 Cobb Middle
 Notes

TO COMPARE NUMBERS
Find the first number on the number line
Find the second number on the number line
If the second number is to the right use less than <
If the second number is to the left use greater than >
TO ORDER NUMBERS
Put a dot for each number on the number line
If least to greatest put an arrow from left to right
If greatest to least put an arrow from right to left
Start at eh binning of the arrow and write the number of the dots in order following the path of the arrow
TO CLASSIFY RATIONAL NUMBERS
Look for a decimal point or a fraction bar
If you see one, the number is a rational number only
If not and you see a negative sign, then the number is an integer and rational
If you don’t see a decimal point, fraction bar or a negative, then the number is whole, integer and rational
Find Least Common Multiple
1. List multiples for each number
2. Circle the numbers that are the same on each list
3. Identify the smallest of the circled numbers
Adding Integers
1. Check the signs of both numbers
2. If both numbers have the same sign add the values3. If they have different signs subtract the values4. Answer will have the sign of the biggest numberSubtracting Integers1. Leave the first number the same2. Change subtraction to addition3. Change the sign of the second number4. Add like normalBreaking down word problems1. Read problem carefully2. Circle the numbers3. Underline question4. Box math action words5. Expression or equation needed?6. Solve the problemMultiplying Integers1. Multiply factors to get product2. Use tic tac toe chart to find the sign of the productDividing Integers1. Divide like normal2. Use tic tac toe chart to find the sign of the quotientConverting fractions to decimals1. Write the fraction2. denominator (long division symbol) numerator.003. Divide like normal4. If it was a mixed number, add the whole number back in front of the decimalMultiplying decimals1. Rewrite problem as long number x short number2. Multiply like normal3. Count how many numbers are behind the decimal in the factors do the same for the answer4. Use tic tac toe chart for the signMultiplying Fractions1. Make sure both numbers are written as fractions2. Multiply numerator x numerator to get the new numerator3. Multiply denominator x denominator to get the new denominator4. Use tic tac toe chart for the signDividing Decimals
1. Write problem divisor (long division symbol) dividend2. Move decimal in divisor to the right to make it a whole number3. Move decimal in dividend to the right the same number of places4. Bring decimal in dividend up and divide like normal5. Use tic tac toe chart for the signDivide Fractions1. Make all number fractions2. Keep first fraction the same3. Change divide to multiply4. Flip second fraction5. Multiply straight acrossAdding FractionsIf the denominators are the same1. Keep the denominator2. Add the numeratorsIf the denominators are different1. Make both numbers fractions2. Swoop: Multiply denominators together3. Cross: bottom R x top L4. Cross: bottom L x top R5. Order of operationsAdding Decimals1. Line up the decimal points2. Add like normalSubtracting FractionsIf the denominators are the same1. Keep the denominator2. Add the numeratorsIf the denominators are different1. Make both numbers fractions2. Swoop: Multiply denominators together3. Cross: bottom R x top L4. Cross: bottom L x top R5. Order of operationsSubtracting Decimals1. Line up the decimal points2. Subtract like normalSimplifying Variable Expressions1. Distribute to get rid of parentheses2. Identify variable terms and move them to the left side3. Identify constants and move them to right side4. Do the required operationsTo Factor1. Find a number that can be divided out of both terms2. Write that number outside of parentheses3. Inside parentheses goes quotientsDistributeMultiply the number in front of parentheses times each term inside parenthesesSolving one step equations1. Separate equation at the equal sign2. Identify operation happening to variable3. Do the inverse operation to both sides of equation4. What you do to one side, do to the other5. Answer is variable = numberSolving two step equations1. Split the equation and identify the variable2. Do the opposite of addition or subtraction on both sides3. Do the opposite of multiplication or division on both sides4. Answer is variable = numberSolving one step inequality1. Separate at sign on equality2. On side with variable do the inverse operation3. What you do to one side, do to the other4. Bring the sign of equality down5. If you multiplied or divided by a negative number, flip the sign of equalityGraphing inequalities1. Draw axis2. Place answer in middle of axis3. Circle around number4. If variable is in gator mouth shade right, if number is in gator mouth shade left5. If line is under sign of equality fill in circle, if not leave it blankWriting 2 step inequalities1. Set up problem (time)x+(constant) (total)2. Fill in total amount3. Fill in initial amount4. Last value or time value goes in front of x5. Choose sign of equality based on context cluesSolving 2 step inequalities1. Separate at sign of equality and identify side with variable2. On side with variable do opposite of +/3. On side with variable do opposite of x/ ÷4. What you do to one side do to other5. Bring down sign of equality flip if multiplied or divided by negativeWays to write ratiosword form: 3 to 2Fraction form: 3/2Ratio form: 3:2Way to find equivalent ratios1. Write the ratio in fraction form2. Either multiply or divide top and bottom by the same numberFinding Unit Rate1. Rewrite question as unit1 per unit22. Create division problemfor decimal unit 2 (bracket) unit 1for fraction unit 1 ÷ unit 23. Divide4. Answer followed by unit 1 per unit 2Identifying Constant rate of Change1. Create fractions for each set of datamoney or distance is a numeratortime is the denominatoror in the order it is given in the problem2. Divide each fractionbottom (bracket) top.003. compare answerif same then proportionalif different then nonproportionalHow to create proportionality equation1. Create fractions from datamoney, distance or y is numeratortime or x is denominator2. Divide all fractionsbottom goes outside
top goes inside division sign add decimal and 0's if necessary3. If answers are the same it is proportional4. If answers are different it is nonproportional5. Write equation y = k xA graph is proportional if:1. it is a straight line2. it goes through the origin3. increases from left to rightTo create an equation from a graph1. Identify a point on the graph2. Divide y ÷ x3. Use answer for k value in y = k xTo change percent to decimal1. Erase percent sign2. Move decimal point 2 units to the left3. If necessary put 0 in front of decimal pointTo change decimal to percent1. Move decimal 2 units to the right2. Add percent sign to numberTo change percent to fraction1. Erase percent sign2. Put number over 1003. Simplify fractionTo change fraction to percent1. Divide numerator ÷ denominator2. Move decimal point in quotient 2 units to the right3. Add percent sign to numberTo solve percent problems1. set up proportion is / of = % / 1002. Fill in values3. Cross multiply4. Divide by number in front of xTo find percent change1. Subtract the values2. Divide the total by the starting amount3. if the numbers got bigger write increaseif the numbers got smaller write decreaseTo find markup or markdown1. Change percent to a decimal2. Multiply original amount times decimal3. If markdown or discount or decreaseoriginal  answerIf markup, tax, or tip or increaseoriginal + answerTo find interest1. Write equation i=Prt2. Plug in the number they give you in for i, P, r, t3. Multiply4. Divide by number in front of variable5. To find total add interest amount to principalLong Division1. How many times can divisor be subtracted from first number in dividendwrite answer above that digit in dividend2. Multiply 'answer' times divisor write product under dividend3. Subtractdifference should be less than divisor4. Bring down next number in dividendif you run out of numbers and still have remainder add decimal to dividend and 3 zeros5. Repeat 14 until either you have 3 numbers after the decimal or you have 0 remainder and no more numbers to bring down.To use scale factor1. Set up proportion fake/real=scale factor as a fraction2. Plug in scale factor in order it was given3. Line up the units and plug in other value4. Cross multiplya/b=c/d becomes a*d=b*c5. Divide by number in front of x on both sidesTo determine if it is a triangle1. Two shortest sides must add to be greater than third side if s1+s2 less than s32. If they give you 1 side between two angles it is a unique triangle3. If they give you 3 angles it could make many different triangles4. The 3 angles in a triangle add up to 180 degreesFinding Area and circumference of a Circle1. Divide diameter by 2 to get radius2. Remember pi= 3.143. Identify which equations to use Area = pi*r*r Circumference= 2*pi*r4. Plug in values for radius and multiply if directions say 'in terms of pi' stop here5. Plug in 3.14 for pi and multiplyFinding area of composite figures1. Break figure into shapes circles, triangles, squares, rectangles, quadrilaterals, trapezoids2. Redraw shapes independently with their dimensions and identify type of shape3. Identify correct equation4. Plug numbers into equations5. Find the area of each shape and add them togetherFinding Volume of Prisms1. Identifying the shape of the base2. Redraw the base with dimensions3. Find the area of the base4. Multiply area times depth of the figureFinding Surface Area of Prisms1. Identify the base of the prism2. Redraw base with dimensions3. Find area and perimeter of baseif circle use 2*pi*r4. Multiply area of base x2multiply perimeter of base x height5. add together 2B+PhUsing data to predict the future1. Setup two fractions specific sample/total sample=specific population/total population2. Cross multiply a/b= c/d becomes axd=bxc3. Divide both sides by coefficientTo find the mean absolute deviation1. Add all values in your data2. Divide sum by number of values added3. Subtract this mean from original data values4. Add all answers together5. Divide sum by number of values addedTo find Probability1. Identify the total number of options or choices2. Identify what you are looking for3. Create probability (what you are looking for)/ (total choices)4. Reduce fractionCompound Probability1. Theoretical Probabilitynumber of ways an event CAN occur (over) the total number of likely outcomes2. Experimental Probabilitynumber of ways an event HAS occured (over) the total number of likely outcomes3. Prediction = probability x total possibilities