This week 7th grade students constructed scatterplots to organize, display, and analyze data. In one of the lessons, they were given multiple data points for odometer readings and prices of cars and were asked to determine if the two factors were related. After analyzing their scatterplots they came to the conclusion that there is a negative association between the two factors - as the odometer reading increases, the price of the car decreases. Students then drew a trend line/line of best fit through their data points and used that line to make a prediction about the price of a car with an odometer reading of 80,000 miles.
Meanwhile, 8th grade students were exploring a few of the strategies used to factor quadratic expressions. We started with a visual understanding of what a quadratic expression looks like. The students were provided an expression and created the rectangular representation using algebra tiles. Once they had their rectangle they identified the side lengths which became their factored form. The second method explored was factoring with the help of generic rectangles and diamond problems. Below is a description of the one student’s step by step process in their own words.
Using a Generic Rectangle and Diamond Problem to Factor a Quadratic Expression
Quadratic Expression: 4x^2 +17x - 15
1. Put in standard form ax^2 +bx +c (this problem already is)
2. Make a generic rectangle with the ax^2 and c diagonal from each other (4x^2 , -15)
3. Multiply those two together (equals -60x^2)
4. Make a diamond problem with that (-60x^2) on top and the bx (17x) on the bottom
5. Find factors for the top that when added together are what is on the bottom, the GCF (-3x. 20x)
6. Put these in the remaining spaces of the generic rectangle
7. Find the answers for the sides of the rectangle (4x-3)(x+5)