Thursday, March 28, 2013

Multiplication and Division Word Problems

After working for over a month on understanding the meanings of multiplication and division, it is time to "kick it up a notch" and use what we know to problem solve.

One of the most important things to know when solving word problems is key words. Key Words can make all the difference in the world. They are by no means the only tool you need to have but they can definitely help hammer out some word problems.

We first learned addition and subtraction key words. We used BAITS to help us remember Addition Key Words.
Both
Altogether
In all
Total
Sum

 Now it is time for some new key words. Here are two words to help you: PEGS and SPEEDS.


Since multiplication and division are related, they share some of the same key words. One way to know when to multiply or divide is to look for your total. Do you know how many total pieces of candy there are? Do you know your total number of people? If you know they total then you must be dividing because a division problem always starts with the total. Many times it will ask for the number of groups or the number in each group in the question.

Do you know how many groups there are? Do you know how many are in each group? If you do then you are multiplying. When you are multiplying you are looking for the total. Many times it will ask for the total in the question.

Below is the PowerPoint I use in class. It contains examples and practice and even some test prep. 

Saturday, November 24, 2012

Diving into Division

When I tell parents that their third grader is going to learn to divide, I am often met with looks of trepidation. It does seem like a very hard concept for wee ones to learn. However, that is what the curriculum calls for these days.

One thing I do to make this easier is to spend a good bit of time on the meaning of multiplication:
  1. Repeated Addition
  2. Groups of
  3. Rows of (Arrays)
  4. Times I count by
 Then when we move to division the concept does not seem near as daunting. I teach the meaning of division as:
  1. Repeated Subtraction
  2. Sharing into Groups
  3. Making Equal Groups
  4. Times I Count by
  5. Invers Multiplication
Here is the PowerPoint I use when teaching about division.

Meaning of Division

 
 
 
Here are some activities that students are asked to complete:
 


 
I love these videos to help students understand the Meaning of Division.
 
 
 














If your child likes to get on the computer, let them practice the concept of division with these online games:

Deep Dive Division
Deep Dive Fun4theBrain Game

Digging Division
Fun4theBrain Can You Dig It? Division Game

Saturday, November 17, 2012

Zero the Hero

One of my favorite concepts to teach is multiplying by multiples of 10's and 100's. Once I teach students The Meaning of Multiplication and how to find the answers to multiplication facts using arrays, groups, skip counting and repeated addition, I love to totally impress them with some major multiplication problems like:

20 x 9=180    
400 x 6= 2,400    
5,000 x 7 = 35,000
 
I help students master this concept by introducing them to Zero the Hero.


He makes multiplying by mutliples of tens and hundreds simple. All students need to do is circle the basic fact. Find the product. Count the zeros and then add them to the answer.

Here is the PowerPoint presentation I use during class.
 

Multiplying By Multiples of 1...

 
 
 
Once students practice a little while, it becomes second nature. It makes estimating with mutliplication a breeze.

Sunday, October 28, 2012

The Properties of Multiplication


Properties, properties. So many to teach and so little time. Not to mention what an abstract concept it is for students to understand. Here are some tricks I use when teaching the properties of multiplication:

1. Commutative- Before I start I have students use a Thesaurus to find lots of synonyms for the word talk. We make a word web of all of the words. One of the words is always communicate. We talk about what communicate means. It means to say something by talking, writing, using sign language.... Then I show the problem 4 x 3= and I ask them what is another way we can say the same problem...3 x 4. We can show that the 2 problems communicate the same thing like this 4 x 3=3 x 4. Since the two are communicating the same things we say that they are the Commutative Property-the order in which you multiply two factors does not matter the product will always be the same.

2. Associative- We start by talking about friends. Friends are the people we choose to be with. When we are on the playground or in the lunchroom, we group ourselves with our friends. Another word for grouping is associating. We associate with our friends. Associate means to group. When we multiply 3 or more numbers, we can't multiply all of them at the same time so we group them or associate them. To show the grouping or associating, we use parentheses to show which numbers we are grouping together first: 3 x (5 x 6)=3 x 30=90. The Associative Property says that it does not matter which two numbers you group together or associate first, the answer will still be the same. We show the Associative Property like this: 3 x (5 x 6) = (3 x 5) x 6. When we are multiplying the factors 3, 5, and 6, it does not matter which two we group or associate together first. When we find the final product, the answer will always be the same.

3. Identity-I like to talk about secret identities. The kids really get into it: Spiderman is Peter Parker, Batman is Bruce Wayne, Superman is Clark Kent, Hannah Montana is Miley Cyrus....They are not two different people. They are the "1" and the same person. Their secret identities (Peter, Bruce, Clark, Miley) are their real identities. It is who they are and adding a costume or a wig does not change who they are. The Identity Property of multiplication shows that a number can stay the same when we multiply it by a certain factor. Then I show them the following facts: 4x0=0, 4x1=4, 4x2=8, 4x3=12. Which one allowed the 4 to keep its identity? 4x1=4. The identity property states that any number multiplied by a factor of 1 stays the same.

Here are the notes that students will have in their notebooks:

And they will be expected to complete tasks like these:





Here is the PowerPoint presentation that I use in class to teach students about the Properties of Multiplication:



Videos are a great way to learn and review. Here are a few of my favorites:










The best way to learn is to practice, and nothing gets kids more excited about practicing than playing games on the computer. Here are some games to help practice the Properties of Multiplication:















Sunday, October 21, 2012

Mysterious Multiplication

This week we will be learning about the Mystery of Multiplication.

When we were young, we only had to memorize our multiplication facts, and we usually did not do that until 4th or 5th grade. Now, not only do third graders have to memorize their facts, they also have to be able to show why.

They can not just say that 3 x 4=12. They have to be able to prove that 3 x 4 = 12 because if you have 3 groups of 4 there are 12 total or if you add 4 three times you will get to 12 or if you count by four three times you will get to 12. They must be able to Prove It Not Just Choose It.

Here are the notes that should be in your child's notebook on Monday:



This is a graphic organizer that really helps show the Meanings of Multiplication:



Here are some examples of the tasks students will be asked to complete during class:

 
This is the PowerPoint Presentation I will use in class throughout the week:


The Meaning of Multiplication

 
 
Here are some of my favorite videos that really illustrate the Meaning of Multiplication:
 
video
 
video
 
 
 
 




Get Your Game On
 

Tuesday, October 16, 2012

Wonderful Word Problems

Did you know that the majority of math questions on standardized tests are word problems? Did you know that many kids who are not great readers score poorly on math portions of tests because they can not read the problems? Did you know that it doesn't have to be that way?

 In fact, in 13 years of teaching I have only had 1 child fail math. I believe one of the reasons for this is that I focus a lot on key words. They help give kids an advantage over word problems.

If a student can find the key words in a problem, then, most of the time, they don't even have to read the rest of the problem to figure out what to do to solve the problem. Key words have made my students successful problem solvers and have significantly increased test scores. Before focusing on key words, my students who were low in reading would score well on everything except for word problems, but now they are finally able to show off their strengths in math!

Here are the main Key Words that are found in most Addition and Subtraction Word Problems.

I teach my students to remember the addition key words by using the word BAITS. And Subtraction is as simple as 3-2-1 3-M's, 2-L's, 1-CDF. When I start teaching multiplication, which usually happens a month or so after solving word problems with addition and subtraction, we use the word PEGS. I teach kids to write these words on their scratch paper any time we are problem solving. 

You should find the following notes in their notebook's math section:


Ask them key words in the car, at Wal-mart, at the ball field...when ever you get a chance. I promise it will do amazing things. 

See my PowerPoint presentation below to see how I teach kids to solve word problems:




Word Problems




The videos below give some great problems solving strategies!


video


video







Get your Game On!













Monday, October 15, 2012

Scary Subtraction

Subtraction is very scary for third graders and their teachers. It seems so simple but is so hard for little brains to grasp, especially when subtracting involves regrouping. There are so many steps and so many ways to make a mistake.

This is why we teach subtracting in such a different way now. We want kids to thoroughly understand what is happening in a sutraction problem. That does not mean there is validity in teaching kids how to "borrow" across numbers, but it is not valid to call it borrowing. In fact, you are not borrowing anything.

You are regrouping. You are literally taking a ten and regrouping it in to ten more ones in the ones place. Borrowing suggests that it stays a ten. But it doesn't.

I teach students how to subtract using these 5 methods:
Drawing
Fair is Fair


Old School

Take a Penny

The most important thing for kids to remember and do is:
1. Always put the big # on top.
2. Before you start circle the largest digit in each place.
3. Think about the song.
Big on to?
No need to stop.
Big on the floor?
Go next door.
Take one ten,
That's ten ones more!

Here are the PowerPoint presentations that I use in class as my lessons. They will really help you understand how I teach and will provide a great review for your child.
There are some really great videos available to help understand subtraction.













Get Your Head in the Game! Check out this great online practice!
Subtraction Games
Subtraction Basketball



Subtraction Games
Match Up Subtraction
Subtraction Games
Subtraction with Regrouping Practice

Subtraction Games
Power Puff Girls Subtraction