Year 6 extension

1. Aroha thinks of a whole number. Rounded to the nearest 10 it is 350. Rounded to the nearest 100 it is 300. How many different whole numbers could she be thinking of?
2. Which number is exactly halfway between 0.08 and 0.3?
3. Tama has more than 1 but fewer than 100 marbles. When he puts them in groups of 4, there is 1 left over. In groups of 5, there is 1 left over. In groups of 6, there is also 1 left over. How many marbles does he have?
4. Mere eats 1/3 of a pizza. Hemi then eats 1/4 of what is left. Then Sione eats half of what remains after that. What fraction of the whole pizza is left?
5. A raincoat costs $80. Shop A takes 25% off. Shop B takes 10% off, then takes a further 15% off the new price. How much more does the raincoat cost at Shop B than at Shop A?
6. A robot starts at (0, 0) on a grid. It moves 1 unit right, then 2 units up, then 3 units left, then 4 units down, then 5 units right, 6 units up, and so on. Each move is 1 unit longer than the one before, and the directions keep going right, up, left, down in that order. Where is the robot after 12 moves?
7. Kahu's mean score on 4 spelling tests is 72. What must she score on the 5th test to make her mean for all 5 tests exactly 75?
8. What is the smaller angle between the hour hand and the minute hand of a clock at 4:30?
9. On a grid, Ana joins the points (0, 2), (2, 0), (4, 2) and (2, 4) in order to make a tilted square. What is the area of her square, in square units?
10. Rāwiri spins two fair spinners. Each is numbered 1, 2, 3 and 4. He multiplies the two numbers. What is the probability that the answer is even?