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
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
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