Is there a largest natural number? And is there one between $7$ and $8$? The set of natural numbers, $\mathbb{N}$, has its own rules that are worth getting clear before you start working with them seriously.
Before you start, make sure you know: Natural numbers (1st ESO)
In the decimal number system, the value of a digit depends on its position. In the number 7 475, state the value represented by the first "7" (starting from the left)…
In the decimal number system, the value of a digit depends on its position. In the number 7 475, state the value represented by the first "7" (starting from the left) and the value represented by the second "7". How many times greater is the first than the second?
The estimated population of a social network in 2023 reached $1.205.040.300$ active users. a) Write how this number is read in words. b) Give its polynomial expansion…
The estimated population of a social network in 2023 reached $1.205.040.300$ active users.
a) Write how this number is read in words.
b) Give its polynomial expansion using powers of base $10$.
c) What is the place value of the digit $5$ in this number?
When an expression mixes additions, subtractions, multiplications, divisions, powers and brackets, the order in which you work is not up to you: there is a fixed order of priority.
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In a mathematical logic challenge, you are given an expression that is missing parentheses for the result to be correct. Place the necessary parentheses so that the…
In a mathematical logic challenge, you are given an expression that is missing parentheses for the result to be correct. Place the necessary parentheses so that the equality holds:
$$5 + 3 \cdot 8 - 6^2 : 4 + 2 = 23$$
Once solved, explain step by step the order of operations you followed to arrive at the result of $23$.
Before the decimal system we use today, numbers in Rome were written with letters. You can still see them on clocks, on the dates of monuments or on the chapters of a book.
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Walking through your city centre, you see a plaque on an ancient monument indicating its year of construction in Roman numerals: MDCCCXCVII. Convert that date into our…
Walking through your city centre, you see a plaque on an ancient monument indicating its year of construction in Roman numerals: MDCCCXCVII. Convert that date into our decimal number system.
Not all natural numbers are equally "interesting": some hide a geometric pattern. You already know the perfect squares ($1, 4, 9, 16, 25\ldots$); there are other similar families, such as the hexagonal numbers.
Also look at palindromic numbers (they read the same forwards and backwards, like $4.774$): they combine conditions on digits with what you already know about expanded form.
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Lucía wants to arrange her collection of $36$ stickers into a perfect square on her album cover. How many stickers must she place along each side of the square so that…
Lucía wants to arrange her collection of $36$ stickers into a perfect square on her album cover. How many stickers must she place along each side of the square so that none are left over? Draw a simple diagram of the solution.
You can do it on paper and send a photo with your answer.
In a logistics warehouse, shoe boxes are arranged to form perfect cubes. If a shelf has a square base of $7 \times 7$ boxes and they are stacked to reach the same height…
In a logistics warehouse, shoe boxes are arranged to form perfect cubes. If a shelf has a square base of $7 \times 7$ boxes and they are stacked to reach the same height to form a cube:
a) How many boxes are there in total on the shelf? Express it as a power and calculate its value.
b) If $150$ boxes are sold, what is the maximum number of boxes that can still form a perfect square on the warehouse floor? How many boxes would be left over in that case?
The Pythagoreans studied polygonal numbers. Look at the following sequence of hexagonal numbers and answer: 1. Draw or describe what the fourth hexagonal number pattern…
The Pythagoreans studied polygonal numbers. Look at the following sequence of hexagonal numbers and answer:
Draw or describe what the fourth hexagonal number pattern ($H_4$) would look like.
How many dots will pattern $H_5$ have?
Knowing that the formula to calculate the hexagonal number in position $n$ is $H_n = 2n^2 - n$, work out the value for $H_{12}$.
You can do it on paper and send a photo with your answer.