Tuesday, October 23, 2012

Mathematizing the World

As educators, we often get asked, "How can I help my child at home?"

One way of supporting children's mathematical development is to help them "mathematize" their world by seeing math all around.  Start by being curious about your child's ideas and what they are pondering.  Notice everyday experiences and ask questions that help build on their mathematical thinking. 

For example, when visiting the Texas State Fair last week, math was EVERYWHERE! 
It was easy to capture some digital images with the use of a smart phone.

How many fair tickets did I purchase?
If each ticket costs $2, how much money did I spend on tickets?
It takes 5 tickets to ride the bumper cars.  How many times can I ride?

How many ducks in the pond?
How could you group the ducks to easily count them? 
How many would there be if you added 1, 10 or 100?
What if you took one away?

Estimate the height of the Ferris wheel.
How many buckets are there?
If a bucket holds 3 people, how many people will the Ferris wheel hold?
If takes 45 minutes for one rotation on the Ferris wheel, how many minutes would 3 rotations take?

Look at the balloon array!
How many rows of balloons are there?
How many columns?
What is the product? 
How many 6x4 arrays can you find?
What fractional part is blue?

How many inches tall are you?
How many feet tall must you be to ride?  
If you are not tall enough, how many more inches must you grow?  
What is the difference between 36 inches and 42 inches?

Howdy BIG TEX!
If Big Tex is 52 feet tall, how many feet taller is he than you? 
How many inches tall is he?  
If Big Tex turned 60 years old in 2012, what year was he built?

When our children are thinking like mathematicians, they make sense of numbers, learn to persevere, are able to reason, and use multiple strategies to solve problems.  All of these things help our children become passionate about math in the world we live. 

I challenge you to "mathematize the world" and have some rich conversations with your child.  


Wednesday, October 17, 2012

Math Word Walls

As part of the Math Classroom Challenge, today's post is about how you can use math word walls to support students in communicating with mathematical language.

Word walls are relatively common in the Language Arts realm, but why might we want to use them in math? How can we set up word walls in a way that give students the opportunity to actually make meaning of the words?

What exactly is a math word wall?
A math word wall is an area of the classroom in which key content words are displayed on a list or chart in order to help students learn mathematical vocabulary. Word walls aid in encouraging students to spell these words correctly and use them when they are speaking, reading and writing about math. You could also have other word walls for science, social studies, etc. It's a great tool!
At River Place Elementary, 1st grade has math word walls right on a large piece of chart paper!
Here's another example. This is simple and eye level for the students to see!
Here is another example from Becky Vaughn's 4th grade classroom at Westside.
Heidi Dominguez, teacher at Westside, set up a spot in her math area for her word wall right at the beginning of the year. It is nice and low for her class of 1st graders!

How often do I change out the words on a word wall?
Math word walls are constantly changing based on student level of understanding, unit of study, and/or real-world problem they are solving. Once students understand the words, you can take them down and add new words.
I like this word wall because of its simplicity. Grab a piece of chart paper, select about 10 core words from your unit of study, gather the students around and hang it up in the math area of your classroom. Add to it as the students learn. Don't buy something that is pre-made! It makes more sense to involve students for a couple of reasons:
1. It supports the LISD curriculum. Teacher stores usually don't have the most rigorous words.
2. Different students understand different words and that will change every year based on your class.
3. If students are involved in the creation of the word wall it sends a message to them that you care what they think and you care that they learn the words. Spotters ready...let's learn these words together!

What is the most important thing to remember about a word wall?
As my language arts friend Diana says, "They are dynamic and interactive!" Students need opportunities to make meanings of words on the word wall so they can communicate. Here are a few ideas:

I Say, You Say!
1. Point to the word on the word wall and have the students pronounce them with you.
2. Point to the words in order and mix them up when students become more fluent with the pronunciations.
3. Have students work together in partners with one partner pointing at the words and the other partner saying the words. Then, the partners switch and do the same thing.

Word Connection
1. Have students pair up.
2. Pick two words from the word wall and write them down.
3. Have students talk about how the words connect.
4. Share answers with another pair or as a class.

Vocabulary Cards
1. Have students use the Frayer model to create a vocabulary card for each content word on an index card.
2. Now the students have their own set of word wall cards!

Ready, Set, Redo!
1. Take down the words from the wall and have students sort them in a new organized way.
2. If students have their own set of cards (like mentioned above with the Frayer Model) they can just use their own.
3. Record the sort in their math journal.

Those are just a few basic strategies that I have found most helpful in getting students to communicate and learn math language, but we know that there are multiple paths to the same solution! What are some ideas that you have to make math word walls interactive and meaningful? Comment below!

Thursday, October 4, 2012


Look who showed up at Reagan Elementary to promote mental math, number talks, and fact strategies! 

The CRAZY MATH LADY!  (I've heard she has also been spotted at Giddens Elementary before.)

The CRAZY MATH LADY dresses up to bring warm-up activities into the classrooms. She enters with clappers, yelling "WooHoo," startling many teachers and students.  She introduces herself as the CRAZY MATH LADY because she is CRAZY about math. (Aren't we all?)   

She always begins her mini-lesson with a chant, "When I say Math, you say Rocks! Math....Rocks! Math....Rocks!" Then she gathers the students on the carpet for a quick number activity.  

On this day, she handed each student a hundreds chart. The hundreds chart is a great model for seeing patterns in numbers. Most children decided to use the hundreds chart, while some challenged themselves to try it mentally and turned their charts over. 

The activity was a series of problems to calculate quickly.  It went something like this: Put your finger on the sum of 10 and 25, add 50, subtract 4. Is the sum of the digits 9? 

Wow, she went CRAZY fast but it was fun and engaging.

Hopefully after a few more weekly visits from the CRAZY MATH LADY, students will become more confident in their mental math ability and less dependent on using their hundreds chart. 

The next day students were still wondering . . . who is the CRAZY MATH LADY???  
One never knows where and when she will show up next!!   

The lesson idea is from Mary Alice Hatchett at http://www.mahatchett.com./

Monday, October 1, 2012

Traditional Algorithms VS Invented Strategies

There are significant differences between traditional algorithms and invented strategies.

The traditional algorithms are based on performing the operation on one place value at a time with transitions to the next position. They involve trades, regrouping, "borrows," "carries" or Dead Monkeys Smell Bad!  The procedures are rigid.

Traditional algorithms take the understanding out of place value. They are "digit oriented." They rely on procedures or steps that must be done in a specific order and usually start in the ones place. 

Look at theses examples of traditional algorithms for addition and subtraction. They follow a procedure.

Think about what is being said as you solve this problem: 7 plus 8 is 15. I put down the 5 and carry the 1.  One plus 5 plus 3 is 9. Three plus 2 is 5. The answer is 595.

Think about what is being said as you solve this problem: 3 minus 7, you can't do it so you have to go next door and borrow 1. Since they don't have any to give you they go next door and borrow one. The 3 becomes a 2 and the zero becomes a ten. Now they have one you can borrow so the ten becomes a 9 and the 3 becomes a 13. Now you can subtract! 13 minus 7 is 6, 9 minus 6 is 3 and 2 minus 1 is 1. The answer is 136.

Invented or flexible strategies develop a good understanding of the operations especially the commutative property and the distributive property of multiplication. Students start to see the relationships of addition to subtraction, addition to multiplication, and multiplication to division. What an important concept! 

Invented strategies involve taking apart and combining numbers in a wide variety of ways. They are "number oriented." Most of the partitions of numbers are based on place value and start in the largest place. 

Now look at the examples of the same problems. Although these may look complicated many invented strategies can be done mentally and just recorded on paper.

Think about what is being said as you solve this problem: 300 plus 200 is 500, 50 plus 30 is 80 and 7 plus 8 is 15. I add them together and 500 plus 80 equals 580 plus 10 is 590 plus 5 more is 595. The answer is 595.

Think about what is being said as you solve this problem: 300 minus 100 is 200. Since I know 67 + 33 gets me to 100 then 200 - 67 is 133. But I still have the 3 ones in 303 that I need to give back. 133 plus 3 is 136. The answer is 136.

Your Turn: 
Think about the traditional algorithms for multiplication and division. Are they rigid procedures? Are they "digit oriented?" Do they build understanding of number relationships? 

Be careful: Don't turn an invented strategy into a "procedure." 

Students must be allowed to develop their own strategies based on their own understandings!