PS/IS 686 | Brooklyn, NY

Grade 6 Math Week of 12/11/17

Algebra: Exchanges and Combinations

Late last week we began our first algebra unit as 6th graders!

We are looking at strategies and tools to evaluate algebraic situations. We’ve looked at two strategies so far.

Fair Exchange


Fair Exchange is a Substitution Method where a number of items are bartered or exchanged for objects of an equivalent value.

In this first strategy, students use their basic understanding of bartering and exchanging items to solve equation-like problems presented in picture form. Within the context of bartering, students are introduced to the concept of substitution, by the method of fair exchange. This method will be used throughout the unit to develop more sophisticated strategies for solving equation-like problems.

Combination Charts


This chart represents the length of cabinets in centimeters comparing combinations of long and short cabinets to determine the total length of the cabinets.

Combination charts are used as a means for investigating situations where there are two unknowns. Since the lengths of the cabinets are either short or long, it needs to be determined which combination of short and long cabinets will fit into the space.

We also began to look closely how fair exchange can relate to the use of the combination chart as a tool for evaluating a situation where values of one quantity can be exchanged for another quantity of another object for the same total.


It is importnat to note that while our work at the beginning of this unit may feel like it is not challenging for some, a solid clear understanding of exchange and determining equivalence in combinations is essential to moving forward successfully in algebra in 6th grade and beyond.