Students are using divisibility rules to Identify primes and factors of target numbers. You might ask for an example of how to use Factor Trees, Prime Pools, and Factor Towers to find and check all the factors of a given number (60 could make a good example…). We worked on building useful Multiple Tables and found the perfect-square diagonal. We played 3-bop and Prime Save, and today we threw composite-numbered water polo players out of the pool. One of the best challenge problems in the history of math was offered, and so far the farthest anyone has gotten is to a 6-digit number that is divisible by 6; perhaps some students will determine whether it is possible to go farther. (Question: Using the 10 digits 0-9, can you choose one digit to make a one-digit number divisible by 1? Then can you add a second digit to the right of the first so that it makes a 2-digit number that is divisible by 2? Can you then place a third digit to the right of those two, so that you now have a 3-digit number that is divisible by 3? How far can you go without using the same digit twice? *If you use all 10, you get to reset the “shelf” with the digits 0-9 again and can continue looking for an 11-digit number that is divisible by 11, etc.). Try it!?!
We just finished our unit using positive and negative integers with the four operations. We also looked at the distributive property with negative numbers. Currently, we are beginning our unit on solving equations using properties of equality. We will be solving single and multi-step equations with positive and negative integers. In the final section of the unit, we will be solving problems with distance (d), rate or velocity (v), and time (t). Students use the equivalent formulas d = vt and v = d/t to solve problems involving constant or average speed. They learn an easy way to remember the formula v = d/t from the unit for speed that they already know, “miles per hour.”
Students are approaching this week’s unit test on Linear Equations – arguably the most important concept in Algebra. In order to thoroughly understand how an equation in the form y = mx + b operates, we have explored slope through tricycle racing (imagined), by drawing a “slope triangle”, and by comparing equations and graphs. We have generated equations for lines when given a graph, a table, a slope, and a point, or simply two points. Growth rate has been observed in patterns of figures made of squares and by comparing a graph of tree behavior over time or a steadily dwindling bank account. Solving equations for one variable (so that one variable is isolated on one side of the equation and everything else is accurately assembled on the other) has proved challenging for many, so directed practice opportunities will be forthcoming. You might ask your favorite 8th grade mathematician(s) what the line is that contains the points (12,4) and (9, -2)…