Creating a perplexing math task with disequilibrium

Last week our district 6-12 math teachers spent the day learning to create math tasks with teacher Zach Herrmann, Evanston Township High School. We experienced three perplexing, high school geometry tasks and observed Herrmann’s delivery before being given time to create our own tasks.

Our sixth grade PLC developed a task based on students discovering that the altitude, not the slanted edge, is used to find the area of  parallelograms, trapezoids, obtuse and equilateral triangles.  

Which figure has the greatest area is actually a trick question. Each polygon has an area of 10 inches sq. The altitude of each figure is 1 inch.

This is a small group task. If the students need help, a representative can ask a question. We want to develop perseverance and resourcefulness so we’ve decided to use the line, “You may use any tools available in the classroom.” We want the students to discover for themselves how the ruler, graph paper, etc. can assist them. We also wanted to create disequilibrium so we positioned each figure so that the base is not necessarily on the bottom.

I really want a polished look so I don’t want to upload a file with hand drawn figures. I’m still learning Sketchpad and I’m having trouble getting the correct size when I paste the figures into Word. As soon as I tackle the problem, I’ll repost.


Experiencing success and creating a sense of hope

If you want to lose weight monitor your calorie intake and the amount of daily excerise. If you want to achieve monitor your learning and the amount of effort you exert. It’s early in the year and we may still be in the honeymoon phase, but student goal setting and progress monitoring are working.

The students just finished their second formative assessment on decimals and nearly every student is at at a 3 or better. They’re keeping track of their progress by shading in a bar chart and comparing the results to the previous formative. Charting has turned out to be a powerful tool because the kids create a visual representation of their progress. As they say, “A picture is worth a thousand words.” The students literally see they are learning and improving. I may be over extrapolating, but I’ll take a cognitive leap to suggest that the less confident student, over time, will become more confident in math.

The students however are still hooked on grades. They asked, “Is this for a grade?”

All I could say was, “If I had to report a grade today, it would be what you see on this knowledge check.” I said, “We are officially done working on decimals but chances are you’ll get another assessment to see how much you remember.” I do have a few students who haven’t reached the level 3 target, but they can arrange for an out of class assessment. They just have to schedule a date and time and come to the session with evidence that they’ve practiced.

I wonder if there is evidence that SBG provides additional student motivation. It seems that a delay in reporting of a grade gives students a sense of hope and as a result they continue to strive to meet the learning target.

Educating parents and students about standards based grading

My phone and email were quiet one week after Open House. A parent however ran into my principal while attending another grade level’s open house and gave him some feedback which he passed along to me. They were two great suggestions: 1) continue to send emails over the next couple of weeks announcing when updates have been posted to the online grade book, and 2) explain once again why I am doing this.

The end of this post details what I sent home. It’s been only one day, but I’ve received just two emails requesting clarification. The clarification was what I anticipated–taking a score of 2 or 3 out of 4 and intepreting it as a 50% or 75%. I reiterated that it was not a grade, but merely a record of where the student is at.

Parents and students are accustomed to a gradebook that captures the end result. They need time to digest the idea that a grade book can be thought of as a running record of progress. This hit home today when a student said to me, “Rumor has it you are counting a pre-test as a grade.”

I told Emma, “No, I entered it in the grade book only as documentation that this is where you are at as of this date. It is not a grade.” She slowly began to understand this grading practice. This is an adjustment period and I hope everyone will come to appreciate SBG over the course of the quarter.

Another student questioned why I don’t just make each assessment worth 10 points. I understand where he is coming from, but returning to a point value defeats the purpose of SBG and students still end up focusing on the grade.

I’m curious as to how others have handled this question. Again I’m doing SBG using a percentage based grade book.

I haven’t forgotten. Here’s the email I sent to parents:


For those interested in learning a bit more about standards based grading, please read the information below. Again, if you have questions or concerns, please contact me via email or phone.

Why SBG?
1.  SBG measures and reports the learner’s progress in a clear, precise manner. An assessment reported in the traditional grade book would have very limited information such as rational numbers test, 85%. This type of grade book entry does not describe the student’s strengths and areas that need more practice.

Continuing with the rational numbers example, in SBG the concepts are recorded and reported individually. This way everyone knows where the student excels and struggles. The grade book reflects individual levels of mastery such as adding and subtracting fractions, mixed numbers, decimals, and integers, as well as a separate entry for multiplying and dividing these concepts.

2.  Another important feature of SBG is maintaining a running record of the student’s understanding of the major topics in each unit. Parents often ask, “How is my child doing?” Seeing your child’s trend moving from 2/4 to 4/4 indicates your child’s learning is moving closer to the learning target and beyond.

Today and tomorrow, Monday and Tuesday, I am explaining the process to the students and returning to them their “pre-test” on the first learning concept(s). In Home Access today you will see your child’s current level of proficiency. If I see your child on “B” days, I will share the pre-test results tomorrow, Tuesday. As I mentioned at Open House, 3 is the target and 4 is more complex content.

Thank you for the opportunity to teach your child and I look forward to a great year of learning.

Is this important?

When students ask, “Why do we have to learn this?” they are truly asking, “Is this important?”  According to Marzano, teachers and the curriculum should connect to students’ lives, connect to students’ life ambitions, and encourage application of knowledge. Chapter 4 of Marzano’s book, The Highly Engaged Classroom, provides a variety of activities to help students connect the content with their life.

  1.  Use a variety of comparison tasks to connect the curriculum to personal interest. Compare characteristics, processes, sequence of events, cause and effect relationships, fame or notoriety, analogical reasoning tasks.
  2. Connect to students’ life ambitions through personal projects. Students identify their long term goals. In certain phases the students identify the need for certain knowledge, skills, critical thinking, etc. and learn the roles of heroes and role models.
  3. Encourage the application of knowledge with challenging tasks using decision making, problem solving, experimental inquiry and investigation.

Here I thought making up a humanitarian word problem was all that’s needed:

A volunteer organization delivered 32 tons of wheat to a drought stricken African nation. This is enough food to feed about 2,080 people for a month.  One ton feeds how many people in a month? If one ton equals 2000 pounds, how many pounds of food does one person eat in a month? Round your answer to the nearest whole number.

The problem is real world, but it’s not enough.

The standard is 6NS2, dividing multi-digit numbers. I originally created this problem as an example of a level 4 problem. In its current form it certainly does not use decision making, problem solving, experimental inquiry, or investigation.  But with some tweaking it can be a rich task.

I have a couple of ideas to create a decision making task that entails comparing two ways to schedule the delivery of food. But I right now they are in my head and not on paper.

How would you alter the problem?