This week the Pre-Algebra class looked more closely at the distributive property and has been starting to work with single variable linear equations. For both concepts, we began our discussions by using the algebra tiles to physically construct algebraic statements with blocks, similar to what is shown in this youtube video. Lots of research suggests that working from physical models gives students a very tangible entrance point to more abstract representations and notation.
In Algebra class we also spent most of the week looking at solving equations with variables; though at a different level of complexity. Mostly we focused on solving equations with multiple variables in terms of one specified variables, for example rewriting the well-known d=rt as r = d/t when trying to find a speed instead of a distance.Part of the discussion was providing a real world context for when it is necessary to do this: writing formulas in a spreadsheet, entering equations into graphing calculators, and in certain programming languages.
The Geometry group moved on from formal logic and is working with proofs relating to parallel lines and/or congruent triangles.
October 19, 2018
This abbreviated week had us all over the math realm. On Tuesday all the students worked on a logic puzzle/tour de mathematics celebrating my 42nd birthday. (All the answers were something about 42–like William Jefferson Clinton or XLII.)
The rest of the week had us investigating numbers in other bases and the concept of place value with the Pre-Algebra group; finishing off formal logic in Geometry and looking at properties of algebra with the Algebra students. The 10 o’clock group also had their first round of “pop quizzes” (untimed and used formatively to frame future assignments).
October 12, 2018
This week the Pre-Algebra class did an exploration with pentominoes, hexominoes and other polyomino tiles. They thought about strategies for listing all of the tiles of one category in an organized fashion and investigated the relationships between the area and possible perimeters of the tiles.
The Algebra students continue to work with algebraic properties, and single variable equations; most of them have begun or are about to begin a chapter assessment. Shortly we’ll be moving into graphing linear equations.
The Geometry class continued to work with formal logic; moving on to rules or replacement (aka which statements are interchangeable); thinking about which binary operators can be used to produce all 16 of the possible bivariate truth tables without the use of any other operator (and how this ties to extremely low-level computer hardware); and delving deeper into formal logic proofs.