Math Talk

A school day is filled with so many objectives we are trying to accomplish with our students. Sometimes we wonder how we can possibly fit in one more activity.

Math Talks are an activity that can be accomplished in 5 - 10 minutes and will not only support student number sense but can give you a quick formative assessment. They can be done any time during the day, not just during math class.

Do you have 5 minutes before a special?

Did a lesson you thought would take 30 minutes only take 20?

Did everyone finish a test faster than you thought?

Pull out a picture and have a

quick Math Talk.

So how do you do a Math Talk?

1. Show students a picture. This picture can come from almost anywhere.  Math Talk by Char Foresten and Torri Richards is a great place to start, but you could use I Spy books, National Geography for Kids, or Time for Kids. You probably have some books in your classroom that would be great. Make sure to check pictures first to ensure they have plenty of opportunities for talking about numbers.
2. Start asking questions, have them tell you what they see or have them share with a neighbor. The goal here is talking about math, but you can tie in other subjects as well.
3. Students can also create a math story about the picture. You can do this through discussion or in a journal.

The following pictures come from Math Talk by Char Foresten and Torri Richards.

Here are some example questions:

A simple question like "what do you see?" will tell you a lot about each student.

"Are there things in this picture we can count?"

"How many sets of 3 do you see?"

"What fraction of the umbrellas are white?"

"How many people would there be if there was one more person on each blanket? How did you figure that out?"

"What is the ratio of white to colors on the umbrellas?"






Have students create stories based on your current math lessons. Students will differentiate based on their understanding and you will gain valuable information. You could ask them to:

•  Create a story that would use 2 in a number bond
•  Create a multiplication story

You can tie other subjects into Math Talks:

"What is the fraction of carnivore to herbivores?"

 

You can also support understanding of math vocabulary words -

"Are there more rabbits or squirrels?"

"What animal is under the log?"

"What animal is above the tree?"

 

 

This would be a great activity to share with parents. Parents could do this at home to support their students' learning. Pretty soon your students will see math everywhere!!

 

Blessings,

 

Shari

 

 

 

 

 

 

 

 

 

 

Number Talks

Joy took a class this summer that ties in well with our new program, Math in Focus. After she shared with me some of the strategies presented in the class, I asked her to write a blog post about what she learned. I copied and put one sheet of information in your box, however, Joy has more information if you are interested.
Thanks for sharing Joy!!

Guest Post from Joy Bartholomew:

This summer I took a class called Instructional Strategies for Math Teachers.  It was a good class that I think helped to prepare me for Math in Focus.  I think it will be offered again next summer if anyone is interested.

 

In this class, they focused a lot on Number Talks.  (We did one in class with the representative from Math in Focus in in-service.)

You give the students a problem they can do mentally and then discuss the different strategies they used to solve the problem.  Sometimes, you can also look at the strategies and order them in a sequence by the different ways they relate to one another.

For lower grades K-2, you can also try something called “Quick Images.”  Looking at various images (usually dots) for a brief period of time (a few seconds) and then asking students “how many dots did you see?”  They then share their strategies to explain how they know the amount they saw.  “How do you know you saw 6 dots?”

Both methods offer opportunity for mental math, math discussions, and seeing more than one way to solve a problem.  I know we are trying to get Math in Focus figured out first, but Number Talks may definitely be something to think about trying in the future.  I know I am. I think they would be a valuable addition.  It is not something you have to do every day, but doing them on a consistent, regular basis is good.

 

Anyway, if you are interested in trying some of these types of problems, here are some resources you can look at.

https://www.teachingchannel.org/videos/visualizing-number-combinations

www.teachingchannel.com (search for videos of teachers doing number talks with their students)

 

 

You can definitely google “Number Talks” or “Quick Images” and find even more information.

 

I have some articles/handouts on Number Talks too.


Joy

Model Drawing

Model Drawing

 

This summer I was introduced to model drawing and immediately -  I was hooked!!!

Before learning about model drawing, my teaching of word problems went something like this ........

"Make sure to read the problem carefully"
"Underline/circle/box the important information"
"Draw a picture"
"Guess and check"
"work backward"


Unfortunately, this didn't always help many students. Although I tried many different ways to teach word problem strategies, I still had students struggle through complex and multi-step problems.

This made me so sad!! I believe God has created us to be problem solvers and to think logically. God created math with order and structure so that we can use it as a tool. But, if we can't use the tool to solve problems we aren't living up to all we are created to be.

None of the strategies and ideas that I used in the past are wrong, they were just missing something. After learning about model drawings I realized what was missing - visualization. 

Why am I so excited about model drawings?

Model drawings help students accomplish many things:

• transition between concrete and abstract (algorithm) by giving them visuals they can manipulate
• gives them a way to handle written information
• gives them strategies to tackle complex, multi-step problems
• allows them to visually communicate their thinking through drawings
• makes algebraic concepts more concrete - develops algebraic thinking
• helps students visualize the part-whole concept

 

Math in Focus begins model drawing in 2nd grade, but the ability to see the part-whole concept was developed starting in Kindergarten. Thanks K/1 teachers!

Singapore teaches students to use rectangles as their model when solving problems.

So, What's Special About These Rectangles?

 

While, there is nothing special about the rectangular shape that is used in Singapore Math, and therefore in Math in Focus, rectangles are used for several reasons.

• When all teachers use the model drawing and rectangles to solve word problems, we are consistently and systematically teaching students to think through complex problems.
• Rectangles are easy to draw and divide.
• They can be used to represent large numbers and show the relationship between numbers.
• Mainly, it helps students visualize the problem.

Watch this video!

Dr. Yeap Ban Har is a fabulous teacher/lecturer from Singapore. I had the opportunity to attend several of his teaching sessions this summer. In this video he explains the importance of bar models to help students visualize the problem. Singapore teachers are consistently asking their students "can you see this" or "can you visualize this". The advanced math students can do this with very little directions, but we need to teach the average and struggling learners to visualize.

We will have our first Math Night, September 24, where I will show this strategy to parents. You are welcome to attend. I also have the book Step-by-Step Model Drawing: Solving Word Problems the Singapore Way. You are welcome to borrow it any time.



Blessings,

Shari

 

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