19 October 2014

Algebra on a Chromebook: LucidChart Diagrams

I've heard more than once that laptops or Chromebooks in a 1:1 environment get relegated under the desk during math class because the classroom teacher struggles with finding ways to integrate the technology into what is usually a much more hands-on process with graph paper, pencil, and exercises.

I think the easiest answer is to have kids using the laptops for watching videos, looking up examples on webpages, or drill and practice on websites. The sexy answer is to have kids engaged in problem-based learning, integrating their math work into relevant reports, graphs, images, and presentations, but first you would have to also sell problem-based learning on the teacher.

In between the easy answer and the sexy answer lies LucidChart Diagrams, whose collection of education templates can facilitate note-taking, critical thinking, the problem solving process, organizing and summarizing, sequencing, and concept mapping.

Let me show you briefly how a student could use LucidChart Diagrams to integrate writing and list the steps to solving an equation.

You can find LucidChart Diagrams in the Chrome App Store

After clicking on "Create," this box pop-ups, giving you a selection of templates. There is an extensive "education" collection.
This is the "sequence chart" which you could use for any technical writing task. 

Your next task is inserting an image of a worked out equation for students to write about. Scroll to the bottom of the menu on the left and select the plus icon to add an image. This box pops up in which you can do a Google search or upload your own (student or teacher created)
Here's what mine looks like after resizing the image some and inserting each of my steps. (click to zoom or pop out to new tab)

mind mapping software

Other charts you might use - 
  • Venn Diagrams
  • Cluster/Word Web
  • Compare and Contrast
  • Concept Map - use to connect similarities and differences in characteristics of functions
  • Planning Chart - problem solving or think alouds
  • Vocabulary Chart - visualizing unit vocabulary, grouping similar/related words
  • T-chart - change the headings and use as guided notes/interactive notebook. students import images of examples and type in on the right side.


17 October 2014

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).
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.

11 October 2014

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.