Problem of the Week

Problem of the Week
I was sitting in a 10 grade Geometry class at Union High School that I observe Tuesdays and Thursdays, and the teacher, Mrs. G, passed out a worksheet that was titled: Problem of the week. I looked at the worksheet and this is what I saw:

Four Step Problem Solving Sequence 

Problem of the week that the students and teacher are going to work on. 

Understanding the Problem

Analyze the problem and establish what is asking you to do or find. Underline any important words or facts. Define any key vocabulary words. 

Create a Plan 

Devise a plan for solving the problem and/or make an illustration to demonstrate your understanding of the problem. 

Carry of the Plan 

Write a complete sentence explaining the answer and remember to attend to precision. 

Reflecting 

Evaluate your solution, is it reasonable? Can you find another valid approach to solve the problem?

Each part of the problem is done in class with the students and the teacher. There are four steps for one problem, one step for each day. On the final day, the students will do a problem to the one similar to the one they worked on all week all on their own. 

Mrs. G finds the problems that are either review from the previous week or a problem that will be coming up in the new week. This problem is challenging to the students, but when the week is done, they be able to do a similar problem.

Below is one of the problems Mrs G presented the class, and I completed the worksheet.

This worksheet can help focus the students attention to what the question is asking and following through with the answer but also another way of looking at the same problem. This worksheet breaks down a problem into steps of thinking, so the students will receive the full understanding of a problem. 

Counting Circle

Counting Circle
"What in the world are you talking about? What in the world is a counting circle?"; you might be asking yourself as you read the title. I will tell you it is exactly as the title says...you are in a circle counting.You may be thinking: "O you are counting 1,2,3,4...1010. that seems way easy." In all reality, the counting circle can be that easy or it can be created into a harder game.

The Game
The set up of the game is very simple. You gather your group/students into a large circle. The teacher (or student) will pick a number for the counting circle to start with. Then the teacher (or student) will decide on the number that will be added or subtracted to the starting number. The first student in the circle will take the original number and add or subtract the teacher's number in his/her head. The next student in the circle will take the previous students answer and add or subtract the teacher's number in his.her head. This will continue around the circle until the teacher decides the number line is done. Then the teacher will pick a student and ask the group what their number would be once it was their turn.

Example
Starting number: 432
Teacher's number: +32
1st student: 464
2nd student: 496
3rd student: 528
continue...

Experience from Game
What can we learn from counting in a circle? When the game is over ask the students to think about the way they got their number in their heads. Then the teacher will randomly pick a student and ask to explain how they came up with their answer. This way will be written on the board. This will continue until all possible ways to come up with the answer is up on the board. This shows students that there are many ways to get the correct answer. Some ways will be easier than others, while others might make more sense to the student might not make much sense to the student standing next to them.

Side note: Continue the counting circle even if a student gets the number wrong-just write the number on the board. This will create a challenge for the following students.