PS/IS 686 | Brooklyn, NY

Gr6 Math, Week of March 20th

Throughout March and April, we will be diving into linear algebra.  We’ve started by looking at visual patterns, discussing how they grew, and representing them with algebraic equations.

For example, below is a pattern that we looked at:

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One way to look at figure 1 is that it has 3 blue tiles plus 1 red tile, figure 2 has 6 blue tiles and 1 red tile, and so on.  The pattern is that each new figure has 3 more blue tiles but the red tile stays constant.  This is an example of a recursive rule for the pattern.

Another way to look at these figures is to see a blue 1 by 3 array in figure 1, a blue 2 by 3 array in figure 2, a blue 3 by 3 array in figure 3, and so on, with the red tile staying constant.  However, by looking at this pattern in this way, students see that that figure number matches the side length and sees this pattern growing as a general rule.  This then leads to the equation:

(figure number) × 3 +1 red tile = total number of squares.  This is an example of a function rule for the pattern.

We’ve included other growing patterns we explored at the end of this post.

After we learned about growing patterns, we spent some time connecting our previous understanding of arithmetic and inverse operations so that we could then use that knowledge to balance equations. Some students are using this as an opportunity to extend our understanding about other arithmetic such as square roots and exponents.

Our next goal of the algebra unit is to develop our reasoning skills about missing information for more than one variable.  Students will use contextual information to exchange and combine equivalent expressions in order to reason through systems of equations. This will prepare them for next year when they further develop their ability to solve systems of equations through graphing and substitution.

Students are using Khan Academy to strengthen their skills through differentiated practice.  The language we are using and the methods of instruction are aligned to the examples on Khan Academy.  When students log in through their accounts, we are able to chart their progress and determine next instructional steps on an individual basis.

At this point, students are expected to be on Khan Academy between 60-90 minutes a week.  We have noticed that students who devote this amount of time are making significant gains in their automaticity and conceptual understanding of the content.

Examples of growing patterns that 6th grade explored: