Math 8 is NOT a math class.  

I repeat:  Math 8 is NOT a math class.  

For those who don’t like math or think that math class is irrelevant to the rest of your life (and even for those of you who enjoy it), I offer up the idea that the greater purpose of our class is not to learn math.  The greater purpose of our class is actually  to build critical thinking skills, analytical skills, and problem solving skills.  Those are skills that are necessary for every field and, in fact, every facet of life.  

So where does math fit into the equation of this class (see what I did there with the pun)????  Math is just one of the many tools in our problem solving toolbelt.  Other tools include logic, common sense, number sense, process of elimination, finding/using patterns, and many more.  

How do we exercise problem solving skills?  It takes a quality problem to utilize quality problem solving skills!

A truly “good” problem is one that doesn’t entail mere mindless number-crunching.  Writing a good problem involves creativity and thinking outside the box so that the actual process of solving the problem also involves creativity and thinking outside the box.

For example, a “boring” number-crunching problem would be:

50+49x100

This problem assesses the following skills:

• Knowing order of operations

• Multiplying a two digit number by a three digit number

• Adding

A more interesting and much richer problem involving the same skills (and more) would be:

What is the sum of all the whole numbers from 1-99?

The tedious, inefficient, and “boring” way of solving the “sum of 1-99” problem is to add one number at a time starting from 1 until you reach 99.  This method is not only time consuming, but the sheer number of calculations involved greatly increases the chance of making errors along the way.

Can you think of a more efficient way to solve this problem?

Can you find patterns within the range of numbers that would make adding them up easier?

Can you figure out why/how the boring math problem above is actually one method you can use cleverly solve the sum problem?

Can you figure out more than one method to solve the sum problem?

While you can certainly Google the answer to this problem, I challenge you to exercise that brain of yours and figure out ways that you can more easily solve this problem (as compared to mass addition).

The AMS 8th grade math department gets very excited when we find resources for “good” problems.  The Area Mazes that were shared in an earlier Math, Learning, and Love entry are one example of terrific brain-working problems.  In today’s edition, we bring you another great resource to exercise those problem solving muscles.

The American Mathematics Competition, better known as AMC, puts out a 25 question test each year that is full of AMAZING questions.  

Here’s what AMC says about their problems/mission:

The AMC is for anyone who loves problem-solving. Notice, we didn’t say, “it’s for anyone who loves math.” At least, there is no requirement that you love traditional school math. Sure, loving math is great, but standard math classes may have sometimes left you bored, and it isn’t really what the AMC is all about. (“OK, class, tell me what seven times eight is.” Again? Really?)

Try this!

Aaron, Darren, Karen, Maren, and Sharon rode on a small train that has five cars that seat one person each. Maren sat in the last car. Aaron sat directly behind Sharon. Darren sat in one of the cars in front of Aaron. At least one person sat between Karen and Darren. Who sat in the middle car?

That’s an actual problem on the AMC-8 from 2020. If you like puzzles and games, the AMC is for you. 

Many researchers have looked closely at what skills lead to dominating at board games, logic puzzles (like Sudoku), or these types of AMC problems. The science is unambiguous: if you enjoy learning and have a growth mindset, you can definitely become a master problem-solver.

What precisely does it take to shine at these kinds of problems? One key is deliberate practice; that’s just a way of saying: do lots of problems in a focused way.  You’ll use your deliberate practice sessions to master these core skills:

Working backward

Working systematically

Looking for patterns

Visualizing

Iterating on an initial best guess

Reasoning logically

Once you have learned these strategies, you’ll be a pro at mathematical reasoning. You’ll be able to summon all of your mathematical knowledge and creativity to tackle super fun problems!

The AMC website contains the AMC problem sets for every year  from 1985-present.  Each set consists of 25 awesome questions for you to puzzle over.  An extensive answer key is also provided for each problem with multiple ways to solve the problems.  Some problems even include video explanations for the solutions.  It’s an awesome resource!!  

For our math classes, students may opt to substitute AMC problems for their CPM problem sets.  Here’s the procedure:

1) Open up the most recent AMC test available on the the AMC website.  

2) Label your assignment with the year of the problem set.  Do the first 13 problems in your notebook (be sure to label the problems).  Show all steps/work and relevant explanations. 

3) Look at the answer key (the key with the full explanation, not just the multiple choice answer) and do at least 2 corrections/additions in pen.  

4) Show the AMC assignment to your teacher for one homework stamp on your current stamp sheet.

5) The next time you want to do an AMC problem set, do the next 12 problems from the same year.  Once you’ve finished all the problems for one year, proceed to the previous year’s problem set.