Friday, March 8, 2019

February -- Inequalities and the Train Tracks

February 8, 2019

Still re-adjusting from the missed days, two of the normal math classes this week were used to work on the lingering second projects (in both ⅚ and ⅞). This meant we only had math two times this week. The two days were quite productive--a lot of work on inequalities, reviewing of the distributive property, learning standard form of a linear equation, and finishing up assessments did happen.

February 22, 2019

This week the Pre-Algebra class has been working more closely with linear equations and introducing linear inequalities in one-variable. We have been especially focused on how to work in an organized fashion (the “train tracks” technique) using the reverse order of operations as a guideline for sequencing the multiple steps that may be required. On Thursday and Friday the class worked on an investigation related to these concepts called “Who is Justice Equilibrator”.

The Algebra and Geometry students have been working independently, finishing up diverse topics from linear equations in two-variables, to geometric concepts of quadrilaterals.

Wednesday, February 20, 2019

January -- Weather Shortened

January 25, 2018 and February 1, 2018

The last few weeks have only had a smattering of math classes between trying to finish up projects and school closings. Despite that all the kids have been making some progress. The Pre-Algebra class has been working on solidifying concepts surrounding combining like terms and solving linear equations in one-variable. The Algebra group continues to study linear equations in two-variables; this week we focused on point-slope form.

Many of the students are now moving on to assessments.


January 11, 2018

Sliding into 2019, we began the week in math by taking a closer look at the number 2019. We reviewed prime and total factorizations, and in the algebra class tried out the challenge of using the digits 2019 to write arithmetic expressions equalling numbers from 1-20--akin to the four 4’s problem. The rest of the week had many students working on assessments and featured lessons on: algebraic concepts for some of the sixth graders, graphing inequalities on the number line, point-slope form, proofs about quadrilaterals.

December in Math

December 14, 2018

This week the Pre-Algebra group has been digging further into solving linear equations. We first looked at one-step equations, like x +3 = 10; modelled those equations with the algebra tiles and then talked about how to formalize the solution process into a replicable algorithm.

The Algebra and Geometry classes have been working on assessments and learning about graphing lines in a coordinate plane.

December 7, 2018

The Pre-Algebra group continues to work on simplifying equations--identifying and combining like terms, applying the distributive property, following the order of operations. On Tuesday we started to explore how the Ti-84 series of calculators is used in math classes, in this case looking at tables to compare the values of the original and student-simplified expressions.

The Algebra and Geometry groups completed and reviewed work on assessments. The Algebra class is now all working on graphing linear equations and we have been reviewing concepts related to coordinate planes and discussing the applications thereof. The Geometry group is working on material related to congruent triangles.

Tuesday, December 18, 2018

November in Math

November 30, 2018

The first few days this week were devoted to reflecting on what the classes have done so far and then getting re-engaged after the week off. A fair number of the students are working on a chapter or unit assessment this week. All of the students working on Singapore math are about to finish and should be moving into the Pre-algebra curriculum shortly. Major topics being worked on this week were: the distributive property, solving single variable linear equations, congruent triangles, parallel lines and graphing on the coordinate plane.

November 15, 2018

The 7/8s only had two days of math this week as we were on field trips or catching up on missed special classes. Our primary math exercise for the week was the AMC 8 test that the students sat for on Thursday; results should be returned in the spring.

The 5/6 students also took the AMC test, and had additional time working in very small groups with me on Wednesday and Friday. The Algebra group spent Wednesday going over AMC 8 practice problems (hint: study combinatorics and probability more if you really want to do well). Most of the 5/6 students in Singapore are wrapping up their textbooks, the pre-algebra students are working on chapter 2 and the Algebra students are starting working with equations of lines.


November 8, 2018

The 7/8 students spent most of this week getting ready for the Julius Caesar performances so math was curbed; students continued working on their textbook assignments.

November 2, 2018

This week was full of special events that interrupted math (Halloween, Julius Caesar rehearsal); but that didn’t stop us.




In the 9 o’clock class--(above): One of the students working on the “King’s Castle’s” enrichment puzzle--a geometric puzzle that asks how to arrange 4 walls (lines), that each have a four (castles) named points into a pattern such that there are exactly ten castles and as many of the castles as possible are surrounded by walls such that they could not be directly attacked without crossing a wall first. Other students continued to work with the distributive property.

In the 10 o’clock group, the Algebra class are working on solving single variable linear equations beginning by modelling those equations with the algebra tiles. The Geometry students are writing proofs involving parallel lines and/or congruent triangles. The whole class spent one days talking about Hilbert’s Hotel and the weirdness of infinity.

Thursday, October 25, 2018

October in Sam's Math Classes

October 26, 2018

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.

Friday, October 5, 2018

October 5, 2018 -- Chapter Tests, Properties,


This week most of the Pre-Algebra students began (and many completed) the chapter one assessment from the textbook. While the chapter assessments in form look like a traditional test--they are literally photocopies from the “tests” manual that comes with the teacher material for the text--we do a lot in class to make the experience more useful and less anxiety provoking than some find the traditional model. After completing the assessment at their own pace, students meet with me individually to review, not correct and wrong answers (though I do make note of those), but rather to discuss what major concepts might need further review and how that is going to be achieved. From this assessment I determined that the whole class needed to go back and look more closely at vocabulary and concepts of mean, median and mode, which we will work on next week.

In the Algebra group the students are working with expressions and equations in some form or another; the students starting algebra are working on basic arithmetic properties--particularly the distributive property; while the returning students are working on solving linear equations in one variable including with fractions and decimals which is new this year.

The Geometry class is doing elementary exercises in formal logic; making truth tables, discussing Boolean operators, tautologies, and proofs using formal symbolic logic.

Sunday, September 30, 2018

September 28, 2018 -- Coordinate Planes, Functions and Proofs

This week the Pre-Algebra group focused on vocabulary and concepts relating to the (XY) Coordinate Plane. We made and labelled a set of axes and then physically moved around the plane to reinforce the difference between x and y and horizontal and vertical.

The students new to Algebra  finished reviewing chapter one and then took a longer look at function notation, and the concepts of functions, relations and mappings. The Geometry class showed the couple of students returning to Algebra the basics of formal proofs using solving single variable equations and the properties of arithmetic as their givens and reasons.