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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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Changing the Base
I can't calculate a base-2 logarithm since my calculator doesn't have a base-2 log key. Young mathematicians use the change of base formula to extend the properties of logarithms to all bases. Among these bases is the natural log base,...
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Modeling with Exponential Functions
These aren't models made of clay. Young mathematicians model given population data using exponential functions. They consider different models and choose the best one.
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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...
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Using Permutations and Combinations to Compute Probabilities
Now that we know about permutations and combinations, we can finally solve probability problems. The fourth installment of a 21-part module has future mathematicians analyzing word problems to determine whether permutations or...
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Looking More Carefully at Parallel Lines
Can you prove it? Making assumptions in geometry is commonplace. This resource requires mathematicians to prove the parallel line postulate through constructions. Learners construct parallel lines with a 180-degree rotation and then...
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Exploring the Symmetry in Graphs of Quadratic Functions
Math is all about finding solutions and connections you didn't expect! Young mathematicians often first discover nonlinear patterns when graphing quadratic functions. The lesson begins with the vocabulary of a quadratic graph and uses...
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Expected Value of a Discrete Random Variable
Discover how to calculate the expected value of a random variable. In the seventh installment of a 21-part module, young mathematicians develop the formula for expected value. They connect this concept the dot product of vectors.
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Determining Discrete Probability Distributions 1
Learn how to determine a probability distribution. In the ninth installment of a 21-part module, future mathematicians use theoretical probabilities to develop probability distributions for a random variable. They then use these...
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Games of Chance and Expected Value 2
Use expected values to analyze games of chance. The 15th installment of a 21-part module has young mathematicians looking at different games involving tickets and deciding which would be the best to play. They calculate expected payoffs...
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Analyzing Decisions and Strategies Using Probability 1
Learn how to increase the probability of success. The 19th installment of a 21-part module teaches future mathematicians how to use probability to analyze decisions. They determine strategies to maximize the chances of a desired outcome.
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The Concept of a Function
Explore functions with non-constant rates of change. The first installment of a 12-part module teaches young mathematicians about the concept of a function. They investigate instances where functions do not have a constant rate of change.
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Linear Functions and Proportionality
Connect linear equations, proportionality, and constant rates of change to linear functions. Young mathematicians learn how linear equations of the form y = mx + b can represent linear functions. They then explore examples of linear...
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First Consequences of FTS
Challenge the young mathematicians to find the exact coordinates of a dilated point. The fifth segment in a 16-part series introduces the class to the converse of the Fundamental Theorem of Similarity. Scholars use the theorem to find...
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Patterns in Scatter Plots
Class members investigate relationships between two variables in the seventh installment of a 16-part module that teaches scholars how to find and describe patterns in scatter plots. Young mathematicians consider linear/nonlinear...
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Scientific Notation
Young mathematicians learn how scientific notation is meant to save time. Part 10, out of a series of 15, asks scholars to recognize the correct use of scientific notation and finish by adding and subtracting numbers using the notation.
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Equivalent Ratios
Equivalent ratios show up on tape. Young mathematicians use tape diagrams to create equivalent ratios in the initial lesson on the topic. They learn the definition of equivalent ratios and use it to build others in the third segment of a...
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Locating Ordered Pairs on the Coordinate Plane
Four quadrants, four times the fun. Future mathematicians learn the terminology associated with the coordinate plane and how to plot points in all four quadrants. A worksheet tests their understanding of the material in the 16th...
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The Order of Operations
Future mathematicians learn how to evaluate numerical expressions by applying the order of operations. They evaluate similar-looking expressions to see how the location of parentheses and exponents affects the value.
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Read Expressions in Which Letters Stand for Numbers II
Reading and writing take on a whole different meaning in math class. Young mathematicians learn to read verbal phrases by focusing on operation words. They write equivalent algebraic expressions for both mathematical and contextual...
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True and False Number Sentences II
Substitution is still the method of choice to verify number sentences. The detailed lesson has young mathematicians determining conditions for when number sentences are true or false through substitution. They learn to express these...
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One-Step Equations—Addition and Subtraction
Just one step is all you need to find success in solving equations. The 27th installment in a series of 36 teaches how to solve one-step equations involving addition and subtraction. Tape diagrams help future mathematicians in this task.
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Writing and Evaluating Expressions—Exponents
Bring your young mathematicians into the fold. Scholars conduct an activity folding paper to see the relationship between the number of folds and the number of resulting layers in the 23rd installment of a 36-part module. The results of...
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Multi-Step Problems in the Real World
Connect graphs, equations, and tables for real-world problems. Young mathematicians analyze relationships to identify independent and dependent variables. These identifications help create tables and graphs for each situation.