Lies your calculators tell you
Lesson 1 of 8
Objective: SWBAT recognize and be more aware of unreasonable answers after making calculator mistakes.
The purpose of today's Launch section is to introduce the idea that errors can occur when using a calculator. The lesson assumes the use of TI graphing calculators, which are probably the most popular.
To start, I project an image of a Cube, on the board and I tell the class, "A student was asked to find the volume of this cube. He used his calculator and determined a volume of 27 cubic inches." I pause for a moment to let the class think and then I ask, "What was the student's mistake?" I give the students a minute or so to talk with an elbow partner.
Following the student's conversations, I ask if something like this has ever happened to anyone in the room. I always get a show of hands. I tell the class that maybe this student didn't know how to find the volume of a cube. Or, as often happens, the student knows exactly what to do, but writes down the answer given by the calculator without assessing its validity. After making the mistake, they don't detect that the answer is unreasonable. I then ask students to turn to their elbow partner and make a list of possible ways students can make mistakes using their calculators.
After a couple of minutes, I call on volunteers to share their responses and I write some of these on the board. Possible responses are:
- hitting the wrong keys
- using wrong procedures
- forgetting negative signs
- Using wrong operations
- Using squaring instead of square root
- Not pressing the "2nd" key when necessary
Teacher's Note: Errors made when working with Scientific Notation are addressed in scientific notation lessons further in the course.
Now I want the students to explore a little on their own with the calculator. I hand out the Exploration Slip for Lies calculators tell you. I will also divide the class into small groups, preferably pairs. Then, I ask each group to take a few minutes to work these problems. I say, "As you work look out for the correct answers and write down an explanation for why each wrong answer was given." I give students about 10 minutes.
As the students work I walk around gauging student understanding by asking questions like:
- What is your estimate for this answer?
- What was that student thinking to get that incorrect answer?
When students are done, I will call on volunteers to share what they wrote for each problem. If this conversation works well, some responses will spark whole class discussions. Based on past experience, here are some expected answers and explanations for the errors made using the calculator:
1. answer: -608
explanation: student used subtraction on calculator instead of the negative sign
2. answer: -608;
explanation: student missed a negative sign
3. answer: 1.7320508...
explanation: student used the x2 instead of the square root key
4. answer: 78.5
explanation: student multiplied 5 by 2, instead of squaring
5. answer: 0.53333...
explanation: student clicked 2x4/3x5 instead of 2/3 x 3/5
6. answer: 1
explanation: student clicked in digits with no grouping symbol.
Once students have discussed the exploration problems and agreed on the possible mistakes made, I distribute the Catch Calculators Lying Application worksheet for the lesson. But before this, I ask that the class stand up and stretch a bit, even take a quick stroll around and back to their seats. My students always enjoy this minute of relaxation. It is definitely good to give the brain a break and move about for a minute.
Once the worksheet is distributed, I tell student pairs to divide the sheet along the dotted line, have each student take a half and then take turns posing questions from the sheet to his/her partner. Students should be allowed to use their calculators to test the answers and discuss a reasonable explanation as to why some were computed incorrectly. It is important that each student make a mental estimate of the answer first, before writing "True" or "False" next to each statement.
As I walk around, I may ask how students determined that the answer was incorrect?, or how could they have done a particular problem mentally, without the calculator? What I want to do is get students to understand that the calculator is simply a tool that they should use wisely and not something they should blindly depend on.
Once all groups have finished, I regroup the class and discuss the solutions, spending some time on how errors could be corrected.
To end the lesson I call on students to share their responses to Catch Calculators Lying. Two of the eight are true (number 4 and 7), the rest are false, so students should give an explanation as to how the student obtained the incorrect answer. Each explanation shouldn't take more than a minute.
Before closing, I ask the class to try and summarize the general goal of the lesson in one sentence. Possible responses are:
- "Calculators don't lie, you tell them what to do"
- "Think to see if the answer is reasonable before you write it down"
- "Use calculators wisely"
- "Don't depend entirely on calculators"