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. 

Looking for Patterns in Math - Working with Exponents

Math is full of patterns, and mathematicians leverage these patterns when they are solving problems; they are all around us, we just have to notice and use them to our advantage.

This is evident in our Mathematical Practice Standards (student behaviors in mathematics); especially Mathematical Practice Standard #7 Look for and Make Use of Structure, where mathematically proficient students look closely to discern a pattern or structure.


We began with this problem:
What patterns do exponents make when the base is 10?
We ran through an example and then students were sent off to explore the patterns.

Students organized their thinking in many different ways. Some created charts, while others wrote the expressions down on separate lines.

And did we find a pattern?  Of course! (Keep reading below to find out what it was...)

One pattern that we discussed was the idea of "add a zero" based on the number of zeros within the sequence of 10 we were multiplying.  So I wrote this on the board:

10 + 0 = ?

We talked about if we were actually "adding a zero". 

Mathematically we aren't "adding a zero", rather the digit 1, in this case, is changing place values and the product (answer) is increasing by a factor of 10.

We then extended out our thinking by determining what 10 with an exponent of 23 might look like. 

Math patterns are all around us, it is so important to notice these patterns to make us stronger math students. 

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.

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.