Howard County Schools
Getting Paid for School
What if you were paid to attend class? What kind of payment schedule would you choose? Learn how exponential functions will eventually exceed linear functions by comparing two different payment schedules for attending class.
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Percent Rate of Change
If mathematicians know the secret to compound interest, why aren't more of them rich? Young mathematicians explore compound interest with exponential functions in the twenty-seventh installment of a 35-part module. They calculate future...
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Examples of Dilations
Does it matter how many points to dilate? The resource presents problems of dilating curved figures. Class members find out that not only do they need to dilate several points but the points need to be distributed about the entire curve...
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Characteristics of Parallel Lines
Systems of parallel lines have no solution. Pupils work examples to discover that lines with the same slope and different y-intercepts are parallel. The 27th segment of 33 uses this discovery to develop a proof, and the class determines...
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There is Only One Line Passing Through a Given Point with a Given Slope
Prove that an equation in slope-intercept form names only one line. At the beginning, the teacher leads the class through a proof that there is only one line passing through a given point with a given slope using contradiction. The 19th...
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The Graph of a Linear Equation in Two Variables Is a Line
Show your class that linear equations produce graphs of lines. The 20th segment in a unit of 33 provides proof that the graph of a two-variable linear equation is a line. Scholars graph linear equations using two points, either from...
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Distance on the Coordinate Plane
Apply the Pythagorean Theorem to coordinate geometry. Learners find the distance between two points on a coordinate plane by using the Pythagorean Theorem. The vertical and horizontal change creates a right triangle, which allows...
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Computing Actual Lengths from a Scale Drawing
The original drawing is eight units — how big is the scale drawing? Classmates determine the scale percent between a scale drawing and an object to calculate the length of a portion of the object. They use the percent equation to find...
Teach Engineering
How Big? Necessary Area and Volume for Shelter
Teams must determine the size of cavern needed to house the citizens of Alabraska to protect them from the asteroid impact. Using scaling properties, teams first determining the number of people that could sleep in a classroom and then...
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Using Trigonometry to Find Side Lengths of an Acute Triangle
Not all triangles are right! Pupils learn to tackle non-right triangles using the Law of Sines and Law of Cosines. After using the two laws, they then apply them to word problems.
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Comparing Linear and Exponential Models Again
Making connections between a function, table, graph, and context is an essential skill in mathematics. Focused on comparing linear and exponential relationships in all these aspects, this resource equips pupils to recognize and interpret...
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Translations
Learn through constructions! Learners examine a translation using constructions and define the translation using a vector. Pupils then construct parallel lines to determine the location of a translated image and use the vector as a guide.
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Basic Properties of Similarity
Does the symmetry and transitive property apply to similarity? The 10th segment in a series of 16 presents the class with a group of explorations. The explorations have pairs show that similarity is both symmetrical and transitive....
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Exponential Notation
Exponentially increase your pupils' understanding of exponents with an activity that asks them to explore the meaning of exponential notation. Scholars learn how to use exponential notation and understand its necessity. They use negative...
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Geometric Interpretations of the Solutions of a Linear System
An intersection is more than just the point where lines intersect; explain this and the meaning of the intersection to your class. The 26th segment in a 33-part series uses graphing to solve systems of equations. Pupils graph linear...
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Problem Solving When the Percent Changes
Use more than one whole to solve percent problems. The ninth installment in a 20-part series has pupils work percent problems in which they must determine two wholes. Individuals use double number lines to represent and solve the...
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Comparing Quantities with Percent
Be 100 percent confident who has the most and by how much. Pupils use percentages to help make the comparisons by finding what percent one quantity is of the other. They also determine the percent differences between the two...
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Populations, Samples, and Generalizing from a Sample to a Population
Determine the difference between a sample statistic and a population characteristic. Pupils learn about populations and samples in the 14th portion in a unit of 25. Individuals calculate information directly from populations called...
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Random Sampling
Sample pennies to gain an understanding of their ages. The 16th installment of a 25-part series requires groups to collect samples from a jar of pennies. Pupils compare the distribution of their samples with the distribution of the...
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Sampling Variability and the Effect of Sample Size
The 19th installment in a 25-part series builds upon the sampling from the previous unit and takes a larger sample. Pupils compare the dot plots of sample means using two different sample sizes to find which one has the better variability.
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Sampling Variability
Work it out — find the average time clients spend at a gym. Pupils use a table of random digits to collect a sample of times fitness buffs are working out. The scholars use their random sample to calculate an estimate of the mean of the...
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Estimating a Population Proportion
Find the percent of middle schoolers who want the ability to freeze time. The 21st installment in a series of 25 has groups collect a random sample of respondents who answer a question about superpowers. Using sample statistics,...
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Population Problems
Find the percent of the population that meets the criteria. The 17th segment of a 20-part unit presents problems that involve percents of a population. Pupils use tape diagrams to create equations to find the percents of subgroups...
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Problem Solving Using Rates, Unit Rates, and Conversions
Find a way to work with rates. The 23rd part in a 29-part series presents work problems for the class to solve given work rates. Pupils compare rates to determine which is faster. Some problems require learners to convert the rates to...