What is Great Group Work?

Many times throughout the year in mathematics students will be explaining and justifying their thinking, as well as critiquing the reasoning of others (Mathematics Practice Standard #3). This not only happens when students write about their math thinking, but also when they are with a partner and small group.

We explored what "Great Group Work" looks like with a fun math activity.

Throughout the activity student teams were looking for patterns while working together to complete the task. 

After the task we reflected on the qualities of great group work. 

Fine-Tuning Our Math Justifications

Communication is a big part of mathematics. Today while learning about decimals students were asked to imagine that our number line containing tenths was now divided into hundredths. 

Then we looked at six-tenths (0.6) and wrote how many hundreds this would be. Students came up with three possible answers: 0.06, 0.02, and 0.60. 

Students were then asked to write down on their own slate the decimal equivalent in hundredths to 0.6. Once students decided on a response they met in partnerships defending and justifying their answer.  During the activity students were able to change their response and modify their thinking.

Students met with three different people during this activity.

At the end of the activity the entire class felt convinced that 0.6 is the same as 0.60. We concluded that there are ten hundredths in one tenth; since I have six-tenths, I would have 60-hundredths. 

I was so impressed with our math communication skills during this activity! 

Math

We were busy making connections between different ways to represent a problem in math. We've been focusing on making these connections to strengthen our understanding of multiplying a whole number by a decimals.

We began with the problem: 5 x 0.35  (five groups of 0.35)

We modeled our thinking on a hundredths grid:

We then modeled our math thinking using an open number line. Students were prompted to begin looking for connections between the hundredths grid and open number line. Check out these examples!  One student took 5 jumps of 0.35, while the other decomposed 0.35 and took 5 jumps of 0.30 and 5 jumps of 0.05. Great strategies!

Then we gave the area model a try. Continuing to make a lot of connections!

And, last but not least, an equation. This is the trickiest for the kids. We are beginning to apply the Distributive Property as one of our strategies, something that will be really important in middle school.

Wow! Such amazing work!  Students were then given the task to show these four math representations for the next problem: 3 x 0.32

Check out the group of one group! They decided to each be responsible for one representation: hundredths grid, equation, open number line, and area model.

Using the Multiplication Table to Subtract Fractions

It is sometimes challenging to keep all of the math strategies we have available straight. This is one way to subtract fractions with unlike denominators.

Math Gallery Walk - Math Practice Standards

Communicating in math can be a challenging task. Not only do students have to make sense of a problem, and pull out the important information, but they also have to take their calculations and put it back into the original story/problem (Math Practice Standard #2). We have worked on this skill quite a bit during the first few weeks of school and the students are improving this skill every day.

Now once student groups solved the problem we asked them to share their thinking with their classmates. This is where being precise in our language (Math Practice Standard #6), and constructing reasonable arguments (Math Practice Standard #2) becomes important.

After groups created posters to show their thinking we took a "Math Gallery Walk"; with post-its in hand they read through the work of other groups, thinking about if the work made sense, how the group's strategies were different from their own, etc.  Students were now being asked to critique the reasoning of others (Math Practice Standard #3).  This was a lot of work, and for some students a new way to work in math!  I was so impressed by the thinking of these 5th graders, they stepped up to the challenge!

We gave students some ways to get their post-its started.....

When we were done with this activity, original groups reformed and read through the post-its. During this time they were able to adjust their thinking or explanations if necessary.