Number Talks

I have to admit, Number Talks are probably one of my favorite parts of the day. So what are they?

At the beginning of math students join me on the carpet without any materials. I will then write a math problem on chart paper. Sometimes it has to do with multiplication, other times fractions, and later this year we will work with fraction and decimal addition and subtraction.

Students think about the strategies they could use to find the solution. Once most of the group is ready I write down the answer(s) that they found. Sometimes we have only one answer (we all agree), but most of the time we have a variety of answers to begin. For this problem students thought the answer maybe 204, 264, or 244.

Students then share their strategy with the group and I will write it down on the chart paper. After students share their strategy, the others can ask them questions or make a comment. This is a fantastic time where students seek clarification or sometimes even challenge the thinking of another student. 

I will sometimes ask if students see connections between the different strategies, but students are just beginning to point these out to the group. 

Multiple Strategies in 5th Grade Math

 Multiple strategies and justifying our thinking are important components of our fifth grade math classroom. Often times I will pose a question and encourage students to show their math thinking not only using one strategy, but also using another method as well. 

Today students were asked to find the area of one of the rectangles on the smart board using any strategy they wanted. 

As students were working I encouraged those who were finishing up their first method to think of another strategy they could use to show their thinking in another way. I also nudged students forward just a bit more, asking them what strategy they felt was the most efficient. 

As students were finishing, I walked around the carpet area and took pictures of  their awesome and diverse math thinking. I then post these pictures on the smart board and ask the "math author" to explain their processes and explain which strategy they felt was the most efficient. 

The rest of the class is able to ask questions for clarification. 

Just take a look at this fantastic and flexible math thinking! 

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.