Friday, June 28, 2013

National Debt, Cell Size and Scientific Notation

The week before spring break I wanted to give the students a chance to explore scientific notation.  

I began by using real life data based on the national debt of a few countries/states: USA, California (our home state), CanadaGreece(it has been in the news and it was during the crisis in Cyprus).  I wanted to use the debts because they are very large numbers and they spark conversations among the students about debt that allow me to give them the chance to explore, research and share with each other.

I wrote each debt up on the board and then I wrote the same number in scientific notation right next to it.  I informed the students that these two numbers are equivalent or the same.  I then asked the groups to come up with the rules I followed to change the large number into scientific notation.  After some time, we came together as a class and listed the things they noticed and formulated guidelines or rules.  

HOMEWORK: use the following link: World Debt Clocks to pick four countries and write their national debt and then convert the numbers into scientific notation.  

For the warm up I had each student pick one of their countries and give that number to the group to re-write in scientific notation.  They would do four to six problems depending on the size of the group.  I took roll and monitored what the students were doing as they worked to guide the discussion.  I posted the guidelines/rules to help the students if they got stuck on the process.  We shared, discussed, and clarified the guidelines.
The discussion revealed the need to do an exploration on the powers of 10.  The students wanted to know why the base of the exponent is 10.  So we took out calculators and started multiplying 5 10’s and 2 10’s and 7 10’s.  After each problem, we looked at the resulting number and wrote out the expanded form of the multiplication and set it equal to the exponential form of the same number.  The light bulb went on and the groups wrote explanations as to why scientific notation uses 10 as it’s base.  The rest of the period students worked on problems from the textbook.  Those that do not have access to a computer at home, completed the homework from the night before on one of the classroom computers.

HOMEWORK: use the following link: World Debt Clocks to pick four different countries and write their national debt and then convert the numbers into scientific notation.

For the warm up I posted a couple of large numbers and asked the students to re-write in scientific notation.  I then introduced really small numbers.  I used the following link: Cells Alive - What is the Size? which is an interactive tour from the head of a pin down to a rhinovirus.  It has conversions which allowed us to write the size of each cell as a decimal.  I then wrote the scientific notation for each number next to it and we started the process of creating guidelines or rules for re-writing numbers less than one in scientific notation.  The rest of the day the students worked on scientific notation problems from the math book knowing that they would have a formative assessment on scientific notation Friday before spring break.

Formative Assessment - What I decided to do for the assessment was give the students 8 multiple choice questions converting a number in standard notation to the re-written scientific notation.  I circled answers on the test and the students had to first decide if my answer was correct or incorrect.  Then if it was incorrect they had to write a detailed explanation about what I did wrong.  They were allowed to use the guidelines we wrote together to help them decide on correctness and write their explanations.

Substitute Plans

There are two things  I dislike about teaching: Not being able to use the restroom whenever I want (a future blog post) and doing substitute plans.  Two Fridays ago my son woke up with pink eye and I had to do what we teachers call "emergency" sub plans.  Of course my desk was a mess and my seating charts were not up to date, but I wanted to provide meaningful activities for my students rather than a list of math problems from the book.  I am going to share how my brain works me through the process of creation.

Keep in mind:
  • my district does not allow substitutes to have access to our computers or technology so sending a link and having the sub print or post it on the projector is not an option.
  • The eighth graders are in the process of registering for their high school classes and have had some presentations on college and careers.
  • We have state testing coming up soon so I would like to review some topics we explored at the beginning of the year.
So Based on some interactions I had had with my eighth grade students about careers and college, I decided to seize the opportunity to search the web for some graphs and articles about earnings of college graduates and earnings of non-college graduates.

Here is the document I created at 5:30 am for my substitute to use with my students: Education and Earnings Activities Worksheet

I wanted to give the students a chance to "interpret" graphs and extrapolate information.  I also wanted to create a buzz of group discussions.  Ultimately I wanted the students to consider how some sort of schooling after high school effects the earning potential of a person.

I continued to collect articles and graphs so that we could keep the discussion going and relate it to the standards we are studying.

Here is a document of the graphs and information I have collected thus far: College Earnings Links.  Now, if you look at the resources one could say that the sources have a certain bias and I did discuss that with the students and we are in the process of seeking counter articles and graphs which I will share soon.

It is interesting what information students will cling to.  This past week we read the Los Angeles Times Article about earnings and education.  I used the activity as a "close read" which all of our departments are now integrating into our content areas in the spirit of Common Core.  I had picked the article because it had percentages which is what we are currently exploring in pre-algebra.  However, the students were fascinated with the earnings of different ethnic groups, the difference between female and male earnings, and the accuracy of the article.  Before we explored any mathematics connections to the article I had the students read silently and jot down any questions or comments that arose as they read and to highlight or underline information they thought might be important.  As a whole class  we collectively discussed and underlined the parts of the article that the students had chosen as important, interesting, or caused questions.  

The best part of creating the substitute plans connected to career choice and college earnings,  is the extended explorations it has provided for my students and me.  

There is a plethora of math that can be explored in the resources I have shared.  Again I want to reiterate that we will be considering other perspectives and articles, especially looking at the cost of college and if it is worth the extra earnings.

Please share any other ideas you have on this topic.

Using to Teach Percent Discounts

This week in Mrs. Beck's Math Class our Common Core connection will explore Percent Discounts.  Again I am using one of Dan Meyer's 3 - Act problems:
Amazon Percent Discounts - Courtesy of Dan Meyer's 3-Act Math

Middle school students love to shop.  Many of my students spend some time during their weekends at the mall that is in our town.  Percent discounts and mark-ups provide a great opportunity to show students the connections between pre-algebra and their lives.

Here is the plan for next week's Common Core math activites:

Monday - Close Read, Clarification of Information, Translation into "math expressions" and Possible Questions to Explore

  1. The students will use their handouts to underline important information, circle things they are unsure about, and finally to translate words into equations/expressions. 
  2. They will do this as individuals to begin.  Once it seems all of the students have had a chance to consider the information, then they will discuss their "note-taking" with their partners before we have a whole class sharing session.  The final partner task is to write at least 2 questions that can be answered using the mathematics that we are studying currently.  
  3. As a class we will share and discuss the important information and translations and questions to come up with the math tasks/questions we will explore during the rest of the week for warm-ups and homework. (This is a bit uncomfortable for some since it is open-ended.  We are letting the students take part in the questioning and planning.  
NOTE: Keep in mind that we as teachers sometimes have a difficult time releasing responsibility to the students.  When I ask for "their" questions, I always have "my questions" on hand in case I need to "guide" the students.  What I most often find is that they come up with the questions I am thinking of and surprise me with ones I was not even thinking of.

Look up three items you would be interested in buying on Amazon or another website (school appropriate).  Make sure you pick items that are on sale.  Write down the original price and the sale price of the three items and bring them to school on Tuesday.

Warm-Up: Make a group chart of the items each member looked up, name of each item, their original price and their sale price.

  1. Since the students looked up original price and sale price, I will white out the percent discount on the first amazon picture and have the students find the percent of the discount for practice.  We will share out and discuss so that they can use the warm up notes for their homework.

Use the link below to pick one of the pictures (or find your own) 
Mrs. Beck's Amazon Shopping (you'll have to white out the parts you want to hide) 

Classwork: Work on Chapter 7 problems tied to the standards we are studying.

Pick three of the items from the chart you made for your warm up and calculate the percent of the discount.


  1. Have the students share their "calculations" and compare answers, make sure everyone understands and can show their thinking.  
  2. I will post an amazon picture from my link above and white out the sale price so that the students can use the information to calculate it.  (Work with groups, show work and be able to explain/justify their thinking.)
  3. I will post another picture that has white out on theoriginal price so that the students can calculate that. (Work with groups, show work and be able to explain/justify their thinking.)
Classwork: Work on Chapter 7 problems tied to the standards we are studying.

Use the two remaining pictures from the link (I will post on my classroom website) to find the missing values (one will beoriginal price and one will be sale price)

  1. Share your solutions, your justification (work) and write an argument for one of your solutions describing mathematically how you know your solution is correct.
  2. Share and discuss with group and class your "arguments"
Classwork: Work on Chapter 7 problems tied to the standards we are studying.

Study for the chapter 7 formative assessment.

How Much Sugar in Soda? Using Ratios and Proportions in a Meaningful Context

This week in Pre-Algebra we will be exploring ratios and proportions using the real life context of the sugar content in the students favorite drinks.  I acquired an article from Mr. McLean to use as a "Close" read, something all departments at my school are integrating due to the common core standard adoption.  Here is my plan for the week:

1. How Much Sugar is in a Can of Soda?  The students will read this passage, highlight and/or underline things they think are important and place question marks next to anything that seems confusing.  We will discuss the information, clarify any misconceptions and answer any questions.

2.  I will review our definitions for ratios that we created from our Nana's Chocolate Milk activity and ask the students to write down 3 - 5 ratios using the information from the second paragraph (working in pairs).  We will share out the different ratios and make sure each student has them listed on their sheets.

Homework - look up the sugar content for three of your favorite drinks, look up the recommended daily calorie intake for teenage boys and girls, bring a baggie with 11 teaspoons of some substance (sugar, flour or rice or anything appropriate) to school.

Homework - Use the ratio 8 teaspoons of sugar to 33 grams of sugar to set up proportions and find the number of teaspoons in 23 grams of sugar, 31 grams of sugar, 44 grams of sugar, and 65 grams of sugar.