Number SenseTechniques to make your mental math faster

Number Sense

The tips and strategies are used to help make solving math problems easier and faster. It requires memorization and practice to become accurate every time and recognize the rules quickly.Always try to practice using a time limit. Speed and accuracy are important.

Number Sense Scoring

-Numbers are written in pen and must be legible. -Showing your work, mark outs, or overwrites will result in an error.-Each correct answer is 5 points.-Each skipped or missed costs 4 points.-Illegible numbers are errors. Numbers written under the line are errors.

Number Sense Rules

-Starred problems are approximate answers and must be within 5% of the correct answer.-Exponentials must be written out into their full number form. 83 must be written 512.-Fractions must be reduced to their lowest terms.

Squaring Numbers

One of the first skills to learn and memorize is your squares. You should know your first 12 from your multiplication facts.12 = 1 42 = 16 72 = 49 102 = 100 22= 4 52 = 25 82 = 64 112 = 12132= 9 62 = 36 92 = 81 122 = 144

Tip for Solving for a 2 Digit Square

4540

50

-5

+5

X

Take 40 x 50 and multiply.

Then add the square of the number added/subtracted.

5 squared = 25.

Now let’s look at the next set of squares

132 = 192 = 252 =

142 = 202 = 262 =

152 = 212 = 272 =

162 = 222 = 282 =

172 = 232 = 292 =

182 = 242 = 302 =

Learning Perfect Squares and Cubes

After you’ve learned your perfect squares, it is time to learn your perfect cubes from 13 = 1 to 252= 15625. You should learn these in both directions:172 = 289 and the 289

Squaring Numbers Ending in 5

752

1. First two digits - take the first digit and take the digit +1

2. Add the last two digits of 25. (You are squaring the 5.)

7(7 + 1) 25 = 5625

Multiplying Consecutive Tens

35 x 451. First two digits = the small ten’s digit times one

more than the large tens digit.2. Last two digits are always 75.

3(4+1) 75

=1575

Ending in 5….Ten’s Digits are Even

45 x 851. First two digits = the product of the ten’s digits plus ½ the sum of the ten’s digit.2. Last two digits are always 25.

4(8) + ½ (4+8) 25 = 3825

Ending in 5….Ten’s Digits are Odd

35 x 751. First two digits = the product of the ten’s digits plus ½ the sum of the ten’s digit.2. Last two digits are always 25.

3(7) + ½ (3+7) 25 = 2625

Ending in 5….Ten’s Digits are Odd & Even

35 x 851. First two digits = the product of the ten’s digits plus ½ the sum of the ten’s digit. Drop the remainder.2. Last two digits are always 75.

3(8) + ½ (3+8) 75 = 2975

The Rainbow Method

FOIL - First outside inside last

23 x 12

2(1) 2(2) + 3(1) 3(2)

276

Multiplying by 25

32 x 25

1. Divide by non-25 number by 4.2. Add two zeroes.

32 divided by 4 = 800

Multiplying by 50

32 x 50

1. Divide by non-50 number by 2.2. Add two zeroes.

32 divided by 2 = 1600

Multiplying by 75

32 x 75

1. Divide by non-75 number by 4.2. Multiply by 3.3. Add two zeroes.

32 divided by 4 = 8 x 3 = 2400

Multiplying by 125

32 x 125

1. Divide by non-125 number by 8.2. Add three zeroes.

32 divided by 8 = 4000

Multiplying Two Numbers in 90s

97 x 941. Find out how far each number is from 100.2. The 1st two numbers equal the sum of the differences subtracted from 100.3. The last two numbers equal the product of the differences.

100 - (3 + 6) 3 (6) = 91 18 = 9118

Multiplying Two Numbers in 100s

109 x 1061. The first number will always be 1.2. The middle two numbers equal the sum of the units digits.3. The last two digits equals the product of the units digits.

1 9+6 9(6) = 1 15 54 = 11,554

Multiplying a 2-Digit Number by 11

92 x 111. Last digit is the units digit.2. The middle digit is the sum of the tens and the units digit.3. The first digit is the tens digit + any carry.

9+1 9+2 2 = 10 1 2 = 1012

Multiplying a 3-Digit Number by 11

192 x 111. Last digit is the units digit.2. The middle digit is the sum of the tens and the units digits.3. The first digit is the hundreds digit + any carry.

1+1 1+9+1 9+2 2 = 2 1 1 2 = 2112

Multiplying a 2-Digit Number by 111

41 x 1111. Last digit is the units digit.2. The next digit is the sum of the tens and the units digits. 3. The next digit is the sum of the tens and hundreds + carry.4. The next digit is the tens digit + carry.

4 4+1 4+1 1 = 4 5 5 1 = 4551

Multiplying a 3-Digit Number by 111

192 x 1111. Last digit is the units digit.2. The next digit is the sum of the tens and the units digits. The next digit is the sum of the units, tens and the hundreds digit + carry.3. The next digit is the sum of the tens and hundreds + carry.4. The next digit is the hundreds digit + carry.

1+1 1+9+1 1+9+2+1 9+2 2= 2 1 3 1 2 = 21312

Multiplying a 2 Digit Number by 101

93 x 1011. The first two digits are the 2 digit number x1.2. The last two digits are the 2-digit number x1.

93 (1) 93 (1) = 93 93 = 9393

Multiplying a 3 Digit Number by 101

934 x 1011. The last two digits are the last two digits of the 3 digit number.2. The first three numbers are the 3 digit number plus the hundreds digit.

934 + 9 34 = 943 34 = 94334

Halving and Doubling

52 x 131. Take half of one number.2. Double the other number.3. Multiply together.

52 divided by 2 13(2) = 26(26) = 676

Fraction Foil

8 ½ x 6 ¼1. Multiply the fractions together.2. Multiply the outside two numbers.3. Multiply the inside two numbers.4. Add the results and then add tothe product of the whole numbers.

(8)(6) + ½(6) + ¼(8) (½ x ¼) = 53 ⅛

Adding Reciprocals

⅞ + 8/71. Keep the denominators.2. The numerator is the difference of the two numbers squared. 3. The whole number is always two plus any carry from the fraction.2 (8-7)2 = 2 1/56 7x8

Percent Missing the Of _______

36 is 9% of ________1. Divide the first number by the percent number.2. Add 2 zeros or move the decimal two places to the right.

36/9 00 = 400

Converting Base N to Base 10

426 = _____10

1. Multiply the left digit times the base.2. Add the number in the units column.

4(6) + 2 = 26 10