When teaching math, I’ve always found that making it fun helps students better remember various concepts.
This idea led me to start using brain teasers to combine mathematical concepts with the challenge to think outside the box. It’s an exciting way to put the skills they’re learning to use without them even realizing it.
Students enjoy it, and I love seeing them master concepts without just doing endless math problems and drills. It’s a win-win for everybody.
What Makes Brain Teasers So Effective
I’m sure I’m not the only one who loves that sense of accomplishment that comes with figuring out a brain teaser. Students love that too. I’d love to say doing a dozen math problems gives that same feeling, but that isn't true for many students. Brain teasers are just more fun...besides, “teaser” sounds less intimidating than “problem.”
Brain teasers are ideal for boosting brain activity, which is why they’re used to help prevent brain decline. They’re also more fun, which reduces boredom, and we know that when students aren’t bored, they pay more attention and have better focus. Another reason they’re so effective is students are able to apply concepts they’re learning in a more real-world style way. This leads to improved memory:-)
How To Make It Content Specific
The great thing about brain teasers is they’re not set in stone. I see new brain teasers all the time, so that means someone, somewhere has to be creating them. This means if they can do it, so can I (and you). To make them more effective for students, create your own or modify an existing brain teaser to make it more content specific. For instance, a single brain teaser could involve both Geometry and Algebra.
Adding a brain teaser to the end of a lesson that reinforces concepts helps students remember more about the lesson. It’s also helpful to combine concepts over time to build on what students are learning over the course of several weeks or months. ProProfs has a simple tool for creating brain teasers. I recommend just checking out various brain teasers to get an idea of how to write your own or alter one for your needs.
How To Incorporate Brain Teasers
Honestly, I don’t think there’s a right or wrong way to do this. As long as students are having fun and learning, you’ve incorporated brain teasers correctly. Professional Learning Board offers some great tips about incorporating brain teasers, such as:
How To Find Great Brain Teasers
This is probably what you’re most interested in! I could list hundreds of resources here, but I’m just going to list some of the most useful ones related to math brain teasers.
Free Number Puzzle!
Turning decimals into a fun, Sudoku-like puzzle is a great way to help students work their way through the different decimal operations.
I love solving Sudoku puzzles using whole numbers, and I encourage students to work on them as well. But when I replace the whole number with decimal problems, I’m able to create a logic puzzle that also gives students a new way to practice skills that can be a challenge to master.
Sudoku puzzles are fun and interesting. They require students to problem solve, in order to ensure that every row, column and group of squares only has one of each number. Some students develop strategies when approaching a puzzle; some learn to use guess and check quite often:-)
When working with decimals in a Sudoku puzzle, students need to consider their target numbers, as well as how to complete the necessary operation. This makes decimal practice a bit more interesting and engaging than working on one problem after another on a worksheet.
As with whole number Sudoku, I start decimal Sudoku with a few squares filled in, so students have a starting point. (If students have never tried Sudoku puzzles before, I recommend starting with a regular Sudoku puzzle, to teach students how they work.)
So far, I’ve only used a 4 X 4 grid, which makes figuring out the target numbers fairly easy. All of the squares have a decimal problem with a missing addend in them (in this example). Within each 2 x 2 section, there is one completed problem, with the target number of 1, 2, 3, or 4 already filled in. The object is for students to figure out the target number for each square and then find the missing decimal number in each individual square. Every row and column must each contain 1, 2, 3 and 4 as the answers to the decimal problems (these are the target numbers). Every 2 x 2 section must also contain 1, 2, 3 and 4.
For example, on the answer key shown here, you can see the target numbers of 1-4 in each row, column and section, and you can see the completed decimal problems. Everything in black (target numbers and decimal numbers) is given. Everything in green is what the students must find (target numbers and missing decimal addends):
I've only used the addition problems (which actually require them to subtract:-), but I plan to try the other operations as well and create larger puzzles (6 x 6 and maybe 9 x 9).
To make students really think things through, I may mix up the operations! For instance, in a 4 X 4 puzzle, the first column could be two multiplication problems and two addition problems. This should keep students paying close attention.
These could be great to complete on mini dry erase boards - easy to erase any guesses that don't work out!
I'm really liking the math wheel idea, so I created a new wheel for fraction, decimal percent conversions:-)
How to use this resource (this information is also in the free download):
Around the outside of the wheel are the different conversion headings – you can use the wheel to introduce the conversions, filling in just the ones you are covering each day. Or, you can use it to review all the conversions at once. In either case, the wheel can be kept in students’ notebooks as a reference/study tool.
1) I like to begin with decimal to percent and percent to decimal. In the arrows in these sections, you’ll see x 100 and ÷ 100. It think it’s important that students understand that these are the operations being used for these conversions before giving them a shortcut, so I let them use calculators to complete the examples. Once the examples are complete, I ask the students to look for the pattern – what happens to the decimal point in each of these cases?
We decide on the “shortcut” rules together and then write them at the bottom of those sections.
2) The fraction to percent and fraction to decimal sections have the rules written already, so the examples just need to be completed.
I always relate fraction to percent to students grades. By the time we get to this topic during the year, students have been figuring out their grades for months (I never write their percentages on their assessments – they need to calculate
them). They know how to find their percentage if their quiz grade was 6/8 or their test was 48/52. However, sometimes they need a reminder that this official fraction to percent “rule” is the same thing they’ve been doing for months! I have them
write a little reminder in that section - “just like test grades!”
3) For percent to fraction, students need to remember that percent means “out of 100,” so the percent number will always go over 100. Then they must reduce.
4) I find that decimal to fraction is sometimes tricky for students. When they have trouble, I ask them to read the decimal number according to place value (“How do you say this number, using tenths, hundredths, or thousandths, etc.?”). Once
they speak it, they know how to write the fraction – 0.27 is 27 hundredths, which is 27/100. After completing the examples, we discuss the idea that the denominator will be whatever the last decimal place is (10, 100, 1000, etc.) and the numerator will be the digits in the decimal number. We write this rule as simply as possible.
5) Students then complete the 10 problems around the page. Above each number is the conversion to complete (F to P, P to D, etc.) They can then color the rest of the wheel background.
I had a great time coloring my answer key! These could make a fun decoration as well:-)
I hope you can use it!!
Do your middle school math students like to play math games? Mine do, but over the past few years I've noticed that many of them aren't familiar with some of the games I played when I was a kid, like Yahtzee, for example. So, as we started working on converting fractions and decimals, I decided to create a game to make practicing the conversions more fun AND give them some more game experience! I based it on the idea of Yahtzee:-)
Here's how it works:
Students roll four dice, and pair the dice up to create "target numbers" that are either decimals or whole numbers.
For example, a student rolls 1, 2, 4, and 6. From these dice, the student may create any two of the following decimal (or whole) numbers:
½ = 0.5 4/1 = 4
¼ = 0.25 4/2 = 2
1/6 = 0.1666... 4/6 = 0.666...
2/1 = 2 6/1 = 6
2/4 = 0.5 6/2 = 3
2/6 = 0.333... 6/4 = 1.5
Once a player has chosen two target numbers, he or she finds the score by adding the dice that were used for each decimal (or whole number). If the player chose to use 1 and 4 to get 0.25, he or she adds 1 + 4 for a sum of 5 to place in the score column. If the second choice used 2 and 6, to equal either 0.333...or 3, then sum of 8 would go in the appropriate column as the score.
On the next roll, this student rolls 1, 1, 3, and 5. This student can pair 1 and 1, to get 1, and pair 3 and 5 to get either 0.6 or 1.666... The score for 1 is 2 (1 + 1) and the score for 0.6 (or 1.666) is
8 (3 + 5).
In many cases, students' scores will be the same, but some of the decimals can be found with different combinations of numbers (1 and 3 = 0.333..., and so do
2 and 6, so students could have a score of either 4 or 8). Some students will notice this sum difference and go for the combination that will give them the higher score....bringing in the possibility of using some strategy, for those higher level thinkers.
The students have really enjoyed playing this game. They do need a few examples at the start, to understand exactly how the game works, so if you decide to try the game, be prepared to go through a few turns together.
You can create a score sheet like this on your own, or go to TPT and use what I've created. Detailed instructions are included, and a complete answer key of highest and lowest possible scores for each target number are included as well. This is handy to quickly check student score cards as you check in on their games.
If you give it a try, please let me know how it goes!
Math rules. How often have you found that students are taught "tricks" to remember math rules? How often do they make procedural mistakes even though they've "learned" the rules?
I have taught decimal operations for more than 20 years, and I have seen, time and again, students who know how to add and multiply decimals but then follow the wrong "rule" for the operation they are completing. Line up decimal points when adding or when multiplying? "Jump" the decimal point over when adding and subtracting? Or is that multiplying? They don't remember when to use which method to place the decimal point.
So, this year, as we approach the decimal unit, I've been feeling like I don't want to talk about the rules for where/how to put the decimal point. I want to focus on logic. Today that feeling was reinforced when I asked my students to solve 35.2 + 7.489 and then explain why their answer made sense. Here are some of the answers and reasons (I didn't teach this yet, but they learned it last year):
"0.11009 makes sense because I tried my best and if I remember correctly, addition problems you don't need to line the decimals together"
"0.7838 makes sense because when I added I knew that it doesn't matter how it's lined up"
"78.42 - I added 9 and 2, then 1, 8 and 5. Next I added 1, 3, and 7. Finally I added 7 and 0 and I put the decimal in the middle."
"7.841 makes sense because with adding you only have to add the decimals on the top. Then you add and finally add the decimal back in."
"426.89 because I put the decimal point four spaces back because there are four numbers behind it"
"79.41 makes sense because you do it just like an addition problem (that's how I remember it anyway)"
"7.841 makes sense because you add like normal and take the decimal from the farthest out and put it with the answer"
A few correct answers, with reasons:
"42.689 - this makes sense to me because this is how I learned it. You do simple addition, but line up the decimal points"
"42.689 makes sense because I used what my fifth grade teacher taught me, line up decimals, add zeros so everything is lined up and then solve."
"42.689 - I don't know how it makes sense, but it's how I learned to do it."
Of the 120 students in my classes, only 8 said the answer made sense because "35 + 7 is 42" or because "I estimated" or "when we're doing addition, we know we end up with a bigger number."
Now, that doesn't mean that they didn't think about those things, but to them answers seemed to "make sense" when they followed the rules - even if the rules are remembered incorrectly; students got right and wrong answers and they all made sense because that's "how they learned it."
So, what is the point of teaching rules? Especially to those students who are a little weaker in math - if they can't remember the right rule, they can't tell if their answer is reasonable! They need to develop their number sense.
In the past, I have asked students to estimate the answer first, so they know if their answer is reasonable, and I have required them write these estimates on their tests. But we've also talked about the rules. I'm thinking that if I take the focus off the rules and put extra focus on the estimating/reasonable answer idea, students will be better able to identify reasonable answers and will feel less dependent on the rules.
I know that multiplication and division logic will be more difficult. Problems like
23.5 times 4.428, won't be as bad because there are whole numbers involved. This could be estimated as 25 times 4 = 100. So when placing the decimal point in 104058, it should be placed so that the answer is about 100 - not 10, or 1, or 1000.
Now multiplying 23.5 and 0.7 may be more confusing, but this will be the time to help them understand why the answer should be smaller than 23.5....but more than half of 23, since 0.7 is more than 0.5.
I think division will be the most challenging, as far as determining reasonable answers, and I need to think about this one a bit more. However, we have already done this activity I found on YouCubed -"Too Big or too Small Maze Board." In attempting to create the largest number possible (using a calculator to compute), many students have already made the discovery that dividing by a number less than one gave them a larger number, while multiplying by a number less than one gave them a smaller number. No rules were taught - they found this "secret" on their own. This will be great to reference and discuss when we begin working on the multiplication and division of decimals.
We'll see how it goes!
We started our Percent Unit last week and we start with converting between fractions and percents and decimals. I had already made the number line for them with the most common fractions, percents, and decimals, but I figured there was a need for a "foldable" to keep all of the "rules" for converting in one place.
We have already worked on converting decimals to fractions and fractions to decimals, but somehow, as we add new concepts, the students forget how to do these things! It's funny - my team teachers and I never write percents on students' papers any more, but always write their grades as fractions, like 18/23. From the first week of school, we teach the students how to change these fractions into their percentages, and every time they get a graded paper back, they are to find their percentages. So, when we say "Figure out your grade," they can do it. BUT, in math class, if I ask them to change 18/23 to a percent, they just look at me. When I give them the hint, "Pretend it's your grade," they look at me, understanding dawning on their faces! Why do they need that cue? Hmmm.....always a question.
Anyway, to keep the conversion rules all in one place, we made this "fold it up."
The triangles are cut in half, with a different rule and an example under each half.
I'm so glad we made these last week, because our schedule has been screwy for the past few school days! Thursday and Friday we had early dismissal due to parent-teacher conferences, so all math classes didn't meet both days; and today, we had a two hour delay, so all classes were short. The "fold it up" was super-handy as we had to work pretty quickly today! And hopefully, they've used it to help them with their homework tonight...
Hi, I'm Ellie! I've been in education for 25 years, teaching all subject areas at both the elementary and middle school levels.