Im trying to teach a teen mental math. How do I go about doing it?

-She SUCKS at counting anything (addition, multiplication, division) in her head. Shes fairly decent on paper.She needs to develop the visual skills needed to do mental math. Start with manipulatives. Base 10 blocks are commonly used to help students learn numbers and more importantly place value. These blocks uses cubes to represent numbers and place value. Small cubes (bits) are ones. 10 bits make a rod, or one set of ten. 10 rods make a flat square, or one set of 100. Stack 10 flats to make a large cube, or one set of 1000. Using this helps to visually demonstrate the place value of numbers. When she's doing calculations on paper, I bet she's just doing it by the steps with little or no understanding of what's going on. Use base 10 blocks to teach this. When she masters these blocks, she'll have an easier time doing mental math.



So for example, "What exactly are we carrying when we carry the 1 in adding?" Say 54 + 69. That's 5 rods, 4 bits + 6 rods and 9 bits. Lay out the correct count of rods and bits for each addend, then combine the rods and bits. That's 11 rods and 13 bits. But since this is base 10, we cannot have 10 or more in any place value. So we cluster and 'carry over' into the next place value. 13 bits = 1 rod and 3 bits, so we carry over the 1 rod. Now we have 12 rods and 3 bits. Cluster 10 rods to make a flat. Now we have 1 flat, 2 rods and 3 bits OR 1 hundred, 2 tens and 3 ones. Answer is 123.



Don't have base 10 blocks? Use money. Pennies are ones, dimes are 10s, dollars are 100s. Just remember you're counting the cents. So the answer above would be illustrated as 1 dollar, 2 dimes and 3 pennies. 123 cents, NOT as $1.23



Teaching expanded form also helps the understanding of place value, which will help when dealing with bigger numbers.



789 x 23

(700 + 80 + 9) x (20 + 3)



If you understand how to solve the above using the distributive property then you can see how this will help her to understand the more traditional way to multiply where you're multiplying each digit from one factor with each digit from the other factor.



Although the above methods are 'long' when solving, they reveal the inner workings of numbers and may help her to understand the process rather just learn the steps. In time she should be better in doing some of this in her head.



Finally teach estimation to get a rough answer, because mental math is mostly about getting a close answer. What's 15% of $167.89, your typical gratuity at a restaurant. 15 is 10 + 5. So 10% of $170 (rounded) is $17. 5 is half of 10, so 5% is roughly $8 (half of $17). 17 + 8 is 25. 15% of $167.89 is about $25. Quick, what's the final bill with gratuity added? $170 +$25...well 175 + 25 is 200, but I'm adding 170 not 175 (5 less)...so 5 less than 200 is 195. The total bill is about $195. If you want to be more accurate, from 195 subtract 2...why? 170 is 2 more than 168...thus the final bill would be closer to $193.
Hi:



try have her visually a sheet of paper and have her visually see the the number and do it like she is writing it on that sheet of paper. and say the answers



another way is to visually beads or dots in her head she can do addition and subtraction that way



if you show her a Chinese or Japanese Abacus than work with that is easier for for her to do mental addition, subtraction,multiplication and division and in some case squares,square root and cube and cube roots this the easiest way to do that due to in simplicity ( all you are do is moving bead up and down along with the top ones )



I hope this helps