Download Math Hints and Tricks

Math Hints and Tricks
1. When working with measurement conversions, remember DSL: Divide Smaller Larger:
Divide if going from smaller to larger unit.
Example: 6 feet = ____ yards.
Divide because going from smaller to larger unit.
smaller
larger
2. When converting decimals to percents and percent to decimals remember the alphabet.
D comes before P: to get from D to P move to the right.
P comes after D: to get from P to D move to the left.
Picture a baby’s bottom to remind you to move two spaces.
3. For the less than symbol: Make the word less out of the symbol: <ess.
The point always points to the smaller number; the wider part of the symbol points to the
larger number.
4. Percent Formula: is/of: I comes before O in the alphabet.
Part/whole: P comes before W in the alphabet.
Part
is #
%
Whole
of #
100
5. Cross multiplying (for proportions): multiply the two numbers that are looking at each
other diagonally and divide by what is left.
3 = .86
2=?
2 x .84 = 1.68
1.68 / 3 = .56
6. To measure height in a geometric shape, you measure straight up and down. (You don’t
measure your child’s height leaning; you make them stand up straight.)
7. Coordinate Grids: Points (3,2), (x,y): x is the first number and y is the second number:
x comes before y in the alphabet.
Y axis is up and down: the bottom of the Y is the line continuing down.
8. Equilateral triangle: All sides are equal, all angles are equal. The lines on the capital E
are equal.
9. Isosceles triangle: two sides are equal and two angles are equal. The lines at the top and
bottom of the capital I are equal.
10. Scalene triangle: no sides are equal and no angles are equal. There is nothing the same in
the capital S.
11. Complimentary Angles add up to 90 degrees. Make a 9 by putting a line from the top of
the C to below the bottom of the C. Then the C and the O make 90.
Or: c is before s in the alphabet, 90 comes before 180.
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12. Supplementary Angles add up to 180 degrees. Make the S into an 8.
13. Acute angle: Picture a heart, and think “What a cutie.”
14. Obtuse angle: Picture a wide, obese angle.
15. Hypotenuse: the hypotenuse looks like the slide on a sliding board. It is the longest side;
you can turn you paper around to make it look like a sliding board to help you find the
hypotenuse.
Sliding board
16. Comparing Fractions: the Zig Zag Method: For comparing two fractions to see which is a
larger number or if they are the same.
1
2
3
4
4
6
1x4=4
2x3=6
17. Volume: Fill the letter V with liquid.
18. Area: Draw a carpet and write the word area in it.
19. Perimeter: Picture a picket fence; peRIMeter.
20. Parallel lines will never meet. They are like railroad tracks. Emphasize ll in parallel.
21. Perpendicular lines form the letter T when they meet.
22. Every whole number has a decimal point behind it even though you don’t see it.
Picture numbering your paper from 1 to 10 for a spelling test in first grade.
You usually put a dot after the number, not in front of it.
23. Every whole number can be written as a fraction by putting a tail under it.
4=4
62 = 62
16 = 16
1
1
1
24. Median: the median strip on a highway is in the middle of the road.
25. Diameter of a circle: diameter is a long word and a long line.
26. Radius: radius is a shorter word and a shorter line.
27. Circumference: The fence around the round pool.
28. pi:
circumference
diameter
c before d in the alphabet
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29. Break a math operation into steps, which the student keeps handy while doing problems.
Model working from the steps with the student.
30. For word problems: DRAW A PICTURE.
31. Play Go Fish or Match Games (Concentration) with equivalent fractions, or with fraction,
decimal, percent equivalents. Make the playing cards out of index cards.
32. For flash cards: Place the problem on one side, and the problem
with the answer on the other side. It helps to remember to see the
problem and the answer together. Put addition or multiplication
facts on a triangle; it helps to show the relationship of part to
whole, and the relationship of addition/subtraction and multiplication/division.
33. Mark a ruler, or design a large paper ruler, with all of the fractions marked.
34. Use graph paper for all problems. The graph paper helps to keep numbers lined up
correctly, and makes diagrams easier.
35. To practice graphing: Make the product a house, or the student’s initials, or some other
design. Or draw the design first, then figure out what the points are.
36. Fractions: Think of a fraction, for example 3/5, as three parts of something that has been
divided into five parts. Use visual fractions.
37. Identifying positive or negative slope: Place your elbow on the table with the hand held
upright. Swing your arm like a windshield wiper. It swings to the right it’s a positive
slope. It swings to the left, it’s a negative slope.
38. Multiply by 9: Take one away from the number that is not a 9. That number goes first.
The second number of the answer is the number you must add to the first number to equal
9. (The numbers in the answer in 9 x # always add to 9.)
39. Consider the rules for multiplying (and dividing) with signed numbers:
a positive times a positive is a positive
a negative times a negative is a positive
a positive times a negative is a negative
a negative times a positive is a negative
Change "positive" to "good" and "negative" to "bad" and add "people" and you get:
When good things happen to good people, it is a good thing
When bad things happen to bad people, it is a good thing
When good things happen to bad people, it is a bad thing
When bad things happen to good people, it is a bad thing.
Much of the previous information is from a presentation Tricks of the Trade for Teaching Math
offered by Susan Bowers at PAACE Midwinter Conference, February 2005.
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Suggestions below are from Thinkfinity Literacy Network: Making Math Manageable
http://literacynetwork.verizon.org/Free-Online-Courses.21.0.html
The sum of three angles in a triangle equals 180o.
A straight line is 180o.
Draw a triangle of any size or shape.
Tear or cut the triangle into three parts, each part containing an angle, as in Figure 1.
Arrange the pieces of the triangle together along a straight edge.
The three angles will form a straight line as in Figure 2.
Factoring Venn Diagram for finding lowest common denominator/multiple, factoring
For adding, subtracting, simplifying fractions.
Write the two numbers you want to factor
on the lines Factors of ___ in the top
circles.
Example: 24 and 18
Factor each number and write the factors in
each top circle.
Ex:
24: 2 x 2 x 2 x 3
18: 3 x 2 x 3
Look for common multiples and write them
in the intersecting area of the lower circles.
2x3
Write the remaining factors for each number
in the isolated part of each circle. 2 x 2 for
24; 3 for 18
To find the greatest common denominator,
multiply the numbers in the intersection.
2x3=6
To find the lowest common multiple, multiply all the numbers in the Venn diagram.
2 x 2 x 2 x 3 x 3 = 72
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Math Hints from Help Yourself
Decide where you need help, and decide what is most important for you to improve.
Start on that first.
Select a strategy for improving, and practice it several times.
If that strategy doesn’t work, select another strategy to try.
Stop confusing + and – signs.
Circle the sign before you start work.
Darken the sign before you start work.
Write out the word plus or minus next to the sign.
Talk to yourself as you do the problem.
Keep numbers lined up on the paper.
Use graph paper.
Turn lined paper on its side.
Use a strip of paper to cover up all except the column on which you are working.
Write the numbers in the correct order when you copy them to your own paper.
Proofread.
Say the numbers out loud as you write them.
Have someone read what you wrote.
Memorize number facts.
Chant the number facts in rhythm.
Keep tables nearby and use them.
Work from facts you know to answer ones you don’t know.
Use tricks:
Multiplying by 5 always ends in 0 or 5.
Multiplying by 10 always ends in 0.
Multiplying by 2 or multiples of 2 always ends in an even number.
When multiplying by 9: The sum of the digits in the answer always equals 9.
6 x 9 = 54
5+4=9
Practice estimating.
Hints with word problems
Read the entire problem before trying to solve it.
Read the problem out loud.
Draw a picture or diagram.
Lightly cross out information you don’t need to solve the problem.
Circle the remaining numbers and their units.
Underline the question.
Reword the question.
Decide on the operations needed: +, -, x, /
Estimate the answer.
Follow the Five Step Plan:
1. Read the problem and decide what information you need.
2. Decide what math operations you need.
3. Estimate the answer.
4. Do the problem and label the answer.
5. Check the answer.
This information is summarized from:
Sonbuchner, Gail Murphy. Help Yourself. Syracuse, NY: New Readers Press, 1991.
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Math Hints from Math and Numeracy Listserv
LINCS Discussion Lists
http://lincs.ed.gov/lincs/discussions/discussions.html
An "expression" is simply a recipe for calculating something -- it describes a specific sequence
of computations to be carried out one step at a time.
If you evaluate a numerical expression you will get a specific number (its VALUE), or you will
be stopped in the process because something is missing, or impossible, such as dividing by zero.
Think of equivalent expressions as different road maps to arrive at the same destination. Most
students have taken a different route home to help visualize this idea. Both trips begin and end at
the same place. Illustrate on mapquest.com.
The symbol = means what most dictionaries say "equal" means, "having the same weight or
value." It does not mean "is the same as" or "two different names for the same thing."
Think "Equals means Balance," not "Equals means The Answer."
Illustrate the idea of balance visually by showing the equals sign as a kind of fulcrum; put the
"answer" in the fulcrum spot and show an expression on either side, such as 5+1 = 6 = 2+3, as
an in-between step to 5+1 = 2+3 .
Or the equals sign lets you "translate" a phrase from one side of the answer to the other.
The letter “stands for” the number we don't know yet.
Think of a variable as a placeholder for an unknown value.
In an equation such as x = 6 - 2, calling 'x' a variable can seem something of a misnomer. In
ordinary speech, if something is variable, then it is allowed to change, but in the equation x = 6 2, x can have only one value: 4.
Explain exponentiation as serial multiplication, just as multiplication is serial addition. Thus 4 ×
5 = 4 + 4 + 4 + 4 + 4 and 4 ^ 5 = 4 × 4 × 4 × 4 × 4.
Demonstrate the value of parentheses:
If I earn $5 an hour and I worked 6 hours one day and 7 hours the next, I tend to appreciate the
value of writing 5 x (6 + 7) rather than 5 x 6 + 7.
Calculators and order of operations:
Different calculators work differently. Practice with the calculator you have. Demonstrate the
differences with different calculators, and discuss the different results. Ex. 3 + 4 x 5 Correct
answer: 23; answer on some calculators 35.
Note: The calculator used in GED test centers is the Casio FX 260 solar understands the order of
operations. You type a math expression exactly as it is written with two exceptions. In an expression
such as 2( 3 +4), the multiplication key must be inserted between the 2 and the open parenthesis. The
second exception is when a vinculum (-----) is used as a division sign. Any expression above this bar and
below the bar must be placed in parentheses to tell the Casio that the expressions above the bar and
below the bar must be resolved first before the division is done. Otherwise the Casio will divide the last
term above the bar with the first term below the bar. It will treat the Vinculum as a solidus (/).
A frequent problem occurs when students are learning the quadratic formula. They'll enter -3^2 ... and
wonder why their answer is wrong, because the calculator used -9 as the answer.
http://mathjourneys.com/slideshows.html Powerpoints describing math topics.
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Notes from Everyday Opportunities to Think Algebraically
presented by Lynda Ginsburg Math at Teacher Institute December, 2011
Introduce algebra concepts:
Review one step addition/subtraction equations:
 Identify the whole in the equation.
o The whole in a subtraction problem is in front of the minus sign
o The whole in an addition problem is at the end of the problem.
 Rearrange addition into subtraction.
 Rearrange subtraction into addition.
 Write an equation to match a situation.
 Practice different ways to subtract.
Students are more willing to review if the review is related to algebra.
Marking for confidence.
 Glance at problems that are incorrect; try to see where the student got off track.
 Comment first on examples where students got the right answer.
o This problem is correct. Tell me your thinking here.
o Get the student to articulate the strategy or thinking pattern used.
o Ask questions to bring out the areas where the students made mistakes on the
problems that were incorrect.
 Ask students to look back at the first incorrect problem.
o Often students see their mistake themselves.
 Comment that finding your own errors is an important math skill.
Combining signed numbers
When teaching integers don’t use the term adding or subtracting integers, use the phrase
combining signed numbers. Getting the add and subtract words out of the way, allows students
to focus on, “If the signs are the same, add and keep the same sign. If the signs are different,
subtract and keep the sign of the larger number.
Take the student’s way of finding the answer, and describe the math properties they were using.
Banana is .19 and drink is .88. What is the cost of snack?
(.19 + .88) or (.88 + .19) The order doesn’t matter for addition. Commutative property
Relate to algebra:
x+y=y+x
or b + d = d + b
Estimate:
.20 + .90 = 1.10, then subtract .03, = 1.07
Look for ways to make an easier problem.
3 x 4 x 25
You don’t have to do it in order, because multiplication is commutative.
First do 4 x 25 = 100; 100 x 3 is easier than 12 x 25.
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Negative x negative = positive
Look at patterns in Four Square.
positive x negative = negative
X
4
3
2
1
0
-1
-2
-3
-4
4
16
12
8
4
0
-4
-8
-12
-16
3
12
9
6
3
0
-3
-6
-9
-12
2
8
6
4
2
0
-2
-4
-6
-8
1
4
3
2
1
0
-1
-2
-3
-4
0
0
0
0
0
0
0
0
0
0
-1
-4
-3
-2
-1
0
1
2
3
4
-2
-8
-6
-4
-2
0
2
4
6
8
-3
-12
-9
-6
-3
0
3
6
9
12
-4
-16
-12
-8
-4
0
4
8
12
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Graphing
Look at sample graphs from various sources, such as USA Today, for examples of how to set up
graphs (variable vs independent variable).
Look at the exaggeration in scales; what looks like a huge zigzag in the graphed line might vary
only 50 over 10,000, for example.
What is the sample? Ex downtown Philadelphia vs all of PA
Encourage students to keep questioning until they truly understand.
Work collaboratively.
Students need to talk about their work, explain it to someone else, see another strategy. In adult
ed nothing is lost by helping others; it is not competition, with only one person being successful.
Math is often organized trial and error as problem solving.
Look at everything through the viewpoint of algebra; how can I relate this to algebra, so algebra
is not so scary later on.
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