Standard 4.3C: Math

Content Area: Math

Index: 4.3C Grade 7 CPI 1

Standard: 4.3 - Patterns and Algebra

Strand: C - Modeling

Cumulative Progress Indicator: 1 - The student will analyze functional relationships to explain how a change in one quantity can result in a change in another, using pictures, graphs, charts, and equations.

Grade: 7

Sample Activities:

· Students predict what size container is needed to hold pennies if, on the first day of a 30-day month, they put in one penny and double the number of pennies each succeeding day. After making their predictions, they calculate how many days it will take to fill that container, and how many containers like that they would actually need for the whole month.

· Students make a chart that helps them understand the charges for a taxi ride when the taxi charges $2.75 for the first 1/4 mile and $.50 for each additional 1/4 mile. They look at rides of different lengths and figure out how much each trip would cost. Then they write an explanation of how they found the cost.

· Students look for a pattern between the temperature in degrees Fahrenheit and degrees Celsius and write an explanation of that relationship.

· Students use tables or two-color chips to help them solve the following problem: A classroom has 25 lockers in a row. The first person to enter the room opened every locker. The second person closed every other locker beginning with the second locker. The third person started with the third locker and changed every third locker from open to closed or closed to open. This continued until 25 people had passed through the room. Which lockers would be open after the 25th person walked into the room?

· Students make pendulums using strings of length 64, 32, 16, and 8 cm with a washer at one end and a screw eye or ruler at the other. The strings are swung from a constant height and the number of swings in 30 seconds is recorded. A graph is made plotting the number of swings against the string length. Students study the results and determine if there might be a pattern they could continue. They attempt to answer questions such as: Will the number of swings ever reach zero? (This activity is a good one to repeat at later grades since the relationship appears linear but when very short lengths and very long lengths are used, it becomes clear that it is actually a quadratic relationship.)

· Students are given the times of the Olympic 100 meter freestyle swimming winners both in the men's event and the women's event. Using different colors for the two genders, they produce a scatterplot and use a piece of spaghetti to eyeball a line of best fit for each set of data. They use their lines to determine times in the years not given (when no Olympics were held) and to predict times in the years beyond those they were given. They also determine if the data supports the assertion that the women will some day swim as fast as the men and predict from their lines when that would happen.

· A plastic rectangular shape is exhibited on the overhead. The lengths of both sides of the image, and the distance from the screen to the overhead are measured. The overhead is moved and the process is repeated so that measurements are taken at six to ten different distances. One group of students is responsible for determining the relationship between the distance from the screen and the length of one side of the image. A second group is responsible for studying the relationship between the distance from the screen and the area of the image. Each group makes a scatterplot of its data and eyeballs a line of best fit using a piece of spaghetti. They then use the graph to answer questions about the relationship between distance and length or distance and area. They also develop a summary statement describing the relationship.