Children

Least Common Multiple

Numbers were also the subject of Euclid Books VII to IX of Euclid’s Elements study properties of numbers. Divisors and multiples are part of a very old investigation that remains useful today. Your turn to investigate: Imagine two wheels marking steps: one from 4 to 4 and the other from 6 to 6. List the positive multiples. Where do brands meet for the first time? Discover the historical source on MacTutor, from the University of St Andrews.

July 18, 2022 Read

Even and odd numbers

The doubles dance Assemble pairs with caps. Add one: an even number turns into an odd one. Twelve is even. Can you rearrange these balls into six pairs? To define who starts in a football match, hide and seek, among others, children use the odd and even game. Who has never used odd and even for hand games. The first use of this concept was in ancient Greece, with the Pythagorean school.

July 10, 2022 Read

Greatest Common Divisor

Euclid and the shrinking problem In the Elements, written in Antiquity, Euclid presented a procedure for finding the greatest common divisor. Instead of listing all the divisors, we can work with smaller and smaller divisions and remainders. Your turn to investigate: Investigate 24 and 18: 24 = 1 × 18 + 6; then 18 = 3 × 6 + 0. What was the last nonzero remainder? Compare with the square explorer in class. Discover the historical source on MacTutor, from the University of St Andrews.

July 10, 2022 Read

Prime numbers

Eratosthenes and the sieve of numbers Eratosthenes lived in the 3rd century BC and is remembered for a method of finding cousins: the sieve. Think of a sieve that removes composite numbers and leaves the primes visible. Your turn to investigate: Write the numbers 2 to 20. Preserve 2 and cross out its multiples greater than it; then do the same with 3. What numbers are there? Discover the historical source on MacTutor, from the University of St Andrews.

July 10, 2022 Read

The number zero

Look at what’s not there Zero is not a forgotten space: it informs you that there are no objects in the box. Now imagine removing the four units: they remain 20. Zero records that there are no loose units. Zero also has a story Brahmagupta registered calculation rules with zero at 628 in India. These include adding zero without changing the number and multiplying by zero obtaining zero. The history of zero involves contributions from different peoples. Your turn to investigate: Write 25 and 205. What does the zero say in the second number? Represent both on the class abacus. Discover the historical source on MacTutor, from the University of St Andrews.

July 10, 2022 Read

Geometry with sequences of numbers

Numbers using Geometry The next row will have 5 points. How many points will the next triangle have? In Elements it shows numbers in geometric perspective. In previous posts, we saw the product of one natural number by another as the area of a rectangle or square. Property Distributive An example of numbers associated with geometry, we can find triangular numbers.

July 5, 2022 Read

Introduction to Geometry

A walk through the city of shapes Look at doors, tiles and streets: where do you find lines like these? Draw a house with these shapes. What figures appear on the doors and windows? Introduction The Greeks of ancient civilization were one of the most famous populations in the art of thought. They were responsible for the golden age in philosophical, scientific, political, social and artistic ideals and had a decisive influence on the Western world.

July 5, 2022 Read

Quadrilateral

Detectives from all four sides Run your finger along the outline of each figure. Count four sides and four vertices. Draw a grid of 3 by 4 squares: it will have 12 squares. This is an area idea. In the previous post, we talked a little about the book Elements of Euclid, which is made up of 13 books.

July 5, 2022 Read

Triangles

Introduction In the previous post, we defined polygons and served to define quadrilaterals and their properties. Now, let’s define triangles, for this, we need the concept of polygons. A triangle is a three-sided polygon, in which we use straight segments for the sides. A diagonal of a convex quadrilateral divides it into two triangles. Vertices: can be defined as meeting points between the sides of a triangle. Generally speaking, vertices are meeting points between sides of any polygon. In particular, a triangle is formed by 3 vertices.

July 5, 2022 Read

Division

Share without losing anyone Check that everyone received the same amount. To divide equally is to share fairly. With 13 marbles and 3 people, each person receives 4 and has 1 left over. The rest are less than 3. Bread, sharing and mathematics The Rhind papyrus includes problems of bread distribution. Sharing was a way of transforming everyday needs into mathematical questions. Your turn to investigate: In a game inspired by these problems, distribute 15 paper loaves among 5 people, without cutting the loaves. How many does each person receive? Discover the historical source on MacTutor, from the University of St Andrews.

June 15, 2022 Read

OBMEP 2018 - Second Phase

In this post we will resolve the OBMEP 2018 questions with comments. Question 1 A crazy machine turns two fruits into one fruit, as follows: Turns two apples into an orange; Turns two oranges into one orange; Turns an apple and an orange into an apple. Q1 Item a a) How many times should the machine be used to turn three apples into one apple? Data: Initially we have 3 apples.

June 19, 2020 Read

OBMEP 2019 - Second Phase

In this post we will resolve the OBMEP 2019 questions with comments. Question 1 Marcelo throws five rings onto a wooden peg, one at a time. When the ring hits the pin, he earns points, as shown in the table below. When the ring doesn’t hit the pin, he doesn’t get any points. The figure shows five throws made by Marcelo, in which only the blue and green rings hit the pin. Note that the green ring was the last one thrown, as it was on top of the others

June 19, 2020 Read