The BuzzMath Blog

(Measurement > Measurement Systems > Conversions)

While most students possess the background knowledge of the decimal system, they seem to struggle with the conversion of metric units. Is it the calculation or the concept of liter, meter, and gram that pose a problem for students? The document, Convert Metric Units of Length, Mass, and Capacity, provides students with practice of both the calculation and the concept of converting metric units. This document begins with benchmark objects that students can relate each unit of measure to. Once students learn that a raisin is about 1 gram, they begin to understand the concept of gram.

As students progress through the document they enhance their understanding of base metric units by exploring equivalent measurements as prefixes are added. They then apply basic concepts of operations with decimals to convert various units of measurements. This document concludes with challenging students to convert units as they attempt to compare different metric units.

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Why does an image become distorted when you enlarge just the width? What would a model of the Statue of Liberty look like if you shrunk just the dimensions of her height and not her width? The answers to these questions are based on the concept of scale factors. In the document, Scale Factors, students will explore and apply the concept of scale factors by finding the ratio of the lengths on a model or drawing to the corresponding length of the original object.

Throughout this document students will identify scale factors, use scales to find scale factors, and convert units to the same unit of measure before calculating the scale factor. This document will get your students thinking about the relationship between real life objects and the scale models they may see in the stores or museums.

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We are currently testing out our new email reporting system. Even though this example below contains data for the whole month, we will be sending them weekly, starting in January 2012:

Our goal is to interest teachers in their classes with useful information.

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The BuzzMath homepage has gotten a makeover just in time for the New Year!

(1) It will be hard to keep your eyes off of our new attention-grabbing banner at the top of the page. This banner contains information on new content, promotions, and features. So be sure to check back often!

(2) Our biggest change! It is now easier to explore our content by simply clicking on the thumbnail images of some of the most popular documents or by entering keywords into our new and improved search field.

(3) You can also view testimonials and BuzzMath news as well as access buttons to try BuzzMath for free or subscribe your class for free for the entire school year.

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(Algebra > Relations and Functions > Functions)

Students will investigate the relationship between equations and functions in the document Evaluating a Function. Page 2 of this document provides students with a comparison of an equation and a function that allows students to connect their prior knowledge of equations to the concept of evaluation functions.

Throughout this document students are provided with numerous practice problems. These problems allow students to explore functions both numerically and graphically. With each problem students have access to detailed solutions and examples to maximize their success.

(Measurement > Using Measurement > Volume)

Volume of a Prism introduces the what, when, why, and how for finding the volume of a prism. On pages 1 and 2 students experience what volume is as they drag cubes to fill a prism.

Page 3 explains how to solve for the volume using the volume formula.

Pages 5 through 9 provides students with real life situations that allow them to see when and why it would be necessary to find the volume of a prism. Students will determine how many boxes will fit into a storage unit and how much water is needed to fill an aquarium as they practice solving for the volume of a prism. 

(Numbers and Operations > Operations with Rationals > Multiplication and Division > Fractions)

To divide a fraction we must multiply the fraction by the reciprocal of the other factor. As teachers, this makes sense. To students, this can be a very confusing concept. The mastery of the algorithm for dividing fractions will almost guarantee a correct solution, but does nothing for the understanding of the concept.

Dividing Fractions Investigating Patterns with Multiplication introduces students to the relationship between multiplication and division and how this relationship is applied when dividing fractions. This document begins with a visual representation of both dividing whole numbers into fractional parts and multiplying whole numbers by a fractional part to arrive at the same answer.

Throughout the document students are guided through an explanation of why we multiply a fraction by the reciprocal of a factor when we are dividing fractions. Students will use a table to input information that is later used to match corresponding multiplication and division statements. They are also given numerous opportunities to practice dividing fractions and mixed numbers as the document progresses.

(Numbers and Operations > Operations with Rationals> Addition and Subtractions > Fractions)

We all have students that have mastered addition of fractions with like denominators, yet when asked to add fractions with unlike denominators they begin to create their own rules. This is evidence that the students have memorized a series of steps but lack an understanding of number sense and equivalent fractions. Adding Fractions with Models provides students with a variety of models to help students visually explore the addition of fractions.

At times, students fail to realize that different denominators reflect different sized unit fractions and adding fractions requires a common unit fraction. Fraction bars, number lines, and fraction circles allow students to investigate this concept and understand the need for a common denominator.

The interactive models in this document are great for engaging a whole class with a lesson on an interactive white board, and also serve as great practice for students when working individually.

(Measurement > Using Measurement > Surface Area)

Surface Area of Prisms allows students to use their existing knowledge of finding the area of a 2-dimensional shape and apply it to finding the surface area of 3-dimensional prisms. This document is full of colorful visuals that provide students with different prospectives of a variety of prisms. On pages 1 and 2 students explore the area of individual faces of a rectangular prism by viewing the prism and its net.

Students use information from this exploration to generate a formula for finding the surface area of a prism. As they progress through the document students are given the opportunity to practice finding the surface area of hexagonal, triangular, rectangular, and pentagonal prisms.

Students are also provided with problem solving situations that demonstrate how surface area can be applied to real life situations. This document provides students with a foundation for understanding, finding, and applying the concept of surface area. They will further this exploration of surface area in another new document, Surface Area of Pyramids, that will be soon to follow.

Try it online: Surface Area of Prisms

(Numbers and Operations > Real Numbers System > Rational Numbers)

Simplifying Square Roots introduces students to simplifying square roots by finding the principal square root of a number. This document begins with an exploration of perfect squares. The detailed solution on page 2 provides students with a visual representation of a perfect square to solidify their understanding of the concept.

As the students navigate through the document they will investigate the relationship between perfect squares and square roots.

This document provides numerous opportunities for students to practice simplifying square roots. The values are dynamic, so they will change each time a student attempts to solve a question. This allows students to practice simplifying square roots until they are successful. The “Show me an example” option provides students with step-by-step instructions for simplifying square roots. Students are given many opportunities to experience success with BuzzMath.

Try it now! Simplifying Square Roots

(Numbers and Operations > Operations with Rationals > Multiplication and Division > Fractions)

To find a reciprocal of a number just turn it upside down. There is no denying that teaching how to write the reciprocal of a number is far from a challenging task. What is a Reciprocal goes beyond just how to write a reciprocal. It explains what a reciprocal is and provides problems that challenge students to think about how a reciprocal is used.

Throughout the document students are guided through the steps to finding reciprocals of fractions, improper fractions, and whole numbers.

The conclusion of this document asks students to explore what happens when a number is divided by itself and when it is multiplied by its reciprocal. This concept prepares students for dividing fractions. Keep an eye out for our new document, Dividing Fractions Using Models.

Try it now! What is a Reciprocal

(Numbers and Operations > Ratios and Proportions > Ratio)

Seeing two numbers separated by a colon, fraction bar, or the word “to”, may have little meaning for students. The symbolic representation of a ratio can be a very abstract concept for young minds. What is a Ratio? provides students with visual representations of ratios so students can better understand the concept and be able to apply it to real life situations.

Students are provided with definitions of both part to part ratios and part to whole ratios. They are then given the opportunity to apply these definitions by finding the ratio in different situations.

An interactive tool on page 8 is used to build an understanding of equivalent ratios.

If is important for students to have a firm understanding of ratios, so that they can apply this concept to other situations. Shortly to follow is Unit Rates, where students will explore special ratios.

Try it now! What is a Ratio?

The BuzzMath team has just returned from an outstanding two days at the NCTM Regional Conference in Atlantic City. We had the opportunity to meet so many great teachers and administrators who were enthusiastic about enhancing their current math curriculum.

There was a lot of excitement at our booth as many educators took advantage of our free class promotion that will give them and their students a free full-access subscription for the duration of this school year!

This week, the excitement will be in booth #8 at the AMTNYS Math Rocks Conference in Rochester, NY. Next month we will be heading down south for the NMSA2011 Conference on November 10 -12 in Louisville, KY. Hope to see you there!

(Measurement > Using Measurement > Volume)

Why is volume such a confounding topic for students? Are there too many formulas and variables to memorize? Is the concept too abstract? Do they lack the experience and understanding of working with 3-D objects? The answer could be yes to any and all of these questions. Volume of a Cylinder provides students with guided questions and visuals to allow students to “make sense” of this concept. The introduction of this document simply asks students to estimate how many jelly beans are in a jar. This is the prior knowledge of a student that will be built upon throughout the document.

In this document students are not simply given the formula for finding the volume of a cylinder, they are asked to identify it.

Finding the volume of a cylinder may seem meaningless if a student can not relate to a situation in which they will need to use this information. Pages 8-11 provides students with situations where finding the volume is necessary.

Try it now! Volume of a Cylinder 

(Numbers and Operations > Relationships Among Numbers > Comparing and Ordering Numbers)

Students everywhere struggle with fractions. The abstraction of this concept can be causing this confusion. Comparing Fractions with like Denominators or Like Numerators attempts to eliminate this confusion by providing students with visual and interactive representations of fractions.

Students will shade in fraction bars to visually represent different fractions and then compare them. They will explore the relationship between fractions with the same numerators and with the same denominators. Their understanding of this relationship will be assessed as they drag and drop different words into a short paragraph that describes this relationship.

The first 6 pages of this document provide visual representation of the fractions that the students are asked to compare. The concluding pages of this document ask students to apply their knowledge by comparing fractions without the visual representation.