Calculadoras
There are "clever" and "silly" calculators. The "clever" ones knows which operation goes first, the "silly" ones don't. Find out which kind is yours doing this operation 2+3·5. Complete on your notebook the following sentence:
My calculator is “......................“ because the result is ... and it should be ...
Formally we say tha our calculator respect (or not) the order of operations.
There are other operations that some calculators don't do correctly, for example: 1/9 · 9. Write the correct answer and the answer given by your calculator.
Use your calculator to find out:
3 - 4 · 5 =
7 + (6 · 52 + 3) =
3 + 6 · (5 + 4) – (–3 + 7 – 2) · 3³ =
9 – 5² + (8 – 3)² · 2 – 6 =
Scientific calculators have more than 25 keys, some of them like "log", "sin" and many others that do weird things. What calculator do you have: scientific or non-scientific one?
If your answer is "non-scientific", you should get a scientific one ASAP.How many digits does your calculator show on its screen? How many keys, at least, do you have to press in order to calculate 0.56 + 0.56 ? Is it possible with six keystrokes?
Perform the following operations without using your calculator. Explain how you did it. Check with the calculator if your answer is correct:
23 · 37 - 13 · 37 = 105 · 105 - 95 · 105 =
27 · 153 + 73 · 153 = 17 · 13 + 7 · 13 =
3 · 7 + 87 · 7 = 34 · 7 + 34 · 6 =
Find out what the following keys does? (or at least, give some information about the possible results): ^, log and sin
¿Qué diferencia hay entre las teclas CE, C, AC y ON? ¿Tienes otras teclas que sirvan para borrar resultados como ← , Clear , DEL , OFF,...? Averigua las diferencias entre cada una de ellas.
Are there two equal numbers whose product is 2? A price for the one who gets closer to 2 without surpassing it. ? · ? ≤ 2.
10. Square root test (only if your calculator has √ key): find out √2 · √2. What do you get? What do you should have got? Calculate the difference between the two results. This test gives you an idea of how precise your calculator is.
Pascalina (1642, Blaise de Pascal). Primera calculadora a base de engranajes.
11. Watch this video by Numberphile team and have a look at the mentioned test and other aspects of some calculators.
12. Calculate by pressing the '=' key once in each subsection:
The price of a 25 euro shirt that is discounted/reduced 12%.
The price of a 5 euro movie ticket after adding a 21% tax.
Calculadora mecánica de Babbage, s. XIX
13. Can you help poor Mariló with this difficult problem?
14. Does your calculator have keys with several functions (for the same key)? Write three examples.
15. How many memories does your calculator have? Do you know how to save a number in its memory? Does whatever is saved get deleted when you turn it off? To answer these questions, try to save a classmate's number. Turn off the calculator and try to show the number in the screen to check if you've done it right.
¿Cuántas memorias tiene tu calculadora? ¿Sabes guardar un número en la memoria? ¿Se borra lo almacenado cuando la apagas? Para responder a estas preguntas intenta guardar el número de teléfono de tu compañero de pupitre. Apaga la calculadora e intenta mostrar ese número en pantalla para comprobar si lo has hecho bien.
Calculadora de Dalton, 1914 (de la Wikipedia).
16. Big and small numbers:
Find out the biggest and the smallest number that your calculator can show.
Work out the smallest positive number and the biggest negative number that your calculator can show.
Type the biggest number that can be squared.
Find out the smallest number whose square root seems to be equal to this number.
Multiply 1 000 000 000 · 1 000 000 000. Write down the result on your workbook and explain it.
17. Use your calculator to perform the following subtitutions:
x² - 4x + 1, when x = 3 (2)
4x³ - 6x² + 2x - 5, when x = -3 (-173)
x⁴ + 4x² - 3x - 10, when x = 3
5x⁴ + 2x³ - x² + 3x - 9, when x = -2
18. Numbers that don't fit.
Type in a 5 and add zeros until it doesn't fit on the screen anymore. Save the last number to be a 1. Add it by the same number. What do you get? What is the exact solution? Is there some variation? What is it due to?
Find 2 numbers whose sum does not fit on the screen.
Do the following operations:
11 234 567 801 + 4 567 890 =
12 345 678 910 - 7 437 =
0,123 456 789 + 10 =
10 · 0,998 877 665 5 =
99 999 999 + 0,1 =
0,000 000 1 : 2 =
10 000 001 : 4 =
19. Does your calculator have a statistics mode?
Curta (calculadora de 1948 que cabía en la palma de la mano)
20. (Only for scientific calculators) Calculate 1/8. Put the mode on fixed with 2 decimals and calculate again. What happens differently? What does that mode do? Put it in normal mode.
21.Indicate what the following keys are used for (if they aren't on your calculator, the professor will tell you which keys are equivalent): EXP, Min, M+, x!, +/-, ab/c, x1/y, shift o inv.
22. Guess without using your calculator the result of these keys sequences. Explain what happens:
3 5 + 4 0 × - · 5 =
3 × 6 C 7 =
7 Min 9 × 3 M+ RM
23. Calculate 1 / 0 . What do you get? Why do you think this happen? Try dividing by numbers closer and closer to 0 to find an answer to the last question.
24. Find out five different operations that show an error as an answer.
25. Complete the following table with the help of your calculator:
Anita, 1961, primera calculadora electrónica de escritorio (foto de MaltaGC, en la Wikipedia)
26. La letra del DNI. Para calcular la letra del DNI se divide el número por 23 y se le asigna una de las siguientes, en función del resto obtenido:
¿Están todas las letras del alfabeto?
¿Por qué se divide por 23?
Calcula la letra de tu DNI para ver si funciona. Trata de "adivinar" la letra del DNI de cinco de tus compañeros.
27. Imagine the square root key doesn't work. Calculate the square root of the following numbers with two decimals and explain how did you proceed without that key: 10, 5 000, 1 000 000 y 357.
28. Las teclas de memoria (I):
Suma 568 + 237 + 1 265 usando la tecla M+ .
¿Qué valor aparecerá en pantalla al pulsar 3 4 M+ 2 1 Min 5 M+ MR ?
29. Juego de acercarse (para dos jugadores). Cada uno escribe un número de tres cifras en su papel, sin que el otro lo vea. Se sortea quién empieza el juego. Al que le corresponda escribe en la pantalla de la calculadora un número de una cifra. A partir de ese momento, cada jugador, por turno, tiene que pulsar una tecla de operación (+, -, x ó /), un número de una cifra o de dos y el signo igual. Gana el que se acerque más a su número en cinco turnos. Si se llega al número exacto se obtienen 5 puntos y si sólo es una aproximación, se obtienen 3. Gana la partida el que pasa de 20 puntos.
30. Juegos de palabras. Comprueba qué números al visualizarlos al revés parecen letras. Encuentra palabras que puedan formarse con esas letras. Busca una operación que dé como resultado una de esas palabras-números. Inventa una historia relacionada con todo ello, similar a la que se muestra en el siguiente vídeo.
31. Broken calculator.
32. Calculator bingo.
33. Start by putting one million (1000000) into the display of your calculator. Can you reduce this to 7 using just these six buttons - the 7 key and add, subtract, multiply, divide and equals as many times as you like? What is the shortest way can you find to do it? (Source: nrich.maths.org).
34. Find a fraction that is as near as possible to 0.46291 where numerator and denominator are both less than 100. How about numerator and denominator values both under 40? What about, instead of division, multiplying two numbers to get as near as possible to 789?
35. Find the closest fraction to pi, with both, numerator and denominator, less than 100.
36. Imagina que sólo funcionan las teclas de operación y el 1 y el 0, esto es, no puedes teclear cualquier otro dígito. ¿Con qué operación podrías conseguir el número 120? Consigue el mismo número con cuatro ochos.
37. Consigue:
111 con seis seises.
123 con siete seises.
100 con todas las cifras del 1 al 9.
Una multiplicación cuyo resultado esté entre el peso de Venus y el de la Tierra.
38. Closer. Play in pairs. Each of the players think of two digits. With the four of them it's formed a number, written in scientific notation.
For example, if the chosen digits are 1, 2, 7 and 9, you get 1.27 · 10⁹, in that order.
Then, all the players try to get close to this number by performing operations with the digits 1, 2, 3, 4, 5, 6, 7, 8 and 9. It's allowed to use every digit just once and any other key of the calculator. The final result must be rounded to three significant figures. It is forbidden to join two or more digits together to get a new number (i.e. 2 and 4 to get 24).
For example, (3⁴)⁵ - 6¹² - 9⁸ = 1266955344 ~ 12700000000 = 1.27 · 10⁹.
Other example: if the chosen number is 3.47 · 10², you can get it by performing 3 · (6+4)² + 7 · 8 - 9 = 347 = 3.47 · 10².
Score: for each round, the player who get the exact number wins 3 points. The player who get closer wins 1 point.