Fraction Mash is a great learning toy for meaningful exploration time during any fraction unit in elementary or middle school. Give kids some unstructured time to play around and create their own mash-ups, then ask each student or group to do some mathematical reflection and justification to bring the lesson back to fractions. You can also provide images that might be relevant to your school or content from other classes for some interdisciplinary flavor. It's also not a bad idea to keep Fraction Mash around as an option to keep kids meaningfully occupied during standardized testing downtime or other lost classroom time.
If you need more structure to get started, check out NYCSI's website for a bunch of thoughtfully prepared lesson plans and ideas or teacher-submitted tips, ideas, and inspirations.Continue reading Show less
Fraction Mash is a math-inflected version of the now ubiquitous face-mash-up apps. Students combine two images by dividing each into equal parts using a variety of division schemes, then select which parts of each image to keep. The resulting mash-up is then displayed, and edges can be blurred to seamlessly blend the two images. Ridiculous combinations of faces, animals, shapes, abstract designs, or almost anything else can be made. Along the way, the selected fractions of each image are displayed as an addition problem, and students can directly change the numerators and denominators of each to see how this affects the image.
The app also features a built-in reflection tool in which students can choose from a variety of templates and insert images or videos. The tool also lets students write about their creations, either as part of a formal unit or for a final presentation or report.
There are three ways that Fraction Mash is great for student learning. First, it uses creative play to keep kids engaged in tinkering, remixing, and exploring, which helps to build curiosity and persistence. Second, it promotes student agency by giving kids a choice about which images to use and how to combine them. Third, it presents fractions as partitions of a whole and keeps the notion of unity at the core of its pedagogy. This strategy has been used by successful learning programs such as Montessori and Waldorf schools for decades because it's such an intuitive way to grapple with numerators and denominators. Ultimately, it would have been nice to see some extensions to the math concepts, such as mixed denominators, subtraction, or fractions that add to less than or more than one. These would be fairly easy to implement but would add a lot to the learning potential.
Ultimately, it would have been nice to see some extensions to the math concepts, such as mixed denominators, subtraction, or fractions that add to less than or more than one. These would be fairly easy to implement but would add a lot to the learning potential.
Key Standards Supported
Number And Operations—Fractions
Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.
Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.
Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)
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