### Sam's 4-6th Math Class

With the 5/6s gone on Thursday and Friday the workload was a little smaller this week. The kids should still try to have their Singapore assignments completed for Monday 10/2. On Tuesday and Wednesday we learned about using the bar model strategy to solve problems with whole numbers, particularly problems involving the idea of consecutive multiples. It is important for the students to develop a way to represent these ideas graphically, as many of them are not developmentally ready to approach these problems abstractly using algebra.

For the problem,

**"The sum of three consecutive even numbers is 36. Find the greatest,"**the students would make a drawing akin to this:
We can then talk about the idea of maintaining equality by removing the same amount from the bars as from the total, such that this problem can be reduced to the three boxes being equal to 30, which then allows the student to figure out that one box is 10, and then carefully re-read the problem to figure out how to answer the question asked.

We will continue to work with this technique for problems with percent, fractions, and ratios in coming weeks.

If you'd like more background on the technique or the rationale take a look at these websites:

### Pre-Algebra and Algebra

The blue and green groups both got some lessons on the need for orthopraxy [our unofficial vocab. word for the week] in the creation of coordinate graphs, which is a fancy way of saying I told them exactly how I want them to make their graphs every time. The key features of a coordinate graph are: clearly labelled origins and axes, consistent and clear numbering of the grid, and in my case I add the requirement that the axes are only labelled with arrowheads in the positive direction, which is a convention I learned to use in physics classes.

The (Blue) Pre-algebra group completed chapter 1 in the text and had their first formal assessment (that's a traditional test in this case). The major topics covered in chapter 1 were variables, the order of operations, exponents, basic absolute value concepts and the coordinate plane.

Maddy uses the Algebra Tiles to investigate inconsistent linear equations. |

The (Green) completing Algebra group is digging into a chapter on systems of linear equations. We've talked about graphing and estimating solutions, using substitution and the elimination by linear combinations method.

The (Red) beginning Algebra group is working on linear equations in one-variable which is partially a review from last year, but now we are adding in the additional complication of working with fractions and decimals. We spent most of Thursday talking about problems that are "weird", where the solution is that the problem is always or never true; things like 2x + 4 = 2x - 3.