Math Strategies

  • 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.  


    Work Backwards
    Draw a Picture
    Create a Table
    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.


    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 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.


    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.

    Use addition to subtract - Use your knowledge of addition facts to subtract
    (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 with 10, 100, 1000 - See below (Multiplication with 10, 100, 1000)

    Partial Quotients

    Area Models


    Partial Products

    Area Models

    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.


    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 do you receive? 
    Start with $3.86. 
    Add one penny : 3.87
    Add one penny : 3.88
    Add one penny : 3.89
    Add one penny : 3.90
    Add one dime: 4.00
    Add one dollar: 5.00

    Change: $1.14 

    Counting Change - start with the bill/coin of highest value


    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)
    Use your Rounding Song
    Add zeros

    Mental Math

    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


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

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


    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


    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.
    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
    denominator, add the numerator. Put the answer over the original denominator.

    PROBABILITY - chance of outcome/ TOTAL 

    ***If there are other strategies you have questions about, please feel free to call me and ask! I am happy to explain them to you!***