- 1. USING MAPS TO READ MATH TEXTS– CONCEPT MAPS, THAT IS… READING WORKSHOP
- 2. MYTH 1: A MATH TEXTBOOK ISN’T FOR READING. IT’S FOR HOMEWORK SETS AND EXAMPLES ONLY. Fact: All the pages before your homework sets—the chapters—contain valuable explanations, examples, detailed processes and instruction beyond what your teacher can provide in class. Learning math is really learning a new and very detailed language, one that has its own symbols and grammar that is often unfamiliar. A student would never expect to learn a different language—like German or Japanese—without taking the time to at least look over and familiarize themselves with the writing of that language. Math, like other languages, has definitions, sentences, paragraphs, syntax, and grammar. Unlike most other languages, math is almost exclusively a WRITTEN language, so if you’re not reading it, you’re not learning it!
- 3. READING MATH IS IMPORTANT… Trick Number below 10 • Step 1: Think of a number below 10. • Step 2: Double the number you have thought. • Step 3: Add 6 to the previous result. • Step 4: Half the answer; i.e., divide it by 2. • Step 5: Take away the number you have thought from the answer-- that is, subtract the answer from the number you have thought. • Answer: 3
- 4. READING MATH IS IMPORTANT… Trick 1089 • Step 1: Think of a 3 digit number. • Step 2: Arrange the number in descending order. • Step 3: Reverse the number and subtract it with the result. • Step 4: Remember it and reverse the answer mentally. • Step 5: Add it with the result. • Answer: 1089
- 5. MYTH 2: EVERYTHING I NEED TO LEARN IN MATH WILL BE DEMONSTRATED BY MY PROFESSOR ANYWAY. While in class, your teacher has 20+ students who all must understand the material being presented. Each student has a different learning style, is at different education levels, and has a different background regarding the information being presented. It is up to you— the student—to take responsibility to learn those things that you personally did not understand, or was not covered at the depth you needed, by reading the textbook. The textbook is there to both complement and supplement the lectures.
- 6. MYTH 3: WHEN READING A MATH BOOK, START AT THE FIRST PAGE AND END AT THE LAST PAGE. DON’T LOOK AT EARLIER OR LATER MATERIAL. • Math is a subject that is learned cumulatively—that is, it is a subject that demands that you understand older, already taught information before you can completely understand new information. • For this reason, you must read in all directions and, more importantly, the author INTENDS for you to skip around and make connections between paragraphs and chapters. • By skipping around you are making mental notes of the connections between the ideas, and the significance of the relationships between the new information you’re learning and the old information you already know. • Examples of skipping might be you skip back a chapter to review how exponents work when you begin a new chapter on multiplying exponents. Or, the author may prompt you to flip to an appendix in the back of your book to look at a chart or table that will help you understand better. Don’t skip the prompting: you may miss an important tool that will make your homework easier.
- 7. MYTH 4: EVEN IF I DO READ, TAKE NOTES, AND STUDY, I’M NOT “NATURALLY” TALENTED AT MATH, SO I KNOW I’LL FAIL ANYWAY! • Think about a skill or talent you have like driving, reading, fixing cars, writing, or playing an instrument. Were you born with this ability? Of course not; with years of training, education, and practice, you’ve learned to drive, read, fix cars, write, or play an instrument. Math is a learned skill. • Of course there are people out there who may possess an ability that allows them to go far beyond the average ability, like race car drivers, famous novelists, or virtuoso pianists but, by and large, they are not the majority. Math is the same: anyone can learn math. There are, of course, people who have more ability who will be able to solve complicated mathematical formulas and study well beyond calculus, but these people are not the majority. • Instead of focusing on how terrible you are at math, be positive and assert yourself into the subject like you would any class in which you feel confident. By staying positive, you’ll be more likely to succeed and you will not suffer the mental pressure of predicting your own failure.
- 8. SO HOW DO I BEGIN GETTING THE MOST FROM MY MATH TEXTBOOK? •Reading • Annotating •Mapping •Practicing
- 9. READING MATH TEXTS ARE LIKE READING ALL TEXTS… • Ask pre-reading questions • Identify unfamiliar terms • Quiz yourself as you go… read the examples, practice them, and then test yourself • Create visuals • Summarize what you’ve read • Teach it to someone else
- 10. ANNOTATING A MATH TEXT
- 11. MAPPING • Shows relationships between ideas and the big picture • Allows students to more easily see the “details” but also how they fit into the bigger picture • Can be done after reading and/or during or after a lecture • May range from simple and general to very detailed and complex
- 12. MAPPING: FROM GENERAL CONCEPTS TO SPECIFIC PROBLEM STEPS
- 14. PRACTICING THE SKILL OF MATH: Do your math homework!
- 15. PRACTICING WORD PROBLEMS: PRACTICAL SKILLS Purple Math.com gives us some great hints and a translation guide chart to understanding illusive, mysterious, and challenging MATH WORD PROBLEMS!
- 16. PRACTICING WORD PROBLEMS 1. Read the word problems in their entirety before trying to solve them. 2. Work in an organized manner! • This means to select clear variables so that you will know exactly which variable is x and which is y so that you will be able to determine exactly what x and y stand for in your answer. • Draw and label pictures clearly. Visual aids are helpful in math! • Write down your reasoning in a linear progression as you go. This improves your cognition and helps you remember your process for later problems.
- 17. PRACTICING WORD PROBLEMS 3.Look for and understand KEY WORDS: Translate! Math Process Translation Math Problem Words Addition Increased by More than Combined, together Total of, sum of Added to Subtraction Decreased by Minus, less Difference between/of Less than, fewer than Multiplication Product of Times, multiplied by Increased/decreased by a factor of* Division Per, a Out of Ratio of, quotient of Percent (divide by 100) Equals Is, are, was, were, will be Gives, yields Sold for *This type can involve both addition or subtraction AND multiplication!!
- 18. TYPES OF WORD PROBLEMS FROM PURPLEMATH.COM • "Age" problems, involving figuring out how old people are, were, or will be • "Area/volume/perimeter" problems, involving very basic geometric formulas • "Coin" problems, involving figuring out how many of each type of coin you have • "Distance" problems, involving speeds ("uniform rates"), distance, time, and the formula "d = rt". • "Investment" problems, involving investments, interest rates, and the formula "I = Prt". • "Mixture" problems, involving combining elements and find prices (of the mixture) or percentages (of, say, acid or salt). • "Number" problems, involving "Three more than two times the smaller number..." • "Percent of" problems, involving finding percents, increase/decrease, discounts, etc. • Quadratic word problems, such as projectile motion and max/min questions. • "Work" problems, involving two or more people or things working together to complete a task, and finding how long they took.
- 19. PRACTICE BY PURPLEMATH.COM •Translate "the sum of 8 and y" into an algebraic expression. This translates to "8 + y" •Translate "4 less than x" into an algebraic expression. This translates to "x – 4" Remember? "Less than" is backwards in the math from how you say it in words! •Translate "x multiplied by 13" into an algebraic expression. This translates to "13x" •Translate "the quotient of x and 3" into an algebraic expression. This translates to " x/3" •Translate "the difference of 5 and y" into an algebraic expression. This translates to "5 – y" •Translate "the ratio of 9 more than x to x" into an algebraic expression. This translates to "(x + 9) / x" •Translate "nine less than the total of a number and two" into an algebraic expression, and simplify. This translates to "(n + 2) – 9", which then simplifies to "n – 7"