Welcome back to part 3 of my math task explanations! I hope that you have found this useful to you and that it answers any questions you may have. If not, please leave your questions in the comment section and I'll try to help clarify.
Part 3: The Actual Task
I will be using a 5th grade level task to walk through. A third grade level task is found in my Free Math Task Explanations set.
I start by briefly reviewing the Math Task Procedures. Then I simply read over the task using the document camera and have the students use their finger to circle in the air any important information. I asked them basic questions like "what are we looking for?" and then put my students into groups of 2 or 3.
Lets look at the 5.NBT.2 Powers of Ten math task called "Sewer Rats".
There are many rats in the sewers. The total amount of rats doubles every seven days. How many rats are there in the sewers after one year? Write your answer in scientific notation.
Extension: One rat has three babies. Each of those babies has three babies. The rats follow this same pattern of birth for 10 generations. How many rats are there altogether?
Now you may look at this at say "Wait a minute! It doesn't tell you how many rats are in the sewer to begin with!". Again, that's the point. This is were the independent thinking and reasonable estimating comes in. The students need to decide what reasonable and what numbers they really want to deal with when doing the task. You will probably have some that will be smart alecks (shocking I know) and choose a number like 5 billion. Well, let 'em! If they can do the math correctly it DOESN'T MATTER WHAT NUMBER THEY CHOOSE!" The purpose of a task is to focus on the mathematical process and mathematical reasoning. Your student will learn quickly that they won't want to be a smart aleck during task time.
If you felt it appropriate you could talk about how many rats would realistically be in the sewer. 1? 100? 1,000? Make sure you let your students decide. This means that every group could potentially use different numbers in their problems and that's fabulous. The numbers they choose don't matter as long as the answer and process are correct. (And by answer I mean as long as their math is correct with whatever number they choose.)
So say your student picks 5 (it's not very surprising that they lean toward benchmark numbers like 1, 5, 10, 50, 100 etc.). That means they take 5 rats and double every seven days. So:
-Day 1: 5 rats
-Day 7: 10 rats
-Day 14: 20 rats
-Day 21: 40 rats
-Day 28: 80 rats
-Day 35: 160 rats
-Day 42: 320 rats
They will need to double it a total of 52 times (for 52 weeks in the year). They could do this by adding, multiplying, drawing pictures, using manipulatives. However they want to solve it is up to them. As you are walking around you can gently guide them (do not give them answers, just suggestions) into easier paths or clearer processes. (FOR THIS TASK I WOULD RECOMMEND THAT THE MAJORITY OF YOUR CLASS START WITH A LOWER NUMBER. In this task the numbers get really big really fast!).
After the students have been working for several minutes, walk around and take note of the different approaches your students are taking on this problem. Then, pull up 1-3 groups and have them share their thinking on the document camera or board. This is a crucial piece that allows for student reflection. It also helps us as teachers see what our students are thinking and where they are in the mathematical process. As much as I wish my students could learn everything from me, sometimes it takes the words of a peer to help something click.
After sharing a few, my students would go back to work. I would walk around and ask questions like: "Okay, explain to me what you are doing." or "Can you tell me more about this?". I tried not to praise to heavily (and the facilitators at our state training said to not praise at all!) because then the other groups think that there might be only one correct way of doing things. I couldn't just look and them and say nothing so I would respond with "I like your thinking here!" or "I really love how you showed me two different ways to solve this!" etc.
Finally, if there was time at the end, we would share a few more groups and talk about their work and answers. The students would turn in their task pages to me and any additional pages they had done work on. I graded these as a participation grade. The tasks are to help my kiddos think and talk about math and help me to see where my students are and where I as the teacher need to take them.
There are many different ways to do a task in your room. How do you run your math tasks?
PEACE, LOVE, AND STICKY NOTES,