Wednesday, December 17, 2014

Common Core Explained Simply

Why is Math Different Now from raj shah on Vimeo. Here is another example. Students and parents are complaining why they are not using the standard algorithm for adding, subtracting, multiplying and dividing sometimes... here's why for multiplying and dividing:

Wednesday, December 3, 2014

Why is (-3) squared different than -3 squared?

A great kick off question that sparked a rich conversation. I believe I selected it because students had trouble explaining it on a CPM homework assignment. Another explanation that also explains why a negative multiplied by a positive is negative. For example, -3(6) is equal to 0-3(6) because you can add zero to anything and not change it's value (Identity Property of Addition). Which results in an order of operation problem. 0-3(6). Multiply 3(6) first to get 18. 0 minus 18 is -18.

This problem below demonstrates a students curiosity at the beginning of class and reflecting in the last 5 minutes. (

MARS Task Re-Engagement - Box Plots

While some students were on the East Coast for our sojourn trip, the 8th graders found the 5 important numbers for a box plot using the data of the US Men's soccer team. They found the minimum and maximum (which connects the whisker), median, upper and lower quartiles (half of each half of the data).

I gave feedback such as how could they spread out their data so the box plot wasn't so close together and we also discussed finding the range of the data. The range of the data is the length of the whisker, which is the maximum subtracted by the minimum.

The format was different because the box plot was plotted on a gridded number line, where optimally each square's interval was worth 0.1 or one tenth. 

Another point of confusion was whether to include the median or not when finding the quartiles. When there is an odd number of numbers you do not include the median. If it's even, you would include the median.

Friday, November 7, 2014

Common Core 8: Using TI 83+ Graphing Calculator Technology

The students worked on a problem from the textbook called "The Big C's". They discovered that the rule was y=6x+3 where x is the figure number and y is the number of tiles in that figure.

They discovered this after making a table of values. We used graphing calculators to graph the table of values and then graph the rule. I'm writing the steps up for my own reference and for students to access later.

First off, press STAT, then press Edit...

Here you will see a screen with 3 columns labeled L1, L2, and L3.

L1 represents your x values, and L2 represents your y values. Enter in a list of points, in this case it was (1,9) (2, 15) (3, 21)

When you press GRAPH in the top right, you'll get 3 points.

For some students, no points showed up. I troubleshooted this problem and found out that you need to press "2nd" "STAT PLOT" (where the Y= button is) and make sure that your Plot 1 is on so that the L1 and L2 values show up.

They seem to form a straight line if they were connected. Since there is no such thing as a Figure 1.5, this is called a discrete graph. The points are separate and are not meant to be connected.

We then pressed the Y= button in the top right and entered in the rule, 6x+3. When you graph that, it connects those previously unconnected points, forming a continuous graph.

I will add a picture of student work to give some context to the problem.

Monday, October 27, 2014

Chapter Test Corrections Policy

If you got under a 3, or a B, on a chapter test I do allow you to make test corrections. To get between a 1/2 point to 1 full point above your current grade, you must do the following:

  1. Show all your work on binder paper and the test if there's a graph on it.
  2. Explain what you did incorrectly.
  3. It must be done with me in homework center (Monday school library, 3:15 to 4:15) or by appointment. You may do the test corrections on your own but we must setup a time outside of class to make sure you did them correctly and that you understand it better.

Friday, October 17, 2014

GCF, LCM: Confusion debunked

A GCF is the greatest common factor of two numbers. It's also sometimes called the GCD, or greatest common divisor. It's the largest number that two numbers can both be divided evenly by ("goes in to"). This number is useful when you are trying to simplify fractions because you would divide by a Giant One. For example, 36/48. The GCF of 36 and 48 is 12. Divide it by 12/12 and you get the simplified equivalent fraction of 3/4.

The LCM is the least common multiple. It's frequent use is to find the LCD or least common denominator of two unlike fractions. For example, if you wanted to add 1/12 to 1/15, you'd have to find the LCM of the denominators, 12 and 15. That's 60 so 1/12(5/5) and 1/15(4/4) gets you 5/60 + 4/60 which equals 9/60 or 3/20.

Here is a method a student taught me to find the LCM of larger numbers. This student clearly understood it:

Study Team Norms for Cooperative Learning

These are challenging for students to follow and for teachers to constantly encourage and enforce. It is so worth it for the culture and exchange of ideas though. I did not create these, I got it from the free professional development CPM offers every summer.

Means of Central Tendency Poems

I do not take credit for coming up with these. I found this from a math teacher from Thomas r pollicita middle school in Daly City when I subbed there a few times years ago. I made it into a poster.

Tuesday, October 14, 2014

Common Core 8 Chapter 2 Closure Activity: Hot Potato

Hot potato is a great activity to force participation amongst a group of 4 students. I give credit to CPM for suggesting it.

Each student gets their own colored pencil and must take turns rotating 1 paper to achieve a multistep task. After each step they rotate the paper. You hold the group accountable for a group grade and you see how they were all participating when they write each of their names in their colored pencil.

The goal here was for students to take a complicated equation and solve it showing all steps using algebra tiles, drawing them, writing the equation, and explaining their steps in words.

I allowed students to choose from 3 equations, all that had an expression in parentheses preceded by a subtraction sign so that they had to use the negative region of the equation mat. With tiles you are "legally" allowed to move tiles from negative to positive region or "flipping the tiles." This makes a connection that you are taking the opposite of each term of tiles in the negative region.

In the example below 3 + 2x - (x-1) becomes 3 + 2x - x + 1.

We also previewed checking their solution by substituting the solution back in to the equation for the variable. I merely asked "how do you know you are right?"

It re-enforces the rules of equality where you can remove or add balanced sets of variables or constants to both sides of an equals sign.

Friday, October 3, 2014

Jo Boaler Math Talk @ Presidio Middle School SF 10/2/14

Jo Boaler spoke to an audience of parents about the shift to Common Core and about fixed versus growth mindsets. She is a Stanford professor and founded the website which has a wealth of information and resources for teachers, parents, and students. I have taken her online MOOC and students can take her course for free via the web site. Coincidentally, I have also already read her great book, What's Math Got to Do with It?

She spoke at length of mistakes creating brain synapses and the brain's plasticity which lends itself to an amazing ability to learn.

Fortune 500 companies don't value computation skills anymore, problem solving and teamwork lead the list. Interpersonal skills (modeling and teaching etiquette, tact, and behavior anyone?) and of course oral communication is up there.

Research to back Common Core principles.

Mothers: take this advice. Even if you are terrible at math, HIDE it. Encourage your child.

Do's and don'ts for how parents can help their kids at home.

OK, if you can't get them off their smartphone, at least get them these apps.

Featured on BBC Radio 4 along with Sal Khan, though she doesn't recommend Khan ever to be used in classroom, which I agree with. Class time is VALUABLE time to be used for collaboration, synthesis, low floor high cieling problems. Link to her interview.

And finally, SF board of supervisors voted to detrack middle school classes. Acceleration point is in students' junior year of high school where they can compress 2 classes or they can continue their path and take AP Stats in their senior year.

At my school I am teaching one section of 32 students Math 7 and 8 curriculum this year and finishing Math 8 and CC Algebra next year. I am following CPM's 3 years in 2 compression guide.

I had a great time hearing her speak. I honestly believe the CPM curriculum backs a lot of the core values she talks about but there is no perfect curriculum. She mentioned that the best teachers use a variety of resources to introduce multidimensional math to students.

Thursday, September 25, 2014

Back to School Night: a success!

I had an awesome time meeting parents and recognized some parents whose siblings I have taught. I'm attaching the PowerPoint I presented in case you missed it or wanted to review what I said.

BTSN PowerPoint 2014

Thursday, September 18, 2014

Back to School Night is this coming Tuesday: September 23rd, 2014

I can't wait to meet you parents! I am excited about this school year and the partnership in responsibility we both share to make the most opportunities to learn this school year.

In their homework they will be practicing checkpoint materials that I may not have taught them directly. Course 3 Checkpoint materials. And Course 2 checkpoint materials.

If you want material to review with your children, I have provided a link to the parent guide for both textbooks we will be using. Math 8 students will be using Core Connections Course 3, there's a 97 page parent guide. Math 7 accelerated will be using parts of it.

Math 7 will be studying Core Connections Course 2 and the parent guide can be found here, at 134 pages.

Their website has smaller versions that go by chapter.

I look forward to seeing all of you so you can see some of your kids work and know the structures of my classroom.

Tuesday, September 16, 2014

Math 7 Students: Theoretical versus Experimental Probability?

Math 7 and accelerated students were given clues about how a spinner was colored in based on percentages and fractions. They came up with the theoretical probability. Then we gathered data from 5 of the groups of students who spun their spinner 10 times using a pencil and a bent paperclip. Here are the results.

What does this tell you? What is the difference between experimental and theoretical probability? What would change if we got data from all 8 groups instead of just 5 groups?

Math 8 Topic and later Math 7: Proportional Relationships

Proportional relationships can be analyzed by creating a t-chart or more commonly known as a table. These data points can then be graphed on an (x,y) coordinate plane. Here are some situations we looked at. Can you come up with an example? How about a non-example?
If your child takes Math 8, ask them to see these notes. We took them yesterday (Monday September 15th) during an interactive lecture.

Here is a link to the Parent Guide for Chapter 1 for extra practice: CC 3 Chapter 1 Parent Guide

California drought

What information can you infer from this graph? Feel free to reply. Courtesy of SF Unified Math twitter feed

Quadrants of the coordinate plane

If you look out at the horizon you'll see a horizontal line. 

I always wondered why the quadrants were numbered in counter clockwise direction. 

I found my answer on twitter. Where does the sun rise? In the east  

I have not found out why they are numbered as Roman numerals yet. Reply and inform me. 

We went over graphing coordinates in math 8 and math 7 accelerated. We had to clear up some misconceptions and I fe we did. 

Via Carrie Wong, ask your self what do you notice about the coordinates in the first quadrant and so on?

Thursday, September 4, 2014

Homework Help

Homework help is offered at In addition I also open my room every Monday or the first day of the week from 3 to 4 to all math students who would like personalized assistance. Come join us in H-1!

Class Expectations

This was also sent home. This details the supplies I'd like students to have, how assignments are graded, and more.

Math 8

Math 7

Math 7 Accelerated

Letter Home to Parents

The first assignment of the school year was for parents or guardians sitting down with their child and reading this over and to return the bottom portion.

Letter Home

Tuesday, September 2, 2014

Math 7 Accelerated Topics and Content

To be completely transparent, the following PDF file links to all the topics the students will learn this year. When it says CC2 that's Core Connections Course 2 which is 7th grade curriculum. Therefore, CC3 is Core Connections Course 3 which is 8th grade curriculum. I've also linked what their 8th grade year would look like with finishing up 8th grade curriculum and completing the full Common Core Algebra course.

7th Grade Accelerated Course Outline

8th Grade Accelerated Course Outline

Edmodo Group Codes

If you are in my Math 8 class, the group code is "gtxwn7".

Math 7 is "hgwfe3" and Math 7 Accelerated is "k928t7".


Edmodo is a great place to ask me questions, ask each other questions, and answer questions that you know the answer to. I will definitely factor in your helpfulness and activity on Edmodo into your participation grade.