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Rotations, Reflections, and Symmetry
Lead your high school class on a journey through the world of symmetry and reflections as you discuss geometric principles. Pupils differentiate between reflections and rotations, explore rotational symmetry, and investigate how to...
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Making Scale Drawings Using the Ratio Method
Is that drawn to scale? Capture the artistry of geometry using the ratio method to create dilations. Mathematicians use a center and ratio to create a scaled drawing. They then use a ruler and protractor to verify measurements.
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Dilations from Different Centers
Can you follow a composition of transformations, or better yet construct them? Young mathematicians analyze the composition of dilations, examining both the scale factor and centers of dilations. They discover relationships for both...
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What Are Similarity Transformations, and Why Do We Need Them?
It's time for your young artists to shine! Learners examine images to determine possible similarity transformations. They then provide a sequence of transformations that map one image to the next, or give an explanation why it is...
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Properties of Similarity Transformations
You can explain it, but can you do it? After learners view a sequence of transformations, the next logical step is creating the transformation. Challenge your classes to construct a composition of transformations and verify the...
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The Side-Angle-Side (SAS) and Side-Side-Side (SSS) Criteria for Two Triangles to Be Similar
Playing with mathematics can invoke curiosity and excitement. As pupils construct triangles with given criteria, they determine the necessary requirements to support similarity. After determining the criteria, they practice...
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The Volume Formula of a Sphere
What is the relationship between a hemisphere, a cone, and a cylinder? Using Cavalieri's Principle, the class determines that the sum of the volume of a hemisphere and a cone with the same radius and height equals the volume of a...
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Perimeter and Area of Polygonal Regions in the Cartesian Plane
How many sides does that polygon have? Building directly from lesson number eight in this series, learners now find the area and perimeter of any polygon on the coordinate plane. They decompose the polygons into triangles and use Green's...
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A Focus on Square Roots
Pupils learn to solve square root equations and rationalize denominators. Problems include those with extraneous solutions.
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The Definition of a Parabola
Put together the pieces and model a parabola. Learners work through several examples to develop an understanding of a parabola graphically and algebraically.
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Extending the Domain of Sine and Cosine to All Real Numbers
Round and round we go! Pupils use reference angles to evaluate common sine and cosine values of angles greater than 360 degrees. Once they have mastered the reference angle, learners repeat the process with negative angles.
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Awkward! Who Chose the Number 360, Anyway?
Don't give your classes the third degree. Use radians instead! While working with degrees, learners find that they are not efficient and explore radians as an alternative. They convert between the two measures and use radians with the...
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Calculating Probabilities of Events Using Two-Way Tables
Tables are useful for more than just eating. Learners use tables to organize data and calculate probabilities and conditional probabilities.
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Calculating Conditional Probabilities and Evaluating Independence Using Two-Way Tables (part 2)
Without data, all you are is another person with an opinion. Show learners the power of statistics and probability in making conclusions and predictions. Using two-way frequency tables, learners determine independence by analyzing...
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Margin of Error When Estimating a Population Proportion (part 1)
Use the power of mathematics to find the number of red chips in a bag — it's a little like magic! The activity asks learners to collect data to determine the percentage of red chips in a bag. They calculate the margin of error and...
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Margin of Error When Estimating a Population Mean (part 2)
Don't leave your classes vulnerable in their calculations! Help them understand the importance of calculating a margin of error to represent the variability in their sample mean.
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Experiments and the Role of Random Assignment
Time to experiment with mathematics! Learners study experimental design and how randomization applies. They emphasize the difference between random selection and random assignment and how both are important to the validation of the...
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Margin of Error When Estimating a Population Mean (part 1)
We know that sample data varies — it's time to quantify that variability! After calculating a sample mean, pupils calculate the margin of error. They repeat the process with a greater number of sample means and compare the results.
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Ruling Out Chance (part 3)
Pupils analyze group data to identify significant differences. They use simulation to create their own random assignment data for comparison.
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Construct a Perpendicular Bisector
How hard can it be to split something in half? Learners investigate how previously learned concepts from angle bisectors can be used to develop ways to construct perpendicular bisectors. The resource also covers constructing a...
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Vectors in the Coordinate Plane
Examine the meaning and purpose of vectors. Use the lesson plan to teach your classes how find the magnitude of a vector and what it represents graphically. Your pupils will also combine vectors to find a resultant vector and interpret...
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Special Lines in Triangles (part 2)
Medians, midsegments, altitudes, oh my! Pupils study the properties of the median of a triangle, initially examining a proof utilizing midsegments to determine the length ratio of a median. They then use the information to find missing...
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Graphing Cubic, Square Root, and Cube Root Functions
Is there a relationship between powers and roots? Here is a lesson that asks individuals to examine the graphical relationship. Pupils create a table of values and then graph a square root and quadratic equation. They repeat the process...
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Characterize Points on a Perpendicular Bisector
Learn transformations through constructions! Pupils use perpendicular bisectors to understand the movement of a reflection and rotation. They discover that the perpendicular bisector(s) determine the line of reflection and the...
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