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TPREP101: SAT Prep

Unit 4: Basic Math   The mathematics section of the SAT includes questions that require knowledge of several mathematical subtopics.  First, before moving into the more advanced subtopics, it is important to review some of the basic mathematical concepts you probably learned in elementary and middle school.  This unit is a quick refresher on these basic concepts, such as order of operations, factors and multiples, fractions, roots, and exponents.  Once you have reviewed and mastered this information, you will be able to more quickly and accurately answer many SAT Math questions.  You will also have a firmer foundation on which to build and review more advanced mathematical concepts.

Unit 4 Time Advisory
This unit should take approximately 4.25 hours to complete.

☐    Subunit 4.1: 1.5 hours

☐    Subunit 4.3: 0.5 hours

☐    Subunit 4.4: 0.25 hours

☐    Subunit 4.5: 0.75 hours

☐    Subunit 4.6: 0.25 hours

☐    Subunit 4.7: 0.25 hours

☐    Subunit 4.8: 0.75 hours

Unit4 Learning Outcomes
Upon successful completion of this unit, the student will be able to: - Explain rules and strategies for answering math questions. - Identify and apply basic number properties and operations. - Translate word problems into algebraic equations and vice versa. 

4.1 The Math Section   - Reading: College Board’s “Mathematics Section” Link: College Board’s “Mathematics Section” (HTML)

 Instructions: Please click on the link above and read this webpage,
which gives a quick technical breakdown of the numbers and types of
math questions you will see on the SAT.  Use this information to
help yourself become more comfortable with the format of the test.  

 Reading this webpage should take approximately 15 minutes.  

 Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
  • Reading: ErikTheRed.com: Erik Jacobsen’s “SAT Math Must-Know Vocabulary” Link: ErikTheRed.com: Erik Jacobsen’s “SAT Math Must-Know Vocabulary” (PDF)

    Instructions: Please click on the link above and select the “SAT Math Must-Know Vocabulary” link on this page to access a PDF with a list of terms that you need to know well in order to best understand the math questions you will encounter.  You may want to print out the PDF, study it as you would vocabulary, and return to review it several times before your test.

    Studying this vocabulary should take approximately 30 minutes.

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Reading: ErikTheRed.com: Erik Jacobsen’s “SAT Math Strategies” Link: ErikTheRed.com: Erik Jacobsen’s “SAT Math Strategies” (PDF)

    Instructions: Please click on the link above and select the “SAT Math Strategies” link on this page to access a PDF with three pages of tips to help you well on the math section.  Read through the document, make note of tips that you particularly need to remember, and keep it on hand as you work through the math units of this course.

    Reading these tips should take approximately 30 minutes.

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Reading: ErikTheRed.com: Erik Jacobsen’s “SAT Math Facts and Formulas” Link: ErikTheRed.com: Erik Jacobsen’s “SAT Math Facts and Formulas” (PDF)

    Instructions: Please click on the link above and select the link to the “SAT Math Facts and Formulas” PDF on this page.  Read the section entitled “Numbers, Sequences, and Factors.”  This will cover the topics outlined in subunits 4.2-4.4.  You may want to make flashcards of each concept and the process, method, or equation that it requires.

    Reading this section should take approximately 15 minutes.

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

4.2 Order of Operations   Note: This topic is covered by the “SAT Math Facts and Formulas” reading assigned below subunit 4.1.  In particular, familiarize yourself with the order in which portions of complex mathematical problems are solved as described according to the “Order of Operations” listing.

4.3 Sequences   Note: This topic is covered by the “SAT Math Facts and Formulas” reading assigned below subunit 4.1.  In particular, familiarize yourself with the formulas for finding “next number (or nth number) in a sequence” as described according to the “Arithmetic Sequences” and “Geometric Sequences” listings.  You may need to practice actually plugging numbers into these equations (in place of the variables) in order for them to make sense to you.  Play around with the equations until they become second nature, so you can easily use them to solve an SAT problem.

  • Web Media: Khan Academy’s “Equations of Sequence Patterns”, “Finding the 100th Term in a Sequence”, and “Geometric Sequences (Introduction)” Link: Khan Academy’s “Equations of Sequence Patterns”, (YouTube) “Finding the 100th Term in a Sequence”, (YouTube) and “Geometric Sequences (Introduction)” (YouTube)

    Instructions: Please click on the links above and watch these videos for a more in-depth explanation of methods for finding numbers in sequences.  “Equations of Sequence Patterns” explains the formula for arithmetic sequences.  “Finding the 100th Term of a Sequence” explains how to apply the arithmetic sequence formula to a commonly encountered sequence problem.  “Geometric Sequences” explains how to set up the formula for finding a number in a geometric sequence.

    Watching these videos and pausing to take notes should take approximately 30 minutes.

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

4.4 Factors and Multiples   Note: This topic is covered by the “SAT Math Facts and Formulas” reading assigned below subunit 4.1.  In particular, familiarize yourself with the methods for factoring a number or finding common factors or multiples of two or more numbers, as described according to the “Prime Factorization,” “Greatest Common Factor,” and “Least Common Multiple” listings.  Pick a few random numbers, and practice factoring and finding common factors and multiples until it comes easily.  You should take approximately 15 minutes to complete this activity.

4.5 Fractions   - Web Media: Khan Academy’s “Representing a Number as a Decimal, Percent, and Fraction”, “Adding and Subtracting Fractions”, “Multiplying Fractions”, “Dividing Fractions”, and “Ordering Numeric Expressions” Link: Khan Academy’s “Representing a Number as a Decimal, Percent, and Fraction” (YouTube), “Adding and Subtracting Fractions” (YouTube), “Multiplying Fractions” (YouTube), “Dividing Fractions” (YouTube), and “Ordering Numeric Expressions” (YouTube)

 Instructions: Please click on the links above and watch these
videos for a review of fractions.  You may not have a lot of
practice with fractions, because we so frequently use calculators,
which give us answers in decimals.  However, fractions frequently
appear on the SAT (partially because all SAT math problems are
designed to be solved without a calculator), so it is imperative
that you are comfortable using fractions.  

 Watching these videos and pausing to take notes should take
approximately 45 minutes.  

 Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.

4.6 Roots and Exponents   - Reading: ErikTheRed.com: Erik Jacobsen’s “SAT Math Facts and Formulas” Link: ErikTheRed.com: Erik Jacobsen’s “SAT Math Facts and Formulas” (PDF)

 Instructions: Please click on the link above and select the link to
the “SAT Math Facts and Formulas” PDF on this page.  Read the
section entitled “Powers, Exponents, Roots.”  Practice writing out
the formulas as they are (using variables) to help yourself
memorize, and also practice writing the formulas out using numbers
substituted in for each variable, so you can see how the formulas
work using real numbers.  

 Reading this section should take approximately 15 minutes.  

 Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.

4.7 Word Problems   - Web Media: Khan Academy’s “Solving Percent Problems” Link: Khan Academy’s “Solving Percent Problems” (YouTube)

 Instructions: Feeling comfortable solving word problems is
important in doing well on the SAT.  One of the most basic and
popular word problems is the percent problem.  Please click on the
link above, and watch this video for a quick review of how to easily
solve these problems.  Write yourself some notes so that you can
remember how to do the problems on your own.  

 Watching this video and pausing to take notes should take
approximately 15 minutes.  

 Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.

4.8 Basic Math Practice Problems   - Assignment: cK-12: Jason Shah’s “SAT Prep - Math Questions” and “SAT Prep - Math Questions with Explanations” Link: cK-12: Jason Shah’s “SAT Prep - Math Questions” (HTML) and “SAT Prep - Math Questions with Explanations” (HTML)

 Instructions: Please click on the first link above “Math Questions”
and complete questions 1 and 2 to apply your new knowledge and to
practice answering questions on numbers and operations.  

 Once you have completed the questions, please click on the second
link above “Math Questions with Explanations” and review the correct
answers for questions 1 and 2.  For any questions you missed, read
and review the provided explanations until the correct answer makes
sense to you.  You may want to look back at the previous sections in
this unit for help.  Once you have studied the correct answer, think
about how you will approach a similar problem in the future and will
avoid making a similar mistake.  

 Completing this assignment should take approximately 15 minutes.  

 Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
  • Assignment: cK-12: Jason Shah’s “SAT Prep II - Math Questions” and “SAT Prep II - Math Questions with Explanations” Link: cK-12: Jason Shah’s “SAT Prep II - Math Questions” (HTML) and “SAT Prep II - Math Questions with Explanations” (HTML)

    Instructions: Please click on the first link above for “Math Questions” and complete questions 1 and 2 to apply your new knowledge and to practice answering questions on numbers and operations.

    Once you have completed the questions, please click on the second link above for “Math Questions with Explanations” and review the correct answers for questions 1 and 2.  For any questions you missed, read and review the provided explanations until the correct answer makes sense to you.  You may want to look back at the previous sections in this unit for help.  Once you have studied the correct answer, think about how you will approach a similar problem in the future and will avoid making a similar mistake.

    Completing this assignment should take approximately 15 minutes.

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Assignment: cK-12: Jason Shah’s “SAT Prep III - Math Questions” and “SAT Prep III - Math Questions with Explanations” Link: cK-12: Jason Shah’s “SAT Prep III - Math Questions” (HTML)and “SAT Prep III - Math Questions with Explanations” (HTML)

    Instructions: Please click on the first link above for “Math Questions” and complete questions 1 and 2 to apply your new knowledge and to practice answering questions on numbers and operations.

    Once you have completed the questions, please click on the second link above for “Math Questions with Explanations” and review the correct answers for questions 1 and 2.  For any questions you missed, read and review the provided explanations until the correct answer makes sense to you.  You may want to look back at the previous sections in this unit for help.  Once you have studied the correct answer, think about how you will approach a similar problem in the future and will avoid making a similar mistake.

    Completing this assignment should take approximately 15 minutes.

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.