See if you know these 10 mental math tricks that will help you teach homeschool mental math with confidence!
Give these ten problems a try, then see below for answers and explanations.
Mental Math Quiz
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30 + 60 =
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46 + 55 =
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176 + 9 =
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Double 147
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377 + 8 =
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34 – 27 =
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23 × 9 =
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17 × 25 =
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12 × 100 =
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366 ÷ 6 =
Answers
1. 30 + 60 = 90.
Trick #1: Use place-value thinking to make this problem a snap. 3 tens + 6 tens = 9 tens, or 90. Use dimes or base-ten blocks to demonstrate this idea for your kids.
2. 46 + 55 = 101.
Trick #2: Use place-value to take numbers apart and put them back together again. Mental math doesn’t mean stacking numbers in your head and solving them like you would on paper! For this problem, you might first add 40 + 50 = 90. 6 + 5 = 11, so the answer is 90 + 11, or 101.
3. 176 + 9 = 185
Trick #3: To add 9, simply add 10 and then subtract 1. For this problem, 176 + 10 = 186. Since I added 1 more than I need, I simply subtract 1 from 186 to find the answer: 185.
4. Double 147 is 294.
Trick #4: Double each digit separately and add them together. Double 100 is 200. Double 40 is 80. Double 7 is 14. Add them all up (200 + 80 + 14) and you get 294.
5. 377 + 8 = 385
Trick #5: Add larger numbers by making several smaller (and easier) jumps. Landing on multiples of 10 makes this strategy especially helpful.
For this problem, you don’t have to add 8 all at once. Instead, do it in 2 jumps: First add 3 to 377 to get 380. Then, you still need to add 5 more, so 380 + 5 = 385. (This works well for subtraction, too.)
6. 34 – 27 = 7
Trick #6: Subtract by adding. When you’re subtracting numbers that are pretty close together, it’s often easier to change the problem to an addition problem. Instead of trying to take away 27 in this problem, think of it as “27 plus how many more equals 34?” Combine this with trick #5 (add in smaller jumps) and you’re good to go!
7. 23 × 9 = 207
Trick #7: Multiply in parts. Remember the distributive property? The formula is complicated, but the idea is simple. Think of 23 × 9 as 23 boxes of chocolates with 9 chocolates in each. (Mmm, chocolate.) First, figure out how many boxes are in 20 of the boxes: 20 × 9 = 180. Then, figure out how many chocolates are in the other 3 boxes: 3 × 9 = 27. So, the answer is 180 + 27, or 207.
8. 17 × 25 = 425
Trick #8: Think quarters. This one looks really hard, until you think of the 25s as quarters. If you had 17 quarters, how much money would you have? Well, every 4 quarters makes a dollar, so 16 of the quarters would be 4 dollars, or 400 cents. The extra quarter adds 25 cents, for a total of 425 cents.
9. 12 × 100 = 1200
Trick #9: Think $100 bills to multiply hundreds. Okay, this one is a little easier. But for kids, the reasoning behind it can still be tricky. Use $100 bills (from your Monopoly game, not your wallet!) to show your child that you can tack on 2 zeroes to the other factor every time you multiply by 100.
10. 366 ÷ 6 = 61
Trick #10: Break up the dividend (the first number in the problem). Instead of getting out pencil and paper for long division, break 366 into 300, 60, and 6 and figure out how many times 6 goes each part. 300 ÷ 6 = 50, 60 ÷ 6 = 10, and 6 ÷ 6 = 1. So, the answer is 50 + 10 + 1, or 61.
How’d you do? Have a question about one of the tricks? I’d love to hear in the comments!
If you’d like more help teaching mental math to your kids, check out: How to Avoid These 3 Common Mental Math Myths
Love the quiz! I learned a lot 🙂 Thanks
Did everything in the same way
I solved most of the problems correctly, but not the way you explained them! I am going to start Right Start math with my second grader and Kindergartner this year. I am excited to learn to think differently about these basic facts. Thanks for the articles!
Glad you enjoyed it, Holly!
Great tips! Thank you! Here is one more: On the last question, it is faster and simpler to look for facts you know within the problem and solve. For example, if you look at the first two digits from left to right (36, in this case), you can access quickly if this is a fact you know. Since 36÷6=6, I can solve for 360÷6 and then add the answer to 6÷6=1. Grouping can certainly make the process faster.
That’s a great way to approach it, too, Amy! (And a really fruitful conversation to have with a child: Why do both approaches work? Which is more efficient? Do both approaches work for all sorts of division problems?)
Happy Math!
Kate
Is there a supplement program that covers basic mental math so our family wouldn’t need to switch from Rod & Staff. Kids are doing well finally and I don’t want to change again next year.
Hi Donna,
If it ain’t broke, don’t fix it! 🙂 Rod and Staff does include some mental math in the older grades, but it can use some supplementing.
Mental Math in the Middle Grades (for about grades 4 to 6) is my favorite supplement. It’s out of print, but used copies are very cheap.
Happy Math!
Kate
I did nearly every problem in my head the way you explained it, and it’s because of mental math problems like these that I’m such a big supporter of the Common Core math method. It basically teaches mental math, but I think people don’t understand that. Instead, they say, “Why would you use such a complicated method to solve such an easy problem?” Well, it only looks complicated on paper, and it only looks complicated when you’re learning it using simple problems. Once you get to more complicated problems, simplifying the numbers by rounding down and up and subtracting or adding makes it SO much easier to do in your head. Thanks for sharing this!
Glad you enjoyed it, Kasey!
Love these examples! I am a math teacher at a classical charter school. I thought about 5 of them differently than you described. Problems like this are wonderful for number talks. I will put up a problem on the board and have students solve it. Then, I will have them share their answers and write their thought process for each one in a different color. There aren’t enough hours in the day to look at every problem from every angle, but number talks provide an opportunity to really go deep on a problem. The mental math I use might not make as much sense to a student as the mental math that a classmate used.
Such a great way to do mental math in a classroom!
Question 7 – I might have used distribution if it had been 23 x 7, but to me multiplying by 9 is automatically multiplying by (10-1). For some reason, calculating 230-23 comes much easier to me than the multiple steps of distribution.
(This might be my engineering bias, too, rather than mathematician, to always think order of magnitude first).
That’s a great way to do question 7! And also one of the beauties of mental math–it teaches kids so many ways to think flexibly about numbers. (Although since you’re an engineer and clearly have a deep understanding of math, I’ll nit-pick: you are actually using distribution, just with subtraction. 🙂 )
Happy Math!
Kate
Any advice for a mama who learned math the old way and has little mental math skills? I am just starting MWC1 with my 6 year old. Thanks!
My main advice is to trust that you are totally capable of understanding mental math and growing your skills. Your kid can do it, and so can you!
Happy Math!
Kate
Did them in my head. Been doing math in my head forever it seems. The trick is how to teach others. I think maybe teaching to visualize the problem would help but I’m not sure. Any suggestions?
I substitute teach in Colorado and have noticed most 5th graders are lacking basic math skills.
At nearly 42 years old I just realized I have no idea on how to do mental math. For me it’s always been putting it “on paper” in my mind and getting frustrated when I can’t keep the picture clear enough to keep up with it! I wonder if that is part of the reason that trying to find the right path for a math curriculum has been so stressful?
You’re definitely not alone, Amber! I hear from a lot of moms who discover that teaching homeschool math helps them develop their own mental math skills right along with their kids’.
Happy Math!
Kate
366 ÷ 6 = 61
could we split it to 6/6 = 1. 36/6 = 6 so 61?