7th Grade News
In the seventh grade, we are just now in the midst of some basic foundational work in preparation for algebra next year. We have plumbed the depths of the commutative, associative, identity and distributive properties and have also identified the identity elements for the four basic operations. We are now putting these properties to work as we study how to simplify algebraic expressions, paying special attention to the applications of integer operations, and the combining of like terms.
As we continue, we will be encountering our first formal work with solving algebraic equations, for the time being limiting ourselves to simple linear equations. This will involve an understanding of the inverse order of operations as well as its application in formal equation solving, inverse operations. Before too long, the students will be solving more complex linear equations which will bring this wide-ranging subject matter into great focus. These complex equations will demand application of each of the properties (especially the distributive property,) and combining like terms as well as inverse operations. We will even be solving equations where we find variables on BOTH sides of the equation!
8th Grade News
The eighth graders are exploring the richness of the concept of slope (rate of change) in great detail. This is one of the central themes of algebra and has utility all the way through to calculus! We are examining continuous rates of change, which correspond to linear equations. The introduction to this intense topic was a piece of creative writing, written by each of the students, describing a fictional trip to Duluth and all of the interesting and often humorous events that happened along the way. The stories were written to describe the facts that were contained on a graph of the fictional trip. The students had a lot of fun with this activity, and it strongly reinforced the concepts of coordinates on the coordinate plane, as well as establishing rate of change (in this case speed!) as the slope of the lines at various points along the journey.
Building on these understandings, the eighth graders will develop more fully their understandings of linear equations, expressed both in slope-intercept form (y=mx+b), standard form (ax+by=c), and point-slope form((y-y1)=m(x-x1). We will also be discussing the implications of parallel and perpendicular lines on their respective equations. Lastly, we will be applying our skills and knowledge to examine trend lines that present themselves in scatter plots.
Okay, you got me. There IS yet one more thing... graphing absolute value functions!
As always, excitement abounds!