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Mental Math Tutorials

Tips and tricks for mastering basic math facts

CarQuiz challenges players to solve math equations quickly
like 13x17 or 124-89. Can you answer these in your head in just a few seconds? Of course you can!

The tutorials below are an example of how to solve these equations quickly without pen and paper. These tutorials are to help kids with Math Practice and to help play CarQuiz Math Game. The techniques on these pages take time to master, but once learned, will last a lifetime, and make all other math classes easier.

 


Addition Examples:

48 + 96 = 40 + 90 + 14 = 130 + 14 = 144

When adding 2 digit numbers together, try adding numbers in the tens place first, then add on the remaining single digit result. Working from the ones place up through the answer to the tens and hundredths place is a common method of calcuation, but can be slower. Try to stack the numbers in your head. Stack the tens over the tens and the ones over the ones. Separate an equation like this in to simpler equations.

This is more of our thought process...

57 + 84 = 50 + 80 or 130, added to 7 + 4 or 11. Stack 130 over 11 in your head. 130 + 11 = 141

28 + 62 = 20 + 60 + 10 = 90. First calculate the tens place and add the result of the ones place.

53 + 49 = 50 + 40 plus the result of 3 and 9 or 12. 90 + 12 = 102

 

We made a video of CarQuiz gameplay from start to finish. In this video we talk out loud how we solve the math equations.

YouTube Gameplay video with voiceover
on how to solve the mental math equations.

In the video the addition calculations include 1 and 2 digit numbers. For many of the equations, I quickly decide if the ones place of the 2 numbers adds up to 10 or more. If it does I know to add a 1 to the total of the tens place. If the ones place of the 2 numbers adds up to 9 or less, I make that calculation and add the tens place. This is one way to quickly calculate the addition of 2 numbers.

It is very important to memorize your addition facts from 1 to 9. Know them by heart. Avoid counting on fingers and counting out loud. Memorize facts like 3+4 and 7+8. There are less than 50 addition facts you need to memorize and you probably already know many of them. Memorize 1+1, 1+2, 1+3, etc., then 2+2, 2+3, 2+4 etc., then 3+3, 3+4, 3+5 and so on. If you commit these to memory, all other calculations will be so much easier!

 


Subtraction Examples:

124 - 89

124 - 89 = 124 - 90 + 1 = 34 + 1 = 35

When subtracting a 2 digit number from a 3 digit number, round the 2 digit number to the nearest 10, subtract that from the 3 digit number and make the adjustment for rounding.

124 - 90 is easier to solve than 124 - 89. 124 - 90 = 124 - 100 + 10 =
24 + 10 = 34 plus the 1 (for rounding 89 to 90) = 35

This is how we break it down to explain it, but not the exact thought process that happens. It's more like this:

I see 124 - 89 and think 124 - 90 instead. 12 - 9 is 3 (or 120 - 90 is 30).
34 plus 1 is 35.

 


Multiplication Examples:

13 x 17

13 x 17 = (17 x 10) + (17 x 3) = 170 + 51 = 200 + 21 = 221

This is how we break it down to explain it, but not the exact thought process that happens in the 10 seconds or less we have to answer the equation during the game. It's more like this:

13 x 17 = 170 + 51. 30 gets me 200 and 21 is left over. 221.
17 x 3 is an equation we've memorized.

--or--

13 x 17 = 130 + 70 + 21 = 200 + 21 = 221

 

As you are memorizing your multiplication facts, don't get intimidated by how many there are to learn. From 1 to 9, there are 72 possible multiplication facts to memorize (9 integers x 8 integers). Once you master your 1's, 2's and 5's there are only 30 multiplication facts left to memorize!

 


Division Examples:

132/12

When dividing numbers in your head try to divide the denominator - the number at the bottom or to the right of this equation in to the top number. 12 is less than 1 (in the 132), so divide 12 in to 13 (the first 2 numbers of 132). 1 time with 1 left over. Take the 1 left over and tack on the 2 in 132, resulting in 12. 12 goes in to 12 once. The answer is 11.

84/7

7 goes in to 8 once with 1 left over. Tack on the 4 from 84 to get 14. 7 in to 14 is 2. The answer is 12.

119/7

7 goes in to 11 (from 119) once, with 4 left over. So the 1st number in the answer is 1. With 4 left over, tack on the 9 from 119. 7 in to 49 is 7, which is the 2nd number in the answer. The answer is 17.

210/7

7 is less than 2 in 210. So divide 7 in to 21. The result is 3, the first number in the final answer. With zero remaining, tack on the 0 in 210. 7 in to 0 is 0, the 2nd number in the final answer. The answer is 30.

64/4

4 goes in to 6 (from 64) once, so 1 is the first number in the answer. With 2 remaining, tack on the 4 and divide by 4. 4 in to 24 is 6, the 2nd number in the answer. The answer is 16.

 


As you practice:

It is important to remember that these techniques take time to master. Once you practice, you will get the hang of it. It is equally important to master memorizing the multiplication table from 1 to 9 as well as addition facts from 1 to 9. You probably already know half of these facts, so you don't have the entire list to learn! You need to solve 7x9 as quickly as you solve 2x2.

You can solve equations like 7 x 8 faster by memorizing your doubles like 7 x 7 = 49. So 7 x 8 is 49 + 7. Most people can multiply 2x2 or 5x2 quickly. 8x7 and 9x6 can be solved just as quickly. Memorization is the only way!

CarQuiz is the perfect game for this type of mental math practice. For example, players can choose Normal mode to practice multiplication from 1 to 9. Challenge mode expands the range of numbers used in the equations, and Hero mode is even more challenging.

Younger players can start in Normal mode while older players can try Challenge or even Hero mode. The trick is to memorize multiplication, addition and subtraction with 1 thru 9, along with a few efficient methods of complex calculations. Then, you'll be able to answer CarQuiz equations with ease!

 


Working with 6
Be sure to work on your addition facts with 6, learning how to split 6 in to 1+5, 2+4, and 3+3 so adding 6 to any number becomes easier. For example, adding 6 to 15 ... 5 gets you 20 with one more to go ... 21.

When subtracting 6, use this same technique. 24 - 6 for example ... subtract 4 gets you 20 with 2 to go. 18.

When multiplying with 6 it is best to memorize your facts from 1 to 9 so all other equations become easier. Memorize 6x2, 6x3, 6x4, etc. and be sure to practice them backwards as well. 2x6, 3x6, 4x6...

A great way to work with 6 is to think in dozens. So 2 6's is 1 dozen. 4 6's is 2 dozen or 24.

 


Math Monster 7 Multiplication with 7
Use the easy to remember 7x7=49 when solving 7x8 or 7x6, because 7x8 is (7x7)+7 and 7x6 is (7x7)-7. Try this trick until you memorize the answer to equations like 7x8 and 7x6.

 


Math Monster 8 Working with 8
The 8 is great, but you might not know it. The '8' is seen in many tricky equations like 8x9 or 8x6 that require memorization.
For now, you can try the same trick as with 7's.
8x9 = (8x8)+8


And don't forget 8x6 is also 6x8 which is 48.
A little rhyme to remember... 6x8 makes 48.

8 is 2 cubed. 2x2x2=8 or 2 to the 3rd power.

8 is .125 of 1 or 12.5%
so 1/8 is 12.5% of a whole, or half a quarter.

For larger equations of addition and subtraction learn how to split 8 in to
1 and 7, 2 and 6, 3 and 5, & 4 and 4.
Master these facts and adding 8 to any equation gets easier.
25 + 8 ... 5 gets you 30 and 3 is left over. 33. 5 and 3 is 8
37 + 8 ... 3 gets you 40 and 5 is left over. 45.

See! The '8' monster is not so scary. He just has a complex personality!

 


Math Monster 9 Working with 9
One fun trick when multiplying by 9 is to subtract 1 from the other number and add the remainder (the remainder of subtracting the result from 9). It works with all single digits from 2 through 9.


4x9. Subtract 1 from 4 to get 3. Subtract 3 from 9 to get 6. 4x9 is 36.
5x9. Subtract 1 from 5 to get 4. Subtract 4 from 9 to get 5. 5x9 is 45.
7x9. Subtract 1 from 7 to get 6. Subtract 6 from 9 to get 3. 7x9 is 63.
Use this trick until you master your 9's in multiplication.

 


Find out more about CarQuiz at carquizgame.com

Questions? email info@smilemorestudios.com

 

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