Probability and Statistics – Using a sample to generalize about a population

“Three out of four people prefer Brand X toothpaste.” We hear these claims all the time. How did these claims come about? Was every single person in the world asked about the brand they prefer? That would certainly take a lot of time and money!

Probability-and-Statistics---Using-a-sample-to-generalize-about-a-population

The activity Using a Sample to Generalize about a Population helps students to understand that it is difficult to gather information about an entire population. They learn that a smaller portion of the population, called a sample, is used to draw inferences about the entire population, and that these samples must be representative of the whole population to make valid generalizations. They also examine the effect sample size and variation can have on their conclusions.

Click here to try: Probability and Statistics – Using a sample to generalize about a population

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New BuzzMath Activity – Creating, Interpreting and Analyzing Scatter Plots

Feeling scattered? Get it together and check out Creating, Interpreting and Analyzing Scatter Plots. This activity begins with a review of plotting points on a coordinate grid and then challenges students to identify trends in the data without connecting the points. As they progress through the activity they will explore, identify and interpret independent and dependent variables and their correlation to each other.

Creating,-Interpreting-and-Analyzing-Scatter-Plots

The utilization of familiar situations in this activity makes it easier for students to grasp the concept. At the conclusion of this activity students will not only be able to create a scatterplot, but also identify a trend and explain the relationship between the variables.

Click here to try : Creating, Interpreting and Analyzing Scatter Plots

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New Buzzmath Activiy – Approximating the Probability of a Chance Event

How do we think about events in our daily lives? How much of it happens by chance? Can we predict any of it?

In the activity Approximate the Probability of a Chance Event students examine the relationship between expected events and the events that actually occur. They look at the expected probability of an event such as rolling a 3 on a number cube and then actually perform the experiment to see if what they get is the same, or even close to what is expected.

Approximating-the-Probability-of-a-Chance-Event

Students use different models like flipping coins, spinning spinners, and of course, rolling number cubes in this activity. They come to realize that as the number of trials increase, the probability in the experiment gets closer to the one they had expected. This is a dynamic activity which allows students to explore this concept in a way that they could not do by simply using a textbook.

Click here to try Probability and Statistics – Approximating the Probability of a Chance Event

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New Buzzmath Activity – Relations, Functions and Coordinate Graphs – Points of Intersection

“I hope our paths cross again.” If someone tells you this, what does it mean? What path? Let’s think about it. If we were walking towards each other there would be a specific moment that we were in the same spot at the same exact time. This is where our paths would cross. At any other time we would be at different locations. On a grid with two intersecting lines there is a point where the lines intersect (or cross). This point satisfies the equations for both lines at the same time. This is the point of intersection.

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Students will find solutions to real world problems by analyzing and creating graphs using linear equations and finding the point of intersection. They will use their understanding of graphing linear equations at the beginning of the activity and work towards using similar graphs to determine the best cost value for adding turf to a training gym.

Click here to try: Relations, Functions and Coordinate Graphs – Points of Intersection

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New Buzzmath Activity – Equations with one solution, infinitely many, and no solutions

Life is a balance….and so is an equation. In our search for balance in both life and mathematics we at times either find many solutions, infinite solutions or no solution to our problems. While this activity is sure to provide students with strategies and practice to identify equations with one solution, infinite solutions and no solutions, there will be no strategies for achieving balance in our lives.
Equations-with-one-solutionStudents begin this activity with a review of the properties of equality as they manipulate a balance scale to represent each side of an equation. From here they will explore patterns in equations that will allow them to determine if it has one solution, infinitely many or no solutions at all. Once they identify these patterns they will be able to practice applying this concept with numerous problems. With each problem they practice they will be given immediate feedback and assistance if needed. This supported practice gives the students the confidence and ability to be successful.

Click here to try: Equations with one solution, infinitely many, and no solutions

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New Buzzmath Activity – Properties of Operations to Factor Linear Expressions with Rational Coefficients

Let’s factorise! That sounds like a workout, doesn’t it? But there’s nothing strenuous about factorising. The term factorise is used in the UK instead of its American counterpart, factor. The activity, Factor Expressions with Rational Coefficients, is about just that…factorising, or factoring expressions!

This activity uses the Distributive Property to factor and expand algebraic linear expressions. Students are already familiar with the Distributive Property from earlier grades where they used it to expand and factor numerical expressions. So this activity should not feel like a workout. They will now use the same concepts to expand and factor algebraic expressions.

Properties-of-Operations-to-Factor-Linear-Expressions-with-Rational-Coefficients

Students begin the activity with rectangular models that build on their understanding of the Distributive Property to expand algebraic expressions. They then use this understanding to factor these types of expressions. To accomplish their tasks, students use a variety of Buzzmath input, matching, and select tools.

Click here to try: Properties of Operations to Factor Linear Expressions with Rational Coefficients

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New Buzzmath Activity – Populations and samples

Many of us like to try before we buy…whether it’s a beauty or household product, a food item or recipe, or even a piece of music. Many consumers like to get a limited quantity of a product so they can learn about and assess the product. The same holds true for population samples–a sample from a population allows you to have an understanding of the entire population.

Populations-and-samples

In the activity Populations and Samples, students learn about sampling a population and understand that they can draw conclusions from representative samples. The activity is an introduction to population study in which students define terms used in this area of mathematics and distinguish between representative and biased samples.

Click here to try: Populations and samples

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New Buzzmath Activity – Unit Rates with Ratios of Fractions

A part of a rate? Is that possible?

The activity Unit Rates with Ratios of Fractions provides many real world opportunities for students to find unit rates when one or both quantities are fractions. A variety of tools and representations are available to help students with this concept: a walking bug, double number lines, tables, and more.

Unit Rates with Ratios of Fractions

The activity extends students’ conceptual understanding of unit rate and reinforces dividing both parts of the rate by the denominator to result in 1 unit in the denominator. The result– a unit rate! The activity further leads them to understand that of course dividing by the denominator is equivalent to multiplying by its reciprocal, and further leads to a shortcut–simply multiply the numerator by the reciprocal of the denominator. Students come to realize that the only difference between a unit rate with fractions and one with whole numbers is in working with the different types of numbers.

Click here to try Unit Rates with Ratios of Fractions

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New Buzzmath Activity – Using Elimination to Solve A System of Equations

Opp-o-sites attract! Right? Thanks to Paula Abdul, we know this is true. Did you also know that opposites eliminate?

This concept will prove to be very helpful when students practice solving systems of equations using the elimination method.

Using-Elimination-to-Solve-A-System-of-Equations

Students are off to an exciting start in this activity as they explore and review the concept of combining opposite integers using an interactive manipulative. They continue to use this knowledge throughout the activity as they select and eliminate one variable in order to solve for another. Each page adds a little more complexity leading to the introduction and application of the Multiplication Property of Equality. Students will practice applying this property as they create equivalent equations that are easier to work with as they solve systems of equations. At the culmination of this activity students may be stateing…2 steps forward and 2 steps back…we go together because opposites ELIMINATE.

Click here to try : Using Elimination to Solve A System of Equations

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New Buzzmath Activity – Equations and Inequalities – Solve and Graph Two-Step Inequalities

This one is a role reversal!

Up to this point, students have been exposed to expressing basic real world problems with inequalities using only positive coefficients. The activity Solve and Graph Two-Step Inequalities is the first opportunity for students to use negative coefficients with inequalities.

Equations-and-Inequalities---Solve-and-Graph-Two-Step-Inequalities

The activity begins by using a number line to show students that when they multiply or divide by a positive number the inequality remains true. This is followed by a review of the similarities between solving an equation and solving an inequality, using only positive numbers. Now students are ready to move to multiplying and dividing by a negative number. Again, the use of a number line shows that multiplying or dividing by a negative number causes the inequality to reverse for the expression to remain true.

Once students have mastered these skills, they solve two-step inequalities, translate between word problems and symbols, show solutions visually on a number line, and interpret their solutions verbally. This activity is a great preparation for inequalities they will encounter in the future.

Click here to try : Equations and Inequalities – Solve and Graph Two-Step Inequalities

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