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Grade 9 ELA Module 3, Unit 2, Lesson 4
It seems like the first result in a search engine is the best source, but how can you be sure? An activity on assessing sources guides ninth graders through an integral part of their inquiry-based research project, based on questions...
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Lines That Pass Through Regions
Good things happen when algebra and geometry get together! Continue the exploration of coordinate geometry in the third lesson in the series. Pupils explore linear equations and describe the points of intersection with a given polygon as...
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Parallel and Perpendicular Lines
Use what you know about parallel and perpendicular lines to write equations! Learners take an equation of a line and write an equation of a line that is parallel or perpendicular using slope criteria. They then solve problems to...
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The Angle Measure of an Arc
How do you find the measure of an arc? Learners first review relationships between central and inscribed angles. They then investigate the relationship between these angles and their intercepted arcs to extend the Inscribed Angle Theorem...
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Properties of Tangents
You know about the tangent function, but what are tangent lines to a circle? Learners investigate properties of tangents through constructions. They determine that tangents are perpendicular to the radius at the point of tangency,...
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Writing the Equation for a Circle
Circles aren't functions, so how is it possible to write the equation for a circle? Pupils first develop the equation of a circle through application of the Pythagorean Theorem. The lesson plan then provides an exercise set for learners...
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Ptolemy's Theorem
Everyone's heard of Pythagoras, but who's Ptolemy? Learners test Ptolemy's Theorem using a specific cyclic quadrilateral and a ruler in the 22nd installment of a 23-part module. They then work through a proof of the theorem.
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Successive Differences in Polynomials
Don't give your classes the third degree when working with polynomials! Teach them to recognize the successive differences and identify the degree of the polynomial. The lesson leads learners through a process to develop an understanding...
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Putting It All Together
Shuffle 'em up and deal! Learners practice operations with polynomials using cards they pass around the room. The activity works with pairs or individuals, so it offers great flexibility. This is the fifth installment in a series of 42...
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Ferris Wheels—Tracking the Height of a Passenger Car
Watch your pupils go round and round as they explore periodic behavior. Learners graph the height of a Ferris wheel over time. They repeat the process with Ferris wheels of different diameters.
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Factoring
Build an understanding of factors and use it to write the prime factorization of numbers. After exploring key vocabulary, learners create prime factorization for given numbers. They then use the prime factorizations to determine the...
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Fibonacci and Other Sequences
Fibonacci is an interesting sequence that forms some unique patterns. Learners explore sequences that do not have the typical arithmetic and geometric patterns. They identify the pattern and find the next consecutive terms....
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Angle Sum Property of Triangles
All triangles have some things in common. Using these properties of triangles, learners find missing angle measures. Scholars use the Angle Sum Property and properties of special triangles throughout the lesson.
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Measurement
Build a basic understanding of units of measure and create a great foundation for your learners. The lesson gives a complete overview of everything measurement, from types of measurement to rounding to conversions — it has it all!
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Perimeter of Common Geometric Figures
Help learners understand that perimeter and circumference are one in the same. Learners apply their skills to determine the perimeter/circumference of triangles, rectangles, and circles. They then use the same strategy to find the...
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Approximating a Line of Best Fit
You may be able to see patterns visually, but mathematics quantifies them. Here learners find correlation in scatterplots and write equations to represent that relationship. They fit a line to the data, find two points on the line, and...
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Line Plots
You can't see patterns in a jumble of numbers ... so organize them! Learners take a set of data and use a line plot to organize the numbers. From the line plot, they find minimum, maximum, mean, and make other conclusions about the...
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Radicals and Conjugates
Make the irrational rational again! Continuing the theme from previous lessons in the series, the lesson relates the polynomial identity difference of squares to conjugates. Learners develop the idea of a conjugate through analysis and...
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Overcoming Obstacles in Factoring
What do you do when factoring doesn't work? Learners complete the square when faced with quadratic expression that don't factor traditionally. They then use factoring by grouping to solve polynomial equations.
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Structure in Graphs of Polynomial Functions
Don't allow those polynomial functions to misbehave! Understand the end behavior of a polynomial function based on the degree and leading coefficient. Learners examine the patterns of even and odd degree polynomials and apply them to...
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Equivalent Rational Expressions
Rational expressions are just fancy fractions! Pupils apply fractions concepts to rational expressions. They find equivalent expressions by simplifying rational expressions using factoring. They include limits to the domain of the...
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Solving Rational Equations
What do fractions and rational expressions have in common? Everything! Learners use common denominators to solve rational equations. Problems advance from simple to more complex, allowing pupils to fully understand the material before...
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Linear Systems in Three Variables
Put all that algebra learning to use! Using algebraic strategies, learners solve three-variable systems. They then use the three-variable systems to write a quadratic equation given three points on the parabola.
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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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