That Common Core Subtraction Problem

Its hard to have NOT seen a variation on this problem over the past year.

The basic premise is this: Students are presented a subtraction problem, but instead of performing the traditional stacking/borrowing algorithm, evil public school common core teachers force students to jump through extra hoops. Students add chunks of numbers to the lower value to get to multiples of 5, 10, and then the higher value in an effort to find the difference between the values.

Every time I see this shared on social media its from a politically conservative non-educator using it as a tool to illustrate how big government getting its hands into our locally controlled schools makes things unnecessarily complicated (and ultimately, worse).

Say no to #CommonCore the moron math pic.twitter.com/YWHlJ9Yrg2
— Guardian Of Freedom (@ClownDogGunny) October 6, 2014

Here's the problem with using this ONE standard to characterize and criticize "common core math" - its the same thinking that our students and families use when they say things like, "all I need to be able to do is count my money. I don't need ______."

This question is meant to address a 1st grade standard about operations and algebraic thinking. The point is getting kids to understand multiple ways to manipulate numbers.

CCSS.MATH.CONTENT.1.OA.C.6Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). (source: corestandards.org)

Before you're ready to confirm your contempt for core standards, think back to your own math experience. I've found that most "non-math" people often prefer problems and learning environments in which there is more than one "right" answer. The point of this question is to build mathematical thinkers that can adapt their thinking to look for solutions when their first or second attempt is unsuccessful.

2 Exercises for "Relevant" Proportion Solving in Algebra 1

One of the first things I realized after becoming a math teacher in my very first Algebra 1 summer school course was that students love to cross multiply. You stick a fraction on the board and ask something like, "Okay, what next," and you will most certainly get some kids that are dying to cross multiply.

Kids that only know how to cross multiply love to get exercises like this:

And they're probably even pretty comfortable with this:

But things might start to fall apart sometimes when students have to set up the proportions themselves in a situation not neatly laid out for them in "word problem" format.

Here are two such attempts that I used in my Algebra 1 class this past week. One is about troop reduction in Afghanistan, and the other is about "total percentage of weight loss" and trying to win the reality show The Biggest Loser.

WAYS TO MODIFY THESE PROBLEMS:

1. You could increase the rigor in both of these problems if you did not initially give either of the numbers I hand out (8000 and 51%, respectively) and instead, had your students figure out what number would be relevant to finding a solution that would satisfy the problem. After deciding what information was needed and/or relevant, students could do a web search to find the information for themselves. 
2. Have an extension question exploring these ratios in a different way.
1. The Afghanistan troop numbers could be compared to Iraq or previous deployments this century in Afghanistan.
2. The Biggest Loser problem could ask students to compare Jerry to other seasons to see if he would have won those years. You could have students set up "teams" of Biggest Loser contestants and find the proportions of weight loss necessary to defeat other fantasy teams from previous Biggest Loser seasons.

10 Writing Prompts for Exit Slips

Exit slips are, of course, a great means of quick, formative assessment over your day-to-day lessons in class. Writing is a means to trigger students' brain to memory and learning connections. Let's do 'em together!

1. "Describe something you previously misunderstood about _______ that was clarified in this lesson."
2. "Give two tips for remembering how to _______."
3. "Give a title and two section headings to your work/the notes for today's lesson."
4. "How would you describe today's lesson to my five year old when she asks what the kids learned today?"
5. (After putting up the graph of a function with each axis labeled): "What would this graph tell us about the relationship between the variables?"
6. Have students answer any of the unit essential questions (this is good for PLC pre and post data, too)
7. "How did something we learned about ______ help your understanding of ______ today?"
8. (After putting up a solution to an exercise). Evaluate this student's work. If the student was wrong, make an inference about where he went wrong or what he needs to relearn.
9. Did today's class rock or suck? Explain your choice with two reasons.
10. Make a list of as many content-specific words we used today. Define their meaning in the context of today's lesson.