Learning Unit

LU Title: The Stock Market and Integers

Author(s): Kristine M. Storms

Grade Level: 7

School : Copenhagen Central School

Topic/Subject Area: Mathematics

Address: Copenhagen, NY

Email: kstorms11@hotmail.com

Phone/Fax: (315) 688-4411

Understand that integers consist of zero and natural numbers and their additive inverses

Locate a point, using ordered pairs of integers on the coordinate plane.

Understand the meaning of the absolute value symbol

Locate the quadrant in which an ordered pair of integers is located

Understand that integers are among the rational numbers

Compare and understand interrelationships similarities, and differences among integers and rational numbers

 Know where the axes, quadrants, and origin are, and how to number the axes on a coordinate plane

Consistently and accurately perform operations on integers

 Determine the absolute value of real numbers expanded to include numerical expressions beyond a single value

 Use symbols ( ) when recognizing numerical relationships

Develop techniques for ordering integers and rational numbers

#

Description of Learning Experience

1.)

Launch: Provide each group (4 in a group) with a copy of the same issue of the local newspaper (i.e. Watertown Daily Times). Have them look to find the "Local Stocks" section. Give them 3 minutes.

Provide each individual with a handout of a copy of the "Local Stocks" section. Have students look through and see if they have heard of any of the companies.

Discuss the numbers provided on each company. Have students make connections to what they know regarding the closing price and the change. Give students 3 minutes to discuss in their group before announcing to class.

Ask students if they know what would happen if you bought a share of stock and it went down, and then if it went up.

Have each group choose eight companies that they are interested in. Provide a handout for each student to record the stocks and each stock’s closing price and change. They are to keep track of all eight for a three weeks so that they know which stocks are the "best buys". Suggest to the groups to figure out a way to make this task the easiest for everyone in the group.

2.)

Provide information of integers, opposites, absolute value, and number line.

Ask students to come up with times where they have seen negative numbers before (thermometer, etc.) Have students practice writing integers for verbal expressions, i.e. a loss of $12. Students then make up their own verbal expression and trade with their partner to have written as an integer.

Have a few number lines taped to the floor. Ask students to practice absolute value and opposites in their groups by standing on the value on their group’s number line. Provide problems and circulate while students are working on activity.

3.)

Launch: Corners: At the beginning of the second round of Jeopardy, John’s score was –800 and Barry’s score was –200. Who is winning?

When comparing integers, think of a thermometer. What words would you use in place of "greater than"? What words would you use in place of "less than"?

Have students practice ordering and comparing integers in and out of word problem form.

Redo corners.

4.)

Launch: Partner up. Find the following cities on the provided map. "Do you remember latitude and longitude? Which lines were latitude? Which were longitude?"

Find the coordinates of the cities.

5.)

Draw this coordinate plane with all the parts labeled. (axes labeled and numbered, quadrants named, origin labeled) Tell each group of four to come up with how the class might remember each of these parts. Give students 5 minutes.

After each group shares with the class, have students decide on what they think is the best way for them to remember each of these parts.

Pairs Check: Have students label a coordinate plane by using what they decided were the ways they would remember each.

Have students decide how they will remember the order that the x-coordinate comes before the y-coordinate. Ask where they are supposed to start counting from (origin), and have them plot a few points and write the coordinate pairs of previously plotted points. Ask which quadrant each is in.

End with students naming four of their own points where one would fall in each quadrant. Then have them graph and label each point in a coordinate plane.

6.)

Schedule time in computer lab for practice on Microsoft Excel. They will record their collected data from the newspaper of the companies they are following. They will set up a table of companies with their close and change listed for the two weeks. Students will practice making line graphs of each company's closing prices, changes, and two comparative graphs, one of the closing prices and one of the changes. They will also have a discussion of what the data means and how to report what they see. A handout will be provided. They are to continue to keep their Excel documents up to date.

7.)

Launch: show students a finished Cartesian puzzle that has been colored in.

Have students do Cartesian puzzles in pairs to practice their plotting points. Have students do pairs check after every 5 points.

8.)

Launch: Game.

Break the room into four squares with desks and chairs moved to the outside as far as possible. (Possibly use the cafeteria.) Break the class into groups, giving each group markers for each student and each group a role of tape and construction paper. Have each group create a coordinate plane on the floor with all its parts labeled. Tell them that they have five minutes.

After they look at each group’s coordinate plane, play this game: pair up. Get with another pair. Round 1: In your pair, decide what point you would like the other pair to "plot themselves" at. Continue for five points per pair.

Round 2: Decide with your partner where one of you will plot yourself. Have the other pair say the ordered pair where you are standing.

9.)

Schedule the computer lab again and have students buy shares of four of the eight companies they have been following, using the prices they get off of http://www.nyse.com/. Choose an amount for them to invest, such as $1,000 per group. They will be starting a new Microsoft Excel document for the time they will be "owning shares" of the companies they choose. This is a time to clear up any confusion after the last time they were working on their Excel and Word documents. Students will also be asked to write an explanation of why they chose these stocks and provide mathematical evidence with the tables and graphs from the last three weeks. A handout will be provided for students to guide them through the next four weeks of collecting and recording daily data and reporting weekly data.

10.)

Launch: After this experience, students will be able to answer the following question: Express your gains/losses to this point for each company as an integer. How much have these companies gained/lost per share all together?

Pairs check. Provide each student with a mat and integer counters. Provide students with simple problems. Ask students to model the problems on the mat with the counters. Have students decide what the answer should be, and then discuss with partner how they could show the process with the counters. (You are looking for them to come up with a positive counter zeroing out a negative counter.) Have them practice this, and then to share a simple rule that each pair followed to come up with the answers. Provide a handout to lead them through the activities. (Goal: when the signs of are the same, add and keep the sign. When the signs are different, subtract and keep the sign of the larger number. The students can and will come up with this themselves.)

11.)

Game: Review of coordinate plane and plotting points.

Coordinate Battleship in teams (2 vs. 2). This is done on graph paper making reference to the Milton-Bradley game "Battleship".

12.)

Question to be answered: what happens when there are two signs in front of a number?

How many signs do we WANT? This is the rule: you need to multiply the signs together that are right in front of the same number. Tell students the rule: odd number of negatives will be negative; even number of negatives will be positive. *Does not matter how many positives there are. Practice rewriting and then evaluating

Evaluation of understanding: FAST CHALLENGE. Ask each student a long, drawn out problem of "a positive times a negative times a negative times a positive … ", one at a time. This is fast paced; it should take about 2 minutes to hit everyone in the class.

Continue applying this knowledge to rational numbers.

13.)

Launch: What has been the change up to this point? Taking into account how many shares you purchased of each company, who made you the most money? Who made you the least (or who lost you the most money?) What is your portfolio worth right now?

Multiplying and dividing integers. Multiply the signs and then multiply the numbers. Follow the same rules for division. Golf is a good tool for students to visualize multiplying: use the same above/below par for a series of holes, and find the score compared to par for the number of holes.

Apply these rules to rational numbers. Again, golf can be used to find the average per hole or per tournament compared to par.

4

The Excel Chart is very neat and organized. The data is completely correct. The reports show no grammatical and/or spelling errors. The reports explain precisely what a reader of the chart and report is seeing/reading. The reports also explain clearly decisions they would make in lieu of their data.

3

The Excel Chart is neat and organized. The data is mostly correct. The reports show no grammatical and/or spelling errors. The reports explain briefly what the reader of the chart and report is seeing/reading. The reports also explain decisions they would make in lieu of their data.

2

The Excel Chart is neat or organized. The data has some errors. The reports show few grammatical and/or spelling errors. The reports are unclear what the reader of the chart and report is seeing/reading. The reports somewhat explain decisions they would make in lieu of their data.

1

The Excel Chart is not neat or organized. The data has many errors. The reports show many grammatical and/or spelling errors. The reports do not explain to the reader of the chart and report what he/she is seeing/reading. The reports do not explain decisions they would make in lieu of their data.

0

The Excel Chart is incoherent, irrelevant, or not done. The data is completely wrong or not done. The written reports are incoherent or not done.

Map

Legend

Ease of map use

4

The map is very detailed with coordinates marking at least 5 places of interest with no mistakes.

The legend is very neat and very organized. It includes a clear description of the location of the axes, the origin, and the measurement between each coordinate.

The map is exemplary with students in the sixth grade being able to follow the map with ease.

3

 The map uses coordinates marking 5 places of interest with no mistakes.

The legend is neat and organized. It includes a description of the location of the axes, the origin, and the measurement between each coordinate.

 The map is good with students in the sixth grade being able to follow the map with little difficulty.

2

The map uses coordinates marking fewer than 5 places of interest or there are few mistakes in the mapping with coordinates.

The legend is neat or organized. It includes a description of at least two of the required parts.

The map is needs improvement with students in the sixth grade having some difficulty following the map.

1

The map does not use coordinates to mark 5 places of interest or marks fewer than 5 places of interest with many mistakes.

The legend is not neat or organized. It includes a description of at least one of the required parts or has very little relevant information.

The map is unacceptable in that the sixth grade students had much difficulty following and/or understanding the map.

0

 The map is not done or makes no sense.

The legend is not present or makes no sense.

The map cannot be followed because of missing information or irrelevant information.

3

The response is complete and correct. It demonstrates a thorough understanding of the mathematical concepts and/or procedures embodied in the task; indicates that the student has completed the task correctly, using mathematically sound procedures; and contains clear, complete explanations and/or adequate work when required.

2

The response is partially correct. It demonstrates partial understanding of the mathematical concepts and/or procedures embodied in the task; addresses most aspects of the task, using mathematically sound procedures; may contain an incorrect solution but applies a mathematically appropriate process with valid reasoning and/or explanation; may contain a correct solution but provide faulty or incomplete procedures, reasoning, and/or explanations; may contain a correct solution but lacks work when required; and may reflect some misunderstanding of the underlying mathematical concepts and/or procedures.

1

The response is incomplete and exhibits many flaws but is not completely incorrect. It demonstrates only a limited understanding of the mathematical concepts and/or procedures embodied in the task; may have addressed some elements of the task correctly but reached an inadequate solution and/or provided reasoning that was faulty or incomplete; exhibits multiple flaws related to a misunderstanding of important aspects of the task, misuse of mathematical procedures or faulty mathematical reasoning; reflects a lack of essential understanding of the underlying mathematical concepts.

0

The response is completely incorrect, irrelevant, or incoherent.

Learning Experience #

Number of days spent

Learning Experience #

Number of days spent

1

2

9

1

2

1

10

2

3

3

11

5

4

1

12

1

5

3

13

5

6

1-2

Culminating Performance P1

 4

7

3

Culminating Performance P2

1

8

2