In this video from PBSLearningMedia, students learn about Native American winter counts in South Dakota and complete an interesting activity. This video is part of Activity Starters, which is an animated video series. In each episode an animated character introduces a concept and an activity
In this video from PBSLearningMedia, students learn about Native American land stewardship in South Dakota and raise money for your local food pantry. This video is part of Activity Starters, which is an animated video series. In each episode, an animated character introduces a concept and an activity.
In this video from PBSLearningMedia, students learn about map borders and complete an interesting hands-on activity. This video is part of Activity Starters, which is an animated video series. In each episode, an animated character introduces a concept and an activity.
In this video from PBSLearningMedia, students learn about the difference between past, present, and future. Then, students can try the hands-on activity in the classroom or at home.
In this video from PBSLearningMedia, students learn about cardinal directions and complete an interesting hands-on activity. This video is part of Activity Starters, which is an animated video series. In each episode, an animated character introduces a concept and an activity
In this video from PBSLearningMedia, students learn as the growth of the automobile industry continued and more and more people purchased cars, a system of good highways was in demand. United States legislators and senators became involved in passing bills to establish federal highways and to provide monies for the construction and maintenance of those roads. This boom in the building of new roadways led to both good and bad practices and called for innovative ways to raise money to match the demand.
In this video from PBSLearningMedia, students learn about the development of a transportation system in Alabama, which first included river towns, then upland towns serving as railroad stops, and then highway towns as roads were built to connect the shortest distance between places. Politics and highway construction have gone hand in hand as elected officials made decisions about where roads would be built and how monies would be spent. President Eisenhower established the Interstate System and automobile travel became the major source of transportation for people and goods.
In this video from PBSLearningMedia, students learn about the development of a highway and byway system leads to growth and prosperity in Alabama, but with the amount of traffic on the roadways comes the rise in highway related accidents and death. National and State safety boards and law enforcement personnel work to make the highways safer and laws are enacted to make road travel less of a risk.
In this video from PBSLearningMedia, students learn that the earliest forms of transportation in Alabama involved trails followed by animals and Native Americans. These trails lead to water, and Alabama rivers served as a gathering place for many early Indian settlements. It is along the paths of Native American trails that the first highway systems were developed.
Students will apply their critical thinking skills to learn about multiplication and division of exponents. This interactive exercise focuses on positive and negative exponents and combining exponents in an effort to help students recognize patterns and determine a rule.
This resource is part of the Math at the Core: Middle School collection.
This video lesson builds on the idea that both graphing and rewriting quadratic equations in the form of expression = 0 are useful strategies for solving equations. It also reinforces the ties between the zeros of a function and the horizontal intercepts of its graph, which students began exploring in an earlier unit.
Here, students learn that they can solve equations by rearranging them into the form expression = 0, graphing the equation y = expression, and finding the horizontal intercepts. They also notice that dividing each side of a quadratic equation by a variable is not reliable because it eliminates one of the solutions. As students explain why certain maneuvers for solving quadratic equations are acceptable and others are not, students practice constructing logical arguments.
In this video lesson, students learn about the zero product property. They use it to reason about the solutions to quadratic equations that each have a quadratic expression in the factored form on one side and 0 on the other side. They see that when an expression is a product of two or more factors and that product is 0, one of the factors must be 0. Students make use of the structure of a quadratic expression in factored form and the zero product property to understand the connections between the numbers in the form and the x-intercepts of its graph (MP7).
Previously in this video series, students saw that a squared expression of the form (x + n)² is equivalent to x² + 2nx + n². This means that, when written in standard form ax² + bx + c (where a is 1), b is equal to 2n and c is equal to n². Here, students begin to reason the other way around. They recognize that if ax² + bx + c is a perfect square, then the value being squared to get c is half of b, or (b/2)². Students use this insight to build perfect squares, which they then use to solve quadratic equations.
Students learn that if we rearrange and rewrite the expression on one side of a quadratic equation to be a perfect square, that is if we complete the square, we can find the solutions of the equation.
In this video lesson, students begin to rewrite quadratic expressions from standard to factored form.
Students relate the numbers in the factored form to the coefficients of the terms in standard form, looking for a structure that can be used to go in reverse—from standard form to factored form (MP7).
(This lesson only looks at expressions of the form (x + m)(x + n) and (x – m)(x – n) where m and n are positive.)
Earlier in this video series, students transformed quadratic expressions from standard form into factored form. There, the factored expressions are products of two sums, (x + m)(x + n), or two differences, (x – m)(x – n). Students continue that work in this video lesson, extending it to include expressions that can be rewritten as products of a sum and a difference, (x + m)(x – n).
Through repeated reasoning, students notice that when we apply the distributive property to multiply out a sum and a difference, the product has a negative constant term, but the linear term can be negative or positive (MP8). Students make use of the structure as they take this insight to transform quadratic expressions into factored form (MP7).
In this video lesson, students encounter quadratic expressions without a linear term and consider how to write them in factored form.
Through repeated reasoning, students are able to generalize the equivalence of these two forms: (x + m)(x – m) and x² – m² (MP8). Then, they make use of the structure relating the two expressions to rewrite expressions (MP7) from one form to the other.
Students also consider why a difference of two squares (such as x² – 25) can be written in factored form, but a sum of two squares (such as x² + 25) cannot be, even though both are quadratic expressions with no linear term.
In this video lesson, students apply what they learned about transforming expressions into factored form to make sense of quadratic equations and persevere in solving them (MP1). They see that rearranging equations so that one side of the equal sign is 0, rewriting the expression in factored form, and then using the zero product property make it possible to solve equations that they previously could only solve by graphing. These steps also allow them to easily see—without graphing and without necessarily completing the solving process—the number of solutions that the equations have.
This video lesson has two key aims. The first aim is to familiarize students with the structure of perfect-square expressions. Students analyze various examples of perfect squares. They apply the distributive property repeatedly to expand perfect-square expressions given in the factored form (MP8). The repeated reasoning allows them to generalize expressions of the form (x + n)2 as equivalent to x2 + 2nx + n2.
The second aim is to help students see that perfect squares can be handy for solving equations because we can find their square roots. Recognizing the structure of a perfect square equips students to look for features that are necessary to complete a square (MP7), which they will do in a future video lesson.
Previously in this video series, students used area diagrams to expand expressions of the form (x + p)(x + q) and generalized that the expanded expressions take the form of x2 + (p + q)x + pq. In this video lesson, they see that the same generalization can be applied when the factored expression contains a sum and a difference (when p or q is negative) or two differences (when both p and q are negative).
Students transition from thinking about rectangular diagrams concretely, in terms of area, to thinking about them more abstractly, as a way to organize the terms in each factor. They also learn to use the terms standard form and factored form. When classifying quadratic expressions by their form, students refine their language and thinking about quadratic expressions (MP6).
In this video lesson, students return to some quadratic functions they have seen. They write quadratic equations to represent relationships and use the quadratic formula to solve problems that they did not previously have the tools to solve (other than by graphing). In some cases, the quadratic formula is the only practical way to find the solutions. In others, students can decide to use other methods that might be more straightforward (MP5).
The work in this lesson—writing equations, solving them, and interpreting the solutions in context—encourages students to reason quantitatively and abstractly (MP2).
In this video from PBSLearningMedia, students learn that using the old Native American trails, white settlers to Alabama begin the first transportation system in the state. Early roads were simply dirt paths widened for wagons and animals. Later corduroy and plank roads covered the dirt helping to eliminate the muddy conditions that followed the rain. River transportation and the first railroads also played a large part in the growth of Alabama’s transportation during this time. The invention of the automobile caused a revolution in the transportation world and increased the need for a better highway system.
Probability is the study of chance or the likelihood that an event will occur. Probability can’t tell us what will happen, only what is likely to happen. At the end of this lesson about probability, students will be able to calculate probability for real-life situations.
One way we analyze data is to look at measures of central tendency—mean, median, and mode. They are the tools to look at the information for the purpose of answering the question, “What is normal?” Understanding the measures of central tendency can help us make important life decisions. For example, averages can help us set goals or plan budgets. At the end of this lesson about central tendency, students will be able to recognize and apply the concepts of mean, median, and mode in real-life problems.
Students analyze economic data to better understand America’s middle class, its role in the economy, and its impact on economic growth. In this interactive lesson, students use media produced for How the Deck Is Stacked, and tables and graphs created from Pew Research Center and government data to examine household income and spending trends and the widening wealth gap between the upper and lower-income tiers. Interim assessments evaluate students’ ability to interpret data, make inferences, and justify conclusions. At the end of the lesson, students write an evidence-based essay on why a shrinking middle-class matters to the U.S. economy.
These interactive tools give students an opportunity to explore more about stemplots, control charts, and histograms as covered in the Against All Odds statistics series. Simulations allow students to explore statistics methods in-depth using their own data.
In this video from PBSLearningMedia, students will join Peg+Cat as they learn about the Muslim holiday Eid-Al-Adha from their friends Yasmina and Amir. In addition to exploring how Muslims celebrate the holiday, students also explore the mathematical concepts of less than (<) and more than (>), fractions, and how to create equal amounts.
Introduce high school students to the art and science of statistics in the 6-minute video, "What is Statistics?" from the Against All Odds series. This video resource will demonstrate how gathering, organizing, drawing, and analyzing data is applicable in everyday life and a variety of careers.
Discover how calculating median and mean reveal different ways to describe a center of distribution in this 9-minute video from the Against All Odds statistics series. This video resource will examine differences in comparable wages for men and women to see practical applications of statistics and data visualization.
This exercise was developed to complement the film The National Parks of Texas by Texas PBS & Villita Media. In this activity, students will learn about estimating the number of trees in a large area based on a smaller area.
This is one way statisticians measure forests and other wide expanses of land. It's also a great way to illustrate how polling works. Scientists will interview a smaller sample size of Americans, rather than every single American, and then make estimations based on their results. In the same way, we counted smaller samples of trees, rather than all of the trees individually to get an estimate of how many trees are in the park total.
Note: The corresponding lesson plan can be found under the "Support Materials for Teachers" link on the right side of the page.
Explore real-life applications for statistical data sets and creating stemplots in the 12-minute program "Stemplots" from the Against All Odds series. Students will learn how designers and engineers calculate uniform sizing for the military by creating a stemplot to visualize the data. A stemplot demonstrates how a data collection of measurements helps the military design gear that fits modern troops.
Statistics and sampling are important for human performance experiments. Students will learn several sampling types including census, random, stratified random, and convenience. Examples of real-life sampling and experimental design are also shown.
Note: This video is available in both English and Spanish audio, along with corresponding closed captions.
Explore how probability can be used to help find people lost at sea, even when rescuers have very little information, in this video from NOVA: Prediction by the Numbers. To improve its search-and-rescue efforts, the U.S. Coast Guard has developed a system that uses Bayesian inference, a mathematical concept that dates back to the 18th century. The Search and Rescue Optimal Planning System (SAROPS) uses a mathematical approach to calculate probabilities of where a floating person or object might be based on changing ocean currents, wind direction, or other new information. Use this resource to stimulate thinking and questions about appropriate uses of statistical methods.
Learn about the origins and meaning of “p-value,” a statistical measure of the probability that has become a benchmark for success in experimental science, in this video from NOVA: Prediction by the Numbers. In the 1920s and 1930s, British scientist Ronald A. Fisher laid out guidelines for designing experiments using statistics and probability to judge results. He proposed that if experimental results were due to chance alone, they would occur less than 5 percent (0.05) of the time. The lower the p-value, the less likely the experimental results were caused by chance. Use this resource to stimulate thinking and questions about the use of statistics and probability to test hypotheses and evaluate experimental results.
Examine a mathematical theory known as the “wisdom of crowds,” which holds that a crowd’s predictive ability is greater than that of an individual, in this video from NOVA: Prediction by the Numbers. Sir Francis Galton documented this phenomenon after witnessing a weight-guessing contest more than a hundred years ago at a fair. Statistician Talithia Williams tests Galton’s theory with modern-day fairgoers, asking them to guess the number of jelly beans in a jar. Use this resource to stimulate thinking and questions about the use of statistics in everyday life and to make evidence-based claims about predictive ability.
Dihydrogen monoxide (better known as water) is the key to nearly everything. It falls from the sky, makes up 60% of our bodies, and just about every chemical process related to life takes place with it or in it. Without it, none of the chemical reactions that keep us alive would happen, none of the reactions that sustain any life form on earth would happen, and the majority of inorganic chemical reactions that shape the surface of the earth would not happen either. Every one of us uses water for all kinds of chemistry every day--our body chemistry, our food chemistry, and our laundry chemistry all take place in water. In this Crash Course Chemistry, we learn about some of the properties of water that make it so special. We explore its polarity and dielectric property; how electrolytes can be used to classify solutions; and we discover how to calculate a solution's molarity as well as how to dilute a solution using the dilution equation.
