### Transcription

1The Authors:Steve Marcy and Janis MarcySanta Monica-Malibu UnifiedSchool DistrictLimited Reproductionlimited to the teacherschool or schoolPermission to duplicate these materials ispurchased. Reproduction for an entirestrictly prohibited.For Jennifer, Matt, Andy, and JazzCover bb Nimbus Designhdlllustratio s by Mark LawlerTechnical art by S teveReiling, Rohini KelkarEdite by Ann Roperight GroupIMcGraw-Hilluden-tialPlazaISBN: k88488-742-1

MIDDLE SCHOOL MATH WITH PIZ21AZI!is a series of five books designed to providepractice with skills and concepts taughtin today's middle school mathematicsprograms. The series uses many of thesame puzzle formats a s PRE-ALGEBRAWITH PIZZAZ! and ALGEBRA WITH PIZZAZ!both published by Creative Publications.have tried to minimize the time spent onfinding answers or doing other puzzlemechanics.3. CAREFUL SELECTION OF TOPICSAND EXERCISES. The puzzles withineach topic area are carefully sequencedso that each one builds on skills andconcepts previously covered. Thesequence of exercises within each puzzleis designed to guide students in incremental, step-by-step fashion towardmastery of the skill or concept involved.A primary goal is the development ofproblem-solving ability. In order to solveproblems, students need not only rulesand strategies but also a meaningfulunderstanding of basic concepts. Somepuzzles in this series are designed specifically to build concepts. Other puzzles,especially those for estimation, also helpdeepen students' understanding byencouraging them to look at numbers asquantities rather than just as symbols tobe manipulated. For puzzles specificallykeyed to problem solving, we have triedto write problems that are interestingand uncontrived. We have included extrainformation in some problems, and havealso mixed problem types within sets,so that the problems cannot be solvedmechanically.We believe that mastery of math skills andconcepts requires both good teaching and agreat deal of practice. Our goal is to providepuzzle activities that make this practicemore meaningful and effective. To this end,we have tried to build into these activitiesthree characteristics:1. KNOWLEDGE-OERESULTS. Variousdevices are used in the puzzles to tellstudents whether or not their answersare correct. Feedback occurs immediatelyafter the student works each exercise.For example, if a particular answer is notin the code or scrambled answer list, thestudent knows it is incorrect. He or shecan then try again or ask for help.Additional feedback and reinforcementoccurs when the student finds a puzzlesolution that is appropriate. Thisimmediate knowledge of results benefitsstudents and also teachers, who nolonger have to spend time confirmingcorrect answers.In addition to these efforts to make thepuzzles effective, we have tried to makethem easy to use. The topic for each puzzleis given both at the bottom of the puzzlepage and in the Table of Contents on pagesiv and v. Each puzzle is keyed to a specifictopic in recent editions of leading middleschool textbooks. Each puzzle requiresduplicating only one page, and manyof them provide space for student work.Finally, because the puzzles are selfcorrecting, they can eliminate the taskof correcting assignments.2. A MOTIVATING GOAL FOR THESTUDENT. The puzzles are designed sothat students will construct a joke orunscramble the answer to a riddle inthe process of checking their answers.The humor operates as a n incentive,because the students are not rewardedwith the punch line until they completethe exercises. While students may decrythese jokes a s "dumb" and groan loudly,our experience has been that they enjoythe jokes and look forward to solving thepuzzles. The humor has a positive effecton class morale. In addition to humor,the variety and novelty of procedures forsolving the puzzles help capture studentinterest. By keeping scrambled answerlists short and procedures simple, weWk hope that both you and your studentswill enjoy using these materials.Steve and Janis Marcyiii

Table of Contents1. RATIO AND PROPORTIONa.b.c.d.e.f.g.Ratio.7Ratio and Rate .8Solving Proportions .9Problem Solving: Using Proportions .10Using a Calculator: Solving Proportions .1Similar Figures .12Scale Drawings .132. PERCENTPercent.I 4-15Percent and Fractions .16-19Percent and Decimals .20Estimating Percents .21Mental Math: Finding a Percent of a Number .22Estimating a Percent of a Number .23-24Finding a Percent of a Number .25-26Finding a Percent of a Number: Percents GreaterThan 1 00% or Less Than 1 %.27i. Problem Solving: Choosing a Calculation Method .28j. Problem Solving: Discounts and Sale Prices .29k. Problem Solving: Simple Interest .30I. Finding the Percent One Number Is of Another .31,33m. Estimating the Percent One Number Is of Another .32n. Problem Solving: Mixed Applications .-34o. Finding a Number When a Percent of It Is Known.35-36p. Problem Solving: Mixed Applications .-37a.b.c.d.e.f.g.h.3. STATISTICS AND GRAPHSa.b.c.d.e.f.g.Mean and Range.38Median and Mode .39Pictographs .40Bar Graphs .4-42Histograms .43Line Graphs .44-45Circle Graphs .46-484. PROBABILITYProbability .49Probability: Expected Outcomes .-50Possible Outcomes .-51d. Independent Events .52e. Dependent Events.53f. Permutations .54

5. INTEGERSa.b.c.d.e.f.g.h.i.j.k.Integers .55Comparing and Ordering Integers .56Adding Integers: Using the Number Line .57Adding Integers: Like Signs .58Adding Integers: Unlike Signs .59-60Subtracting Integers .61Review: Addition and Subtraction .62Multiplying Integers .63Review: Addition, Subtraction. Multiplication .64Dividing Integers .-65Review: All Operations with Integers .666. COORDINATE GRAPHINGa. Graphing Ordered Pairs: First Quadrant .67b. Graphing Ordered Pairs: All Quadrants .-68-697. EQUATIONSa.b.c.d.e.f.g.h.Equations: Concept of Solution .70Solving Equations: x a b .71Solving Equations: x - a b .72Solving Equations: ax b .73Solving Equations: b .74Review: Solving One-Step Equations .75Solving Equations: ax b c .76Equations in Two Variables .778. ENRICHMENTa. Test of Genius .789. ANSWERS .7 9.96

NOTES ABOUT USING THE PUZZLESThe selection of topics for MIDDLE SCHOOLMATH WITH P I Z A Z Z ! reflects recent thinkingabout what is important in an updated middleschool math program. Virtually every puzzle canbe matched with a particular lesson in recenteditions of popular textbooks. After studentshave received instruction in a topic and workedsome sample exercises, you might assign apuzzle along with a selection of textbookexercises.Students in the middle grades should begin [email protected] many mathematics problems andexercises into one of three categories:1 . MENTAL MATH. Problems for which an exactanswer can be obtained mentally.2. ESTIMATION. Problems for which a napproximate answer, obtained mentally, issufficient.3. TOOLS. Problems requiring a n exact answerthat cannot be obtained mentally. Studentswill use paper and pencil and/or calculators.Some of the puzzles in this series focusspecifically on one'of these categories. A fewpuzzles actually present problems in all threecategories and ask the student to make theclassification.By the time they reach the middle grades,students should generally be permitted to usecalculators for problems that require tools(Category 3).The most common argumentagainst calculator use is that students willbecome overly dependent on them. This concern,though, appears to be based primarily on fearthat students will rely on the calculator forproblems in Categories 1 and 2, those thatshould be done mentally.To solve problems in Category 3, calculators arewonderful tools for computing. Students mayalso need paper and pencil to make diagrams,write equations, record results, etc., so they willneed both kinds of tools. On the other hand,students should not need calculators forproblems in Categories 1 and 2, problems thatcall for mental math or estimation. Skills inthese areas are essential not only in daily lifebut also for the intelligent use of the calculatoritself. The puzzles in this series reflect thesethree categories and the distinction betweenthem.When students do use calculators, you maywant to have them write down whatevernumbers and operations they punch in and theiranswers. This makes it easier to identify thecause of any error and assists in classmanagement. Even when students do mentalmath or estimation puzzles, have them write acomplete list of answers and, where appropriate,the process used to get the answers. Encouragestudents to write each answer before locating itin the answer list. Students should complete allthe exercises even if they discover the answer tothe joke or riddle earlier.One advantage of using a puzzle a s a nassignment is 'that you can easily make atransparency of the page and display theexercises without having to recopy them on theboard. You can then point to parts of a problema s you discuss it. It is often helpful to cut thetransparency apart so that you can displayexercises on part of the screen and writesolutions on the remaining area.Other books by Steve and Janis Marcypublished by Creative PublicationsPre-Algebra With Pizzazz! in a BinderCovers most topics in a pre-algebra curriculumAlgebra With Pizzazz! in a 6inderCovers most topics in a first-year algebra curriculum

. .What Happened When There Was aKidnapping at Bizarre Middle School?Write each ratio in simplest form, then find your answer at the bottom of thepage. Write the letter of the exercise in the box above the answer.I. Write .each [email protected] Stars to squaressquares to [email protected] Stars to [email protected] Circles to starsStars to all [email protected]@ Squares to all figures-II. A TV screen is 15 in. high and 20 in. wide. Write each [email protected] Height to [email protected] Width to heightIll. A magazine photograph is 24 cm long and 16 cm wide.Write each ratio.24 [email protected] Length to [email protected] Width to lengthIV. The