W5 Discussion about Real-life Problems

Take a look at the following table.

- What observations can you make about this table?
- How would you describe the shape of a graph of this data?
- Have you worked with data in tables elsewhere? If so, describe the data and how you analyzed it.

Year |
1998 |
1999 |
2000 |
2001 |
2002 |
2003 |
2004 |
2005 |
2006 |

Sales- millions of dollars |
201 | 219 | 233 | 243 | 249 | 251 | 249 | 243 | 233 |

# W8 Group Discussion of Real-life Problems

“The number of words in a child’s vocabulary is a function of the child’s age. A typical child at the age of 20 months has a vocabulary of 300 words. At the age of 50 months, the child’s vocabulary has increased to 2,100 words. ”

On your own, graph the pairs of points generated from the last two sentences, where the age is the independent variable and the vocabulary is the dependent variable.

Now, as a group, discuss how many words a 30-month old child would know? How many words would a 40-month old child know? What assumptions are you making when you give these estimates?

How many words would you predict a typical child learn each month from the age of 20 months to the age of 50 months? Could a graph be used to estimate how many words a 10-month old child knows? Explain.

Once these questions have been addressed, get creative. What other situations can be described by a linear relationship? Suggest some possibilities and see what others think. Ideally, come up with an equation.

# W 12 and 13 Discussion about Real-life Problems

**Here’s a problem that uses systems of equations:**

At a carnival, $2,941.25 in receipts were taken at the end of the day. The cost of a child’s ticket was $20.50, an adult ticket was $29.75 and a senior citizen ticket was $15.25. There were twice as many senior citizens as adults and 20 more children than senior citizens. How many of each type of ticket was sold (adult, senior, child)?

Discuss in an entry how you would approach this problem, using what you have learned about systems of equations. Play around with the numbers. It’s doubtful these are real prices- too much need for quarters! Can you think of a way to simplify prices? Share possible rewrites for this problem. This may get you thinking about what to propose for your final project!