"Mental math" means performing calculations "in your head." The ability to do mental calculations is an invaluable skill and is used almost unconsciously by most adults. Fifth grade boys should already know the basics of mental math, but they will benefit from consistent practice, as well as explicit instruction in specific mental math strategies. Fifth grade boys are particularly receptive to learning how to impress their friends with mental math "tricks," and they enjoy being able to perform calculations with speed.
To reinforce the concepts being learned, fifth graders should practice mental math calculations on a daily basis. Five to ten minutes of practice per day is a good rule of thumb. Emphasizing that there is more than one way to arrive at a correct answer will free students from the restriction of having to solve a problem the "right" way. Likewise, discussing how the students arrived at an answer helps students begin to understand relationships between numbers and number facts or operations.
One of the easiest strategies to remember is when adding three consecutive numbers, the sum is three times the middle number. Another strategy, the "breaking up the numbers" strategy, utilizes regrouping: one of the addends is broken up into its expanded form before being added to the other addend. For example, 35 + 27 might be calculated as: 35 + 20 is 55 and 7 more is 62. A similar strategy is the "compensation strategy" in which you substitute a number for one that is more easily computed mentally. For example, 63 + 18 could be calculated as (63 + 20) - 2.
A good subtraction strategy for fifth grade boys is visualizing the numbers on a number line. For example, to subtract 16 from 92 you need to move 4 segments from 16 to 20, then another 70 segments to make 90, then another 2. The answer is 4 +70 + 2 = 76. Or, when there is no need to carry, try the "front-end" subtraction strategy where you subtract from left to right. To subtract 372-121, think 300 - 100 =200, 70-20 = 50, and 2 -1 = 1.The answer is 251.
Multiplication strategies are efficient and easy to learn. For example, multiplying by 9 is really multiplying by 10 minus 1. For example, 9 x 32 = 10 x 32 - 32 = 320 - 32 = 288. You can use the same strategy to multiply by 99: just multiply by 100 - 1. To multiply by 10 you just need to add a zero at the end of the number. To multiply by 5, multiply a number by 10 and then divide by two. For example, 13 x 5 = (13 x 10)/2 = 130/2=65.
Knowing the connection between percentages and fractions is invaluable to fifth grade students. For example, 20% is 1/5 and 25% is 1/4. So to find 20% of a number, just divide it by 5. Another good fifth grade strategy is to divide the dividend into parts. For example, 2150/5 = (2000/5) + (150/5) = 400 + 30 = 430. The "think multiplication" strategy is good for estimating answers to division problems. For example, to divide 4812 by 8, think what number you multiply 8 by to get 4812. Eight times 600 is 4800.
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