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I love seeing students problem solve and brainstorm. There is something about seeing the concepts connect and the light in their eyes as they say, "don't tell me!"

When reviewing the order of operations (or as a holiday filler, or when 1/2 the class is gone on a field trip, or.) I love to give my students the four 4s challenge.

The idea is to reach the given number using the order of operations using only four 4s.

I like to give lots of examples of different combinations to get their minds thinking. Here a few examples to help your students get started:

$1=\frac{44}{44}$
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$9=(\frac{4}{4})+4+4$
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$47=(4!+4!)-\frac{4}{4}$
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$60=4*4*4-4$
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$81=(4-(\frac{4}{4}))^{4}$
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$100=4*4!+\sqrt{4}+\sqrt{4}$
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I like to give them time to play with them. Some of my classes will need more examples, and some will not want one more answer. I allow them to work together. I love hearing their conversations as they work. I like to give them a leveled challenge, and I don't allow this challenge to go home or let anything that connects to the internet as the answers are too easy to find.

If they can get at least ten additional answers, they get ___ points

If they can get at least 20 additional answers, they get ___ points

Etc.

This strategy allows me to personalize it for each person's needs if necessary.

I love seeing the students think outside of the box to get these answers. It truly is amazing! The students that are not usually my "star" performers will often be excellent at this because they don't have to follow an algorithm. Each problem is different.

Before we finish, I like to ask some questions to help them see the patterns.

• Which numbers are the hardest to find?
• Is there anything special about prime numbers?
• Can there be more than one answer for each number? Prove it.
• What other patterns can you find?
• Where there strategies that helped you move quickly through this sheet?

I love the development of language during these discussions. It took a fun puzzle and increased it's value even more.

Here is a great answer key with a lot of variations: http://mathforum.org/ruth/four4s.puzzle.html

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