Fractured Fraction Puzzles - MathPickle PDF Free Download

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Fractured Fraction Puzzles1/21/31/41/21/31/7

ContentsMost of the first classwill be spent here. .Rules for FracturedFraction Puzzles3. .Common Core Standards4. .Puzzle to project andsolve as a class5First worksheet. .8. .9Projectable solutions of first worksheet. . 22Second worksheet. .Projectable solutions of second worksheet23. . 34Multi-color puzzlesMore projectable . .puzzles38Some students benefit fromcreating their own puzzles. .Pictures for creatingyour own puzzles62Blanks for creating. .your own puzzles71About MathPickle. . 77Copyright 2014 MathPickle - All rights reserved

Fractured Fraction PuzzlesThese puzzles belong in any classroom learning about equivalent fractions.Here’s an example: Cover the 7x7 tiles of the yellow submarine with threerectangles One rectangle must be half yellow; one must be a thirdyellow, and one must be a quarter yellow.After a little exploration you’ll find one or both of these solutions to theyellow submarine.8/16 1/27/21 1/33/12 1/41/21/38/16 1/27/21 1/33/12 1/43/128/163/127/211/48/16The following looks like it might be correct. The upper left rectangle hasgot 4/12 grey which is equivalent to 1/3. Good we’ll check off that.7/21Students inventing their own puzzles may decide to use multiple colors. Inthis case, when a fraction is specified, the color must also be specified. Forexample here is the solution to Lauren & Noelle’s cupcake puzzle:4/121/21/3 1/41/31/31/41/7Unfortunately, the bottom rectangle is 7/21 grey which is also equivalentto 1/3. The upper right rectangle (which is also a square) is 7/16 which is adisaster because it doesn’t simplify.

Standards forMathematical PracticeAll MathPickle puzzle designs, includingCommon CoreState StandardsFracturedFraction Puzzles, are guaranteed to engage a wideFractured Fraction Puzzlestargets the following Common Core State Standards:,spectrum of student abilities while targeting theGrade 3following Standards for Mathematical Practice:MP1 Toughen up!This is problem solving where our students developgrit and resiliency in the face of nasty, thornyproblems. It is the most sought after skill for F.A.1Explain equivalence of fractions in specialRecognize and generate equivalentcases, and compare fractions by reasoningfractions.about their size.CCSS.MATH.CONTENT.4.NF.A.2students.MP3 Work together!This is collaborative problem solving in which studentsdiscuss their strategies to solve a problem and identifyGrade 4CCSS.MATH.CONTENT.3.NF.A.3.ACompare two fractions with differentUnderstand two fractions as equivalentnumerators and different denominators,(equal) if they are the same size, or thesame point on a number line.missteps in a failed solution. MathPickle recommendspairing up students for all its puzzles.CCSS.MATH.CONTENT.3.NF.A.3.BRecognize and generate simple equivalentMP6 Be precise!fractions.This is where our students learn to communicate usingprecise terminology. MathPickle encourages studentsnot only to use the precise terms of others, but toinvent and rigorously define their own terms.CCSS.MATH.CONTENT.3.NF.A.3.DCompare two fractions with the samenumerator or the same denominator.MP7 Be observant!One of the things that the human brain does very wellis identify pattern. We sometimes do this too well andidentify patterns that don't really )

Yellow Submarine1/21/31/4

ElephantJellyfishRabbitFrogPiranhaCamel

Piranha1/21/3

Camel1/21/31/4

Rabbit1/21/31/7

Jellyfish1/21/31/4

Frog1/21/31/4

Elephant1/21/31/4

Spiral1/22/3

Yellow Submarine1/21/31/4

Eyeball1/71/41/3

House number 113/1111/2011/2811/33

Shopping Cart1/211/81/41/36/7

Shopping Cart1/211/216/71/41/81/81/41/31/36/7

Uncomfortable Clog⅓⅓⅓⅓⅓⅓

Sunrise½½½

Broken Heart1/101/42/52/3

Garbage Can1/22/53/53/73/8

Garbage Can3/51/22/53/71/23/53/73/82/53/8

Fractured tree1/101/43/74/5

Fractured tree3/71/101/41/43/74/54/51/10

1/21/121/21/33/52/51/21/31/53/52/33/5

21/33/52/51/21/31/53/53/52/3Blast-Off

Fraction 91/22/3

Fraction 88/108/15

Fraction Seven1/21/5

Fraction Six1/22/32/3

Fraction Five1/21/5

Fraction four1/21/31/5

Fraction 31/93/53/52/3

Fraction 21/22/5

Fraction 11/121/23/5

Fraction 01/21/3

elibss rpo taim s1/21/33/41/229/11

Robot1/32/51/27/9

Robot1/21/32/51/27/92/57/91/3

Pick-Up Truck

The Red Balloon

Pointer

Loud Music

Pointer Finger

Put Your Students in a Pickle!I’m a father of two elementary school children, a mathematician, anddesigner of puzzles and board games. Students call me Dr. Pickle. There isnothing I enjoy more than stumping students and having them stump me.I founded MathPickle.com in 2010 to inject new ideas into the classroom.MathPickle’s primary objective is to get thirteen curricular unsolvedproblems into classrooms worldwide - one for each grade K-12. Aconference in November 2013 established the thirteen unsolved problems.To aid with the dissemination of these awesome problems, MathPickle islooking at setting up a 1,000,000 reward for each - the prize money tobe split between the person who solves the problem and their mostinspirational K-12 educator.MathPickle is also developing a range of curricular puzzles like the onesyou’ll find at TpT. These help teachers them with their number onechallenge:“How to engage the spectrum of student ability?”Whenever an elementary school teacher wants to teach addition, she willinvariably face 20% of students who already know how to add andanother 20% who are struggling with last year’s curriculum. How can sheengage the top students without losing the bottom students? How can sheengage the bottom students without boring the top students?One solution: Parents of top students often ask that their child be allowedto accelerate through the curriculum. This exacerbates the problem forfuture teachers, and sets up a failure-impoverished education experiencefor the bright student.A wiser approach is to use curricular puzzles, games and mini-competitionsto simultaneously teach curriculum to the students who need it, and todeflect top students into tough problem solving activities. This is nevertime wasted, because problem solving is the primary reason we teachmathematics.The experience of mathematics should be profound and beautiful. Toomuch of the regular K-12 mathematics experience is trite and true.Children deserve tough, beautiful puzzles.Gordon HamiltonMMath, PhD

All MathPickle puzzle designs, including Fractured Fraction Puzzles, are guaranteed to engage a wide spectrum of student abilities while targeting the following Standards for Mathematical Practice: