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:

The Properties of Multiplicat...

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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:

Math Basketball

AAA Math Properties

Properties Quiz

Fourth Grade Multiplication Properties

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

More PowerPoint presentations from Elizabeth

 

 

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

 

 

 

 

 

 

Get Your Game On

 

Tons of Lessons and Games on Multiplication

Math Racing



Multiplication Picnic

 


Multiplication As Arrays

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

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The videos below give some great problems solving strategies!

Get your Game On!

Grand Slam Math

Model Problems Like We Do In Class

Monster Word Problems

Tons of Games about Word Problems

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.

Subtraction

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Take a Penny

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There are some really great videos available to help understand subtraction.

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

Subtraction Basketball

Match Up Subtraction

Subtraction with Regrouping Practice

Power Puff Girls Subtraction

Addition With and Without Regrouping

We have just finished our addition unit. We learned different techniques and strategies for adding whole numbers. I do teach kids to add numbers using the traditional algorithm, which we refer to as "Old School" but I also provide them with many different ways.

Our standard states that third grade students should be able to "fluently add numbers within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction".

What it means in normal people terms is that students need to be able to add numbers less than 1,000 using lots of different ways and be able to check their answers by using subtraction.

Here are the PowerPoint presentations that I use in class (if it doesn't come up on your Apple product just click on the link and you can view it on the site):

Adding without Regrouping

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Addition With Regrouping

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This is how I teach kids to draw out problems. This strategy works really well for those kids who are not good with basic addition facts.

Branching is about taking an addition problem and break it into expanded form and grouping the tens and ones together to make adding easier. This is really how you add numbers together when you do it mentally in your head.

 Give and Take is a strategy that I teach students who have difficulty remembering to regroup or add the "1" that was regrouped into the tens place. It takes the regrouping out of adding with regrouping!

 To teach checking, we focus on fact families. Every number sentence is made up of 1 "Big Number" and 2 "Small Numbers". The rules are:

S + S = B

&

B - S = B

If you know the rules, you can check addition by taking the answer "the big number" and subtracting one of the addends "the small numbers". If you added correctly then your answer should be the other "small number".

Here are some of the videos I use in class and some others to help you understand these new "crazy" methods this "crazy teacher" is teaching your kids. 

Branching

Expanded Form or Partial Sums Addition



Old School Song

Some online games that make learning and practicing fun can be found below:

Our most favorite video that really helps when we do the "Give and Take" method.

Properties of Addition

The properties of addition are the rules that make adding numbers easier. In third grade, we focus on three properties: the Commutative, Associative, and Identity Properties.

The Commutative Property is also known by younger students as "The Switch-a-roo". It tells us that it doesn't matter what order you add two numbers in the answer will still be the same. 3+4 is the same as 4+3 or 3+4=4+3.

The Associative Property is about grouping numbers that we are adding. When you add 3 or more numbers at a time, you naturally group two together first and then add in the next number. The Associative Property is shown by using parenthesis to show which numbers we are grouping together first to make adding easier. (3+4)+6 means that we are adding 3 and 4 together first then we add 7+6 to get 13. We can also add those numbers by adding 4+6 first to get 10 and then add 10+3 to get the sum of 13. It is shown as (3+4)+6=3+(4+6).

The Identity Property is about helping a number keep it's identity. Remember: identity is who or what something is. When adding two numbers together, the only way one of the numbers can stay what it is, is to add 0 to it. 5+0=5, because when you add nothing to a number the number does not change.

Here are the notes students should have in their notebook.

 

Below you will find the PowerPoint presentation that I use in class over the week long period that we are learning about The Properties of Addition.

 

Properties of Addition

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I also like to show the following videos.

 

Let your child have fun while reviewing the Properties of Addition with some of the following games.

Properties Quiz


Properties of Addition

Rounding

This is a new focus for third grade. In the past, it has been in second grade. Rounding is about making mental math easier. We use mental math every day, whether we realize it or not. To teach students how to round, we focus on 10's, 100's, and 1,000's numbers...because the only "round" number is a zero.

Students should have these notes in their binders.

 

If you know my teaching style at all, you know that I have to have a song to go with this concept. This songs helps students decide whether they should round up or round down.

 

 

This is the presentation that I use throughout the week to teach children about rounding numbers.

 

 

Round Up Time

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I love incorporating videos throughout my presentations and here are just a few of the ones I use to help students understand the concept of rounding.

 

 

 

 

Let kids have while learning while having fun!

Rounding Sharks


Rounding Spaceships


Which One Rounds?

Place Value

The most important concepts students learn is place value. It is the foundation for all other concepts in math. To round, estimate, add, subtract, multiply, and divide, you must know place value. I use a variety of techniques and strategies for teaching place value.

Our standard and goals for this unit are below:

These are the notes that should be in your child's notebook.

 

 

We even learned a song about place value.

 

 

 

I use the following PowerPoint presentation while I am teaching during the week. It allows students to work along with me and see many visual representations of place value.

 

Learning Place Value

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 Your child will be expected to answer questions like:

The Chattahoochee National Forest covers 13,567 acres. What is the value of the digit 5 in the number 13,567?

 

A. 5

B. 50

C. 500

D. 5,000

 

Aubrey wrote a number on the board. The number was the greatest number you can write with the digits 6, 2, 5, and 8. What number did she write?

 

A. 8,652

B. 6,258

C. 5,628

D. 8,625

 

In the number 54,872, what is the value of the 7?

 

A. 7

B. tens

C. 700

D. 70

 

In the number, 7,345 what digit is in the hundreds place?

 

A. 7

B. 3

C. 4

D. 5

 

What is another way to write 5,872 using values and sums?

 

A. 500 + 80 + 7 + 2

B. 5,000 +80 +70 +2

C. 5,000 + 800 + 70 + 2

D. 5,000 + 800 + 20 + 7

 

Check out the following videos about Place Value found at United Streaming and on YouTube:

 

 

 

If your child wants to have fun practicing place value, click on the following pictures to be taken to some awesome and engaging online games!

 

Football Math

 

Place Value Millionaire

 

 



 



 Place Value Puzzler

 

 

Place Value Game