‘Sum’mer camp to multiply new maths lovers
The Connemara Maths Academy, based in Kylemore Abbey in the heart of Connemara, aims to add to maths fans experience through an innovative approach to the teaching of a subject that can still cause fear in many students.
“Our aim is to facilitate the learning of maths through discovery and the use of creative technologies,” said the academy’s director, Aengus O’Connor.
“We want to connect students with the key mathematical concepts in their syllabuses through a range of stimulating and enjoyable academic and artistic projects.”
Mr O’Connor stressed that, unlike the current Channel 4 series, Child Genius, which focuses on child prodigies, the academy’s courses are aimed at students of varying ability in maths.
He claimed that there was a big demand for such a fresh approach to the teaching of maths as, he said, many teachers and parents had concerns about how the new project maths syllabus was being implemented.
Mr O’Connor said technology had also greatly facilitated new methods of teaching maths, although he added that students still needed to practice quick mental arithmetic.
In addition to classes focused specifically on maths, students also participate in activities including music, kayaking, archery, ziplining, windsurfing and team sports, while they also explore the mathematics behind each of those pursuits.
“For example, when the students use zip wires, we examined the dynamics of pulleys on ropes and how fast they can travel along a zip wire,” said Mr O’Connor.
“In music, we look at how natural numerical sequences are used in musical composition.”
The academy is also organising today’s gathering of 80 of the most mathematically gifted students aged 11-16 years at the first Mathletes Ireland Challenge Alumni in Mullingar.
The event is a reunion for all the finalists in the Mathletes Challenge 2014 earlier this year where students competed for a prize fund of €20,000.
The tournament is the brainchild of businessman and entrepreneur, Seán O’Sullivan, who is probably best known as one of the regular mentors on Dragon’s Den.
His company, SOS Ventures, is also sponsor of today’s event.
The mathlete summer camp posed questions such as the following:
In an enchanted forest, there are two kinds of talking creatures: bears, whose statements are always true, and foxes, whose statements are always false. Four talking creatures, Maeve, Tony, Colin, and Fiona, make the following statements:
Maeve: “Fiona and I are not the same species”
Tony: “Colin is a fox”
Colin: “Tony is a fox”
Fiona: “Of the four of us, at least two are bears”
How many of these four creatures are foxes?
Start with Tony. If tony is a fox, then he is lying. So, Colin is in fact a bear. If Tony is a bear, then he is telling the truth. So, Colin is a fox. Either way, there is one fox and one bear between them.
Now, suppose Maeve is a bear. Then, since Maeve is telling the truth, Fiona must be a fox. But this cannot be, since Fiona is telling the truth. Thus, Maeve must be a fox. And therefore, so must Fiona.
All together, there are three foxes in the group.
What is the smallest two-digit number that is not the sum of three one-digit numbers?
The largest two-digit number that is the sum of three one-digit numbers is 9 + 9 + 9 = 27. Switching a 9 to a 10 — so that the sum 9 + 9 + 10 is not the sum of three one-digit numbers — produces 28.
Lucas is spending a weekend in Limerick, and wants to see the Seven Limerick bridges. All seven bridges run across the same river. He will start at his hotel in the beginning of the day, and must end up on the same side of the river that his hotel is on at the end of the day. It costs €4 per crossing on Bridge One; €4 per crossing for Bridge Two; €4 per crossing for Bridge Three; €4 per crossing for Bridge Four; €3 per crossing for Bridge Five; €1 per crossing for Bridge Six; €1 per crossing for Bridge Seven once.
If Lucas has €25 when he leaves the hotel in the morning and plans to cross each bridge at least once, what is the maximum number of crossings he can make?
At minimum he will spend €22, making the 7 mandatory bridge crossings (€21) and the 1 cheapest return (€1). If he does an extra round trip on a €1 Bridge he will have €1 remaining. He cannot cross again, even if he has €1 left, because that will leave him on the wrong side of the river.
When a barrel is 40% empty it contains 40 litres more than when it is 40% full.
How many litres does this barrel hold when it is 100% full?
Let X denote the full capacity of the barrel. Then we have, (60% – 40%) X = 40. Hence, X = 200.
Tommy drops a rubber ball from the roof of his house, at a height of 10 meters. With every bounce the ball returns to 4/5 its previous height. Tommy’s brother, Eli, is looking straight out of a window with bottom edge at a height of 5 meters, and top edge at 6 meters.
How many times will Eli see the ball appear through his window?
We begin by calculating the heights of the first several successive peaks: 10, 8, 6.4, 5.12, 4.096, etc.
From peak 1 to peak 2 (10m to 8m), the ball appears before Eli twice (once going down and once going up). From peak 2 to peak 3 (8m to 6.4m), the ball again, appears twice before Eli. And from peak 3 to peak 2 (6.4m to 5.12m), Eli sees the ball two final times. In total, 6 times.
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