Thursday, October 19, 2017

Intro to Graphing Linear Equations

I basically started by having students create a table with x inputs from -8 to +8. I then gave the class a rule and asked them to find the outputs for each of those inputs, and have one group member write it on the table on the white board and pot the 2 sticky dots with the coordinate (x,y) written on it. I asked students to show their work and to confirm with their group, and once it came time to practice, I circulated targeting students I suspected would not know how to get an output for their input.

Instead of creating axes and doing the same rule from the book each period, I decided to make 2 classes have negative growth, and 2 of the classes have negative y intercepts and 2 with positive ones. I also carefully selected linear equations in y=mx+b form that would have clearly visible x and y intercepts.

I used y=5x-10, y=4x+12, y=-5x+10, and y=-4x-12.

So, once students had finished plotting their values, I asked if they agreed with the outputs written in the table, then copy them onto your table in your notebook. One student forgot a negative sign, and one had a calculation error, but it created a talking point for the class discussion.

I asked students if they noticed any patterns on the table. They would notice that it was increasing or decreasing by 4. I then asked them if they notice anything in the equation related to that. They said it was before the x. I tried to stress that since you are repeatedly adding the 4, repeated addition is multiplication, which is why it multiplies x.

I then directed students attention to the graph. I asked if there were any points that were easy to spot from their seat. Volunteers would identify either the x or y intercept because "the point is on the 'line' or axis." I then added the academic language of y-intercept. They then knew the latter's name since it must be the x-intercept.

Now I have butcher paper that I can reference for all my classes of various features.

Students then practiced on their own filling out a table for inputs -4 to +4 for the rule y=2x +1. Then they have to figure out how to scale their y axis based on the smallest and largest values. Some kids mistakenly scaled their x axis by 2. It's their first time, so there were plenty of issues with evenly spaced intervals, but I took photos of student work using the Google Drive app to display for our closure discussion. We also showed a rule with y=x^2. I asked them if they remember that from the Algebra walk at the beginning of the year and some remembered it's called a parabola. I asked them if it was increasing or decreasing, they said both. It decreases then increases.

All in all, a fun day in graphing linear equations for the first of many times. Here is the sample student work I shared with the classes. (having trouble uploading them, Blogger isn't updated for the new iOS version of the app I have)

Friday, October 13, 2017

Strength in Numbers by @ilana_horn book review

I had heard a lot about the book Strength in Numbers: Collaborative Learning in Secondary Mathematics from other math teachers in the #MTBoS. I also follow the author, Ilana Horn, on twitter, which offered a unique experience reading it where I could ask her clarifying questions, which we answered!

Here's what it looks like:

I borrowed the book from the San Mateo County Math coordinator, Kim Bambao, and it is definitely worth buying. I am definitely going to buy her newest book called Motivated. I am writing this blog post so that I can refer back to it later, and hopefully encourage other teachers to read it. If you use CPM curriculum, this is a must read because it mentions some of the study team strategies and the team roles that CPM encourages.

I am a big fan of group work, because it allows me to listen to my students ideas and misconceptions that I can't hear if I'm doing all the talking. Some teachers, students, and parents do not like group work because kids get off task. Yes, this can be a first instinct, but like any skill, they must practice it to become proficient at it. It takes a lot of work, and patience. When group work has no structures, norms, or reinforcements, it can be a disastrous environment.

An important idea that is suggested in the book, as well as on Youcubed's Week of Inspirational Math, is co-developing study team norms with each class period. A teacher friend of mine, Aristotle, had great success with this last year with students referencing the norms regularly through out the year. I am working on compiling mine into a universal list. I have two lists for each period. The first list, is what students DON'T like people saying or doing during group work:

This naturally leads to what they DO like when working in a group:

In the book, these norms are also suggested to be added myself, which I will be doing:

Another important strategy is using participation quizzes. You basically focus on one norm that students are struggling with and then give them feedback on how they are doing with it. Ilana suggests naming kids by their team roles to reinforce those as well, which I am working on doing. Here are some examples:
A great tip offered in the book is putting a plus or minus before the idea, like this example:

I was able to improve my feedback during my debrief with my 7th graders in this recent example:
Like I mentioned before, it's so important to listen to student conversations carefully. These are some moments when to intervene in a group, and questions to ask yourself when the learning isn't going as smoothly as expected:
I absolutely love this quote from Lampert:
What I also love is that the 5 practices for Orchestrating Mathematical discussions is referenced heavily. I convinced my principal to buy copies for the whole math department as a book study. It's also highly recommended by Illustrative Mathematics, the curriculum published by Open Up Resources that we MAY be piloting next year. I've already used a bunch of their warm-ups, their 8th grade unit on 3D volume, as well as some of their integer lessons for 7th grade. That's for another blog post though, back to the book.

Equitable teaching focuses on four principles: learning is not the same as achievement, achievement gaps often reflect gaps in opportunities to learn, all students can be pushed to learn mathematics more deeply, and students need to see themselves in mathematics.

At the end of the book I love how Ilana has practical suggestions for your school and math department. Some are discussing common language that is precise that we want all teachers to use in hopes that students also use that language. Also, since we all want the same goal, students learning, why not agree on some common structures like homework routines, warm-ups testing routines, and general rules?

There is also a big discussion in the text about status. If students see others as lower status, they are more likely to dismiss their ideas. We as teachers need to be intentional in not valuing speed, but deep thinking. It's also important to positively reinforce students asking each other why they think the way they do about a particular concept. In the book they describe a concept called "assigning competence." It's when we as the teacher publicly praise a students specific idea or thought in relation to the task, valuing a way they approached or explained their thinking.

The book also mentions the status students assign themselves when they say "I'm so bad at math." This is mentioned quite frequently in Jo Boaler's research and can be quite damaging to the student and others. Suggesting to the student that saying "I don't understand this fully... yet" is a much more positive outlook on it and can be seen as encouraging to others and themselves.

I feel my short review of the book does not do it justice, but I hope that by reading this, you are encouraged to pick up this fabulous book. At many points I was nodding my head at things I was already doing, and then paying attention to ideas for solutions to problems I was having.

Wednesday, October 4, 2017

Retaking Skill 4 Proportional Relationships & others

If you want to improve your grade follow these steps:
To retake, you must tell me beforehand so I have it ready. I can sometimes meet at 8:05am and after school by appointment. The best time is Monday after school in the homework center in the Taylor Library.

  1. Correct all mistakes on your 3 attempts on skill 4 assessments.
  2. Do at least 7 practice problems on Khan Academy: https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-linear-equations-functions/cc-8th-graphing-prop-rel/e/comparing-proportional-relationships
  3. Revise and show me your Learning Log on the piece of binder paper. Be sure all aspects of the prompt are answered.
  4. Retake the assessment.
Remember how we proved my diaper buying options were not proportional by finding the unit rate:

If you want to retake Skill 1 diamond problems, prove that you can add like and unlike fractions as well as add and subtract integers. Show me

For Skill 2, points in the coordinate plane and the quadrants, practice at least 7 or more of this Khan Academy activity and show me your corrections https://www.khanacademy.org/math/basic-geo/basic-geo-coord-plane/quadrants/e/graphing_points_2

For Skill 3, percent error, show me your estimation 180 warm-up and lets practice some percent error and correct and analyze all your mistakes. Then take a retake.


7th graders:

For Skill 1, there's practice finding mean and median here: https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-data-statistics/mean-and-median/e/calculating-the-mean The link for median is right below it.

Skill 2 is converting fractions to decimal and percents and back. Fractions to decimals: https://www.khanacademy.org/math/arithmetic/arith-decimals/arith-review-decimals-to-fractions/e/converting_fractions_to_decimals . Writing decimals as fractions: https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-fractions-decimals/cc-7th-fracs-to-decimals/e/converting_decimals_to_fractions_1 Converting percents and fractions: https://www.khanacademy.org/math/pre-algebra/pre-algebra-ratios-rates/pre-algebra-percent-decimal-conversions/e/converting-between-fractions-and-percents

Skill 3's big issues are area of triangles and trapezoids. That can be practiced here: https://www.khanacademy.org/math/basic-geo/basic-geo-area-and-perimeter/area-triangle/e/area_of_triangles_1 and https://www.khanacademy.org/math/basic-geo/basic-geo-area-and-perimeter/area-trap-composite/e/areas_of_trapezoids_rhombi_and_kites