#NCTMDance : Fun and mathematics in Boston at NCTM 2015

Did you know that more than 8,000 of your math education peers are in attendance at the NCTM Annual Conference? It is the perfect opportunity to have some fun!

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We kicked off the festivities at our booth with the Buzzmath #NCTMDance contest. Educators from across the country are being challenged to perform a dance move representing a math function of their choice to win a premium classroom subscription to Buzzmath!

Rules are simple:

The two most liked comments here will be crowned Queen or King of Math-dancefloor on our Facebook page (and win premium classroom subscription to Buzzmath).

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The two most liked pictures on our Instagram account  with hashtag #NCTMDance or #Buzzmath will be named Bowtie dancers (and win premium classroom subscription to Buzzmath).

The two most retweeted tweet with hashtag #NCTMDance or #Buzzmath will win be our social media champions (and win premium classroom subscription to Buzzmath).

If you are in Boston be sure to come boogie with Buzzmath and be part of the #NCTMdance!

Visit our #441 booth, follow us on social media and please be sure to subscribe to our newsletter.

NCTMdance

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New BuzzMath Activity – Factor 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.

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.

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New BuzzMath Activity – Introduction to Cube Roots

Are you perfect? If you are a 4, 16, or 36 you are. You also are if you are an 8 or 27. By perfect we mean, a perfect square or a perfect cube.

Students will use unit tiles to cover a large square as they explore perfect squares and then use unit cubes to fill a large cube as they explore perfect cubes. This manipulation and visualization of squares and cubes introduces students to these concepts while providing a foundation that students will build upon later in this activity as well as in additional activities. They will apply this understanding as they find the cube the root of some numbers and cube others.

Introduction to Cube Roots

Click here to try New BuzzMath Activity – Introduction to Cube Roots

New BuzzMath Activity – Proportional Relationships

Proportional relationships are all around us–in nature, music, design, art, and a myriad of other real-world spheres. Patterns, prediction, efficiency, and aesthetically pleasing objects result from proportional relationships. How do we know when relationships are proportional?

In the activity Proportional Relationships, students learn how to identify these relationships. They complete tables and graphs, and use select, drag and drop, and input tools to show off their skills when determining proportional relationships. They also learn that the unit rate is the constant of proportionality, and determine these from tables, graphs, and real-world situations.

Proportional Relationships

Click here to try  New BuzzMath Activity – Proportional Relationships

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New BuzzMath Activity – Proportional Relationships and Graphs

When you go to buy something, if you don’t buy it, you pay nothing. In other words, zero of that item cost you zero dollars. But if you do buy it, for each item that you buy, you will pay a certain amount. This is a description of a proportional relationship. If you were to graph this relationship, you would get a straight line going through the origin, (0, 0). Well, that’s exactly the focus for the activity, Proportional Relationships and Graphs!

Proportional Relationships and Graphs

In this activity, students examine graphs of proportional relationships. They focus on two special points on the graphs–the point at the origin, (0, 0), and the point that shows the unit rate.

Students begin the activity with a review of unit rates and quickly move to tables and graphs of proportional situations. Over the ten pages of the activity, students interpret points on the graph focusing on the point at the origin, and the point that represents the unit rate.

Click here to try it: Proportional Relationships and Graphs

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New BuzzMath Activity – Rational and Irrational Numbers

Is it rational or irrational? The answer depends on who you ask! In the real world, if it is reasonable or logical, then it is rational. But ask a mathematician and you will find out that if it can be expressed in the form of a fraction, only then is it rational. Does that make it logical or reasonable?

In the Rational and Irrational Numbers activity, students identify different types of numbers and classify them as rational or irrational. They learn that rational numbers have decimal equivalents that are either terminating or repeating.

Rational and Irrational Numbers

In previous grades, students learned to convert terminating decimals to fractions using models and by writing and simplifying fractions with denominators containing powers of 10. In this activity, they convert repeating decimals to fractions by completing step-by-step procedures in which they write and solve equivalent equations. Although students may have previously converted fractions to repeating decimals, this is the first time they are converting repeating decimals to fractions.

Click here to try Rational and Irrational Numbers

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New BuzzMath Activity – Operations with Decimals

In a perfect world everything would be whole and we would not have to deal with parts of a whole. But in real life, a whole is often broken in parts. This is most evident in our monetary system–a cent is a part of a dollar, and we use a decimal to separate the whole (dollars) from the part (cents). Because money and decimals are a huge part of our daily lives, we need to be able to add, subtract, multiply, and divide decimals fluently.

In the activity Operations with Decimals, students use standard procedures to perform the four basic operations (addition, subtraction, multiplication, and division) with decimal numbers.

Operations with Decimals -2

Students begin with models that help them to perform an operation, and then connect the standard procedure to the operation they performed on the model. For example, students use a grid to add two decimal numbers, and then use the standard procedure by aligning the decimal points in the numbers, and then adding the digits in the same place value. By the end of the activity students are exposed to real world situations they must solve by performing the appropriate operation(s) with decimal numbers.

Operations with Decimals

Click here to try it: Operations with Decimals

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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.

Properties of Negative Integer Exponents to Generate Equivalent Numeric Expressions -2

 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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