Now, what about the use of the graphing calculator? If students are using it for simple computations, it might help a student who is weak in the basics to continue processing the algebra, but otherwise this is not an appropriate use of the graphing calculator for students at that level. However, if the graphing calculator can multiply binomials, or if Nancy allows students to go to the web and access one of the sites that do that, then students who are using the technology to check their actions, or to generate numerous binomial products to verify patterns, or to find new patterns, are engaging the full power of the technology to promote higher thinking. (Use Google and search for Algebra Tile calculator. Unfortunately, most calculators that multiply binomials also provide rules, so the teacher needs to find one having the least guidance or to be prepared to make the best use of it. As of October 7, 2016, the following sites were available, https://www.mathpapa. com/free-algebra-calculator.html; http://mathbits.com/MathBits/AlgebraTiles/AlgebraTiles/ AlgebraTiles.html.)
Alternatively, the calculator or a website with a calculator for multiplying binomials could be used as the manipulative for helping students initially see the process to derive a rule. To do so, Nancy could give students a worksheet with problems and ask them to: 1 2 3 4 5 6 7 8 9 10
- 1. use the calculator to complete the worksheet on multiplying binomials;
- 2. look for a pattern to guess the calculator’s rule;
- 3. create three problems to verify your pattern or rule;
- 4. compute the answers to your problems using your rule;
- 5. have a partner check the answers to your problems;
- 6. use the calculator to check your rule;
- 7. if your rule fails, discuss with your partner and go back to step 2;
- 8. share and justify your rule;
- 9. if the website already gives a rule, then justify why that works and how it connects to yours;
- 10. think of real-life situations to model some of your problems and, in your journal, explain how
to solve them.
In addition to the informal assessment Nancy gathers as she monitors the groups, she can collect the journal from Step 10 for information on individual students’ conceptual understanding of the lesson to decide who needs help and how to assist.