Properties of Negative Integer Exponents to Generate Equivalent Numeric Expressions

If you are going to be negative, you are on the wrong side of the line. If you are an exponent, that is. If an positive exponent tells you how many times to multiply a base number, what does a negative exponent mean? It means that you will do the opposite and divide. 

Properties of Negative Integer Exponents to Generate Equivalent Numeric Expressions

Students will explore patterns and properties of negative exponents as they work through this activity. They will gain an understanding of why a base number with a negative exponent in the numerator is equivalent to that same base and positive exponent in the denominator.  Using the same table that was used in a previous activity, Properties of Positive Integer Exponents to Generate Equivalent Numerical Expressions, they will be able to determine that positive, zero or negative exponents are part of the same simple pattern.

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 Click here to try it : Properties of Negative Integer Exponents to Generate Equivalent Numeric Expressions

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New BuzzMath Activity – Opposite Quantities

I take two steps forward

I take two steps back

We come together ’cause opposites attract

I’m like a minus, she’s like a plus

One going up, one coming down

But we seem to land on common ground 

Like some of the above lyrics from a popular song in the late 1980’s called Opposites Attract, the activity Opposite Quantities examines situations that combine to make zero.

In this activity, visual models combine with symbolic and verbal representations to illustrate situations that combine to make zero. Students are presented with many familiar real world situations that help them to understand this concept, and prepare them for adding positive and negative numbers.  Using a variety of input modes that include matching, number lines, as well as positive and negative clickable buttons, students demonstrate their understanding of situations that combine to make zero.

Opposite Quantities

Click here to try it : Opposite Quantities

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New BuzzMath Activity – Division of Rational Numbers

Imagine trying to divide a set of books among zero people! That doesn’t even make sense….does it? This activity takes this idea one step further, using the relationship between multiplication and division to demonstrate why division by zero does not work.

As students work with rational numbers in this activity, they come to understand that when division of integers is represented with a fraction bar, the signs on the integers determine the overall sign of the fraction (that is, the sign of the quotient). Many different representations for division of rational numbers are presented in this activity. And as a culmination, students get a chance to interpret quotients of rational numbers in real world situations.

Division of Rational Numbers

Click here to try it : Division of Rational Numbers

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Properties of Positive Integer Exponents to Generate Equivalent Numerical Expressions

Exponential growth…we love it when it applies to our bank account, we hate it when it applies to the dishes in the sink! As we multiply the same number over and over again we can rewrite it using exponential notation. Once this value is in exponential equation, we can use the properties of exponents to simplify and produce equivalent expressions.

In this activity, students will be guided through pages of practice as they explore and apply the properties of exponents. They will analyze exponential terms written as repeated multiplication in order to generate a rule for multiplication and division. They will then apply these rules as they simplify a variety of exponential expressions.

Properties of Positive Integer Exponents to Generate Equivalent Numerical Expressions

Click here to try it : Properties of Positive Integer Exponents to Generate Equivalent Numerical Expressions

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Operations with Numbers Expressed in Scientific Notation

How can you measure a year? Besides, daylights, sunsets, midnights and cups of coffee, we can say a year is 525,600 minutes or 31,536,000 seconds or .001 of a millennium. Whew! These numbers can get really large or really small based on our units. I don’t know about you, but I don’t want to spend all day writing these numbers and either do scientists and mathematicians. The good news is that we don’t have to! Scientific notation can be used to write really large and really small numbers in a more compact way.

Operations with Numbers Expressed in Scientific Notation

Operations with Scientific Notation allows students to add, subtract, multiply and divide large and small values using scientific notation. The students start by reviewing how to write numbers in scientific notation and then learn how to perform operations using values that are in this form. They will gain an understanding of not only how to solve problems using scientific notation but also see the value in the ability to do so.

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Click here to try it : Operations with Numbers Expressed in Scientific Notation

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New BuzzMath Activity – Multiplication of Rational Numbers

In previous grades, students have been multiplying positive rational numbers, which include integers, fractions, and terminating decimals. In this activity, they extend their understanding to positive and negative rational numbers.

The activity opens with something that may be familiar to students; that is, multiplication patterns that lead to the rules for multiplying signed numbers. But over the next pages, explorations using properties of operations lead them to products that really demonstrate the rules for signed numbers. This will be new for most students, and just may present an aha moment. Not only do they come to better understand the rules, but they will also understand different ways to proceed when applying the rules.

Later in the activity, students have an opportunity to test out their rational number multiplication skills before they are faced with real world situations where they must interpret the product of rational numbers. This way they really get to see these rational numbers in action!  

Multiplication of Rational Numbers

Click here to try it : Multiplication of Rational Numbers

 

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Calling all Heroes! Save Buzzcity

Looking for extra fuel to motivate your students? Tell them the story of BuzzCity! Your Buzzmathematicians can help Dr. Bowtie by collecting enough gold stars to unlock missions to recover important mathematical artifacts.

Alfred Bowtie, the great inventor, was in his time traveling machine (called the BuzzPorter) when the mysterious Mr. Haze stole the world’s math knowledge! Now BuzzCity is in shambles–there are no right angles, circumferences or diameters cannot be measured, and so on–but wait, Alfred Bowtie was safe in his time machine and did not lose his math knowledge. He plans to undo Mr. Haze’s work and restore all our mathematical knowledge.

Watch the video

Watching the mission video will introduce you to the BuzzMath storyline where you will find out why BuzzCity needs to be repaired and how you can help. The video is approximately 2.5 minutes in length and could easily be watch in your classroom!

What is a mission?
A mission is a more challenging problem solving activity that links students to math history and to the BuzzMath storyline. Students must solve each page in order to move to the next page. Each mission features a famous mathematician in a fictional storyline that is integrated with mathematical history. Upon completion of a mission students collect an object (such as Euclid’s lost Book of the Elements) that will help restore lost mathematical knowledge and ultimately the beauty and architecture of BuzzCity.

The current missions are The Lost Talisman, The Secret Rule, Mystery in the Sand of Egypt, Measure Under Pressure, Reaching the Possible,Knowledge is the Key, the Dawn of Algebra.

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As Buzzmath evolves, stay turned for more missions and more opportunities to save our city!

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Buzzmath Friday at Philippa Schuyler Intermediate School

The  Buzzmath team was  back in NYC last week to collaborate with teachers and other ed tech developers as part of the NYC DOE Innovation Zone Short Cycle Evaluation. While there, we had the opportunity to talk with the students, teachers and administrators at the Philippa Schuyler Intermediate School.

Students were eager to give us feedback on the activities they were working on and the teachers provided us with valuable information regarding the role Buzzmath plays in their classroom. From our visit we not only got to see Buzzmath in action, we also gained great insight into data reporting, parental involvement and bowties. In honor of Alfred Bowtie, the students and teachers wear bowties on Buzzmath Fridays…amazing!

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GIFs That Explained Math Better Than Your Teacher Ever Did

Where was this post when I was in school? Amazing how a little animation can help illuminate the most confusing of math concepts. Thanks to Lisa Winter from iflscience website, we now have 21 GIFS that neatly illustrate math concepts better than anyone could have expected.

From solving Pascal numbers to dealing with pi, these moving pictures make everything look easy. Try it with your students! Visual-spatial learner will absolutely love this.

Our favorite? The Pythagorean theorem one.

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Click here to see the article and don’t forget to share your thoughts in the comment section below.

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Buzzmath iPad App Update !

Buzzmath iPad App Update

A new Buzzmath version is now available on the App Store just in time for back to school! Update your application now to access the following additions and improvements:

  • iPad Retina display support. Enjoy our content with absolute clarity.
  • Improved scrolling speed inside activities.
  • Fullscreen mode; making it easier to view and interact with hundreds of objects. Read our blog Say Hello to Full Screen Mode for more information.
  • Various bug fixes

We hope you enjoy these new features, so please share your experience with the others in the comment section below.

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