Fawn Nguyen, a creative and inspiring teacher, had a great idea for Math Taboo on her blog. What a great way to teach math vocabulary with a fun diversion. Check it out!

# Category Archives: Tools and Tips

# Excellent free resource: Online Graphing Calculator

Desmos has a free online graphing calculator available here. https://www.desmos.com/

# Standards Map

Activity Library Volume 2 is nearly here! All of the new activities are mapped to the Common Core State Standards for Mathematics. As of March 2012, these learning standards had been adopted by 45 of the 50 states in the United States. We’ve uploaded a reference document which maps each of the new activities to the core standard by grade level. The new library will be available on our site soon. Very soon.

# 2012 TeamUp Presentation

Make It Real Learning activity developer and award-winning author, Frank Wilson, will be part of an all-star lineup of authors and educators at the Cengage Learning TeamUP Faculty Programs Mathematics Conference in Scottsdale, Arizona on Feb 10, 2012. Wilson’s workshop, entitled*Captivating Contexts for College Algebra*, will feature intriguing real-world contexts that interest and engage students in learning. By creating mathematical models for real-world situations, students learn more than math: they learn about the world in which they live. Participants will receive an activities packet featuring fascinating contexts ranging from the Nintendo Wii to the Apple iPod. A copy of the presentation and packet may be freely downloaded.

# Sweet Fractions – Free Activity

Recently, I was asked to substitute for an arithmetic class at a community college. As you might expect, many of the students had little experience being successful at mathematics. My goal for the day was to help the students understand basic fraction concepts. I decided to use an activity I had created for a teacher traning workshop I had conducted at Arizona State University. The activity was a hit and the students loved it!

Since it’s back to school for many of us. We thought we’d celebrate by providing the activity as a free download. Enjoy!

Free PowerPoint show: Sweet Fractions Math Activity

# The Make It Real Learning Approach

One important component of the Make It Real Learning approach is making sense of mathematics and mathematical models of real-world contexts. For example, consider the following sample exam question for an algebra class and its corresponding solution.

Based on data from 1985 - 2004, the difference between US oil field production and net oil imports may be modeled by million barrels where ** t **is the number of years since 1985 (Source: Modeled from Statistical Abstract of the United States 2007, Table 881). When the value of the function is negative, the US is importing more oil than it is producing. What is the practical meaning of the 2251 and the -278.3 in the equation?

This question doesn’t require any computations but it does require an understanding of quadratic function models.

The 2251 is the initial value of the function. Since 1985 is the initial year (*t =* 0) for the model, US oil field production exceeded net oil imports by 2251 million barrels in 1985.

The -278.3 is the initial rate of change of the function. In 1985, the difference between US oil field production and net oil imports was decreasing at a rate of 278.3 million barrels per year. According to the model, the difference in 1986 was predicted to be about 278 million barrels less than the difference in 1985.

# Real-World Math

Students always ask, “When am I ever going to use this?” The following is a list of a few common math function types and associated real-world math contexts.

## Linear functions

**Anything that has a constant rate of change is a linear function.**

The total cost of bowling n games at a price of $5.00 per game when the shoe rental is $4.00:

A cell phone plan costs $59.99 for 1000 minutes. Additional minutes are $0.45 each. The monthly cost of the plan when you go over by x minutes:

Gasoline currently costs $3.799 per gallon. The cost of buying g gallons:

Degrees Fahrenheit and degrees Celsius are both used to measure temperature. Water freezes at 32 degrees Fahrenheit or 0 degrees Celsius. Water boils at 212 degrees Fahrenheit or 100 degrees Celsius. The temperature in degrees Fahrenheit when the temperature is c degrees Celsius:

## Exponential functions

**Anything with a constant percentage change is an exponential function.**

According to the Central Intelligence Agency, Argentina had a population of 41.8 million people in 2011 and was growing at a rate of 1.017% per year. The population of Argentina (in millions) t years since 2011:

According to the Central Intelligence Agency, Japan had a population of 126.4 million people in 2011 and was declining at a rate of 0.278% per year. The population of Japan (in millions) t years since 2011:

The future value of a $1000 investment earning 3.21% interest compounded monthly after t years:

## Piecewise functions

**Anything where different rules apply in different situations.**

The monthly cost of a cell phone plan with 1000 included minutes for $59.99 and extra minutes costing $0.45 when m total minutes are used:

The cost of n greeting cards when cards cost $1.29 each when 10 or less cards are ordered and cost $0.99 each when more than 10 cards are ordered:

# 31 years ago today…

Mount St. Helen’s in Washington State, USA, erupted 31 years ago today, and the Make It Real Learning team experienced the eruption first-hand. In commemoration, we’ve posted a free real-world math activity focused on the Mount St. Helens eruption.

If you’re unfamiliar with the event, a great visual history is available here.

# Rule of 4

The *Rule of 4* refers to representing mathematical functions with *graphs, tables, equations*, and *words*. As learners discover how to represent functions in each of these ways, the mathematics becomes more meaningful. For example, consider the following cell phone plan offered by T-Mobile in 2011, represented using the *Rule of 4*.

**Words Representation (from website)**

Even More 1000 Talk + Unlimited Text

$59.99 includes 1000 whenever minutes

Additional minutes $0.45 per minute

Despite the fact that each of these representations of the cell phone cost function looks different, the same function is represented in each representation. All learners should practice to increase their ability to “see” the other forms mentally even when only one form is given.

# TeamUP Presentation

Make It Real Learning activity developer and award-winning author, Frank Wilson, will be part of an all-star lineup of authors and educators at the Cengage Learning TeamUP Faculty Programs Mathematics Conference in Chicago on March 4, 2011. Wilson’s general session, entitled* Captivating Contexts for College Algebra*, will feature intriguing real-world contexts that interest and engage students in learning. By creating mathematical models for real-world situations, students learn more than math: they learn about the world in which they live. Participants will receive an activities packet featuring fascinating contexts ranging from the Nintendo Wii to the Apple iPod. A copy of the presentation and packet may be freely downloaded.