Day 40: HWD Concept Tests

The last time I gave a chapter test was student teaching.

Before my first year of teaching I met with my principal and pitched a modified 10 point version of Dan’s assessments. He was on board with the whole thing. I was excited about this.

Testing has been a work in progress for me with several changes along the way (I now use a 5 point scoring system). Feel free comment below if you have any criticism, questions, or want to share an idea.

Here’s how things go:

Tests are broken into major conceptual ideas* rather than chapters:

I pick 3 to 4 concepts to put on each test, with one to two questions for each concept.The concepts cycle out after appearing roughly three times. (My first test had concepts 1 and 2, my second had 1,2,3 and 4, my sixth test had concepts 6, 7, and 8) Once they are out of the cycle, it is the student’s responsibility to come in and re-test to raise their scores.

*My list of major conceptual ideas for Algebra is located at the bottom of this post


Return + Checklist:

I return the tests within a few days and students record their scores on a concept checklist, which they hang onto. They shade up to their highest score for each concept. After two 4’s on a particular concept they call me over and get a signature; indicating they don’t have to test over that concept anymore.



Each concept is scored between 0 and 4 points. After a student scores two 4s on a specific concept (i.e. multi-step equations) they are not required to test any further on that concept. Here is the Rubric I follow (this came from another blogger… I can’t remember who though!!)

If a student’s score increases, I replace their previous score with their new one. No new gradebook entry. If the score drops I do nothing.


The second time students see a concept, the questions are harder. The difficulty levels-out after this. I consider the questions from the 2nd time on to be at a mastery level.

Other things I do:

  • Each week I put up the percentage of students in each class that have a 4 or 5 broken down by each period (this adds a little competition).
  • I make up a question or two on the spot when students come in and retest. Nothing too fancy.
  • I limit retests to once a day.
  • No tutoring + retesting on the same day.
  • I grade hard.

Things I have changed:

  • From a 10 point scale to 5 point.
  • Shifted from one perfect score to receive a signature up to two.
  • No longer require their checklist on the desk during testing.

What my students from last year thought about concept tests:



Tests (Algebra) 1    2    3    4    5

Tests (Geometry) 1    2    3    4    5

Algebra Concept List

Blank Concept Checklist




Day 32: HWD Visual Patterns

My school has 3 days a year that are used as “attendance incentive days”. Basically, if a student has less than 2 absences and maintains higher then a D in all their classes they are not required to attend school these days. Today was one of those days. It was nice to have time to work with students who were behind and fill in a few conceptual holes in the process.

I have been wanting to write about How We Do Visual Patterns, so here it is. (I cycle through several openers each week; Visual Patterns, Number Talks, Mental Math, Would You Rather, and Estimation)

This process has been evolving since the beginning of the year. I started off with something very similar to Fawn’s first hour found here. And I want to lead you through where things started and where they are right now.

For the first couple weeks, every pattern was about finding the squares/circles/shapes in a particular step;


At this point, students were too focused on numbers. They wrote out tables and looked for patterns within the numbers.


In the example above, most students overlooked the shape and saw a +3, +5, +7 pattern, which is fine, but I wanted to shift their thinking towards writing rules.

So I started asking for an equation. I went through about 2 visual patterns asking: “Find an equation to solve for the number of ________ in any step”.

This was WAY too complicated, so I changed the question:


Things started falling into place at this point., Almost every student can now contribute to our discussions; a simple rewording drastically lowered the entry point for all students.


Now instead of throwing around variables students write it as they see things, which in my opinion is awesome. The picture above gives an idea of how students create a rule:

S1 (Blue):From step 1 to step 2 you take the original pattern and add 4″

S2 (Red): “I did almost the same thing but called the pattern before the one we want to find x”

S3: (Green): “It also works if you take the step, multiply it by 4, and add after”

S4: (Green): “I did the same thing but called the step we want to find x” 

This was all facilitated by the students; no joke.

So, right now here is how we do visual patterns.

  1. The bell rings and I let students know we are opening with a Visual Pattern.
  2. I pull up a stopwatch in front of students and tell ’em how long they have (2-3 minutes).
  3. I remind students that it is OK if they don’t reach a rule, we are more interested in the process of finding one. It is also OK if the rule doesn’t work.
  4. I put something like this up on the board and start the timer.VP.5
  5. By themselves, students create a rule; no talking during this time.
  6. The timer goes off and I pull up our seating chart; I have the option to randomly choose a student. I do this in front of them.
  7. Whoever is called on shares where they are at in the process of writing a rule; it doesn’t have to be anything fancy. Sometimes the share what they see changing, sometimes they have a rule, they used to try and opt out; that didn’t fly.
  8. After 3 people have been randomly chosen I open things up for discussion; sometimes it ends there, other times it goes on for 10+ minutes.

Here’s the deal: I don’t help students along or provide a “correct” rule at the end. Things have gone this way since they very first Visual Pattern. Sure there are always times where I want to step in and some days we don’t get very far into creating a rule.But, I believe that students deserve opportunities to engage in discussions and share their thinking without being critiqued.

So much of what happens in math classrooms is about the teacher; we provide correct answers, solution methods, assignments, and assessments. The focus needs to shift towards the students and their perspectives. Taking 10 minutes out of one period, once a week to provide students with this opportunity has directly impacted what my students get out of the other 240 minutes each week and created an amazing culture of patient problem solving in my classes.


Here are a couple resources for Visual Patterns

OUSD Instructional Toolkit

Day 11: HWD (How We Do) – Homework

In Geometry we played around with formulas and put some visual patterns into the mix as well. However, today we calculated perimeter instead.


In Algebra we wrapped up Crossing The River and talked about the equation 25 = 4A + 1. I spent some class time going through a few examples of one and two step equations introducing some vocab along the way.

After we fished up I gave students some practice problems for the last 20 minutes of class.

I want to use today to write about how homework/classwork goes in my classes.

I have students who come from 6 or 7 different schools so there is a wide range of abilities. I don’t believe that giving ever student a single assignment  of 2 – 50 evens reaches students the best way. So here is how classwork/homework goes.

day12Two different assignments for two different ability levels. Students pick one and get to work. I explain that the /homework part of this only comes into play if they choose not to use their time in class productively. I do not ask students to take the problems they didn’t complete home and work on them there. I am more interested in the quality of student’s work over the quantity.

With two minutes left in class I throw up something along these lines:


Student pick one of the two questions and bring it in complete the next day.