• Throughout the year, students learn different strategies to help them approach math problems. Here is a list of different math strategies you may encounter while helping your children complete their homework.

WORD PROBLEMS

Work Backwards
Draw a Picture
Create a Table
Estimate/Round
Write an Equation
Find a Pattern
Relate it to a Simpler Problem
Make a Graph
Make a List
Guess and Check

Act it Out

Draw a Bar Model

BAR MODELS - Bar models allow children to create a visual representation to solve their
wordproblems. Most of the children will either create a part/part/whole bar model, or a
comparison bar model. It is important to label each bar, and decide which operation is
used to find the missing section.

NUMBER BONDS

Visual Representation showing that two parts make a whole. Cover one "part" up to help
with subtraction problems. Can be used for fact families.

Counting on - start with the higher number, then count up to find the sum

Doubles - two of the same number - these should be memorized

Doubles plus one - just like doubles plus one more. Use your double fact then add one
more.  (As students get older, they refer to these as "doubles" as well).

Using a Base Ten Frame - Using the visual of a ten-frame. A ten-frame is a rectangle
with ten boxes inside. When half of the boxes are filled the students easily identify that as
"5." When they are all filled the students identify that as "10." This allows the students to
visualize other numbers as well.

Decimals - line up the decimals - "the hula."
(Helps with addition and subtraction of decimals)

For remembering place value - words get longer as they move to the right of the decimal.

Adding Bigger numbers - use base ten blocks (easily drawn) and show how you can
regroup.  (Units, Longs, Blocks: Ten units = One Long. Ten Longs = One Block)

Commutative Property - The property states that you can change the order of the
addends, but you still have the same sum.

Associative Property - The way in which you group the addends does not affect the sum.

Identity Property - Any number plus zero is equal to that number.

SUBTRACTION

Count up - when you are subtracting numbers that are close to each other,
count up from the smaller number. (the numbers must be close to one another)

Count back - when you are subtracting 1,2, or 3 from the larger number. Often
a number line helps the child visualize this process.

Doubles - Use your knowledge of doubles, helps you subtract from the total.

(like fact families)

Decimals - Line up the decimals

Subtracting bigger numbers - use base ten blocks to help visualize borrowing
from other place values. Visualize breaking down a larger base ten blocks into
its pieces (a 1 hundred block into 10 tens) or (1 ten into 10 ones).

Subtraction Across Zero - Visual representation using base ten blocks is helpful.
Show the necessity of borrowing all the way from the left side, and continuing to
take one away, break it apart, and then have only nine (not ten) left as you move
to the right.

Trouble with REGROUPING, try this:  take the number and subtract 1, then
subtract regularly, and then add one at the end. For example: 4,000 - 285. Turn it
into: 3,999 - 285 = 3,714. But, then add one more back to the difference
(since you subtracted it originally) to make the final answer 3,715.

DIVISION

Division with 10, 100, 1000 - See below (Multiplication with 10, 100, 1000)

Partial Quotients

Area Models

MULTIPLICATION

With decimals - First multiply (as if the decimals are not there). Count how many
digits are to the right of the decimal in each number, and then move the decimal
over from the right that many times.

Commutative Property - the ability to reverse the factors and still have the same product.

Associative Property - the way in which you group the factors does not affect the product.

Property of One - any number multiplied by one equals itself.

Property of Zero - any number multiplied by zero equals zero.

Multiplication with 10, 100, 1000 - anytime you multiply a number by a multiple of 10,
we follow these 3 simple rules:
1. Hide the zero, multiply, bring back the zero.
For example: 20 x 6 =
1. Hide the zero (2 x 6).
2. Multiply (2 x 6 = 12).
3. Bring back the zero (120).

Distributive Property - Distribute the digit evenly amongst both digits in the
parenthesis. Will arrive at the same product.

MONEY

Counting Up - starting with the amount of money you have and counting up to
find your total (often used with problem solving)
(For example: A jump rope cost \$3.86 cents. You paid with a \$5 bill. How much

Change: \$1.14

ROUNDING

Rounding Song -
0,1,2,3,4 Round that Number to the floor

5, 6,7,8 and 9 Pump it up and you'll be fine

Rounding Rhyme -
0 to 4 - Touch the floor

5 to 9 - Climb the Vine

Number Line - plot your points on a line with a low ten/hundred/thousand
and a high ten/hundred/thousand

House Rule - Underline the Given place value (draw a house around it)
Look to the right (at the neighbor/helper)

Mental Math

Compensation- altering numbers to make mental math easier

Compatible Numbers - numbers that easily combine to form multiples of 10
ex. (3 and 7; 16 and 24; 18 and 12)

Breaking Apart - break down numbers into their place values to make math easier.
For example: 73 + 24 = (70 + 20) + (3 + 4) = 90 + 7 = 97

ODD/EVEN

Song -
0, 2, 4, 6, 8 Being Even is just great

1, 3, 5, 7, 9 Being Odd is really fine!

MEASUREMENT

When making conversions between units of time, length, capacity, or mass,
some students may learn to SLIDE TO DIVIDE...that means when going from
a SMALLER unit to a LARGER unit, they divide.
For example, if solving the problem; 120 seconds = _______ min,
we would divide 120 by 60 because we are moving from a smaller unit to a larger unit.

On the other hand, when going from a LARGER unit to a SMALLER unit,
we do the opposite, or INVERSE operation, which is multiplication.
For example, if solving the problem; 2 mins = _____ sec.

we would multiply 2 by 60 because we are moving from a larger unit to a smaller unit.

KHDBDCM - Metric Units - works for ALL units of metric measurement.
Stands for: King Henry Died (Basically) Drinking Chocolate Milk
Kilo Hecto Deka Base unit Deci Centi Milli

FRACTIONS

numerator / denominator ("D"enominator stays "D"ownstairs)

Reducing Fractions - find a number that can divide into both the numerator and
denominator (for older students, find the GCF). Divide both by that factor until
the only common factor is "1."

Equivalent Fractions - Use fraction strips (make sure both whole bars are of equal size.
OR
Think: Like bunkbeds, if you multiply/divide the numerator by a factor, you
MUST ALSO multiply/divide the denominator by the SAME number

Adding Fractions - denominators MUST be the same. Then add straight across

Subtracting Fractions - denominators MUST be the same. Then subtract straight across.

Multiplying Fractions - multiply numerator by numerator. Multiply denominator by denominator.

Dividing Fractions - Change the division sign to a multiplication sign. Since you change
the operation to the inverse, you also have to create the inverse of the second fraction (flip it).
Then multiply the two fractions.

Changing improper fractions to mixed numbers - (numerator divided by denominator)
Divide the numerator by the denominator

Changing mixed numbers to improper fractions - multiply the whole number by the