Mathematics Vision Project
Module 5: Rational Functions and Expressions
Where do those asymptotes come from? Learners graph, simplify, and solve rational functions in the fifth module of a 10-part series. Beginning with graphing, pupils determine the key characteristics of the graphs including an in-depth...
EngageNY
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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Chance Experiments, Sample Spaces, and Events
Want a leg up on the competition? Show classes how to use mathematics to their advantage when playing games. Learners calculate probabilities to determine a reasonable scoring strategy for a game.
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Solving Equations
Teach solving equations through an exploration of properties. Before pupils solve equations they manipulate them to produce equivalent equations. The activity switches the focus from finding a solution to applying properties correctly.
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Matrix Addition Is Commutative
Explore properties of addition as they relate to matrices. Using graphical representations of vector matrices, scholars test the commutative and associative properties of addition. They determine if the properties are consistent for...
Illustrative Mathematics
Dimes and Pennies
Help your fourth graders make cents out of fractions and decimals with this short word problem. After learning that dimes are one-tenth and pennies one-hundredth of a dollar, students write a fraction and decimal for a given number...
Curated OER
Get in Shape with Geometry
Using geoboards, computer programs, and hands-on manipulative materials, elementary schoolers engage in a study of two and three-dimensional geometric shapes. This instructional activity is chock full of good teaching ideas on the...
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Making Scale Drawings Using the Parallel Method
How many ways can you create a dilation? Many! Individuals strengthen their understanding of dilations by using various methods to create them. The new technique builds on pupils' understanding of the ratio method. Using the ratio,...
Mathematics Vision Project
Similarity and Right Triangle Trigonometry
Starting with similar triangles and dilation factors, this unit quickly and thoroughly progresses into the world of right triangle features and trigonometric relationships. Presented in easy-to-attack modules with copious application...
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Analyzing Graphs—Water Usage During a Typical Day at School
Connect your pupils to the problem by presenting a situation with which they can identify. Individuals analyze a graph of water use at a school by reasoning and making conclusions about the day. The lesson emphasizes units and...
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Exponential Growth—U.S. Population and World Population
Show how exponential growth can look linear. Pupils come to understand the importance of looking at the entire picture as they compare the US population to the world population. Initially, the populations look linear with the same rate...
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Using Expected Values to Compare Strategies
Discover how mathematics can be useful in comparing strategies. Scholars develop probability distributions for situations and calculate expected value. They use their results to identify the best strategy for the situation.
Curated OER
Avoiding Consumer Fraud: Financial Scams and Schemes
Young consumers get a hefty dose of information on how fraud can put their financial health at risk. The resource provides detailed lecture notes, scaffolded notetaking sheets, vocabulary worksheets, transparencies, and seven links to...
EngageNY
Distributions and Their Shapes
What can we find out about the data from the way it is shaped? Looking at displays that are familiar from previous grades, the class forms meaningful conjectures based upon the context of the data. The introductory lesson to...
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Measuring Variability for Skewed Distributions (Interquartile Range)
Should the standard deviation be used for all distributions? Pupils know that the median is a better description of the center for skewed distributions; therefore, they will need a variability measure about the median for those...
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More on Modeling Relationships with a Line
How do you create a residual plot? Work as a class and in small groups through the activity in order to learn how to build a residual plot. The activity builds upon previous learning on calculating residuals and serves as a...
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Conditional Relative Frequencies and Association
It is all relative, or is it all conditional? Using an exploration method, the class determines whether there is an association between gender and superpower wish through the use of calculating conditional relative frequencies. The...
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Relationships Between Two Numerical Variables
Working in small groups and in pairs, classmates build an understanding of what types of relationships can be used to model individual scatter plots. The nonlinear scatter plots in this activity on relationships between two numerical...
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Graphs of Piecewise Linear Functions
Everybody loves video day! Grab your class's attention with this well-designed and engaging resource about graphing. The video introduces a scenario that will be graphed with a piecewise function, then makes a connection to domain...
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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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Similarity
Learn similarity through a transformations lens! Individuals examine the effects of transformations and analyze the properties of similarity, and conclude that any image that can be created through transformations is similar. The...
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The Definition of Sine, Cosine, and Tangent
Introduce your classes to a new world of mathematics. Pupils learn to call trigonometric ratios by their given names: sine, cosine, and tangent. They find ratios and use known ratios to discover missing sides of similar...
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Tangent Segments
What's so special about tangents? Learners first explore how if a circle is tangent to both rays of an angle, then its center is on the angle bisector. They then complete a set of exercises designed to explore further properties and...
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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...