11+ Taster Day – Maths Activity
The three activities are arranged according to level of challenge (1 star, 2 star, 3 star). Choose which level of task(s) you feel most comfortable with.
Take a Leaf Part A An examination paper is made by taking 5 large sheets of paper, folding the pile in half and stapling it. The pages are then numbered in order from 1 to 20.
etc... What is the sum of the three page numbers that are on the same sheet of paper as page number 5? Part B A newspaper is assembled in a similar way to the examination paper above. Here is a sheet of a newspaper. Each sheet has four pages. How many sheets are there altogether?
Back in Time Beatrix has a 24-hour digital clock on a glass table-top next to her desk. When she looked at the clock at 13:08, she noticed that the reflected display also read 13:08, as shown. How many times in a 24-hour period do the display and its reflection give the same time?
Climbing the Stairs When I climb the stairs I can climb either one step or two steps at a time. This means there are three ways that I can climb a flight of three stairs (see diagram).
1-1-1
1-1-1
1-2
2-1
1-2
2-1
A. Show that there are eight ways of climbing a flight of five stairs
B. The average flight of stairs in a house contains 13 steps. How many different ways can I climb a flight a 13 stairs. Hint: Try counting the ways for smaller flights of stairs to see if you can find a pattern.
Climbing the stairs – 377 different ways to climb 13 steps. Back in time – 96 times a day Answers: Take a leaf – part A: 37, part B: 17 sheets (68 pages)
Investigations from nrich.maths.org