Math Mosaics
Emotional Frogs
Math Tools
Awesome, Outstanding, Excellent, Great, Amazing, Really Cool, 5th Graders!
Math Tools For Building Confidence
Area Constructs
Fractions Sushi
Entrepreneurial Place Value
Fundamentally Fractions
Alex and Chase Challenge

Alex and Chase Challenge

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Voluminous challenge tackled piece by piece

Students spent the morning engrossed in reading a blockbuster cereal hit of sorts. It was the challenge booklet for the Alex and Chase math challenge. It’s about a frog named Alex and a turtle named Chase and a disagreement over how to furnish their college apartment. Alex is studying to become a doctor; Chase, who is good at math and art, doesn’t know what he wants to be yet. He does know that he does NOT want Alex to bring all of his things inside the apartment; it will suck up all of the air. Alex owns all of the round things and Chase owns all of the cubes. Students will have to calculate the volume of several rooms in order to help the hapless roommates to settle their differences. It is an honor to watch children eating their cereal with one hand and reading your work with other.

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Imagination takes on a very important function in human behavior and human development. ~ Vygotsky 1967

Fundamentally Fractions

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Hands-on work with the common fraction

Numbers are abstractions. For young mathematicians, fractions can be some of the most baffling abstractions ever. Even the way we write fractions is baffling: a one with a bar and a four beneath it is read as ‘one fourth’ and ‘one fourth’ is actually a number. What on earth can this baffling set of symbols really represent? Even before children are taught that decimals, ratios, and percentages are also fractions, they need support to understand how the strange configurations we call common fractions work.

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Entrepreneurial Place Value

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Banking for a practical number sense

Students in sole proprietorships or partnerships keep the banker busy as they earn base-ten units with each roll of their dice. By placing their groups of ten on the correct columns of their company’s place-value mat, they trade units for longs, and longs for flats as their mats fill with earnings. Student entrepreneurs who maintain orderly transactions should be able to tell the banker what the value of their business is whenever prompted. This gently competitive exercise helps students learn and improve their knowledge and understanding of  place value.

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Math Tools For Building Confidence

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Dignity and support for struggling mathematicians

Students in small group math sometimes need help learning a particular concept. Some are missing understanding of some basic skills and concepts. Some are nervous about math—period. Some are reluctant to admit they need help at all. Each student signs an individual job bag. This bag holds work. This is engaging work designed to help students to overcome their math anxiety. The weekly assignments coincide with and reinforce concepts the general class will learn in the unit. Students don’t fall behind, plus they have the confidence to participate more in the general math class. Basic skills building exercises are created to help students gain the math know-how they’ll need in order to keep up with the general math unit.

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Awesome, Outstanding, Excellent, Great, Amazing, Really Cool, 5th Graders!

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Community building packets for 5th Graders

In two consecutive classes, students returned from their recess break to find packets on their desks. Each packet contained 3 paperclips and a leaf. Each packet instructed an Awesome, Outstanding, Excellent, Great, Amazing, or Really Cool 5th Grader to make a chain, then find another 5th Grader with a specific attribute and to connect their chains made from the paperclips and the leaf. The result was a chain that cascaded the length of the classroom, plus, an opportunity for the new students to interact with each other on a positive and fun reminder that they can all plant seeds of greatness.

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Emotional Frogs

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Strategies for managing healthy classroom communities

Anyone here ever tried to catch a frog? I asked. Hands wave in the air. Tell us about it, was it difficult to catch? Where did you keep it? Did it try to escape? From that conversation, emotional frogs was born. Emotions are a lot like frogs; they’re hard to take care of, and even harder to catch once they get away. In this exercise, students in groups of six were given the task of coloring two frogs. They had only six minutes, they had to take turns, each of them had to use the one pencil, crayon, or marker they were given, and when the two minute timer went off, they had to stop…and pass the frogs! This was a huge test of community. We discussed what it felt like to wait and watch their teammates coloring the frog differently than they would. We discussed what it felt like to worry that they wouldn’t get a chance to contribute. We talked about all of the emotions they felt while they scrambled to complete the task and learn to trust their classmates at the same time. These are just some of the emotional frogs the teams colored. They are double because the exercise was done by two sets of 5th Graders. In weekly SecondStep classes, now called ’emotional frogs’ by the students, we’ve discussed everything from lying and stealing, to cheating, anger, and bullying. The habitat for the emotional frogs grows every week. The grass and foliage are made from reflections written on green paper triangles. The character words came from discussions of the underlying reasons students gave for the decisions they make.

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Play creates a zone of proximal development in the child. In play, the child always behaves beyond his average age; above his daily behavior; in play, it is as though he were a head taller than himself. As in the focus of the magnifying glass, play contains all of the developmental tendencies in a condensed form and is itself a major source of development.  ~ Lev Semionovich Vygotsky

Math Mosaics

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Patterns and perspective in problem solving

Faced with a block of plywood, a grid, and two sizes of mosaic tiles—one is a quarter the size of the other—students design one of their initials. They struggle to make shapes appear to angle or curve using square patterns of 4 to 1. Up close, their attempts do not appear to be letters at all. Yet, when the perspective is changed a different picture emerges. This is what happens with any mathematical challenge. We have to zoom in to see what the challenge is and to collect important information and details. We might zoom out to see the whole picture, to determine what the goal is, to think, predict, or estimate. Next, we zoom in to see the details, to understand how the challenge works, what it needs; we choose a strategy and carefully try it out. We zoom out again to see if the strategy worked, if the results matched our prediction, if our estimate was even close. We’re not done until we’ve zoomed in once more, this time, to check our work. This exercise helps students learn that beautiful solutions are not all about the right or obvious answer.  A creative approach to mathematical challenges often involves a search for patterns and many changes in focus. In this case, students were pleasantly surprised to see that, in most cases, their initial struggles did in fact result in recognizable and beautiful letters.

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