tag:blogger.com,1999:blog-1667542146821160523Mon, 13 May 2013 12:47:51 +0000shapesbalance scale problemsdecimalscommon core state standards for mathematicsreflectionpre-algebraintroductionmathlandequivalent fractionsmath word problemsratiosfactorsgraphsfunctionsmath conceptsmath equationspythagorean theoremproblem solvingratioordering fractionstrig functionsgraphingproportionperimetervisual math modelsspirographintegersmulti-step problemsmindstormslearningadditionequation of a linebar modelsteachingpattern blockstranslationprogrammingareamath gamesleast common multipleseymour papertThinking Blockstimedivisiongeometryvisual equationsrotationmultiplicationmisconceptionsalgebramath manipulativesgeoboardcurvessubtractiongreatest common factorlinear functionsfractionsmodel drawingproblem solving with fractionsregroupingcomparing fractionssymmetryprojectile motionproportionsconversion factorsalgebraic thinkingbasic factsmoneyEducational resources, thinking games, learning activities, and teaching ideas for math educators.http://blog.mathplayground.com/noreply@blogger.com (mathplayground)Blogger25125tag:blogger.com,1999:blog-1667542146821160523.post-6582146377615336267Tue, 15 Jan 2013 01:38:00 +00002013-01-14T20:38:02.640-05:00visual math modelsratiodivisionmodel drawingfractionsproportionadditionThinking Blockssubtractionmultiplicationcommon core state standards for mathematicsbar models Thinking Blocks is an online problem solving tool that enables students to build physical models of math word problems. Using brightly colored blocks, students represent mathematical relationships and identify known and unknown quantities. The model provides students with a powerful image that organizes information and simplifies the problem solving process. By modeling increasingly complexhttp://blog.mathplayground.com/2013/01/thinking-blocks-and-common-core.htmlnoreply@blogger.com (mathplayground)0tag:blogger.com,1999:blog-1667542146821160523.post-7206856129588571714Fri, 16 Nov 2012 14:00:00 +00002012-11-26T19:47:24.364-05:00fractionsmoneypre-algebraadditionintegerstimesubtractionbasic factsdivisionratiosproportionsmath gamesdecimalsmultiplication For the past ten years, our math learning center has offered a program called Stay Sharp! to help students maintain fluency with basic math facts during the summer months. We convert one of our larger classrooms into a math arcade and provide a variety of learning games and challenges. Students may opt to work in teams or attempt the challenges on their own. This is a favorite among children http://blog.mathplayground.com/2012/11/stay-sharp-math-arcade.htmlnoreply@blogger.com (mathplayground)1tag:blogger.com,1999:blog-1667542146821160523.post-5277703516383329014Mon, 29 Oct 2012 12:00:00 +00002012-10-29T08:00:00.649-04:00perimetergeoboardgeometryareaThe geoboard just might be my all-time favorite math manipulative. There are so many interesting questions that can be explored with this easy to use math tool. When I first introduce students to their geoboards, I encourage open-ended exploration. At this phase, students usually create various shapes without consideration of each shape's properties. Once they're comfortable with this, I then http://blog.mathplayground.com/2012/10/geometry-and-more-with-geoboards.htmlnoreply@blogger.com (mathplayground)0tag:blogger.com,1999:blog-1667542146821160523.post-846260014211346389Sun, 21 Oct 2012 17:00:00 +00002012-10-21T22:10:31.015-04:00pattern blocksfractionsteachingproblem solvingmath manipulatives Pattern blocks have many uses and ours are as quiet as a mouse! Use them to explore transformations, discover symmetry, compose and decompose shapes, investigate fractions, introduce algebraic thinking, create patterns, and engage students in authentic problem solving. These colorful shapes can provide learning opportunities for students throughout elementary and middle school. One of my http://blog.mathplayground.com/2012/10/versatile-pattern-blocks.htmlnoreply@blogger.com (mathplayground)0tag:blogger.com,1999:blog-1667542146821160523.post-2744951427253420219Tue, 16 Oct 2012 12:00:00 +00002012-10-21T20:50:55.224-04:00comparing fractionsproblem solving with fractionsordering fractions Would your students be able to create and order fractions if doing so meant they could help Cleo the Cat escape from the spooky and dangerous Fraction Manor? In this fun problem solving game, students collect cards as they journey through three levels of Dr. Fractionstein's castle. Watch out for the monsters! They will try to prevent students from finding all of the cards. When each http://blog.mathplayground.com/2012/10/escape-from-fraction-manor.htmlnoreply@blogger.com (mathplayground)1tag:blogger.com,1999:blog-1667542146821160523.post-2843148584227752222Fri, 12 Oct 2012 13:30:00 +00002012-10-22T08:49:58.456-04:00curvesconversion factorsratiosgraphsproportionspythagorean theoremtrig functionsperimeterlinear functionsarea Year after year, students make the steady ascent along the rocky trails of Math Mountain. Arithmetic gives way to algebra. Polygons lead to polyhedra. Functions progress from linear to quadratic to exponential. But what's at the summit? What will students do with all this knowledge? When will we ever have to use this stuff? Math Apprentice hopes to answer that question. Designed http://blog.mathplayground.com/2012/10/real-world-math.htmlnoreply@blogger.com (mathplayground)0tag:blogger.com,1999:blog-1667542146821160523.post-6220248836476085840Mon, 08 Oct 2012 18:00:00 +00002012-10-21T20:12:04.401-04:00curvesspirographmath equationsFor our first real world project of the year, I introduced my precalculus students to a Spirograph* toy. I passed out a variety of gears and asked half of the group to rotate a gear around the outside of another fixed gear while the others rotated gears around the inside. Stunning images appeared from both groups. We compared the two processes and looked for patterns. The images depended http://blog.mathplayground.com/2012/10/spirograph-math.htmlnoreply@blogger.com (mathplayground)0tag:blogger.com,1999:blog-1667542146821160523.post-2511297679273724686Thu, 04 Oct 2012 12:30:00 +00002012-10-20T23:02:22.526-04:00fractionsproblem solving This fraction game introduces students to a character with an interesting dilemma. Walker wants desperately to get home but the road has gaps that prevent him from reaching his destination. At each gap, Walker is presented with increasingly challenging tasks involving fraction pieces. Students must help Walker solve these problems in order to move him closer to home. In the process, studentshttp://blog.mathplayground.com/2012/10/problem-solving-with-fractions.htmlnoreply@blogger.com (mathplayground)0tag:blogger.com,1999:blog-1667542146821160523.post-1238099769425492996Tue, 25 Sep 2012 15:00:00 +00002012-10-20T23:11:34.291-04:00balance scale problemsalgebraic thinkingSolve for A, B, and C using the following equations. 2A + B = 18 B + C = 12 3A = 15 My third graders can! However it looks more like this: My students think this is great fun. They have no idea they are exploring linear functions or algebraic relationships. All they know is that these problems make them think and they seem to like that. I usually introduce algebraic thinking problems http://blog.mathplayground.com/2012/08/can-your-third-graders-do-this.htmlnoreply@blogger.com (mathplayground)0tag:blogger.com,1999:blog-1667542146821160523.post-9192623978668570971Tue, 18 Sep 2012 15:30:00 +00002012-10-20T23:05:33.804-04:00symmetryreflectionrotationshapestranslationgeometry I designed the math game, Shape Mods, and the accompanying Transformation Workshop to provide students with opportunities to practice geometric transformations. The object of the game is to transform the starting green figure into the final red figure using anywhere from one to four transformation blocks. The blocks include translation, rotation about the origin, and reflection across http://blog.mathplayground.com/2012/09/teaching-transformations.htmlnoreply@blogger.com (mathplayground)0tag:blogger.com,1999:blog-1667542146821160523.post-2549363659757396617Sat, 15 Sep 2012 13:30:00 +00002012-10-20T23:20:50.466-04:00math conceptsteachinglearningdecimals I generally work with students who would be considered above average in school. But every so often a student comes into my life for whom each new math concept is an exhausting struggle. Math is an endless menu of incomprehensible and unrelated steps to be memorized and catalogued. That there could ever be any purpose to, let alone any joy in, this cryptic jumble of numbers, formulas, and http://blog.mathplayground.com/2012/08/stories-for-em.htmlnoreply@blogger.com (mathplayground)0tag:blogger.com,1999:blog-1667542146821160523.post-8807494174892582413Wed, 12 Sep 2012 15:00:00 +00002012-10-21T20:23:59.022-04:00visual equationsalgebraic thinkingSolve for A, B, and C using the following equations:A + B = 26B + C = 45C + A = 33How would you go about it? Would you begin by combining equations? Or would you start by making substitutions? Is this a problem a 5th grader could solve? Without guessing and checking?What if the problem looked like this?   Is it easier to solve? It's exactly the same problem, isn't it? The visual http://blog.mathplayground.com/2012/09/algebra-for-all.htmlnoreply@blogger.com (mathplayground)0tag:blogger.com,1999:blog-1667542146821160523.post-3189492070689364022Mon, 10 Sep 2012 14:30:00 +00002012-10-20T22:26:32.875-04:00projectile motionprogramming While foraging for markers, a student in one of my math and programming classes stumbled upon some old science equipment I keep in the closet. The air-propelled rocket launcher was promptly brought out of retirement and set up in the long rectangular space at the rear of the math center. It wasn't long before a rousing game of "hit the target" was underway. Based on the number of times the http://blog.mathplayground.com/2012/09/tactical-rescue-missions-for.htmlnoreply@blogger.com (mathplayground)0tag:blogger.com,1999:blog-1667542146821160523.post-5436066838684072701Fri, 07 Sep 2012 16:00:00 +00002012-10-20T23:08:55.416-04:00misconceptionsfractionsteachingfactors A seventh grade student came to the math center to prepare for a test on fractions. She brought in a review sheet with various practice problems which she completed with time to spare. The student, somewhat anxious about the test, asked if I could make up problems on the whiteboard. I complied and wrote out the following problem: My student proceeded to simplify by canceling common http://blog.mathplayground.com/2012/09/stumbling-upon-misconceptions.htmlnoreply@blogger.com (mathplayground)0tag:blogger.com,1999:blog-1667542146821160523.post-8150130743926779194Tue, 04 Sep 2012 15:00:00 +00002012-10-20T23:08:39.308-04:00programmingleast common multiplegreatest common factor A student in my middle level programming course brought in a word problem from school. "The Billy Bonkers candy factory is having a contest. The candy makers placed a silver ticket in every 600th chocolate bar and a golden ticket in every 720th chocolate bar. Anyone who purchases a chocolate bar containing both tickets wins the grand prize. If 10,000 chocolate bars are sold, how http://blog.mathplayground.com/2012/09/euclid-comes-to-programming-class.htmlnoreply@blogger.com (mathplayground)0tag:blogger.com,1999:blog-1667542146821160523.post-243913507833972114Thu, 30 Aug 2012 13:00:00 +00002012-10-20T23:09:29.008-04:00teachinglearning Many of my students attend a private K-8 school that offers a very traditional math curriculum. Students in grades 5, 6, and 7 spend many months studying shopkeepers' math. The main focus is percentages - discounts, sales tax, tip, simple and compound interest, commissions, annuities, etc. Each of these variations is taught as a series of formulas to be memorized. The vocabulary is beyond http://blog.mathplayground.com/2012/08/busy-learning.htmlnoreply@blogger.com (mathplayground)0tag:blogger.com,1999:blog-1667542146821160523.post-6518634891727435337Tue, 28 Aug 2012 21:30:00 +00002012-10-20T23:07:30.506-04:00teachinglearningprogrammingalgebra One of the advantages of teaching in a learning center rather than a classroom is that I often get to see the same student at various stages of his or her academic life. A student who is in one of my precalc classes today was the very first student I ever taught. Back then it was number facts and place value. Today it's trig identities and parametric equations. While I haven't seen this http://blog.mathplayground.com/2012/08/a-math-problem-revisited.htmlnoreply@blogger.com (mathplayground)0tag:blogger.com,1999:blog-1667542146821160523.post-1746263265411771818Mon, 27 Aug 2012 07:00:00 +00002012-10-20T22:10:58.154-04:00teachingI drive my students crazy. I know I do. And this is why. Student: Is this right? Me: What do you think? Student: I don’t know. Me: Well, how did you get your answer? Student: I just did what you showed me before. Me: Ok, but what does that look like for this problem? Student: (utterly exasperated) Why can’t you ever just say yes or no? Me: (to myself) Because saying yes or no is the easy http://blog.mathplayground.com/2012/08/fun-for-whom.htmlnoreply@blogger.com (mathplayground)0tag:blogger.com,1999:blog-1667542146821160523.post-624793725679267229Fri, 24 Aug 2012 13:30:00 +00002012-10-20T23:12:17.610-04:00equation of a linegraphingfunctions "Four frightened Zogs have left the safety of their planet and are floating around in space. The Duplicators, a band of space travelers with the ability to imitate others, have infiltrated the floating Zogs. This is making the rescue mission very difficult.Fortunately, the Zogs are very clever. They can assemble themselves along a straight line path. The Duplicators cannot exist on this http://blog.mathplayground.com/2012/09/save-zogs.htmlnoreply@blogger.com (mathplayground)0tag:blogger.com,1999:blog-1667542146821160523.post-3360794212711014155Wed, 22 Aug 2012 12:30:00 +00002012-10-20T23:06:55.864-04:00teachingsubtractionregrouping I had an opportunity to spend some time with a very enthusiastic group of third grade students at a local school. They were subtracting three digit numbers by regrouping and were doing quite a spectacular job. That is, until we reached the dreaded Middle Zero. The problem was 601 - 347. The following is an actual transcript of the dialogue that ensued. Me: Does anyone know how to do this http://blog.mathplayground.com/2012/10/middle-zeros.htmlnoreply@blogger.com (mathplayground)0tag:blogger.com,1999:blog-1667542146821160523.post-3200978633026153227Mon, 20 Aug 2012 14:30:00 +00002012-10-20T21:57:06.355-04:00comparing fractionsequivalent fractions My fourth grade students are learning how to compare fractions. They've mastered this concept for very specific types of comparison problems, for example, when the denominators are the same and when the numerator is 1. Now I'm trying to teach them how to decide if a fraction is less than or greater than 1/2. They seemed to really grasp the idea that there are many ways to express the http://blog.mathplayground.com/2012/08/comparing-fractions.htmlnoreply@blogger.com (mathplayground)0tag:blogger.com,1999:blog-1667542146821160523.post-6412932682977293490Fri, 17 Aug 2012 16:00:00 +00002012-10-20T21:52:48.861-04:00divisionfractionsteaching When it comes to the dividing fractions, I have to admit that I graduated from the school of "Don't Ask Why, Just Invert and Multiply". Were you taught something similar? There are so many things wrong with that approach. It reinforces misconceptions that students may have about the mysterious and magical nature of math. Is dividing 1/4 by 1/3 really so incomprehensible that we shouldn't http://blog.mathplayground.com/2012/08/invert-and-multiply.htmlnoreply@blogger.com (mathplayground)0tag:blogger.com,1999:blog-1667542146821160523.post-233775510209572574Fri, 10 Aug 2012 13:00:00 +00002012-10-20T21:39:26.994-04:00multi-step problemsmath word problems Engaging students has always been a considerable challenge for teachers. Fortunately, there are a vast amount of resources and technologies available to help meet that challenge. One resource for upper elementary and middle school students is a catalog of animated word problems that guide students through the process of solving multi-step problems. The narrator and animated host is a http://blog.mathplayground.com/2012/08/animated-word-problems.htmlnoreply@blogger.com (mathplayground)0tag:blogger.com,1999:blog-1667542146821160523.post-3911797606553058094Tue, 07 Aug 2012 00:21:00 +00002012-10-20T21:46:21.078-04:00mindstormsmathlandseymour papert The book that influenced my approach to teaching mathematics to children is Mindstorms by Seymour Papert. Subtitled Children, Computers, and Powerful Ideas, this book provided a glimpse into a world of which I knew little but eagerly wished to learn more. As promised, powerful ideas emerged quickly and continued to be revealed at every turn. The most compelling idea for me, the one that http://blog.mathplayground.com/2012/08/learning-in-mathland.htmlnoreply@blogger.com (mathplayground)0tag:blogger.com,1999:blog-1667542146821160523.post-8299627157886734647Fri, 03 Aug 2012 14:00:00 +00002012-10-20T21:20:03.947-04:00introduction Welcome to the Math Playground blog. My name is Colleen and I've been deeply immersed in teaching and learning math for the past 15 years. It all began when my husband and I co-founded a math learning center in the Boston area called Math Advantage. Over the years, we've taught math to thousands of K-12 students. Some of our students come to review math concepts they're studying in school; http://blog.mathplayground.com/2012/08/an-introduction.htmlnoreply@blogger.com (mathplayground)0