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  Teachers in Brookline, Massachusetts, selected the following problems as their favorites. |
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Mystery addition
In this group of questions students are asked to attach units to numbers in the addition examples so that arithmetic is correct. (Date Revised: 3/12/2001).
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Age-related algebra
Students will use their understanding of basic algebra to translate between verbal age-related descriptions and algebraic expressions. (Date Revised: 6/27/2001).
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Graphing motion with numbers
Students will use their understanding of linear functions to extract information from the graphs describing motion at constant speed. (Date Revised: 3/15/2001).
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Triangle with restricted angle sum
In this very short problem, students employ proof by contradiction in a non-formal way, while examining relationships among angles in triangles. (Date Revised: 2/27/2001).
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Balance the cookies, or balance the variables
Students solve a system of linear equations by using a balance model. Credits: The idea came from the problem in a Japanese textbook.. (Date Revised: 4/9/2001).
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Checkers challenge
Students learn addition and subtraction of signed whole numbers by playing two games. One models the numbers using checkers or colored counters; the other uses the same play structure but has students use the numbers themselves. (Date Revised: 3/8/2001).
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Lattice Point Polygons
Under constraints that make the problem a puzzle, students seek ways of creating various polygons whose vertices have integer coordinates. They review and practice the classification and characteristics of various polygons, and ways to determine the length and perpendicularity of segments. Suitable for homework.Credits: Robert J. Reed, Brown Middle School, Newton, MA. (Date Revised: 3/20/2001).
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Maximum Areas
Students investigate maximum area of triangles with two fixed sides and parallelograms with fixed sides. (Date Revised: 6/28/2001).
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Fill the Square
Students use their knowledge of area and perimeter of triangles, rectangles, and trapezoids to solve puzzles.Credits: Robert J Reed, Brown Middle School, Newton, MA. (Date Revised: 4/11/2001).
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Number line
Students develop their understanding of representing numbers as points on a number line while practicing their problem solving skills. Credits: Adapted from a curriculum written by Alexander Shen, Moscow, Russia. (Date Revised: 5/14/2001).
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What's the distance between these points?
This problem about the distance between points on a line helps students learn to consider all possible cases. (Date Revised: 5/31/2001).
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About sushi
These problems informally introduce students to combining linear equations. They can be used prior to solving systems of linear equations.Credits: By Mark Saul. (Date Revised: 5/31/2001).
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When perimeter equals area (right triangle)
Students are asked to find right triangles with whole number dimensions for which the perimeter and area are equal. Students must find a reason why there are only two such triangles. (Date Revised: 7/9/2001).
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Coins in my pocket
Students must find the least number of coins that can be in a given number of pockets, if each pocket must hold a different number of coins.Credits: by Gil French. (Date Revised: 9/13/2001).
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What is it?
Various angles and sides of these inaccurate pictures of quadrilaterals are marked congruent. Students analyze the figures and use their knowledge of basic definitions and theorems to determine precisely what kind of quadrilateral the figure is. (Date Revised: 10/4/2001).
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Arithmetic Expressions / Equations / Inequalities