Skip to main content

THE FOUR FOURS!

Hi All,

Here's a mathematical exploration that will literally make kids want to know what a factorial is and how to use it! I know, crazy, right? But, true!

I love this one. It is particularly good for a class that is learning about order of operations, so typically 5th or 6th grade, but you can use it all the way through high school because it is just so darn intriguing and fun. You should try it too. It does give your brain a workout, and makes you think flexibly with numbers.

The premise is simple. You get four "4's." Using any of six operations; addition, subtraction, multiplication, division, square root, or factorials, write mathematical expressions to represent all the integers from 0 - 25. You may use operations as many times as you want and you may use a variety of operations within an expression. You can also use brackets and parentheses as needed.

For example to represent 16, you could write 4 + 4 + 4 + 4
Remember, 4 is the only digit you can use, and you can only use it 4 times in the expression. In fact, you must use it four times.

How about trying to make 0. I like 44 - 44. Yes, that's right, you can put those 4's together to make a 44. Another way to get 0 is (4 x 4) - (4 x 4).  Or (4 + 4) - (4 + 4). Play around with the operations and the numbers, the parentheses and the brackets.

There is usually more than one expression that will yield a particular number. Try to list them all. And you don't have to go in order. Start with any number 0 - 25.

This is a very popular exploration and is done all over the world from elementary school through graduate school. Lots of answers are available online, but try to steer your students away from that and let them explore.

Most kids don't know factorials, but it is really very simple. 
4 factorial is written 4! It means 4 x 3 x 2 x 1 = 24
3! is 3 x 2 x 1 = 6
2! is 2 x 1 = 2

Most kids don't need to know this for the math they will be doing in upper elementary grades, but it is very handy in trying to create a higher number using just a 4. It's simple to understand and kids think it's pretty cool to know.

I'm also attaching a practice sheet on order of operations as this is really helpful in setting up those expressions. Order of operations is crucial with this one!

Try this out before you look at the answer sheet! Some numbers come easy, some are pretty darn hard. 

Some students will use a lot of paper working out possible expressions. I would suggest using a white board and markers or you can make copies of the manipulative sheets I've attached here with all of the operations, parentheses, brackets, and braces you might need. As well as the four 4's of course. You can cut these up and make cards. This really supports playing around with the possibilities. 

Here's the link to the worksheet and answer sheet and all that other neat stuff. https://drive.google.com/file/d/1gnEZsowpCLMbqZwGVYKFdbWSxQ7oZxmx/view?usp=sharing

Take care everybody! Have fun with this.
Best,
Bob

Comments

Popular posts from this blog

What Does Not Belong?

 Hi All,   "What Does Not Belong" is such a great little concept and can be applied to so many different areas of math as well as other content areas. Great little game when you are waiting, like for buses to be called or for the day to begin. Also a great game for long car or bus rides where if there are no written numbers or pictures you really have to do the mental math. Present a group of numbers. Start with maybe six. Say, 10     56     17     122     4     98 Ask the players to identify which number does not belong and have them explain why. We want players to look at the characteristics of the numbers and compare them to try to find the selection criteria or "rule" so they can determine which does not belong. For example, we have a mix of 1, 2, and 3 digit numbers, so it's not the "rule" is not the number of digits. We have five even numbers and only one odd number. That's it! 17 does not belong,...

EGG BOX SHAKE! IT'S WHATEVER YOU WANT IT TO BE.

Hi All, Shake it up! Egg Box Shake is noisy and fun! That's a big plus right there for most kids. Students like to create and keep their own math tools, and this is a great opportunity to do that as well. And, teachers can adapt the game to fit any level or mathematical operation. Win. Win. Win. Egg Box Shake originated as a coin identification and addition game for grades 1 – 3. I had students bring in an egg carton from home and then provided them with play money or coin stamps, ink pads, and card stock. They stamped out pictures of the coins onto card stock, front and back images, and then cut out the pictures. Students glued these pictures into the bottom of the twelve sections of the egg carton. Each player would get two beads, beans, chips, marbles, or any other small manipulative. They put these into the box and closed it. They then shook the box. When they stopped they opened it and saw where the beads had landed. Players added those two coins o...

What's in a Name? A lot of Math!

Hi All, Welcome back! With school starting one way or another in various parts of the country, I figured it was time again to bring back the math blog. No matter what's going on or how it's going on, I'm hoping this content will still be useful to you.  So, let's talk about names! When classes start, one of the first things both teachers and students must learn about each other are their names. A child's name is a very powerful and important thing. It's also a great springboard to learning. Kids are always interested in their own names. "Names Add Up" is an easy activity for K-2 (though older kids like it as well) that combines counting, addition, and money, as well as vowel and consonant identification. You'll need a pile of pennies and nickels. Explain to children that for this activity vowels will be worth a nickel and consonants will be worth a penny. Have children take the coins that correspond to the letters in their first names and...