Virtual Manipulatives As a Learning Tool in Integer Addition and Subtraction

Student Sample One
Student Sample Two
Student Sample Three

Name: Michelle Marceau
Grade: 7
School: Ogdensburg Free Academy

1. Title/Context Of Learning Experience
   Seventh grade students will be going to the computer labs for two consecutive days in order to explore the use of virtual manipulatives as a learning tool for the concepts of integer addition and integer subtraction. Through the use of two different applets, students will be able to see how the two processes are related, and they will also discover certain patterns and rules that apply as well. If time permits, students will be able to combine and practice the two concepts by playing Tic-Tac-Go on the computers. On the third day, students will be able to practice a number of different problems (addition and subtraction) using the dry erase boards during class.

   Objectives: By the end of this lesson, students will be able to:

   • Add both positive and negative integers
   • Subtract both positive and negative integers
   • Recognize the relationship between adding and subtracting integers
   • Recognize the significance of positive and negative pairs (ex: -1, 1)

   Prior Knowledge: (what students will need to know from previous learning experiences)

   • Definition of an integer
   • Knowledge of positive & negative numbers
   • Concept of place value
   • Process for ordering integers
   • Concept of absolute value

   Outcomes: (what the students should be able to do as a result of the learning experience):

   • Add integers
   • Subtract integers
   • Use the 2 applets in order to solve problems involving integer addition & integer subtraction
   • Complete in-class activity worksheets

   Standards:
   - 7.PS.1 Use a variety of strategies to understand new mathematical content and to develop more efficient methods
   - 7.PS.7 Understand that there is no one right way to solve mathematical problems but that different methods have advantages and disadvantages
   - 7.RP.1 Recognize that mathematical ideas can be supported by a variety of strategies
   - 7.CM.11 Draw conclusions about mathematical ideas through decoding, comprehension, and interpretation of mathematical visuals, symbols, and technical writing
   - 7.N.13 Add and subtract two integers (without the use of a number line)

2. Essential Question
   1. How are integer addition and integer subtraction related?
   2. Does the use of virtual manipulatives enhance student understanding of integer addition and integer subtraction?
3. Assessment Plan
   For the first two days, students will be assessed both informally and formally. Students will be assessed informally by checking for understanding throughout the lessons in the computer labs, by asking them questions about what they have been asked to do, by having them explain what they had to do in order to solve the problems, by having some groups show how they came up with their solutions, by monitoring student progress as they work through the two days in the lab, and by checking for correct answers on the dry erase boards on the review day. The formal assessment will be the completion of the two in-class activity worksheets. The two in-class worksheets (to be completed as a homework assignment if not finished in class) will be graded using a homework rubric.
4. Procedure
   Day 1
   • Students will be given a copy of the in-class activity worksheet (see link below “In-Class Activity Worksheet Day 1”) and a copy of the directions on how to use the integer addition applet (see link below “Directions for Integer Addition Applet”) at the beginning of class. Go through the directions on how to use the integer addition applet, modeling a few problems on the smart board so that everyone has an idea of what is expected (see link below “Integer Addition Applet”). Once confident that students have an understanding of how the applet works, start the in-class worksheet with them.
   • The rest of the class period will be spent working on the in-class activity worksheet. Students can opt to work alone or with a partner, with the understanding that both partners will hand in the worksheet. As they are working, monitor student progress by checking for understanding. If they do not finish the worksheet, it is to be completed for homework.

   Day 2

   • Students will be in the computer labs again today. Today the main focus will be on integer subtraction. Start the lesson by giving them a copy of the in-class activity worksheet (see link below “In-Class Activity Worksheet Day 2”) and the directions on how to use the integer subtraction applet (see link below “Directions for Integer Subtraction Applet”). Slowly go through the directions on how to use the subtraction applet with the students, allowing adequate time for questions (see link below “Integer Subtraction Applet”). Then, model a few problems on the smart board so that everyone has an idea of what is expected. Similarly to yesterday, once confident that the students have an understanding of how the applet works, start the in-class worksheet with them.
   • The rest of the class period will be spent working on the in-class activity worksheet. Students can opt to work alone or with a partner, with the understanding that both partners will hand in the worksheet. As they are working, monitor student progress by checking for understanding. If they do not finish the worksheet, it is to be completed for homework. If time permits, some students may have the opportunity to play the game Tic-Tac-Go (see link below “Tic-Tac-Go Game”). This particular game integrates both concepts.

   Day 3

   • Students will be staying in the classroom today. The class period will be spent using the dry erase boards in order to review that which was taught during the two previous days. Once students are finished with a question, they are to hold it up so that it can be checked for correctness.
     • Integer Addition Applet
     • Integer Subtraction Applet
     • Tic-Tac-Go Game
     • In-Class Activity Worksheet Day 1
     • In-Class Activity Worksheet Day 2
     • Directions for Integer Addition Applet
     • Directions for Integer Subtraction Applet
5. Resources
   Websites Used in Learning Experience:
   • Integer Addition Applet:http://nlvm.usu.edu/en/nav/frames_asid_161_g_1_t_1.htmlInteger Subtraction Applet:
   • http://nlvm.usu.edu/en/nav/frames_asid_162_g_2_t_1.html
   • Tic-Tac-Go Integer Game
   • http://www.fi.uu.nl/toepassingen/03088/toepassing_wisweb.en.html
6. Instructional/Environmental Modifications
   This particular learning experience does not necessarily involve instructional modifications, other than the change of classroom setting (the computer labs).
7. Time Required
   • Planning–5 day Summer Institute Workshop (five 6hr days) & additional time outside of the workshop (3-5 hours)
   • Implementation–3 days (three 42 minute class periods)
   • Assessment-enough time to grade the homework assignments (in-class activity worksheets)
8. Reflection
   I liked the project for the following reasons:
   1. Students were exposed to a variety of strategies to solve integer addition and integer subtraction problems. I heard comments such as “This is fun” and “This makes it a lot easier to do the problems.”
   2. Students enjoyed the change of pace by going to the computer labs for two consecutive days. The change in the classroom setting made a big difference to those students who prefer hands-on learning situations. I also noticed that students who are not typically strong math students, but know a lot about computers, felt more comfortable with these two assignments.
   3. It gave students an opportunity to see that the use of virtual manipulatives can help enhance student learning and comprehension.
   4. I really liked the fact that when my students were asked to come up with four questions on their own, they chose to draw pictures (like the plus and minus chips used in the applets). This reinforced the fact that the use of the virtual manipulatives did enhance student learning and comprehension.

   Things I would reconsider or do differently:

   1. I would like to see more collaboration throughout the learning experience. I gave my students a choice-to work with a partner or to work alone. When I teach this again, I would require them to work with a partner (of my choice).
   2. I would grade both assignments, instead of just the integer addition applet worksheet. My students had trouble understanding how to use the subtraction applet, which resulted in confusion regarding the assignment. In this, I collected and graded the In-Class Activity Worksheet Day 1 only. This may mean that in the future, I will have to devote more than one day in the computer labs for integer subtraction.
   3. I graded the in-class worksheet using the same rubric that I utilize for their homework assignments. In hindsight, I think that I would require the students to complete a mini-project in addition to the two in-class activity worksheets or in place of the two worksheets. I am not sure what a project based on integer addition or subtraction would look like, however, it may be something that I would like to explore in the future.
   4. I would take time to go over the significance of +,- pairs so that less time would have to be spent during day 2 in the computer lab explaining why there is no limit to the number of +,- pairs that can be dragged into the work area (the circle).