Basic Arithmetic Skills Basic Arithmetic Skills WorkshopWorkshop

Accompanied by a Study Accompanied by a Study PacketPacket

About the Accuplacer ExamAbout the Accuplacer Exam

• What is the Accuplacer?What is the Accuplacer?

• Passing Requirements for both Passing Requirements for both ATB and Non-ATBATB and Non-ATB

• What happens when you fail?What happens when you fail?

• How much time do you have?How much time do you have?

• Testing center Testing center RULESRULES

Basic Skills WorkshopBasic Skills Workshop• What this workshop coversWhat this workshop covers

• What this workshop does not coverWhat this workshop does not cover

• Expected Learning OutcomesExpected Learning Outcomes

• Can this workshop guarantee a Can this workshop guarantee a passing grade?passing grade?

• What next steps you should take What next steps you should take when you leave here today?when you leave here today?

LET’S GET STARTED, SHALL WE?!?!?

• What is a fraction?? What is a fraction??

• What are the parts of a fraction?What are the parts of a fraction?

FRACTION EXAMPLESFRACTION EXAMPLES !!!!

• What would a fraction look like to What would a fraction look like to represent the triangles with smiley represent the triangles with smiley faces below? faces below?

If you said 2/7 you’d be correct!

MORE FRACTIONSMORE FRACTIONS

• Now what’s the fraction of smiley Now what’s the fraction of smiley faced triangles?? faced triangles??

• What changed?What changed?

If you said 3/7 you’d be correct!!

ADDING AND SUBTRACTING ADDING AND SUBTRACTING WITH FRACTIONSWITH FRACTIONS

• Adding with Like DenominatorsAdding with Like Denominators• Adding with Unlike DenominatorsAdding with Unlike Denominators

– Finding the Least Common MultipleFinding the Least Common Multiple• Subtracting with Like DenominatorsSubtracting with Like Denominators• Subtracting with Unlike DenominatorsSubtracting with Unlike Denominators

– More with the Least Common MultipleMore with the Least Common Multiple

REVIEWREVIEW

• Add 2/3 + 1/5Add 2/3 + 1/5

• Add 3/4 + 1/2Add 3/4 + 1/2

• Subtract 1/4 - 1/3 Subtract 1/4 - 1/3

• Subtract 5/8 – 1/2 Subtract 5/8 – 1/2

Multiply and Divide Multiply and Divide FractionsFractions

• The Rule for Multplying FractionsThe Rule for Multplying Fractions

• The Rule for Dividing FractionsThe Rule for Dividing Fractions

Multiply and Divide the Following Multiply and Divide the Following

FractionsFractions

• Multiply 3/5 * 2/3Multiply 3/5 * 2/3

• Divide 11/12 Divide 11/12 ÷ 1/2÷ 1/2

• Multiply 4/6 * 7/8Multiply 4/6 * 7/8

• Divide 4/5 ÷ 1/3Divide 4/5 ÷ 1/3

GOOD LUCK!

• What does “Lowest Terms” mean?What does “Lowest Terms” mean?

• How do I know when a fraction is in How do I know when a fraction is in “Lowest Terms”?“Lowest Terms”?

• What is the GREATEST COMMON FACTOR?What is the GREATEST COMMON FACTOR?

• What does Relatively Prime mean?What does Relatively Prime mean?

• What does Equivalency Mean?What does Equivalency Mean?

• How can I tell when 2 fractions are How can I tell when 2 fractions are equivalent?equivalent?

• What’s the USE??What’s the USE??

REVIEW!REVIEW!

Create fractions Create fractions from the shaded from the shaded parts of each parts of each figure, and then figure, and then reduce that reduce that fraction to lowest fraction to lowest termsterms

• What is an Improper Fraction?What is an Improper Fraction?

• What is a Mixed Number?What is a Mixed Number?

REVIEWREVIEW

• Convert into a mixed number 23/7Convert into a mixed number 23/7

• Convert into an improper fraction 2 Convert into an improper fraction 2 4/54/5

• What is a Ratio?What is a Ratio?

• What is the Difference between a What is the Difference between a Ratio and a Fraction?Ratio and a Fraction?

Review

•If the ratio of chocolate candies to strawberry candies is 3:1, and you have 36 chocolate candies, how many strawberry candies do you have?

•How did you solve that?

DECIMALSDECIMALS

• What is a Decimal?What is a Decimal?

• How do you turn a Fraction into a How do you turn a Fraction into a Decimal?Decimal?

Decimal Place ValueDecimal Place Value

• The number of digits after the decimal point will determine the number of decimal places in the number.

• The last digit in the number will determine the label used to write decimal numbers in words

Computing with DecimalsComputing with Decimals

• Adding and SubtractingAdding and Subtracting

• Multiplying and DividingMultiplying and Dividing

• Turning Decimals Back into FractionsTurning Decimals Back into Fractions

• Turning Decimals into PercentsTurning Decimals into Percents

%%%%%PERCENTS%%%%% %%%%%PERCENTS%%%%%

• What does Percentage mean?What does Percentage mean?

• Calculating PercentsCalculating Percents

• Calculating with PercentsCalculating with Percents

• Knowing that a percent is the same Knowing that a percent is the same as both a decimal and fraction is very as both a decimal and fraction is very useful when trying to solve for an useful when trying to solve for an amount based on the percentage amount based on the percentage value value

FORMULA (IMPORTANT!!)FORMULA (IMPORTANT!!)

• PercentPercent PartPart

100100 = Whole = Whole

• Percent = percentage valuePercent = percentage value

• Part = fractional part (numerator)Part = fractional part (numerator)

• Whole = the entire group (denominator)Whole = the entire group (denominator)

• 100 = remains always, since a percentage is 100 = remains always, since a percentage is always a fraction over 100. always a fraction over 100.

Percent Part 100 = Whole

REVIEWREVIEW

• If 400 people are in at a wedding, and 17% If 400 people are in at a wedding, and 17% of them ordered the beef entry, how many of them ordered the beef entry, how many beef entries must the chef prepare? beef entries must the chef prepare?

• If at that same wedding, you count 257 If at that same wedding, you count 257 female guests, what percentage of the female guests, what percentage of the guests are female?guests are female?

• If 92% of the guests the bride and groom If 92% of the guests the bride and groom invited attended the wedding, how many invited attended the wedding, how many people did they invite?people did they invite?

More ReviewMore Review

• A survey was conducted using a sample of NYC A survey was conducted using a sample of NYC residents that found that 72% of people use mass residents that found that 72% of people use mass transit. If the total sample size they used was 600 transit. If the total sample size they used was 600 people, how many people responded that they use people, how many people responded that they use mass transit?mass transit?

• If you ate 8 chocolates out of a box of 20 chocolates, If you ate 8 chocolates out of a box of 20 chocolates, how percentage of the chocolates did you eat?how percentage of the chocolates did you eat?

• If 560 of students vote to extend summer break at a If 560 of students vote to extend summer break at a local school, representing 80% of their schools total local school, representing 80% of their schools total enrollment, how many students attend the school?enrollment, how many students attend the school?

• Of the most dreaded tasks to tackle in mathematics, Of the most dreaded tasks to tackle in mathematics, the word problem beats them all by a mile. Often the word problem beats them all by a mile. Often believed to be confusing and filled with needless believed to be confusing and filled with needless information meant to throw a student off track (and information meant to throw a student off track (and often they are), a word problem is not always often they are), a word problem is not always difficult in the problem it is asking you to solve, but difficult in the problem it is asking you to solve, but first determining what it is asking you. Here are first determining what it is asking you. Here are some key words for examining a word problem. some key words for examining a word problem.

• DifferenceDifference: means subtraction: means subtraction• SumSum: means to add: means to add• QuotientQuotient: is the answer to a division problem: is the answer to a division problem• ProductProduct: is the answer to multiplication: is the answer to multiplication

4 Steps to Problem 4 Steps to Problem SolvingSolving

1. UNDERSTANDING THE PROBLEM 1. UNDERSTANDING THE PROBLEM – Can you state the problem in your own Can you state the problem in your own

words? words? – What are you trying to find or do? What are you trying to find or do? – What are the unknowns? What are the unknowns? – What information do you obtain from What information do you obtain from

the problem? the problem? – What information, if any, is missing or What information, if any, is missing or

not needed? not needed? •    Adapted from "Science World," November 5, 1993 (Adapted from "Science World," November 5, 1993 (http://teacher.scholastic.com/lessonrepro/lessonplans/steppro.htm ) )

2. Devise a Plan2. Devise a Plan

• Look for a pattern. Look for a pattern. • Examine related problems, and determine if the Examine related problems, and determine if the

same technique can be applied. same technique can be applied. • Examine a simpler or special case of the problem Examine a simpler or special case of the problem

to gain insight into the solution of the original to gain insight into the solution of the original problem. problem.

• Make a table. Make a table. • Make a diagram. Make a diagram. • Write an equation. Write an equation. • Use guess and check. Use guess and check. • Work backward. Work backward. • Identify a subgoal Identify a subgoal

3. CARRYING OUT THE PLAN3. CARRYING OUT THE PLAN

• Implement the strategy or strategies in Implement the strategy or strategies in step 2, and perform any necessary step 2, and perform any necessary actions or computations. actions or computations.

• Check each step of the plan as you Check each step of the plan as you proceed. This may be intuitive proceed. This may be intuitive checking or a formal proof of each checking or a formal proof of each step. step.

• Keep an accurate record of your work. Keep an accurate record of your work.

4. LOOKING BACK4. LOOKING BACK

• Check the results in the original problem. (In Check the results in the original problem. (In some cases this will require a proof.) some cases this will require a proof.)

• Interpret the solution in terms of the original Interpret the solution in terms of the original problem. Does your answer make sense? Is it problem. Does your answer make sense? Is it reasonable? reasonable?

• Determine whether there is another method of Determine whether there is another method of finding the solution. finding the solution.

• If possible, determine other related or more If possible, determine other related or more general problems for which the techniques will general problems for which the techniques will work. work.

TIME TO TAKE THE EXAMTIME TO TAKE THE EXAM

Tips to pass the entrance examTips to pass the entrance exam

• 1. Take the exam when you are 1. Take the exam when you are readyready

• 2. Be rested and fit on testing day2. Be rested and fit on testing day

• 3. Don’t be rushed3. Don’t be rushed

• 4. Stay confident. 4. Stay confident.

On behalf of the Staff of the Learning Enhancement Center We would like to wish

you…