Tracking Stocks and Distance on the Coordinate Plane

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Objective

SWBAT: • Find absolute value of rational numbers • Compare absolute values • Plot points on the coordinate plane • Calculate length of horizontal and vertical lines on the coordinate plane

Big Idea

Which stock price had the largest change? How do you know? What is the distance between (a, 5) and (a, -3)? Students continue tracking their investments and work on strategies for calculating length of horizontal and vertical lines.

Do Now

10 minutes

See my Do Now in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day.  Today I want students to review finding and comparing absolute value of rational numbers.  A common mistake is that students ignore the absolute value signs and put the numbers in order.  If I see this I ask students what it means to find the absolute value of a number.  I want students to be able to explain that absolute value is the distance between a number and zero.

I ask for a volunteers to share out their thinking and answer for each question.  I am interested to hear how students compared the absolute value of the fractions in part b.  Some students may have created equivalent fractions with common denominators, while other students may have converted the fractions to decimals to compare them.  Other students may have recognized that ½ is less than 2/3 and 3/5 and then used a strategy to compare 2/3 and 3/5.  

Tracking Investments Practice

7 minutes

Note:

  • I give each student a calculator to calculate change in stock price.  I want students to focus their energy in analyzing the changes in stock prices.  Furthermore, adding and subtracting rational numbers is a 7th grade standard.

I present my investment information and explain that students will be going through the same process with their investments today.  We calculate the change in stock price by subtracting the Day 3 Closing Price by the Day 2 Closing Price.  We check our calculations by looking at the change.  It makes sense that Amazon’s change in stock price was negative, since the closing stock price decreased from Day 2 to Day 3.  On the other hand, it makes sense that Toyota’s change in stock price is positive, since the closing stock price increased from Day 2 to Day 3.

Next we find the absolute value of each change in stock price.  Then I ask students to identify which stock price had the largest stock price and smallest.  Students participate in a Think Write Pair ShareI call on a couple students to share their ideas and ask other students to share if they agree or disagree and why.  Students are engaging in MP3: Construct viable arguments and critique the reasoning of others.

We review the rubric on page 9 of the “Tracking your Investments” packet.  I have volunteers read the descriptors for each number, and then I ask students to rate their own work on this practice page.

Tracking Your Investments

13 minutes

Notes:

  • Students began this project with the lesson Absolute Value and Stocks.
  • Students should have Part 1 and Part 2a completed.
  • I create a spreadsheet with the closing stock prices of each company.  I post a number of these around the room for students to use.

I have a volunteer read over the to-do list for this part of the lesson.  I explain that if part 2b is not completed during class it will be additional homework.  I call students by rows to find a Closing Price Spreadsheet around the room.  They copy the closing price of the companies they have invested in on their packet. 

Students work independently with their calculators.  Students are engaging with MP2: Reason abstractly and quantitatively.  As I walk around, I monitor student progress.  A common mistake is that students find the change in closing price by subtracting day 2 – day 3.  If students do this, I refer them back the practice page to review.  I also ask them if the closing price increased or decreased from day 2 to day 3.  If the closing price increased, does it make sense that the change in price is negative? 

If students successfully complete part 2b, I remind them to read over the rubric and make revisions.  Once they are finished they can work on the Unit 3 Challenge about percent change.  I allow students to use calculators.  This challenge can carry over the next few lessons.

Distance on the Coordinate Plane

10 minutes

We work on problem 1 together. I ask volunteers to brainstorm the similarities and differences of point A and B.  Students may share which quadrant each point is in and they may notice that the points have the same y coordinate.  We plot the points on the coordinate plane and I ask a volunteer if the line is vertical or horizontal.  If students struggle with this, I share that a horizontal line is like the horizon and I draw a quick example.

I ask students to find the length of line AB.  Students participate in a Think Pair ShareI ask students how they figured out the length.  Some students may count, other students may think of the distance each point is from the y-axis and then add them up.  I point out that the latter strategy is using absolute value.

Students work on problem 2 and 3 in partners.  They complete the work and then compare with their partner.  I walk around and monitor student progress.  After a few minutes, we come together and share answers.  For question 3, I dramatically ask students, “How can we find the length of point C and D if we can’t even plot them on our coordinate plane?!?”  I am looking for students to recognize that they don’t need to be able to plot the points to calculate the length.  Since the points have the same y coordinate it is a horizontal line.  To find the length, we only need to look at the x coordinates.  I draw an example of line CD and I ask students to share their different strategies for finding the length.

Practice

10 minutes

Students work on the practice independently.  Common mistakes include switching the x and y coordinate and making a careless mistake calculating the length.  If I encounter these mistakes, I refer students back to our notes and have them look at our examples.

I Post A Key so that students can check their work once I take a look at it.  If students successfully complete the practice they can move onto the Distance Challenge.

Closure and Ticket to Go

10 minutes

 For Closure I write two coordinates on the board: B (a, 5) and C (a, -3).  I ask:

  • What kind of line is this?  How do you know?
  • If I connect points B and C, how long is line BC?  How do you know?

Students participate in a Think Pair Share.  Students are engaging in MP7: Look for and make use of structure and MP8: Look for and express regularity in repeated reasoning.

I pass out the Ticket to Go for students to complete independently.  At the end of class I pass out the HW Tracking Stocks and Distance.