Percent Error

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Objective

SWBAT review circumference and other topics that use pi.

Big Idea

students play games to celebrate pi day (memorization and calculation)

Do Now

10 minutes

Students enter silently according to the Daily Entrance Routine. A timer is set with 3 minutes and Do Now assignments are placed face-down on student desks. The directions on the board read:

Sit down quickly and silently. Take out a pencil. Write your name on the paper, but don’t turn it over! You have 3 minutes. Raise your hand if you finish before the end of 3 minutes.

Students complete as many problems as possible within 3 minutes. If they raise their hand before the timer expires, I walk by and pick up their paper. At the end of 3 minutes, I redistribute the papers for students who finished within the allotted time so that they can help me check the answers. No student gets their own paper back.

I call on different students to call out the answers and I make sure to review mental math tricks that would help student speed up while calculating their answers. For example, quickly visualizing a bar model for #10, 1/3 of 30 is much faster than calculating using the algorithm. These sprints are a great way to keep up with fluency skills.

Class Notes

10 minutes

After reviewing answers and quickly celebrating those who finished with 80% or more correct (I give them achievement stickers) we begin with our class notes. I distribute this worksheet and students must copy the aim and complete their heading.

After copying the aim I have one student read it.  I explain to students that sometimes when estimating numbers, such as the measurement of something really small, you can be off by a certain number of units.

The percent error describes how far off you are as a fraction out of the true value. This will require multiple examples:

  • If I measure a bug to be about 3 cm long, but it actually measures  2 cm, I’m off by a centimeter out of the true value, 2, so I am off by 50%
  • The percent error in using 3.14 as an approximation of pi is the difference over the true value:

    .00159265358979323846..../pi is about 0.05%

    We’re only off by less than 1% when we use the approximation 3.14, which makes it a pretty good estimated value!

 

I break down this complex idea by beginning to explain that error can be calculated by:

Subtract the approximated value from the actual/true value. Ignore any negatives that appear. In other words, you are finding the difference between then exact and the approximate value.

I then use an example to check for understanding. Students must write their answers on their papers as I come by to look around.

Next I explain that the percent error shows the “error” as a percent, and also introduce the formula. We calculate the percent error for the one example I have given.

I have found that teaching complex concepts through one, broken down example is best. In other words, rather than giving students the problem, “I estimated that 260 people would come to my party, but 325 came. What was my ‘percent error’”? right away, I break it down as I explain the concept in chunks by first asking for the error then for the percent error.

Students are then asked to complete the two problems on the back of their class notes silently and independently. Answers must be clicked into Senteo clickers. I will be suing the results to determine which students can work independently in booths and which should be working in groups or with me.

Students are provided with calculators for this lesson and a timer is set for 4 minutes. The assessment for the Senteo clickers is stopped at the end of 4 minutes.

 

Task

20 minutes

Students who answered both problems correctly are offered booth seats. Those students with one problem correctly may join booths if there is still room. There should not be more than 3 students per booth. I limit the number of students at times to reduce the distraction of having too many students in booths.

Any student who answered both problems incorrectly will be working with me or within close proximity. I will be focusing on the strategy of attending to precision of the substitution of numbers and paying close attention to the true value in each problem (MP6). Showing work neatly also impact the correct calculation of these problems.

 

The class work also includes other percent problems students need to review and enter into Senteo clickers.

Once there are 5 minutes left in this section, all students will be asked to return to their seats to continue working silently for the last 5 minutes of this section. I will be asking individual students to put individual problems and the work involved to solve on the board. Students will also be reminded that answers need to be clicked into Senteo clickers.

Closing

10 minutes

After the timer is stopped, those students who were asked to display their work on the board will be asked to explain the work and answers. Other students will be allowed to ask questions (MP3). 

The best part about pushing to have students reviewing work at the board on their own is that it allows me to take one last walk around the room to assess how much work students are completing. 

The homework given includes area and circumference problems to prepare students for pi day.