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The Volume Formula of a Pyramid and Cone
Our teacher told us the formula had one-third, but why? Using manipulatives, classmates try to explain the volume formula for a pyramid. After constructing a cube with six congruent pyramids, pupils use scaling principles from...
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Recursive Challenge Problem—The Double and Add 5 Game
Math is all fun and games! Use a game strategy to introduce the concept of sequences and their recursive formulas. The activity emphasizes notation and vocabulary.
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Properties of Trigonometric Functions
Given a value of one trigonometric function, it is easy to determine others. Learners use the periodicity of trigonometric functions to develop properties. After studying the graphs of sine, cosine, and tangent, the lesson plan...
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Introduction to Simultaneous Equations
Create an understanding of solving problems that require more than one equation. The lesson introduces the concept of systems of linear equations by using a familiar situation of constant rate problems. Pupils compare the graphs of...
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Existence and Uniqueness of Square Roots and Cube Roots
Teach cube roots by building on an understanding of square roots. The third installment of a 25-part series asks learners to solve simple quadratic and cubic equations using roots. Scholars compare square roots and cube roots throughout...
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Pythagorean Theorem, Revisited
Transform your pupils into mathematicians as they learn to prove the popular Pythagorean Theorem. The 16th lesson in the series of 25 continues by teaching learners how to develop a proof. It shows how to prove the Pythagorean Theorem...
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Using Tree Diagrams to Represent a Sample Space and to Calculate Probabilities
Cultivate the tree of knowledge using diagrams with two stages. Pupils create small tree diagrams to determine the sample space in compound probability problems. The lesson plan uses only two decision points to introduce tree...
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Interpreting and Computing Division of a Fraction by a Fraction—More Models II
No more inverting and multiplying to divide fractions. Applying concepts of measurement division from the previous instructional activity, pupils consider partitive division using fraction bars and number lines. They first convert...
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Even and Odd Numbers
Even or not, here I come. Groups investigate the parity of products and sums of whole numbers in the 17th lesson in a series of 21. Using dots to represent numbers, they develop a pattern for the products of two even numbers; two odd...
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Ordering Integers and Other Rational Numbers II
Individuals build on prior knowledge to order a set of rational numbers from least to greatest or greatest to least. As part of the lesson, they order rational numbers written in different forms.
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Comparing Distributions
Data distributions can be compared in terms of center, variability, and shape. Two exploratory challenges present data in two different displays to compare. The displays of histograms and box plots require different comparisons based...
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Sine and Cosine of Complementary Angles and Special Angles
Building trigonometric basics here will last a mathematical lifetime. Learners expand on the previous lesson plan in a 36-part series by examining relationships between the sine and cosine of complementary angles. They also review...
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Equations for Lines Using Normal Segments
Describing a line using an algebraic equation is an essential skill in mathematics. The previous lesson in the series challenged learners to determine if segments are perpendicular with a formula. Now they use the formula to...
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Secant Angle Theorem, Exterior Case
It doesn't matter whether secant lines intersect inside or outside the circle, right? Scholars extend concepts from the previous lesson to investigate angles created by secant lines that intersect at a point exterior to the circle....
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Dividing by (x – a) and (x + a)
Patterns in math emerge from seemingly random places. Learners explore the patterns for factoring the sum and differences of perfect roots. Analyzing these patterns helps young mathematicians develop the polynomial identities.
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The Remainder Theorem
Time to put it all together! Building on the concepts learned in the previous lessons in this series, learners apply the Remainder Theorem to finding zeros of a polynomial function. They graph from a function and write a function from...
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Comparing Rational Expressions
Introduce a new type of function through discovery. Math learners build an understanding of rational expressions by creating tables and graphing the result.
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Graphing Systems of Equations
Expand on learners' understanding of quadratic-linear systems. Building on the graphic understanding developed in the previous instructional activity, pupils learn algebraic methods of solving the systems.
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Using Sample Data to Estimate a Population Characteristic
How many of the pupils at your school think selling soda would be a good idea? Show learners how to develop a study to answer questions like these! The lesson explores the meaning of a population versus a sample and how to interpret the...
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Ruling Out Chance (part 1)
What are the chances? Teach your classes to answer this question using mathematics. The first part of a three-day lesson on determining significance differences in experimental data prompts learners to analyze the data by...
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Drawing a Conclusion from an Experiment (part 2)
Communicating results is just as important as getting results! Learners create a poster to highlight their findings in the experiment conducted in the previous lesson in a 30-part series. The resource provides specific criteria and...
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Euler’s Number, e
Scholars model the height of water in a container with an exponential function and apply average rates of change to this function. The main attraction of the lesson is the discovery of Euler's number.
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Graphs Can Solve Equations Too
There are many equations Algebra I students are not ready to solve. Graphing to solve gives them a strategy to use when they are unsure of an algebraic approach to solve the problem. The lesson exposes learners to a wide variety of...
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Multiplying and Factoring Polynomial Expressions (part 2)
If you can multiply binomials, you can factor trinomials! This is the premise for a lesson on factoring. Pupils look for patterns in the binomials they multiply and apply them in reverse. Examples include leading coefficients of one...