tag:blogger.com,1999:blog-1667542146821160523Sat, 28 Jun 2014 06:20:42 +0000teachingfractionsdivisionlearningprogrammingsubtractionadditionalgebraic thinkingareacomparing fractionscurvesdecimalsgeometrymultiplicationperimeterproblem solvingproportionsratiosDonorsChoose.orgThinking Blocksalgebrabalance scale problemsbar modelsbasic factscommon core state standards for mathematicsconversion factorsequation of a lineequivalent fractionsfactorsfunctionsgeoboardgraphinggraphsgreatest common factorintegersintroductionleast common multiplelinear functionsmath conceptsmath equationsmath gamesmath manipulativesmath word problemsmathlandmindstormsmisconceptionsmodel drawingmoneymulti-step problemsordering fractionspattern blockspre-algebraproblem solving with fractionsprojectile motionproportionpythagorean theoremratioreflectionregroupingrotationseymour papertshapesspirographsymmetrytimetranslationtrig functionsvisual equationsvisual math modelsMath PlaygroundEducational resources, thinking games, learning activities, and teaching ideas for math educators.http://blog.mathplayground.com/noreply@blogger.com (mathplayground)Blogger26125tag:blogger.com,1999:blog-1667542146821160523.post-3898285579831335898Sun, 01 Dec 2013 14:00:00 +00002013-12-03T12:04:50.915-05:00DonorsChoose.orgMath Playground and DonorsChoose.org
Since 2009, Math Playground has helped more than 22,000 students get the supplies they need through DonorsChoose.org. Our goal is to triple that number by the end of 2013.
During the month of December, Math Playground will contribute $1 to DonorsChoose.org every time our Facebook page gets a new like. We are set to donate a maximum of $12,000 to classroom projects around the country. But we http://blog.mathplayground.com/2013/12/math-playground-and-donorschooseorg.htmlnoreply@blogger.com (mathplayground)0tag:blogger.com,1999:blog-1667542146821160523.post-6582146377615336267Tue, 15 Jan 2013 01:38:00 +00002013-01-14T20:38:02.640-05:00additionbar modelscommon core state standards for mathematicsdivisionfractionsmodel drawingmultiplicationproportionratiosubtractionThinking Blocksvisual math modelsThinking Blocks and the Common Core
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 +00002012-11-26T19:47:24.364-05:00additionbasic factsdecimalsdivisionfractionsintegersmath gamesmoneymultiplicationpre-algebraproportionsratiossubtractiontimeStay Sharp Math Arcade
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 +00002012-10-29T08:00:00.649-04:00areageoboardgeometryperimeterGeometry and More with GeoboardsThe 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 +00002012-10-21T22:10:31.015-04:00fractionsmath manipulativespattern blocksproblem solvingteachingVersatile Pattern Blocks
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 fractionsordering fractionsproblem solving with fractionsEscape from Fraction Manor
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 +00002012-10-22T08:49:58.456-04:00areaconversion factorscurvesgraphslinear functionsperimeterproportionspythagorean theoremratiostrig functionsReal World Math
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 +00002012-10-21T20:12:04.401-04:00curvesmath equationsspirographSpirograph MathFor 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 solvingProblem Solving with Fractions
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 +00002012-10-20T23:11:34.291-04:00algebraic thinkingbalance scale problemsCan Your Third Graders Do This?Solve 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 +00002012-10-20T23:05:33.804-04:00geometryreflectionrotationshapessymmetrytranslationTeaching Transformations
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 +00002012-10-20T23:20:50.466-04:00decimalslearningmath conceptsteachingStories for Em
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 +00002012-10-21T20:23:59.022-04:00algebraic thinkingvisual equationsAlgebra for AllSolve 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 +00002012-10-20T22:26:32.875-04:00programmingprojectile motionTactical Rescue Missions for Intergalactic Good
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 +00002012-10-20T23:08:55.416-04:00factorsfractionsmisconceptionsteachingStumbling Upon Misconceptions
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 +00002012-10-20T23:08:39.308-04:00greatest common factorleast common multipleprogrammingEuclid Comes To Programming Class
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 +00002012-10-20T23:09:29.008-04:00learningteachingBusy Learning
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 +00002012-10-20T23:07:30.506-04:00algebralearningprogrammingteachingA Math Problem Revisited
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 +00002012-10-20T22:10:58.154-04:00teachingFun For Whom?I 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 linefunctionsgraphingSave the Zogs
"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 +00002012-10-20T23:06:55.864-04:00regroupingsubtractionteachingMiddle Zeros
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 fractionsComparing 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 +00002012-10-20T21:52:48.861-04:00divisionfractionsteachingInvert and Multiply
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 +00002012-10-20T21:39:26.994-04:00math word problemsmulti-step problemsAnimated 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 +00002012-10-20T21:46:21.078-04:00mathlandmindstormsseymour papertLearning in Mathland
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)0