 The Oakland Public Schools
 Math Strategies All Grades (Parents please read)
Manito Math
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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 CheckAct it OutDraw a Bar ModelBAR MODELS  Bar models allow children to create a visual representation to solve theirwordproblems. Most of the children will either create a part/part/whole bar model, or acomparison bar model. It is important to label each bar, and decide which operation isused to find the missing section.
NUMBER BONDSVisual Representation showing that two parts make a whole. Cover one "part" up to helpwith subtraction problems. Can be used for fact families.
ADDITION
Counting on  start with the higher number, then count up to find the sum
Doubles  two of the same number  these should be memorizedDoubles plus one  just like doubles plus one more. Use your double fact then add onemore. (As students get older, they refer to these as "doubles" as well).Using a Base Ten Frame  Using the visual of a tenframe. A tenframe is a rectanglewith 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 tovisualize 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 canregroup. (Units, Longs, Blocks: Ten units = One Long. Ten Longs = One Block)Commutative Property  The property states that you can change the order of theaddends, 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.Use addition to subtract  Use your knowledge of addition facts to subtract(like fact families)
Decimals  Line up the decimalsSubtracting bigger numbers  use base ten blocks to help visualize borrowingfrom other place values. Visualize breaking down a larger base ten blocks intoits 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 totake one away, break it apart, and then have only nine (not ten) left as you moveto the right.Trouble with REGROUPING, try this: take the number and subtract 1, thensubtract regularly, and then add one at the end. For example: 4,000  285. Turn itinto: 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.
DIVISIONDivision with 10, 100, 1000  See below (Multiplication with 10, 100, 1000)
Partial Quotients
Area Models
MULTIPLICATIONWith decimals  First multiply (as if the decimals are not there). Count how manydigits are to the right of the decimal in each number, and then move the decimalover 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 theparenthesis. 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 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
ROUNDINGRounding Song 0,1,2,3,4 Round that Number to the floor5, 6,7,8 and 9 Pump it up and you'll be fine
Rounding Rhyme 0 to 4  Touch the floor5 to 9  Climb the Vine
Number Line  plot your points on a line with a low ten/hundred/thousandand 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
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/EVENSong 0, 2, 4, 6, 8 Being Even is just great1, 3, 5, 7, 9 Being Odd is really fine!
MEASUREMENTWhen making conversions between units of time, length, capacity, or mass,some students may learn to SLIDE TO DIVIDE...that means when going froma 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 anddenominator (for older students, find the GCF). Divide both by that factor untilthe 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 changethe 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 denominatorChanging mixed numbers to improper fractions  multiply the whole number by thedenominator, 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!***