We are thinking mathematically every day, and students have made some intriguing connections and a few valuable discoveries. We have completed an introductory unit in which the many mathematical backgrounds that got students thus far have been reviewed and often challenged to be sure that the things we are doing mathematically - the algorithms and the "shortcuts" - make logical, explainable sense. We are working on precise language for describing our reasoning when working with peers at Erasable Wheeled Mathematical Surfaces (EWMS!) or when explaining an observation to the entire class. In the process, we have reviewed a couple of models for multiplication, the addition and multiplication of fractions, the use of "versions of 1" (like 3/3 or 17/17) to find equivalent fractions or common denominators, and we have used factor trees, factor towers, and prime pools to break down numbers into usable parts. If you haven't been taken on a tour of the new textbook yet, please ask your favorite sixth grade mathematician to show you how to navigate the structure and substance of Illustrative Mathematics's Accelerated Grade 6 curriculum for both Students and Families. We just began working in this electronic text last week, so please take some time to explore this resource together. This is also a good time to start assessing learners' progress, so if you have questions, feel free to open or continue the conversation. And be sure to ask about tangrams (the seven shapes that collectively measure 8-square units in area) with, which we explored today.
We are just finishing up our unit on rigid transformations. We will be having a unit exam later in the week. In our next unit, students will learn to understand and use the terms "scaled copy," "to scale," "scale factor," "scale drawing," and "scale," and recognize when two pictures or plane figures are or are not scaled copies of each other. Students then refine their thinking about scaled copies as they learn to understand and use the term "dilation" and to recognize that a dilation is determined by a point called the "center" and a number called the "scale factor." Students will then learn the terms "slope" and "slope triangle" and use the similarity of slope triangles on the same line to understand that any two distinct points on a line determine the same slope.
Eighth graders are diving deeply into linear equations now and are perched on the precipice of trying to solve simultaneous equations. We are comparing slopes and intercepts in equations and graphs and will look at systems of equations through similar lenses. This exploration also allows for the introduction and review of several relevant topics - order of operations, combining like terms (and not combining unlike terms!), solving for a variable (even in a multivariable equation), and performing various operations with positive and negative whole numbers and fractions. If you want to support the progress of these algebraic explorers, you could share thoughts and suggestions on these topics or trade relevant problems to solve (i.e., "I'll make one up while you make one up, and then we'll trade and solve" (making errors for each other to correct and modify). We are working on justifying and explaining our reasoning at each step and in the big picture. Feel free to ask for a tour of the electronic textbook, some time to look over the results of the first big "test",” and a glimpse of the upcoming "practice packet" that will provide optional "vitamins" for those wanting some more practice with the core skills previously named.