Mental Math Tutorials Tips and tricks for mastering basic math facts
CarQuiz challenges players to solve math equations quickly 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 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 = 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).
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. 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 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.
Multiplication with 7
Working with 8
8 is 2 cubed. 2x2x2=8 or 2 to the 3rd power.
8 is .125 of 1 or 12.5%
For larger equations of addition and subtraction learn how to split 8 in to See! The '8' monster is not so scary. He just has a complex personality!
Working with 9
