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Special Lines in Triangles (part 1)
Allow your pupils to become the mathematicians! Individuals explore the properties of a midsegment of a triangle through construction and measurement. Once they figure out the properties, learners use them to draw conclusions.
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Mid-Module Assessment Task: Grade 8 Module 1
Assess your young mathematicians' knowledge and understanding of the properties of exponents. The questions in the seventh lesson of 15 incorporate the properties learned in the first six modules of this series. Individuals use and apply...
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Examples of Functions from Geometry
Connect functions to geometry. In the ninth installment of a 12-part module, young mathematicians create functions by investigating situations in geometry. They look at both area and volume of figures to complete a well-rounded lesson.
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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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Real-World Area Problems
Not all structures take the shape of a polygon. The 21st lesson in a series of 29 shows young mathematicians they can create polygons out of composite shapes. Once they deconstruct the structures, they find the area of the composite figure.
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Writing Addition and Subtraction Expressions
Symbols make everything so much more concise. Young mathematicians learn to write addition and subtraction expressions — including those involving variables — from verbal phrases. Bar models help them understand the concept.
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Solution Sets to Simultaneous Equations (part 2)
Do you want your budding mathematicians to be able to explain 'why' and not just 'do'? This lesson encourages an understanding of the process of elimination. Pupils are expected to understand how and why the elimination method is a valid...
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Modeling Relationships with a Line
What linear equation will fit this data, and how close is it? Through discussion and partner work, young mathematicians learn the procedure to determine a regression line in order to make predictions from the data.
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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 and...
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Adding and Subtracting Expressions with Radicals
I can multiply, so why can't I add these radicals? Mathematicians use the distributive property to explain addition of radical expressions. As they learn how to add radicals, they then apply that concept to find the perimeter of polygons.
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The Volume of Prisms and Cylinders and Cavalieri’s Principle
Young mathematicians examine area of different figures with the same cross-sectional lengths and work up to volumes of 3D figures with the same cross-sectional areas. The instruction and the exercises stress that the two figures do not...
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Arc Length and Areas of Sectors
How do you find arc lengths and areas of sectors of circles? Young mathematicians investigate the relationship between the radius, central angle, and length of intercepted arc. They then learn how to determine the area of sectors of...
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Secant Lines; Secant Lines That Meet Inside a Circle
Young mathematicians identify different cases of intersecting secant lines. They then investigate the case where secant lines meet inside a 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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Graphing Factored Polynomials
Young mathematicians graph polynomials using the factored form. As they apply all positive leading coefficients, pupils demonstrate the relationship between the factors and the zeros of the graph.
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Basic Trigonometric Identities from Graphs
Have young mathematicians create new identities! They explore the even/odd, cofunction, and periodicity identities through an analysis of tables and graph. Next, learners discover the relationships while strengthening their understanding...
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Tides, Sound Waves, and Stock Markets
Help pupils see the world through the eyes of a mathematician. As they examine tide patterns, sound waves, and stock market patterns using trigonometric functions, learners create scatter plots and write best-fit functions.
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Proving Trigonometric Identities
Young mathematicians first learn the basics of proving trigonometric identities. They then practice this skill on several examples.
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Solve for Unknown Angles—Angles and Lines at a Point
How do you solve for an unknown angle? In this sixth installment of a 36-part series, young mathematicians use concepts learned in middle school geometry to set up and solve linear equations to find angle measures.
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The Zero Product Property
Zero in on your pupils' understanding of solving quadratic equations. Spend time developing the purpose of the zero product property so that young mathematicians understand why the equations should be set equal to zero and how that...
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Using the Quadratic Formula
What is the connection between the quadratic formula and the types of solutions of a quadratic equation? Guide young mathematicians through this discovery as they use the discriminant to determine the number and types of solutions, and...
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Some Potential Dangers When Solving Equations
Need a less abstract approach to introducing extraneous solutions? This is it! Young mathematicians explore properties used to solve equations and determine which operations maintain the same solutions. They eventually find that squaring...
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Creating and Solving Quadratic Equations in One Variable
Give your classes practice at modeling using quadratic models with a resource that uses area and integer problems to allow individuals to create second degree polynomials. Young mathematicians solve equations using factoring and then...