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Problem Solving in Mathematics
Seventh graders discover that there are multiple strategies to be used in problem solving. They explain a problem solving situation in their own words and determine a possible strategy for solving the problem.
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Toothpick squares
Students state the general rule for a practical situation. They describe a continuing pattern. They use toothpicks to help visualize the problem and answer it correctly.
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Triangular Numbers
Pupils are introduced to the problem and brainstorm ideas for approaching the problem and keeping track of what has been done. They work in pairs and share their answers, explaining their reasoning.
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The Farmer's Sheep II
Fourth graders listen to the story of a farmer who only likes to be able to see nine sheet from his window. His wife has brought him another sheep - what now? They work together in pairs to solve the problem and share solutions.
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You Gotta Have Heart
Ninth graders investigate the concept of relations and interpret graphs and tables. They analyze given data and look for a pattern to determine if the numbers represent a function. Students practice solving scientific word problems that...
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The Basketball Tournament
Students estimate how many games are played if six teams play each other once. They investigate their own way and discuss possible strategies they might use. They then share their findings with the class.
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The Topsy-Turvy Twins
Fourth graders read the problem and brainstorm for ways to solve the problem - list these on the board for the students to refer to as they solve the problem. They work in pairs and focus on the strategy selected.
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Tetrominoes Cover-Up
Third graders are given square tiles and participate in a demonstration on how to arrange them. Using the tiles, they work with a partner to discover how many two-dimensional tetrominoes they can create. To end the lesson, they must...
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QwikQure Algebra
Fourth graders are introduced to the problem using a bottle of medicine. They estimate the volume of the medicine and predict the instructions on the bottle. They then think about how they might solve the problem before asking them to...
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Geometry /Tessellations
Students investigate the concept of tessellations and how they are formed using angles. They categorize how different patterns do and not tessellate and separate them into two different places for assessment. The teacher draws examples...
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Rows of Numbers
Students generate patterns from a structured situation, find a rule for the general term, and express it in words and symbols. They also devise and use problem solving strategies in a systematic way.
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Multiplicative Sequences
Students investigate the concepts related to the practice of multiplication facts. They look for number patterns in order to create an algorithm in order to find the correct sequencing of number patterning. The solutions are then...
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Jo's Table
Second graders work on the problem with a partner. They examine what they are supposed to be doing. They share the students's solutions making sure than they are looking for patterns along the diagonals.
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Chessboard Challenge
Second graders read "The King's Chessboard" by David Birch. The teacher reads the story aloud and pauses at several points for students to calculate the next number in a pattern of doubling.
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Basic Crypto Systems
Pupils try to solve codes mathematically. The use of a code needs a key. Students try to decipher a code with a mathematical key. This requires focus and higher order thinking skills like analysis.
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No-Three-In-A-Line Game
Students use logic and reasoning to answer problems. Through interpreting information and results in the context to examine patterns. They examine how to solve the problems using strategy in mathematics.
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Irregular Fractals
Students study and research irregular fractals and construct a few based on their research. Students practice pattern recognition skills and plane geometry skills calculating dimensions on the Fractured Pictures activity.
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The Great Button Sort
Young scholars practice figuring out how items have been sorted. They also sort buttons in small cooperative groups. They color and sort their own paper buttons and then give their button sort to another student to see if he or she can...
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Pepe Cleaners
Seventh graders gather data to determine the relationships between the base and height of rectangles with fixed perimeters and express the relationships using words and symbols. Students build rectangles with pipe cleaners. They create...
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Properties of Fractals
Students build a working definition of regular fractal, look carefully at the concepts of dimension and scale, and are introduced to logarithms. They solve simple exponential equations for the exponent both by trial and error and using...
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Properties of Fractals
Students build a working definition of a regular fractal, they measure the concepts of dimensions and scale, they explore the concept of a logarithm and they attempt to solve simple exponential equations for the exponent both by trial...
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The Mandelbrot Set
Students explore the Mandelbrot Set. They are introduced to the concept of a complex number and function in order to motivate the discussion of Julia and Mandelbrot sets. Students investigate fractals and how they are built.
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Visual Arts
Students recognize warm and cool colors in a different medium. They look carefully at slide of medieval stained glass.
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Exploding Numbers
Students discuss how numbers increase when exponential growth is occurring. They view a video and compare exponential and linear growth with a graphing calculator.