Friday, November 17, 2017

Week of November 17

November 17, 2017
The highlight of this week was the AMC 8 contest on Tuesday. All of the students in my math classes participated. We spent Monday looking at sample problems and talking about test taking strategies, especially that the goal is to get as many correct as possible in a short time frame and NOT to do every problem correctly and in order. We also talked about identifying which problems might be solvable, but would require such a large investment of time as to not actually be worth completing.

Sam’s 4-6th Math Class

In addition to the AMC contest and the usual work in Singapore math we also started to look at some basic problems in combinatorics, including a lengthy discussion about strategies to stay organized while counting and enumerating possibilities. Specifically, the students worked on these two problems:
  • You have 3 pairs of jeans (we called them X,Y and Z), 7 T-shirts, (called one, two, three, four and five) and 5 pairs of socks (A, B, C, D, and E). Make a list of all of the possible outfits you can wear.
  • What are all the possible outcomes when three normal six-sided dice are rolled, and how likely are each of the possible sums of the three dice.
Algebra and Pre-Algebra

All of the students in these classes are working on finishing up the chapters we’ve been working on with a goal of being done by Thanksgiving break. Some of the students got to the assessments on Thursday or Friday but most will be studying this weekend and working on the assessment on Monday and Tuesday.

Week of November 10

November 10, 2017

Sam’s 4-6th Math Class

On Wednesday we began a new recurring exercise--the timed quiz. This first timed quiz was 3 minutes to complete 60 single-digit multiplication problems. We were practicing quick factual recall; everyone in the class can do these problems, speed, dealing with anxiety and the educational concept of automaticity, were the focus of the discussion post-quiz. On Thursday and Friday the class worked on their Singapore assignments while meeting with Wendy’s class,
Algebra and Pre-Algebra

Because of the aforementioned short week and absences (mine and the students) the pre-algebra group didn’t meet with me this week. They should all be continuing work independently in chapter 3 of the text. The Beginning Algebra group did have a lesson on Wednesday going over the concept of slope--using the “staircase” analogy and as a ratio. The Completing Algebra group also met formally on Wednesday to begin our discussion of exponents and exponential functions, though so far we are only looking at the properties of exponents and vocabulary.

Friday, November 3, 2017

November 3, 2017 -- Coordinate Graphs

November 3, 2017

Sam's 4-6th Math Class

This week we focused on the coordinate plane. Many students were familiar with number lines; introducing the full coordinate plane requires introducing negative numbers (which most students had not worked with formally before) and moving from one-dimensional to two-dimensional thinking. This can be a rather dry conversation, so instead of lecturing on the topic, we talked about the basic ideas and then transitioned right into an activity: making a picture from a set of points--basically an advanced form of connect the dots, but the students had to put the dots in the correct place. After they finished the initial exercise, everyone made a coordinate picture of their own by reversing the process used to make the kitty cat--first make the drawing, locate the important points (places where the line changed direction--vertices), and then right out the list of points as line 1, line 2, etc, so that someone else could recreate their picture. IMG-2990.JPG

Here is one a child made in class if you want to try it at home.

Algebra and Pre-Algebra

We have also been doing quite a bit of graphing on the coordinate plane in the ⅞ math classes. The Completing Algebra group worked on some basic exercises in linear programming as an application and review of graphing systems of inequalities. The Beginning Algebra group is just starting to work with linear equations in two variables and this week talked about graphing lines from an equation by finding points and a little bit about intercepts and horizontal and vertical lines. They also had a brief “pop” quiz, which will be a recurring feature of the class. [One of my professional concerns about timed assessments is that the goal of any timed assessment is to get as many points as possible, not to answer the all questions correctly, our students need practice switching their mindset before being asked to take many timed assessments in high school.] The Pre-algebra group continued their work with linear equations in one-variable.