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

You can purchase my Meaning of Multiplication PowerPoint and my Mystery of Multiplication packet at my TpT store

 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

I use a great PowerPoint when teaching about division. It is called The 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


Digging Division

Multiplying by Tens and Hundreds

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...

More PowerPoint presentations from Elizabeth

 

 

 

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

Popping about 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.

 

I use a PowerPoint presentation to teach students about the Properties of Multiplication. You can find it at my TpT store.

 

 

I also use this packet that has tons of printables, activities, games, student notes, an assessment, and so much more to teach students about the properties of multiplication.

 

 You can find the Popping about the Properties of Multiplication at my TpT store.



See how I use all of this in my classroom at my classroom website, Mrs. Hill's P.I.R.A.T.E.S.

 

 

 

Freebies for Upper Grades

Hocus Pocus with a Giveaway Focus!!  Halloween's just around the corner, and I have to admit it's one of my favorite holidays!  Ghost stories, pumpkins, candy corn and excitement fill the air. It can only mean that we teachers need to prepare for our classroom gremlins' dynamic desires to Trick-or-Treat this season AND fast! Why not get ready for celebrating this festive occasion by entering my HUGE Halloween giveaway?

It even includes a $25 gift card to the amazing black-and-orange company, Amazon.com!

Not to mention, you
have a chance to win 19 high-quality HALLOWEEN products specifically designed for upper grade students from some amazing
and very generous TpT sellers!

The Mystery of Multiplication

Multiplication has come a long way since we were in elementary school. We were handed a list of facts and told to memorize. I don't think we even questioned why 4 x 9 equaled 36. We just accepted it.

Things are so different today. Kids not only have to know that 4 x 9 equals 36, they also have to know why. In other words, how do you know? Prove it to me. Which is perfect for my math motto: PROVE IT! DON'T JUST CHOOSE IT!

Our standards no longer just require students to answer the basic fact. The new standards require students to show what 4 x 9 looks like using groups of objects, arrays, and repeated addition. I have created the following products to help my students master these concepts:

I use this Meaning of Multiplication PowerPoint presentation over a week long period. I take each meaning one day at a time. I embed videos and online games into it, so that we can just click and go.

I also use The Mystery of Multiplication lesson and activity packet to provide lessons, printables, games, activities, graphic organizers, and more.

Give and Take

In my previous post, I discussed different ways of teaching addition with regrouping. One strategy I teach is the Give and Take Method. It allows students to completely avoid regrouping by getting one of the addends to the nearest ten. And whatever they give they have to take from the other addend.

The first step is to look in the ones place. Decide which digit is closer to a ten. In the example, it is the 8. What do you add to 8 to get it to the next tens number? 2. If you add 2 to the 8, then you have to take 2 from the 4. Now look at your new problem. You can solve it without regrouping. The method works really well with 2 digit numbers. I use it with kids who have trouble remembering to regroup or add in the ten that was regrouped. I also use it as a way to check problems that have been worked out using a different strategy. Plus, it gives kids extra practice with addition and allows some practice with mental math. After a while, many use this method to work problems out in their heads.

To introduce and review tens bonds, I show the following video. It is a favorite of my students! We watch it over and over again. It warms them up for this strategy and makes it so much easier. Check it out!

Awesome Addition

Wow! We have come along way from when we were growing up and learning how to add. When we were learning facts, we were just told to memorize. You didn't need to know why 4 + 3=7. All you needed to know was that it was 7! You just learned your facts.

Then when we moved to adding 2 and 3 digit numbers, all we knew was that we stacked up the numbers and remembered those facts. If there was a number bigger than 9 in a position, we "carried" the other number to the next place. No one explained why. No one told us that the 1 in 12 was really 10 ones that could be regrouped into 1 ten and then that is why it was moved to the tens place.

Now we not only teach kids this but we expect them to be able to convey it on state and national tests. We no longer want to know that 53 + 29 is 82. We want to know "how did you find that answer", or "what method did you use to solve your problem", or "how did you use mental math to help you".

In other words, students must be able to show the "how" and the "why" and not just the "what". The problem is that anyone who has been teaching more than five years never learned how to teaach like this. All we know is the "old school" algorithm.

Through out my thirteen years of teaching, I have been criticised for teaching students using unconventional methods, especially when it comes to addition, subtraction, multiplication, and division. Teachers have told me that kids have to know how to do it the traditional way! Why? Does it say it in a standard somewhere? Oh, it is in the book? Well, guess what...math books are becoming obsolete...so you might want to stop resting on your laurels and the way we have always done it and spread your wings a little bit.

I have created 2 different PowerPoint presentations on Addition With Regrouping and Addition Without Regrouping. These presentation include many different strategies for adding numbers, like drawing the problem out, expanded form, branching, a method called Give and Take, and even...Old School. You can see my

I have also created a packet entitled Autumn Addition that includes lessons on each method of addition without regrouping. It includes printables, rules, games, and more!

Finally, I have created a unit for teaching addition without regrouping entitled Game On:Addition with Regrouping. It includes lessons on each of the methods of branching, drawing, expanded form, give and take and old school. It has printables, activities, games, and songs to make learning about the "how" and "why" of addition with regrouping engaging and fun!