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.

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!

Pirate Place Value

 

Place Value is the most important concept students learn in any grade. Without the mastery of place value, students will struggle with every other concept. It is always the first concept I teach each year, and throughout the years I have acquired many strategies, methods, and activities to aid students in learning about place value.

I utilize many strategies from Singapore Math along with methods and techiniques that I have developed myself throughout the year. One of those methods is teaching students a unique song I developed one year, 9 years ago, after being in complete desperation with my students lack of mastery of the concept. So I created this song and taught kids to point at the places in numbers while singing which allowed them to identify the place where digits sat in a number. I still use this method in my classroom today!

 

 

In the last few years I created a PowerPoint presentation that took students through place value by focusing first on identifying the places where digits sit in a number and then using that knowledge to help determine the value of a digit because of where it sits in a number. You can check out my Learning Place Value PowerPoint Presentation at my TpT store.

 This year I changed the theme in my room to P.I.R.A.T.E.S. Prepared, Informed, Responsible, and Truly Engaged Students. So how better to begin math than with a Place Value unit with a Pirate theme.

 

The packet includes a place value chart, activities, student notes, practice sheets, and a matching game. I used it in my classroom this past week and it is an awesome resource. Coupled with my Learning Place Value PowerPoint presentation it ensured the success of all of the 75 students I teach in mastering the concept of place value. Check out Pirate Place Value at my TpT store.

 

 

Check out my favorite videos and other activities.

Take a Penny and Take Regrouping Out of Subtraction

"Take a Penny" is a 2 step strategy that allows students to subtracting across zeros without having to go through the complicated steps of regrouping. In fact with "Take a Penny", students can subtract across zeros without regrouping at ALL!

I learned the "Take a Penny" strategy last summer, and it has transformed the way my students subtract. I was at one of those workshops that you really don't want to be at but are required to go to, and boy was I amazed. The man that came to talk to us knew exactly how it felt to be in our shoes and did not waste one second of our time. 


He taught us all kinds of strategies to make learning about math not only easier but fun. He only talked to us for two days, but I swear I would have sat there for a week just to learn more ways to help children understand and comprehend math in ways that we have never heard of. 


I have used many of his strategies this past year, but the one that has had the most monumental change is the "Take a Penny" strategy. I actually feel like I have cheated my past classes by not teaching them this strategy. Not only is it faster, but because there are less steps students rarely make mistakes. 

And it works every time, no matter how many zeros you have. The reason it works is quite simple. When you are subtracting two numbers, you are finding the difference between them or how far apart they are. When you "Take a Penny", you are not changing the distance between the two numbers because you are doing the same thing to both numbers. You are just make it easier to find the distance between the numbers.

I created a 23 slide PowerPoint presentation to help students and teachers master this innovative strategy. This product introduces how to "take a penny" and then provides an abundance of practice in working subtraction problems that require regrouping across zeroes using this extremely innovative strategy. Check it out at my TpT store.  I promise that it will forever change the way you and your students subtract!

Esti...Who?

Estimation! I love teaching estimation. It is so much fun when students realize how much easier it is to estimate the answer to two numbers than to add, subtract, or multiply them together.  Over the years I have developed all kinds of tricks for teaching estimation.

My most effective trick in helping students remember how to round and estimate is the integration of some of my unique songs, chants, and raps. The first song I created help students remember when to round up or round down.

Next I created a song to help students remember the steps to estimation. Students frequently want to add, subtract, and multiply first and then round their answers. The problem is that it could result in a wrong answer on a test. They need to remember to round first and then add, subtract, or multiply. You can hear the tune of the song when you purchase my Estimating with Addition and Subtraction PowerPoint Presentation at my TpT store. (I honestly could not figure out how to add the sound here and I made up the tune.)

Finally, I (with the help of a class a few years ago) created a song to help students remember how to multiply after rounding by multiplying by multiples of 10's, 100's, and 1,000's.

You can hear the unique tune of Zero the Hero and get so fantabulous teaching tools, tips, and lessons when you purchase my awesome PowerPoint presentation Estimation with Multiplication from my TpT store.

Here are some of my favorite videos and songs from YouTube and United Streaming that I use when teaching my units on Estimation:

Math Confusion

      My idea for Math Confusion came from the fitness craze, Cross Fit. The goal with Cross Fit is to do many different activities in a short amount of time, switching it up so that your muscles never know what is coming next. You work out your arms, then do cardio, then do abs, then do legs...and repeat as many times as you are able to make it through the circuit. It makes your muscles stronger and burns more calories because the muscles are working harder when the exercises are not repetitive.

     So as we were coming back from a field trip one day, I thought about using the same idea for a math review. Math Confusion uses the same idea as Cross Fit. Students work on lots of different math concepts in a short amount of time. They rotate from station to station working on place value, fractions, multiplication, addition… They get 2 minutes at each station and must try to get as many questions right as possible. The Confusion continues until time is up. The goal is for students to make it through the circuit as many times as they can in the time allowed and to get as many cards right at each station as possible.

I created 11 stations 2 place value, 2 addition, 2 subtraction, 2 multiplication, 2 fraction, 1 number forms. I printed the circuit (instruction) card and activity cards on card stock and laminated them for safe keeping. I folded the circuit card in half and added Velcro to the inside to make a little pocket for the cards to fit in. All 11 stations fit nicely into a gallon Ziploc bag. 

I set the stations up so that none of the same skills are side by side, hence the CoNfUsIoN! Here is an example of how I set up the stations: 

Next I divide the students into groups of 2. Each group rotates from station to station spending 2 minutes at each station. There are 32 activity cards at each stations so it is rare for any group to finish a station before time is called. 

Here is how I explain the confusion to the students:

There are stations set up around the room. At each station, there is a set of cards face down. I am going to assign you to stations where you will sit and wait until I say go. When I say go, you are to turn over the first card and write, down the answer as quickly as you can. After you have written down the answer, turn the card upside down and check to see if you got it right. Remember, don’t cheat. If you cheat your muscles (brain) want get any bigger (smarter). If you get it right, put it off to the side. If you get it wrong, put it back into the deck of cards on the bottom. When I say stop, you must stop writing and count the cards you got right. Then place all the cards back in the deck face down, and return the station to how it was when you started. Do not rotate to the next station until I give the signal. When I give the signal, rotate to the next station. Sit down and don’t touch anything until I say to start. Remember, the goal is to get as many right at each station as you can and to get around to every station. Are there any questions?

This was one of the best reviews I have ever done in my classroom. It reviewed every concept in Numbers and Operation in less than a 30 minute period. Check it out at my TpT store! Download the free preview, or get it to use in your classroom. I was so pleased, and I am going to soon begin working on the Geometry, Measurement, and Algebra versions. 

Detecting Key Words

To go along with my Wonderful Problem Solving PowerPoint presentation, I have created a packet of Key Word goodies. This packet has everything you need to ensure that students completely understand how to use key words in problem solving. It includes an attractive Key Word poster.

It also has a blank graphic organizer for students to fill in and student and teach notes. It uses acrostics and other mnemonic devices to help students remember the key words for addition, subtraction, and multiplication problem solving. There are 4 different printables which focus on addition key words, subtraction key words, multiplication key words, and a mix of key words. These also include word problems for students to solve. 

The final part of the packet is a Key Word game, which asks partners to sort word problems into the operations of addition, subtraction, and multiplication. It includes 24 word problem cards, which partners are to read and decide together which operation the key word is asking them to perform. 

You can download a preview of the packet or purchase it at my TpT store.

Multiplying by Multiples of Tens

Third grade begins multiplication. Whereas in years past, students only had to learn their multiplication facts, they are now required to take those facts to a whole different level. Third grade students are required to, also, master how to problem solve with multiplication and to multiply 2 and 3 digit numbers by a 1 digit number.

One way to help make the transition from basic facts to "big" multiplication easier is by taking it step by step. One of those steps is learning how to multiply by multiples of tens, hundreds, and even thousands. Over the years I have developed, with the help of some students, an easy way to teach this concept.

The first step is to circle the basic fact. EX: 40 x 6=   The basic fact is 4 x 6. Once you know the basic fact-4 x 6=24, then just count the zeroes and add them to the basic fact-24 + 1 zero=240.

My students even helped me make up a song to help students remember the steps:

Zero is the Hero
He just won't stop!
All you do is count him,
At the top!
You add those zeroes,
To the basic fact,
And you will get the answer,
Just like THAT!

We use Zero the Hero to help us any time we are multiplying by multiples of tens and hundreds. It comes in really handy when multiplying with partial products and estimating.

I have a fabulous PowerPoint presentation that takes students through multiplying by multiples of tens and hundreds step by step. It even includes the song with me singing :) It provides examples, activities, and test practice.
Check it out at my TpT store.

Here are some of the videos and games that I embed into my presentations:

The Properties of Multiplication

One of the keys in problem solving is to understand the fundamental properties of operations. I swear, I would give anything for kids to understand that they already know that 9x3=27 because they know that 3x9=27. But,for some reason, it is a hard concept to grasp.

When I teach the Properties of Multiplication I focus just on the identity, commutative, and associative properties with my third graders, and I take one property at a time. To guide us through our learning I use a PowerPoint presentation which you can download at my TpT store. It is full of concrete examples, activities with manipulatives, real life examples, and much more.

In addition to the presentation and the activities included in it, I use several other tools in my classroom when teaching about the properties of multiplication. I have an interactive bulletin board where students can sort the properties using index cards. I also use several of the following Internet games:
Math Playground Basketball
AAA Math
CoolMath Games

At the end of the unit students create a book about the properties. To create this book the fold their papers in quarters and cut along one of the middle lines. Next they place the 2 halves together and fold them to create a book. Each page of the book is used to write and illustrate about the properties of multiplication.

Here are some of the videos that I embed into my presentation to make for a smoother lesson:

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 low and reading 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?

My lower performing students always do so much better in math than they do in reading. Why? Because if they can barely read, how can they comprehend a word problem. In fact, in 12 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!


I start off teaching addition key words. I help students remember the words that tell you to add by using the acronym BAITS.
Both
Altogether                                                  
In all
Total
Sum

I spend a day or two solving addition problems and then move on to subtraction. These are the ones that really seem to elude kids. After several years of gathering subtraction key words, I finally got a list of the most frequently used words that tell students to subtract.

I teach to them as 3-2-1:
3 M's, 2 L's, CDF
Many more
Much more
Much _______er (shorter, longer, fatter, hotter, taller...)
Left
Less
Change
Difference
Fewer

It is amazing how much key words help students understand how to problem solve. I teach addition and subtraction key words during the first nine weeks. Later, after my units on rounding, estimation, the meaning of multiplication, and several other units I do a quick review of addition and subtraction key words and start teaching the word that tell students to multiply.

There are many different words that clue students in to multiplying to find the answers to problems.  To help students remember, I teach them the acronym PEGS:
Per
Each
Groups.
Set


Armed with key words, students can solved almost any problem. 95% of key words have key words. For the ones that don't I teach them to draw problems out using unit bars. Unit bars are Singapore Math strategy that have revolutionized my students' problem solving.

I use a great PowerPoint presentation when teaching addition and subtraction problem solving. Check it out at my TpT store.

I also have a graphic organizer that I use with my students. You can download it here for free.

Here are some videos and songs I also use during class. I embed them into my PowerPoint presentation to make the whole lesson flow smoother.

Giving Meaning to Multiplication

Any time someone thinks about third grade, they think about two things: cursive writing and multiplication. Now, in my opinion, cursive writings is a thing of the past. I mean other than signing your name, when do you really use it. Every paper turned in has to be typed, and soon every child will carry around a laptop or iPad with which to take notes.

Multiplication on the other hand is a fundamental skill in life. It is one math concept that I can honestly say I use every day. There are 4 of us and each of us will eat 4 chicken nuggets, therefore I need to cook 16 chicken nuggets. I workout (Ha!) to 8 different songs that are about 4 minutes in length and I am able to know that I worked out for a little over 30 minutes! There are 170 calories in a single serving of ice cream and I had 2 servings, so I know that I really blew my diet with a whopping 340 calories just for dessert. See what I mean! We use it everyday.

But to be able to use it effectively we must truly understand the meaning of multiplication. This is a concept students must thoroughly understand in order to be successful in mathematics. I teach students that multiplication can mean different things in different situations but that all of these situations revolve around 4 central elements:

Multiplication Means...
1. Groups of- 3 x 4 means 3 groups of 4
2. Rows of-3 x 4 means 3 rows of 4
3. Repeated Addition-3 x 4 means 3 times I add 4
4. Counting by- 3 x 4 means 3 times I count by 4

The fundamental tool I use when teaching this unit is a 27 slide PowerPoint presentation that thoroughly explains the meaning of multiplication to students. It provides examples of the meaning of multiplication as it is seen in groups, arrays, and repeated addition. It even shows how the answer to a multiplication problem can be found by counting by certain numbers. It is a standards based lesson that could be used in one setting or spread apart over a few days taking each meaning one day at a time. It also provides notes for students and test prep practice. It has been tried and tested in my third grade classroom. You can download a preview of it or purchase it to use in your own classroom at my TpT store. 


I also use several different activities including grouping, grouping, and more grouping of manipulatives. We use colored tiles and Geoboards to create arrays. We also create graphic organizers and individual student books to illustrate one multiplication fact explained in 4 different ways.

In order to thoroughly engage students in learning about the meaning of multiplication, I incorporate many videos in songs. You can find some of my favorite below:

Sinister Subtraction

I don't know about y'all, but in all my years of teaching I have yet to find something as difficult for students as subtraction. It is the one concept students will have one day and lose the next. In fact, sometimes they will work one problem correctly and when they get to the next one they completely lose it.

Yet, subtraction is one of the most important concepts students must master. Without it, figuring out change, calculating elapsed time, dividing and countless other skills are out the window. The one way to make sure that the concept of subtraction sticks is by making sure students understand the "Why?" of subtraction.

I am frequently asked by parents, "What happened to borrowing? Why is it called regrouping now?" Well, when you borrow something like a shirt that shirt doesn't change. It is still a shirt and eventually (hopefully) you return it. When you are "borrowing" with subtraction, you are never giving anything back to the tens or hundreds place where you took it from, and you are changing that ten or hundred into something else like ones. In other words, regrouping what you took into something totally different.

I spent many hours creating a PowerPoint presentation demonstrating the different ways students can subtract to solve problems. Some of these methods incorporate strategies from Singapore Math. Other methods have been gleamed from countless workshops and conferences. And some I found while scouring the Internet for ways to help make subtraction easier for students.

The four methods I teach students are:
1. Drawing (With this method, students do not even need to know their facts. It works really well with students who have a hard time remembering their basic math facts.)
2. Old School (The way we learned it, but with a few twists)
3. Take a Penny (This method has revolutionized my methods of subtracting across zeroes as well as my students.)
4. Fair is Fair (This works really well with 2 and 3 digit numbers and keeps students from having to regroup.)

Check out my Subtraction With and Without Regrouping at my TpT store. In the presentation, which I use over a 9 day period, I insert several videos that help illustrate the different methods.

Become a Math Whiz with Whiz Quiz

Ask any elementary teacher what the number one thing students need help with in math and you will hear a resounding MATH FACTS. Knowing basic math facts is the most important skill students can have in math. It is also the one thing that can major inhibit a child's ability to score well in any math situation be it homework, a class assignment, weekly tests, or major state assessments.

Students begin working on math facts in kindergarten but they aren't expected to begin memorizing math facts in first grade. By fourth grade, students should have mastered all of the basic addition, subtraction, multiplication, and division facts. Basic facts are defined as 0-9, i.e 3+9= 18-9= 3x7=  24/6=.

Now there is much controversy over basic facts tests. Many teachers and administrators believe that students should not memorize facts by practice with flashcards and tests, but should constantly interact with numbers and fact families in order to best understand the putting together and pulling apart of numbers.

This is absolutely true! Students must understand why and how numbers equal certain things. Students will better understand mathematical concepts if they are able to understand what happens when numbers are put together or taken apart.

However there comes a time when children must memorize their basic facts. Otherwise they will spend time figure out answers to basic facts rather than solving more complicated problems. Not being able to quickly recall basic facts will, without a doubt, impede students when problem solving.

Therefore in my classroom I use the Whiz Quiz. Each day students have 1 minute of fact practice. This minute consist of a strip of paper with 20 problems related to one set of facts, i.e. 2's addition or 4's multiplication. If students mastered that set of facts, they move on to the next set of facts on the next day. If not then, they must practice that set of facts that night for homework. They can practice in whatever way you decide (but I prefer writing 5 times each).

Whiz Quiz is a fast and effective method of fact practice. It takes about 2 minutes to distribute (if you are organized), one minute and 5 seconds to administer, and a couple of minutes to grade. It is differentiated and allows students to move at their own pace through the basic math facts. For instance, I have many children who are almost finished with all of their division facts and I have some children who are still on addition.

I have a bulletin board set up with stars. Each one has a set of facts on it "2's", "3's", "4's"...Since my classroom has a sports theme, students each have a football player or cheerleader. Each time they pass a set of facts they move their person to the next number.

To make it easy to pass out my Whiz Quizzes, I have a file box which has all of the strips organized numerically starting with the addition facts and working back to division. I call out each fact and students come up when I call out the fact they are on. Ex: "2's multiplication....4's division".

Once they get their strip, they write their name on it and then turn it face down on their desk. When everyone has been "served", I tell them to Get Ready, Get Set (turn paper over) and Go! I give them 1 minute and 5 seconds. When time is up I say, "Everybody stop! Pencils drop!" They pass their tests down to me and I quickly grade them. I can do it quite fast, but I recommend making a key for yourself if you find it taking too long. To make it easy, I do not even grade ones that are missing more than 2. I just circle the ones they did not get to and have them write those for homework.

If you would like to use Whiz Quizzes for yourself, please check out Whiz Quiz at my TpT store.

Decimals: Understanding that Little Dot

After teaching my unit on fractions, I move on into teaching decimals. It just makes sense because they are both used to represent parts of a whole. Plus 5/10 and 0.5 mean the same thing so it helps kids to start decimals while they are still in the fraction frame of mind.

Check out my PowerPoint presentation at my TpT store.

I spend a week on decimals. The first day I introduce the concepts of decimals by relating them to fractions. I use a graphic organizer to help kids grasp the concept and several other activities, which you can check out at my TpT store.

The next day we watch the following video:

Then we review the graphic organizer with more examples. Next I allow them to show me what they know with a worksheet or matching game.

The rest of the week is spent on adding and subtracting fractions. Here is a video that my kids really love and it helps them understand the most important thing when adding or subtracting decimals.