Illustrative Mathematics
A Midpoint Miracle
Young geometers develop one of the fundamental properties of quadrilaterals (connecting side midpoints gives a parallelogram) in this short but thought-provoking exercise. Using a combination of hands-on techniques and abstract algebraic...
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V-Numbers
High schoolers explore problem solving strategies. Gin a novel situation, students develop a mathematical theory. Through models and mathematics, high schoolers justify their solution. Students definea V-sets and discuss conjectures...
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The Distributive Property
Students review how to solve problems using the Distributive Property of Mathematics. They solve problems using the paper and pencil method and then use the graphing calculator to discover the property over addition while making a visual...
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Consecutive Numbers
Like all of the Problem Solving units, this one aims to introduce students to the underlying ideas of mathematics through a problem. The problem here requires a knowledge of arithmetic and the use of some algebra. In this unit we see how...
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Hot Wheels
Students observe the action produced by toy cars. In this geometry lesson, students discuss motion and distance as they relate to the movement of a spherical object.They collect data and make conjectures based on their data.
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Perimeters, Patterns, and Conjectures
Students discover patterns and write conjectures relating to perimeters and polygons. Working in cooperative learning groups, they use manipulatives and graphic organizers to solve problems then answer a series of questions in which they...
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High School Mathematics Problems from Alaska: Extensions of Data: Barrow, Alaska Sunrise/Sunset Information
Students using given data to extrapolate new information, using a linear equation to predict later behavior, and using previous knowledge to synthesize new conjectures.
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Graphs of Linear Functions and Rate of Change
Discover an important property of linear functions. Learners use the slope formula to calculate the rates of change of linear functions. They find that linear functions have constant rates of change and use this property to determine if...
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Trigonometric Identity Proofs
Proving a trig identity might just be easier than proving your own identity at the airport. Learners first investigate a table of values to determine and prove the addition formulas for sine and cosine. They then use this result to...
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First-Person Computer Games
How do graphic designers project three-dimensional images onto two-dimensional spaces? Scholars connect their learning of matrix transformations to graphic design. They understand how to apply matrix transformations to make...
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Worksheet 1: Fibonacci Numbers
In this Fibonacci learning exercise, students prove by induction the Fibonacci numbers are recursive. They find a recursive definition for a given set of numbers. This two-page learning exercise contains five multi-step problems that...
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Four Color Theorem
Students identify and interpret how the Free Response questions are graded on an AP Exam. They also discuss coloring the included map, placing several examples on the board to determine the number of colors necessary to color each....
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Mathematics in Robotics
Students build and create using math. In this geometry lesson, students differentiate between congruent and similarity as they observe polygons. They create robots with different functions using properties of geometry.
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Conjectures For Intersecting Circles
Young scholars identify properties of circles. In this geometry lesson, students identify the center of two intersecting circles.They use Cabri software to create circles and move it around to make observation.
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What is s and t?
Students formulate and solve various types of equations. They become familiar with different types of patterns and apply the knowledge to solving mathematical problems from analyzing them.
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Tennis Tournament
In this secondary mathematics worksheet, students determine the how many matches that must be palyed in a tennis tournament given the number of players and the tournament constraints. The one page worksheet contains one problem with the...
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The Secret of the Crystal Ball
Eighth graders use mathematical expressions to solve problems. In this basic properties of operations, 8th graders use prior knowledge and logical reasoning to solve equations. Students analyze an equation by solving a trick problem to...
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Exploring Characteristics of Triangles
Students draw triangles and explore the classification of each using the measures of interior angles and lengths of sides. They investigate the sum of the interior angles of various triangles and conjecture and prove the theorem: The...
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The Pythagorean Theorem
Learners create both a visual and formal proof of the Pythagorean theorem, as well as view four additional geometric demonstrations of the theorem. They construct a square and conjecture the following theorem: The sum of the areas of...
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Exploring Centers of a Triangle: Part 2
Students model and solve a real-world problem by constructing the centroid of a triangle. They explore relationships of the medians of a triangle and investigate how the centroid partitions each of the medians. Students investigate...
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Investigating Patterns to Develop Logarithm Rules
In this logarithmic worksheet, students make conjectures regarding the rules for condensing and expanding logarithms by investigating patterns. This is designed to be done as a group activity.
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Which Quadrilateral Is It?
Young scholars prove conjectures about geometric figures on the plane or in space using coordinate geometry. They develop fluency in operations with real numbers, vectors and matrices using mental computation or paper-and-pencil...
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Polydron Fun
Young scholars investigate nets as they relate to volume and area. In this geometry lesson, students use nets as a visual to deepen their understanding of surface area and volume of objects. They make conjectures about different objects...
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Patterns and Possibilitiies
Students gain an understanding of the value and importance of patterns in mathematics. Through video, interaction and hands-on activities, students identify concrete and abstract patterns incorporating logic and deductive and inductive...