My MT divided the
students into groups of 3 or 4 and worked on word problems such as the one above.
They had to solve the problem and demonstrate how they figured it out. In this
problem the following question is asked, “Charles wants to plant 35 flowers in
5 flower beds. He decides to plant the same number in each flower bed. How many
does he plant in each?” Each student group had a different problem and had to
present their solution to the rest of the class. They had to walk through how
they solved the problem. Each problem that the groups worked on was a concept
they have previously worked on. The big idea was to figure out a way to solve
the problem and demonstrate the division, multiplication or addition in a
picture or another way to explain the class. My MT wanted to make sure the
students worked in a group since there are many ways to solve this problem.
One
possible effect way to approach this problem is to introduce the concept of
division with a word problem like this. Since division is basically dividing
groups into equal parts this word problem demonstrates this completely. It also
allows students to relate division to real life problems such as gardening.
Another way you can approach this problem is to have manipulatives for the different
parts of this problem so in this case 35 flowers and 5 flower beds. This way
the students can manipulate and move around the pieces until the groups are
divided evenly. After the groups are even the students can write a sentence
explaining the grouping of the manipulatives. One anticipated student approach
is for students to come up with a simple division problem such as 35 / 5 = 7.
In this case the students are able to pull out the numbers needed to create the
problem. Another approach is that the students draw a picture demonstrating
equal groups for this problem. They draw 5 flower beds with a certain number of
flowers in each group.
It seems like this group figured out that it was a
division problem and solved for 7 as their answer. From there they drew an oval
represent a flower bed and circles representing the flowers. For each flower
bed they wrote ‘7’ meaning it was one group of 7. There are 5 flower beds drawn
with 7 flowers so there are 5 groups of 7 in all. They could have counted the
groups by 7’s to get to 35 to check their answer. Or they could have counted
all of the circles in all to get 35. These students demonstrate the ability to
create a drawing to explain a division word problem. They correctly used the
variables in the word problem to solve the equation. These students
demonstrated that they can solve a division word problem using images and
variables. One way to advance their thinking is to give them many word problems
similar to this by dividing groups into equal parts and division with
remainders to see if they are able to determine what to do with unequal groups.
As well, I would want these students to create their own word problems similar
to this style and teach it to their peers.
This analysis is a very good start, though there are some elements that I would continue to push you to think about.
ReplyDeleteWhen you say that "The big idea was to figure out a way to solve the problem and demonstrate the division, multiplication or addition in a picture or another way to explain the class", it is great that you are trying to identify the big idea, but the way you describe it is a little too vague to be meaningful or useful in terms of planning instruction or evaluating the students' work. Think more about the mathematical concepts or relationship that the task is asking the students to explore.
Also, as you analyze the students' work, be sure to pay particular attention to the representation that they used and the other representations that are possible and the possible connections between the different representations (thinking in this way (connections between representations) is a very direct way at decoding what the students' current mathematical understanding is...e.g., they understand in one representation but not another).