February 2013

In this issue:

Introducing a New eXpLoration: Petabyte |
DISCOUNT! |
Win Our Latest Activity |
Average Precipitation: Free activity |
Like Us! |
Möbius Strip Fun |
World Maths Day |

**Introducing a new eXpLoration: Petabyte!**

**Middle School - Common Core Standards Aligned - 18 pages - Includes teacher edition with worked-out solutions**

MIRL is helping students answer the "why" of mathematics through a collection of engaging real-world math activities that give you the tools to answer the question, "when am I ever going to use this?"

Explorations extend the standard MIRL two-page math activity into a much larger investigation of the mathematics of a real-world context. Explorations are ideally suited for group work, individual work, or even group competitions. This Exploration activity includes a student version of the activity as well as a teacher edition, complete with worked-out solutions and Common Core Standards mapping.

Explorations are intended to enhance, support, and be used alongside existing curricula. Explorations reinforce mathematical concepts learned prior to completing the activity.

The Petabyte Exploration is focused on the following areas:

- Problem solving and making sense
- Computing rates
- Using rates to create graphs
- Modeling with mathematics
- Working with very large and very small numbers
- Working with exponents
- Looking for patterns
- Creating formulas
- Converting units in the context of a word problem
- Communicating effectively using mathematical ideas

Included in this Exploration:

- Welcome and copyright
- Student edition of the Petabyte eXpLoration activity. (21 pages)
- Teacher edition of the Petabyte eXpLoration activity. (22 pages)
- Worked-out solutions. (Teacher edition only)
- Common Core Standards and Common Core Standards for Mathematical Practices. (Teacher edition only)

A portable document file (PDF) detailing the Common Core Standards alignment is available here.

**20% DISCOUNT!**

We're offering our newsletter subscribers a **20%** discount on any single product this month, including bundles. Just enter coupon code * FEBNEWS* on the checkout page. Discount ends March 15, 2013.

**Win a Petabyte eXpLoration!**

Let us know how we're doing for a chance to win our new Petabyte eXpLoration! We'll randomly select a winner from respondents of a short survey. We'd love your feedback! Take the survey.

We'll announce the winner in March's newsletter.

**Free classroom activity for Grades 7-12.**

**Introduction**

The ability to graph information and to read and interpret information from a graph are essential skills for mathematics students. Experience suggests that by the time students complete high school they have much exposure to graphs but may still struggle to accurately interpret them and understand what a point on a given graph represents in context. This can be a significant barrier to achievement in upper levels of mathematics (such as Calculus, Differential Equations, and Statistics) and can even impact success in other fields like business and medicine. Furthermore, the Common Core standards stress the importance of representing and interpreting data as early as Grade 4 (CCSS.Math.Content.4.MD.B.4) and the skill permeates nearly every focus area in the high school standards.

The activity included here provides practice with graphing data and interpreting the information from a graph. It’s designed so that students must continually confront the questions “What is being represented in this graph?” and “What does a point on the graph communicate about the context?” We believe that training students to ask these questions whenever they confront a graph sets them up for future success in mathematics.

This activity can address the following standards, depending on how the activity is used.

- CCSS.Math.Content.8.F.A.1

- CCSS.Math.Content.8.F.B.5

- CCSS.Math.Content.HSF-IF.B.4

- CCSS.Math.Content.HSF-BF.A.1a

**Activity**

*Average precipitation* in a location is a useful number for meteorologists (people who study weather patterns). It gives them an idea of how much precipitation (rain, snow, hail, etc.) to expect in a certain location over a certain amount of time. Other people might be interested in this number as well. For example, a farmer might want to know how much rainfall to expect in a given month to determine if he or she will need to bring in additional water for certain types of crops. Homeowners may want to know the average precipitation to determine if a certain type of flower or plant can live in their yard without installing a sprinkler system. When the amount of actual precipitation is below the average precipitation for a long period of time then the area could be experiencing a drought. When an area receives more than the average precipitation rivers may swell and flooding can occur. (Data for this worksheet was collected from www.weather.com unless otherwise noted and is rounded to the nearest tenth.)

1. The table below gives the average precipitation (in inches) per month for Dallas, TX.

Month of the year (1 = Jan) | Average precipitation (inches) |
---|---|

1 | 2.1 |

2 | 2.7 |

3 | 3.5 |

4 | 3.1 |

5 | 4.9 |

6 | 4.1 |

7 | 2.2 |

8 | 1.9 |

9 | 2.8 |

10 | 4.8 |

11 | 2.9 |

12 | 2.7 |

a. Graph this data on the given axes. Be sure to label your axes and provide a title for your graph.

b. Pick a point on your graph. Explain what this point tells us about the context.

2. The graph below shows the difference in average precipitation per month between Indianapolis, IN and Kansas City, MO (calculated by subtracting the average precipitation in Kansas City from the average precipitation in Indianapolis).

a. Pick two points on the graph and explain what they tell us.

b. The graph below shows the average precipitation per month for Kansas City. Use this graph and the previous graph to create a graph of the average precipitation per month for Indianapolis. Be sure to label your axes and provide a title for your graph.

c. What is the total average annual precipitation in each of these locations?

d. Construct a graph showing the total average precipitation per month for both locations together. Be sure to label your axes and provide a title for your graph.

e. Pick a point on the graph in part (d) and explain what it tells us about this context.

3. Use the given graphs to construct a graph of the average precipitation per month for New Orleans, LA as accurately as possible. Be sure to label your axes and provide a title for your graph.

4. While the average precipitation per month tells us the total amount of precipitation we might expect to see in a given month in a certain location, the actual amount of precipitation might be different.

a. The tables below give the average precipitation per month in Portland, OR as well as the actual precipitation for Portland in 2009. Construct a graph showing the difference between the actual precipitation in Portland in 2009 and the average precipitation each month. Be sure to label your axes and provide a title for your graph. *(Data for 2009 collected from www.wrcc.dri.edu.) These values are sometimes called the deviations from the expected values.*

Month of the Year (1 = Jan) | Actual Precipitation in Portland in 2009 (in inches) | Average precipitation (in inches) |
---|---|---|

1 | 4.5 | 6.1 |

2 | 1.4 | 4.8 |

3 | 3.4 | 4.5 |

4 | 2.3 | 3.4 |

5 | 3.3 | 2.6 |

6 | 1.3 | 1.7 |

7 | 0.3 | 0.6 |

8 | 0.8 | 0.7 |

9 | 1.4 | 1.5 |

10 | 3 | 3.4 |

11 | 5 | 6.7 |

12 | 3.8 | 6.9 |

b. Pick a point from your graph and explain what it represents.

c. Was the total precipitation greater or less than expected in 2009?

5. Our friend noticed that it seemed to rain and snow more often when the weather is cold than when the weather is warm. We’ve decided to collect some data and see if we agree. The table below shows the average high temperature and the average precipitation per month for Portland, OR.

Month of the Year (1 = Jan) | Average precipitation (in inches) | Average high temperature (in °F) |
---|---|---|

1 | 6.1 | 47 |

2 | 4.8 | 51 |

3 | 4.5 | 56 |

4 | 3.4 | 61 |

5 | 2.6 | 67 |

6 | 1.7 | 73 |

7 | 0.6 | 80 |

8 | 0.7 | 80 |

9 | 1.5 | 75 |

10 | 3.4 | 63 |

11 | 6.7 | 52 |

12 | 6.9 | 49 |

a. Create a graph showing *average precipitation in a month (in inches)* vs. *average high temperature for the month (in °F)*. Be sure to label your axes and provide a title for your graph.

b. Does the graph in part (a) prove that our friend is correct? Explain.

c. The table below gives information about New Orleans, LA. Create a graph showing *average precipitation in a month (in inches)* vs. a*verage high temperature for the month (in °F)* for New Orleans. Be sure to label your axes and provide a title for your graph.

Month of the Year (1 = Jan) | Average precipitation (in inches) | Average high temperature (in °F) |
---|---|---|

1 | 5.1 | 62 |

2 | 5.5 | 65 |

3 | 4.6 | 72 |

4 | 4.6 | 78 |

5 | 4.6 | 85 |

6 | 8.1 | 90 |

7 | 5.9 | 91 |

8 | 6 | 91 |

9 | 1.5 | 75 |

10 | 4.0 | 80 |

11 | 4.5 | 72 |

12 | 5.3 | 64 |

d. Does the graph in part (c) change your answer to part (b)? Explain.

**NOTE: A PDF version of the activity with worked-out solutions is available ****here**. If you download this activity, please take a couple of moments and like us on Facebook.

**Fun with Möbius Strips!**

Maria Miller at Homeschoolmath.blogspot.com has posted an entry, including a video by Vi Hart, that captivated my family. Enjoy! (And be prepared with paper, tape, and scissors.)

**World Maths Day 2013 is nearly here!**

Save the Date: March 6, 2013 is World Maths Day, where students compete in 60-second mental arithmetic races in which they have to answer as many questions as possible. This event measures mental arithmetic and numeracy skills. More than 5.9 million students are expected to participate in this real-time online math challenge. Learn more here!