Mathematics for Children

Proportions and Geometry

In previous posts we talked about proportions and their main applications. Here, we will approach it in geometric form and it is very important for continuity in mathematics studies. These concepts were heavily addressed by Euclid, who was a Greek mathematician who lived in the 3rd century BC and who was responsible for creating the geometry we know today. This type of situation appears a lot in geometry, for example, triangle similarity, Thales’ theorem, among others.

August 15, 2022 Read

Quantity Analysis

Dimensional analysis is very important for high school subjects, more specifically, physics (phýsis). In this post, we will show that 80% of the physics entrance exam questions are solved by dimensional analysis. The author who initiated dimensional analysis was Galileo Galilei. Below we present the work of Galileo. Galileo’s work Galileo Galilei Linceo Dimensional Analysis (Descartes, Leibniz, Newton and Galileo) Today, we study in physics the units of the International System (SI), which emerged as a global standardization. All of this is due to globalization, or specifically, world trade.

August 14, 2022 Read

Fees

In cases where a ratio is compared in different units, such as speed, telephone tariff, among others. This ratio (division or quotient), which is a rational number, is called rate. Common rate examples: Example of Rate with Speed a dog travels 2 meters in 2 seconds; rate is 1 meter per second $$\text{taxa} = \dfrac{2~m}{2 ~s} = 1 m/s$$ Example of Rate with Telephone Tariff a telephone company charges R$ 1,00 per minute; rate is R$ 1,00 per minute $$\text{taxa} = \dfrac{R\\$~ 1,00}{1 ~\text{min} } = R\\$ ~1,00/ \text{min}$$

August 13, 2022 Read

Rule of 3

The rule of three is widely used by chemists for stoichiometric calculations. This rule is taught in elementary school and was used by Galileo in his work Variar Opera Mathematica of 1679. Help us build the math website. Donate as much as you can. Donation via Mercado Pago. Donation via PagSeguro. Below are some historical fragments about the rule of three:

August 12, 2022 Read

Proportions

The first concepts of proportion were seen in the works of Nicomachus of Gerasa, composed of two books, with Pythagorean doctrine. The concept of proportion is linked to the art of comparing and historically we have seen these concepts in: Ancient Egypt, Greece (Pythagorean School) in Crontona between the 6th and 5th centuries BC. Euclid’s Elements at approximately 300 B.C. Ancient Egypt Pythagorean School Euclidean School In Euclid’s Elements, he defines ratio as a kind of relationship with respect to size between two quantities of the same kind. This concept seemed a bit confusing to later generations of civilizations.

August 7, 2022 Read

Percentage Basics

The garden of a hundred flowers Color 25%, 50% and 75%. How many flowers are colored in each case? Explore the controls and explain what changed in your own words. Ative o JavaScript para ver esta figura interativa. Percentage can be defined as a quantity in relation to another evaluated over a hundred. This quantity is a value between zero and 100. It is present in the news, financial markets and everyday life in general.

August 3, 2022 Read

Operations with Rational Numbers

Positive rational numbers were widely used in Egypt in the centuries before Christ. After years as nomads, homo sapiens began the agricultural revolution and with it, the need to use rational numbers. Their use in land markings was the main need for the use of these numbers. On the Nile River, land flooding forced land to be re-marked. In this way, rational numbers were used to remark the lands. Definition Until now, in the history of mathematics, we have noticed that rational numbers are represented by a fraction in which:

July 22, 2022 Read

Introduction to Rational Numbers

The notion of dividing is present in our daily lives, for example, dividing a pizza is a simple process that reminds us of the notion of fraction. The first word we see in fraction is half or half. $$\dfrac{1}{2}$$ History of the representation of rational numbers The great mathematicians took a long time to understand the representation of rational numbers, including the notation for fractions. Next, we show the types of writing for fractions.

July 19, 2022 Read

Introduction to Integers

A journey that crosses zero Start at −3 and apply +5. Then try returning 4 units. Where does each route end? Em telas pequenas, deslize o gráfico na horizontal para ler os detalhes. Explore the controls and explain what changed in your own words. Ative o JavaScript para ver esta figura interativa. In the study of naturals, we use numbers to count, including zero. Now let’s expand this set with negative numbers and know the integers. Naturals are represented as:

July 18, 2022 Read

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