Place Value

I had so much fun teaching a 5th grade math lesson Wednesday!  Thank you Laura for allowing me to come in your classroom. It was exciting to watch and listen as students explored the concept of place value.

 

The focus of the lesson was to compare and order numbers to millions. We started with simply building numbers with place value disks. These manipulatives were new to the students, so it took some training on procedures and rules.  Simple rules like having a "builder" and a "supplier" helped encourage communication between partners and kept everyone involved.



Soon they were building numbers with their partners.

 

 

While it was easy for them to build the number on their chart, it was a challenge for them to think about numbers in a different way.  For example, students built the number 224,827 and then I asked them to build it differently.  Mrs. Bailey and I walked around and asked the groups questions, leading them to see that numbers can be expressed in different ways - for example 1 ten and 7 ones can also be expressed as 17 ones.

Students shared the different ways they made numbers and we talked about each one to see if everyone agreed with their answer. Of course, normally students will build the number with the fewest place value chips or base ten blocks, but the time spent allowing them to explore the meaning behind numbers gave us valuable information on their understanding of place value.

These discussions allowed us a chance to build vocabulary and correct misconceptions. For example, when asked to give the value of the 2 in the tens place, many of them said 20 tens - hmmmm. That gave us a good chance to explore what 20 tens actually means and compare that to a 2 in the tens place.

Here is a short blog post from SDE on number sense that brings up some interesting ideas on allowing students time to explore numbers.  http://sde.com/blog/?p=45

This transition to building deeper understanding will be different and challenging, but very rewarding.  Don't be afraid to "go slow" in the first few weeks. The foundations you are building will pay off with deeper understanding.

Thanks for all your hard work!

Shari

Humbling Homework

Humbling Homework

I recently worked through a problem from Math in Focus that caused me to think reflectively about the new math strategies we will be implementing at HCS. Here is the problem.

At a school 3/4 of the students were girls and the rest were boys. 2/3 of the girls and 1/2 of the boys attended the school carnival. Find the total number of students in the school if 330 students did not attend the carnival.

My first thought was …............   

Then I gave myself a silent pep talk, "Ok, I've just spent a week learning about math and model drawing - let's give this a try".

Here is what I tried (I don't know why the pictures are sideways and upside down - sorry):

This shows the total students -  ¾ girls and ¼ boys.



Because 2/3 of the girls attended the carnival and ½ of the boys, I divided the girls into thirds and boys in half.

The lines don’t match, so I asked myself, what can I do to make this easier to compare – change it to sixths.

2/3 of girls went and ½ of the boys.  So I have 9 "units" or rectangles that didn’t go to the carnival.

9U = 330

U = 36.66666666667

Now, however, I was stuck because I thought "you can't have a remainder of a kid, so I must have done something wrong".

My math minded son happened to be in the next room so I asked him.

He, of course, said, "you do this, and this, and this and there you go".

 Here was my reaction…………..




Was it solved? Yes. 

Was it correct? Yes.

Was I a better and more confident problem solver after his help? No!

Still sure I didn't understand how to solve the problem using model drawing, but wanting to figure it out, I asked an unnamed middle school math teacher here at HCS.

Instead of just telling me what to do next, she asked me several guiding questions.

Yes a unit is 36.666666666667, but there are 24 units and when you multiply 36.666667 X 24 you get 880 students – woo hoo!!!!

 After her guiding questions am I a better problem solver? Yes, I think I am. More than that, I have become more confident in my problem solving ability, having tried and persevered through, what was a challenging problem for me.

As I attempted to be reflective, these are some of the lessons I took from this.

• Don't walk into a lesson cold. In the last blog I said several presenters at the SDE conference recommended, before you begin a unit, work - Every. Single. Problem. What would have happened if I was teaching this lesson and hadn't worked the problem before teaching?
• Be careful about sending home homework. If a student gets stuck and doesn't have the problem solving tools to get them "unstuck" they will either give up or ask their parents for help. It is possible parents will be able to help their student visualize and work through a problem, but more likely they will be like my son, "do this, do this, do this and there you go".
• As you teach students to solve word problems, using the bar model method, make sure to empower parents to help their students. Give parents tools to help students think critically.
• Don't rush to give students the answer. I am guilty of this!! I see a student struggling and want to help, so I tell them what to do instead of letting them struggle. If I let them struggle and guide them through the struggle they will become better problem solvers.

But the biggest AHA I had was -

• Ask for help. This curriculum is new for everyone. If we aren't afraid to admit we are stuck and ask for help from others at HCS, we will become more effective math teachers. Your PLCs are a great place to present problems and ask for help.

Happy problem solving!!                              

Shari