Roger Antonsen

01 Similarity

How can two figures be the same, even though they look different? Roger and Andreas talk about what similarity means, that two things have the same shape.

02 The Equality Sign

It is easy to use the equality sign incorrectly. Roger and Andreas solve equations and talk about why it is so important to use the equality sign correctly. What does it really mean for two things to be equal?

03 Multiplication is Repeated Addition

One way to understand multiplication is to think of it as repeated addition. Roger and Andreas talk about how we can easily write 2+2+2+2+2+2+2+2+2+2.

04 Multiplication is Also Scaling

Multiplication is not just repeated addition. Roger and Andreas discuss how we can look at multiplication as stretching and shrinking (scaling).

05 Percentages and Permille

What does percentage mean? Why is 50% exactly half? Roger and Andreas talk about what percentages and permille mean and how percentages can be shortened.

06 Can All Numbers Be Written as Fractions?

Can all numbers be written as fractions? Or are there numbers that can't be written as fractions? Are all numbers exactly fractional?

07 Puzzles and Problem Solving #1: Buckets

Roger and Andreas discuss how we can attack a difficult problem by first solving a simpler version of the problem.

08 What Are Functions?

What is a function? Roger and Andreas pretend to be functions and try to guess who the other one is. How do you write down functions?

09 What Are Prime Numbers?

Roger and Andreas talk about why we can look at prime numbers as the smallest building blocks among numbers, and how other numbers can be broken down into prime numbers.

10 Undoing and Finding the Opposite

Roger and Andreas discuss how plus and minus are opposite operations, in the same way as multiplication and division, and talk about why we say we can't divide by 0.

11 The Art of Thinking Backwards

When we calculate backwards, plus becomes minus and multiplication becomes division. Roger and Andreas talk about how we think backwards to the answer and how this relates to equations.

12 What is π Really?

What is π really? How can you explain and define – in a simple way – what π is? And why is π not equal to 3.14?

13 Fibonacci Numbers

Fibonacci numbers are one of the most well-known number sequences. Roger and Andreas discuss how we create Fibonacci numbers and other exciting number sequences.

14 Puzzles and Problem Solving #2: Bottle of Soda

Even the simplest tasks can create trouble if we don't think carefully about what the task is actually asking for. Roger and Andreas demonstrate how easy it...

15 Perfect Numbers

What do we mean by perfect numbers, and how many of them are there? Roger and Andreas talk about numbers with very special properties, and how rare such numbers can be.

16 Decimals of π

Why do many say that π is an infinite number? Is there a pattern in the decimals of π? How many decimals do we actually need?

17 Shortening Fractions

How do we shorten fractions? Is 6/8 actually the same as 3/4? Can 3/4 be shortened? Roger and Andreas talk about ways to shorten and simplify fractions.

18 Squares, Triangles and Area

Roger and Andreas try to find out exactly why the area of a triangle drawn inside a rectangle is exactly half the area of the rectangle. How can a task be broken down into smaller pieces.

19 Prime Number Factorization

How can numbers be broken down into smaller pieces? Are there multiple ways to do it? And what does this have to do with prime numbers? Roger and Andreas explore dividing numbers and why it is wise to think of prime numbers when shortening fractions.

20 Improper Fractions are also Fractions

Roger finds it a bit strange that fractions are called improper. His favorite fraction is 4/3, and it is "improper". What is actually proper and improper fractions? Are there fractions that are not proper? How can an improper fraction be divided into an integer and a proper fraction?