately how many Kiwi soldiers took part in the

war?

7.In 1915 New Zealand’s population was approximately one million.

How many males would there have been?

8.What percentage of those males went to war (use your answers to

Q6 and Q7)?

9.What percentage of New Zealand’s population was killed in WW1?

10.Name a town in NZ now that has a population of about 20 000

people. Clue, Hastings has a population of about 60 000.

Mums Kitchen Floor

Mum’s kitchen floor is square and is fitted by 64 square tiles in a 8 x 8 array. Mum has chosen black and white tiles. She could have the tiles laid so that they looked like a chessboard but she was hoping for something a bit unusual. The tile man sketched something that had reflective and rotational symmetry. What did he suggest?

The Treasure Map

Captain Blackheart had buried his treasure and committed the biggest sin a pirate can commit – he had lost his treasure map! But all was not lost. His trusty crew all remembered different bits of the map.

"I remember drawing it with 5 squares each way", said the Captain. ("He can’t count over 6", the cabin boy John said.)

"There was a row of three trees running due East from the square (1,1)", Peg Leg Pete said. "You put each one of them on a different square."

"Weren’t there four granite boulders going due South from (5,5)?" John asked. "I think you put one of them each in a square too."

"Ah!. Now I remember!" yelled the Captain. "I buried the treasure half way between the first rock and the most western tree!"

Where is the treasure?

Robots

Robots can move around the 4 x 4 board below. They can do so at the rate of one square per second. Start the red robot at (1,1) and give it instructions (square by square) to move in a square of side length 3 around the square (2,2).

Noughts

In the game of Noughts, each player takes a turn to place a nought on the board (see below). Each new nought goes into a new square. The winner is the first person to place three noughts in a row. Is it possible for either the first player or the second player, to always win? (Assume that each player plays to win and plays as well as is possible.) If so, what is the winning strategy? If not, why not?

Carrie’s First Cubes

Carrie has glued some cubes together to make a large

solid cube with nine small cubes showing on a face. She

paints the large cube red.

How many of the original small cubes have

(i) three faces painted red; (ii) two faces painted red;

(iii) one face painted red; (iv) no faces painted red