STANDARDS:
- Evaluate and simplify expressions.
- Simplifying Radicals
PERFORMANCES:
- The students will construct a step by step blueprint for simplifying radicals.
- The students will submit items to be used in constructing a bulletin board of several examples of radicals becoming simplified.
SETTING:
SMARTSKILLS:
The radical symbol is to be recognized visually.
PREFERENCES:
Special Education Accommodations - Students with special needs will require calculators.Use of Resources - The
school will provide classroom time to complete the task, and the students
will provide classroom materials such as pencils, paper, notebooks, and
homework time.Customer for Student Work - The student will present their work as evidence of task completion to teachers and their peers.Assessment of Student Work - The following people will be involved in assessing student work generated to complete the task: The student's teacher and peers.
ACTIVITIES:
Ask the students to define a square root and give an example**Step 1:****.**Ask the students to define cube root and give and example.**Step 2:**: Check the homework on yesterday's lesson.**Step 3**
Example: Simplify the square root of 20. Show students how to break the radical into separate radicals with one radicand containing a square. Example: the square root of 20 becomes the square root of 4 times the square root of 5. Find the square root of the square radicand and remove the radical. The answer will be 2 times the square root of 5. The teacher shows an unsimplified radical which has a 3 for its index, and shows how factors of the radicand which are cubes must be identified. The rest of the problem is reduced to the above procedure. Example: simplify the cube root of 40.
Example: The square root of the fraction 4 over 9. Example: The square root of the fraction 2 over 5.
Example: simplify the cube root of the fraction 1 over 4.
Example: simplify the square root of x to the 5th power. Note: Many examples can be taken from the Text Book: Algebra and Trigonometry structure and method Book 2 published by McDougal Littell. Simplifying radicals is in section 6-2 of this text and there are many fine examples on pages 267 and 268.
It is typical to present the task
for the day and allow students to solve it in their own way. Often, the task
can be solved using a method the students have learned recently.Note:(Estimated time: 10 minutes) Create radicals which need to be simplified with an index of 2.**Step 1:**
Create radicals which need to be simplified with an index of 3.**Step 2:**< Each group adds their 2 radicals to a sheet passed around the room.**Step 3:**
It is unusual for students to
work this long without a class discussion. Also, it is typical for students
to struggle with the task before the teacher intervenes.Note:(Estimated time: 20 minutes) Clarify and troubleshoot problems that groups are having.**Step 1:**
- The 1996 Third International Mathematics and Science Study (TIMSS)
- Stigler, J. & Hiebert, J. (1999) The teaching gap: Best ideas from the world's teachers for improving education in the classroom. New York: The Free Press.
- Describe what skills you needed to complete this task.
- Explain how you solved the goal, problem, or issue in this task.
- Do you feel that you are good in simplifying radicals?
- Did you find this task to be difficult?
- Did you enjoy the task?
RESULTS:
I also noticed that although the students were confident in their abilities based on the metacognition questions, their scores on the unit test were quite low in the subject area. The class average for the 10 questions requiring simplifying radicals was only 68, even though the 10 questions were of the type for which students created their own examples. This is much lower than the usual class average in this topic based on results from previous years. I also noticed that this task took the students four class periods (41 minutes each) to complete. This is twice the amount of time that is usually used to present the topic of simplifying radicals, so I was very disappointed in the testing results. Twice as much time on task with lower test results indicates an inefficient method of teaching the lesson. What worked and what didn't work: The students demonstrated enthusiasm for the task. They generated many good questions. What didn't work initially was the tendency for students to try and create the hardest examples to simplify. They needed to be reminded of the Real World Setting that we were using; they are math teachers trying to teach the topic. Therefore, the task wasn't to create the most difficult examples, but to create examples that would be useful to teach someone who didn't already know how to simplify radicals. This reminder helped. As
mentioned earlier, the Blueprints created by the students lacked detail and
failed to accommodate all situations. I believe that the students need
to have a few examples of blueprints from other topics given to them before
this task. This may provide the needed guidance.
My next standards-based task will focus on:1. Plan -Title: Creating quadratic equations to solve using the quadratic formula Content Area: Mathematics, Algebra II, Quadratics Learning Standard(s): 4.3, D, 2 Intent: (Instruction or Assessment) Students create quadratic equations which have rational solutions, irrational solutions, and complex number solutions. Students create the data base to be used for their test in this topic. |
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