Welcome to the HMH math activities hub where you can find engaging math lessons and activities for every grade level. Explore the activities shown below, or visit our full teaching resources page to find even more ideas for your classroom and school.
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When you think of spies and secret agents, you might think of lots of things; nifty gadgets, foreign travel, dangerous missiles, fast cars and being shaken but not stirred. You probably wouldn't think of mathematics. But you should.Cracking codes and unravelling the true meaning of secret messages involves loads of maths, from simple addition and subtraction, to data handling and logical thinking. In fact, some of the most famous code breakers in history have been mathematicians who have been able to use quite simple maths to uncovered plots, identify traitors and influence battles.The Roman GeezerLet me give you an example. Nearly 2000 years ago, Julius Caesar was busy taking over the world, invading countries to increase the size of the Roman Empire. He needed a way of communicating his battle plans and tactics to everyone on his side without the enemy finding out. So Caesar would write messages to his generals in code. Instead of writing the letter 'A', he would write the letter thatcomes three places further on in the alphabet, the letter 'D'. Instead of a 'B', he would write an 'E', instead of a 'C', he would write an 'F' and so on. When he got to the end of the alphabet, however, he would have to go right back to the beginning, so instead of an 'X', he would write an 'A', instead of a 'Y', he'd write a 'B' and instead of 'Z', he'd write a 'C'.Complete the table to find out how Caesar would encode the following message:
Easy as 1, 2, 3This all seems very clever, but so far it's all been letters and no numbers. So where's the maths? The maths comes if you think of the letters as numbers from 0 to 25 with A being 0, B being 1, C being 2 etc. Then encoding, shifting the alphabet forward three places, is the same as adding three to your starting number:
For example, encoding the letter 'A' is 0+3=3, which is a 'D'.Coding 'I' is: 8+3=11, which is 'L'.However, you do have to be careful when you get to the end of the alphabet, because there is no letter number 26, so you have to go back to number 0. In maths we call this 'MOD 26', instead of writing 26, we go back to 0.Have a go at coding your name by adding 3 to every letter. Then have a go at coding your name by shifting the alphabet forward by more places by adding greater numbers eg adding 5, then adding 10. Then have a go at decoding. If your letters are numbers and encoding is addition, then decoding is subtraction, so if you've coded a message by adding 5, you will have to decode the message bysubtracting 5.
Treason!If you've got the hang of coding messages by shifting the alphabet forward, then you might have realised that it is actually pretty simple to crack this type of code. It can easily be done just by trial and error. An enemy code breaker would only have to try out 25 different possible shifts before they were able to read your messages, which means that your messages wouldn't be secret for verylong.So, what about coding messages another way? Instead of writing a letter, we could write a symbol, or draw a picture. Instead of an 'A' we could write *, instead of a 'B' write + etc. For a long time, people thought this type of code would be really hard to crack. It would take the enemy far too long to figure out what letter of the alphabet each symbol stood for just by trying all the possiblecombinations of letters and symbols. There are 400 million billion billion possible combinations!This type of code was used by Mary Queen of Scots when she was plotting against Elizabeth the First. Mary wanted to kill Elizabeth so that she herself could become Queen of England and was sending coded messages of this sort to her co-conspirator Anthony Babington. Unfortunately for Mary, there is a very simple way of cracking this code that doesn't involve trial and error, but which doesinvolve, surprise, surprise, maths.
To be fast at maths, you need to avoid writing down long divisions and multiplications because they take a LOT of time. In our experience, doing multiple easy calculations is faster and leads to less errors than doing one big long calculation.
Caroline Delbert is a writer, avid reader, and contributing editor at Pop Mech. She's also an enthusiast of just about everything. Her favorite topics include nuclear energy, cosmology, math of everyday things, and the philosophy of it all.
Cheap artifacts that can be cracked to get mana and/or draw cards. Almost always seen in the context of Second Sunrise decks like Stanislav Cifka's winning deck from Pro Tour Return to Ravnica.[26]
Also known as "Goodstuff.dek" in online variants of magic. "Goodstuff" refers to a deck that is usually built by including the "best" cards in a single deck. "Delver" decks in Eternal formats are a common example of a Goodstuff deck.
A style of play that involves hardcore/dedicated counter-magic. The permission player attempts to counter every important spell the opponent plays, and simply to draw plenty of extra cards to ensure more counters are available. The term "permission" comes from the way the opponent will end up asking whether each of their spells resolves or is countered.
By itself, a ratio is limited to how useful it is. However, when two ratios are set equal to each other, they are called a proportion. For example, 1/2 is a ratio and 3/6 is also a ratio. If we write 1/2 = 3/6, we have written a proportion. We can also say that 1/2 is proportional to 3/6. In math, a ratio without a proportion is a little like peanut butter without jelly or bread.
In math problems and in real life, if we have a known ratio comparing two quantities, we can use that ratio to predict another ratio, if given one half of that second ratio. In the example 1/2 = 3/?, the known ratio is 1/2. We know both terms of the known ratio. The unknown ratio is 3/?, since we know one term, but not the other (thus, it's not yet a comparison between two ratios). We only know one of the two terms in the unknown ratio. However, if we set them as a proportion, we can use that proportion to find the missing number.
The mathematics problem is a bit like Sudoku on steroids. It's called Euler's officer problem, after Leonhard Euler, the mathematician who first proposed it in 1779. Here's the puzzle: You're commanding an army with six regiments. Each regiment contains six different officers of six different ranks. Can you arrange them in a 6-by-6 square without repeating a rank or regiment in any given row or column?
Using some fun strategies while approaching the subject helps parents and teachers to inculcate some interest among Kids. Dedicate time to solve these puzzles and make your day. We tried providing some of the amazing with Answers to help you out. Kids can easily crack these riddles if they pay some concentration, apply critical thinking, and logical reasoning.
Those who love to challenge their problem-solving skills can try out these Math Riddles. Logic Puzzles and Riddles can be great to enhance kids learning abilities and math problem-solving skills ability.
There are many math riddles out there that are easier as well as the ones that need a lot of concentration. But, the kind of satisfaction you get on solving them is much greater. Children can learn to associate concepts and develop lateral thinking with these puzzles.
There are a very large number of special symbols and notations, too many to list here; see the short listing $\LaTeX$ and $\mathcalA_\Large\mathcalM\mathcalS$-$\LaTeX$ Symbols prepared by Dr. Emre Sermutlu, or the exhaustive listing The Comprehensive $\LaTeX$ Symbol List by Scott Pakin. Some of the most common include:
Don't use \frac in exponents or limits of integrals; it looks bad and can be confusing, which is why it is rarely done in professional mathematical typesetting. Write the fraction horizontally, with a slash:
$$\beginarraycc\mathrmBad & \mathrmBetter \\\hline \\e^i\frac\pi2 \quad e^\fraci\pi2& e^i\pi/2 \\\int_-\frac\pi2^\frac\pi2 \sin x\,dx & \int_-\pi/2^\pi/2\sin x\,dx \\\endarray$$
For double and triple integrals, don't use \int\int or \int\int\int. Instead use the special forms \iint and \iiint:$$\beginarraycc\mathrmBad & \mathrmBetter \\\hline \\\int\int_S f(x)\,dy\,dx & \iint_S f(x)\,dy\,dx \\\int\int\int_V f(x)\,dz\,dy\,dx & \iiint_V f(x)\,dz\,dy\,dx\endarray$$
It is worth noting that MathJax should not be used for formatting non-mathematical text. The preferred way for striking out text is to use the HTML strikethrough tag, [text to be striken], which renders as [text to be striken].
If you are asking (or answering) a combinatorics question involving packs of cards you can make it look more elegant by using \spadesuit, \heartsuit, \diamondsuit, \clubsuit in math mode:$$\spadesuit\quad\heartsuit\quad\diamondsuit\quad\clubsuit$$Or if you're really fussy:\colorred\heartsuit and \colorred\diamondsuit$$\colorred\heartsuit\quad\colorred\diamondsuit$$
Some formulas such as $\overline a+\overline b=\overline a\cdot b$, $\sqrta-\sqrtb$, do not look quite right when it comes to vertical spacing. Fortunately, there is more than one way to fix this. One can for instance employ the \mathstrut command as follows: 2ff7e9595c
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