Mastering Multiplication Facts

There's no way around it - - - fourth graders must memorize multiplication facts. If they don't, mastering 4.NBT.B.5 (multiply four-digit numbers by one-digit numbers and two-digit numbers by two-digit numbers) just isn't going to happen.

Kids are overwhelmed by the multitude of facts they need to know, and they're defeated as they fail timed tests again and again. Teachers can help!

First, determine which facts each student knows. This video on Math Playground explains how to use grids like those below. The first grid gets parents on board; the second allows teachers to determine which facts a student knows and assign the next facts or fact groups a student must learn.

After determining which facts each child needs to learn, it's time for practice. Check out Quick Flash II from multiplication.com. Students can click on the set of facts they need to learn (e.g., their 3's) and set to work practicing them until they reach mastery. For hard copies of flash card sets, try this webpage.

As students master their facts, we move to the next step: fluency. Multitudes of games, also found on Multiplication.com, help students with their fluency, but in my opinion, nothing beats Fact Navigator. It is the most helpful multiplication tool I have found on the Internet EVER!

This week I took my students into the computer lab to try Fact Navigator. Each student set the app for testing multiplication facts to 9 x 9. Fact Navigator generated a 36-question test. As each student finished, Fact Navigator displayed the number correct and time it took the student to finish the test. Wow!! So helpful! If a student could correctly complete 100% of the problems in two minutes or less, I deemed him ready for long multiplication and called out: "DING! DING! DING! DING! DING! ____________ has passed his multiplication facts!" If students could not pass or their times were over three minutes, they moved back to Quick Flash II to work on specific sets of facts.

During that half hour in the computer lab, I saw my students' savvy with multiplication facts increase by leaps and bounds. Using Fact Navigator and Quick Flash II as a one-two punch really knocks out those dreaded times tables!

How can teachers help their students master multiplication facts? Here's the recipe that works for me:

1. Find out which facts a student does and does not know.
2. Focus practice on one small set of unknown facts at a time.
3. Once mastery is achieved, use games and timed tests to increase fluency.

P.S. If you're looking for a fun, whole-class facts game, try Math Facts Baseball!

Teaching About Dr. Martin Luther King, Jr.

On this fiftieth anniversary of Martin Luther King's "I Have a Dream Speech," let's honor the memory in our classrooms. Today I will show my students this video of Dr. King's speech and explore messages he sent to us through his quotes. (You may download either of these by simply clicking on the image.)

I Wish I Had More Science Activities Like This!

If you haven't checked out the E-Activities at AIMS Education Foundation, now is the time! These low-cost ($2.00) activities integrate math and science to make your teaching powerful. Here's just one example, Layers of the Earth, which my class recently completed. (The following presentation was created to display for Open House.)

Was it challenging? Yes. Did it take several class periods to complete? Of course. Was it worth the effort? You bet! I urge you to push your students to new heights with this activity and others from AIMS. You won't be sorry.

To the Left, To the Left, Everything's Ten Times in the Place to the Left

Here's a little Beyonce to get you thinking about 4.NBT.A.1:

To the left, to the left

Everything's ten times in the place to the left

This standard asks fourth graders to "recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right." Its fifth grade counterpart (5.NBT.A.1) takes it one step farther by asking students to understand that a digit represents "1/10 of what it represents in the place to its left."

With that said, how do we teach it? Last year I talked about it - - - over and over and over. My students could repeat it, they could write it, and they said they understood it, but did they really? This year I decided to employ constructivism. Each child received a set of manipulatives like this:

After cutting out the number strip, whole number pieces, and zero pieces, they were ready to explore. I gave them self-guided sheets like this:

Some students were able to work through the process on their own, but most needed help. Next year I'll change the process and provide an example of how to move the pieces before asking them to work independently. I do, however, want them to arrive at the answer to the final question on their own. My hope is that each child will think, "Aha! The value of a number is always ten times greater than the value of the digit to its right!" Then it's time for me to emphasize the concept - - - over and over and over.

You don't need anything fancy to do this activity in your own classroom. Student-created place value strips and number pieces will work just fine. Instead of a worksheet, you can work together, asking students to move their non-zero digit to make the number 10, 100, or 1000 times bigger. 

If you would like everything ready-made, this activity is available in my Teachers pay Teachers store as a part of Multi-Digit Whole Numbers - Differentiated, which includes student-guided activities (like the one shared today), worksheets, a review, pre- and post-assessments, related activities, and an "I Have, Who Has?" game for 4.NBT.A.1, 4.NBT.A.2, and 4.NBT.A.3.

Let's look at a few more resources. Howard County Public School System has gathered lesson plans, activities, and more on this site. Scroll down to Number of the Day Organizers to grab an awesome free resource. And check out their place value problems (which directly address 4.NBT.A.1). 

Now that we've covered reading, writing, comparing, rounding, and conceptualizing large numbers, we need a grand finale. Wouldn't it be fun to ask students to continue the lyrics to Beyonce's song, "IrrePLACEable"? It might start out like this:

To the left

To the left

Mmmm to the left, to the left

Everything's ten times in the place to the left

In the ones place, that's single stuff

Yes, if you move it, baby, it's ten times enough...

Rounding Multi-Digit Whole Numbers

What exactly is rounding, and how can we help students understand it? When I was in fourth grade, my teacher told me to look at the neighbor to the right to round. If that number was 0-4, I should round down; if it was 5-9, I should round up.

Fast forward several decades, and I became the fourth grade teacher. The traditional strategy just didn't seem to help my students "get" rounding. I wanted my class to understand that rounding involved finding the closest multiple of 10, 100, 1000, etc.

Let's eavesdrop on this week's class discussion:

• Me: What is rounding?
• Student: It's sort of like estimating.
• Me: Why do we round?
• Students look around and act unsure.
• Me: Let's say I go to the store with $50 in my pocket. I want to purchase three items. One item costs $19, another is $11, and the third is $13. I want to make sure I have enough money when I get to the counter to pay, so I round each amount then add to see if it's more than $50. I use rounding to figure out about how much each item costs (in this case to the nearest $10) then I add them together. That final step, adding rounded numbers, is estimation.

The conversation continued, and we discussed situations when we would round to the nearest 100; 1,000, 10,000, and even 100,000. My students were clearly comfortable with rounding to the nearest 10 and 100; they'd learned how to do that in third grade, but 100,000? Wow, they just weren't sure they could do that.

This year I've decided to have students take notes for each concept. Here's our page for 4.NBT.A.3:

When rounding, the first thing I want my students to do is ask themselves, "What is the closest 10 (or 100 or 1000, etc.)?" To me, this is the highest level of conceptualization. If that doesn't work, they draw a number line, as shown. This also allows students to conceptualize the process (with the aid of a diagram). Finally, if neither of these two strategies are working, they may use the next-door neighbor. Finding the next-door neighbor has little or no conceptual value, but for those who struggle, it will work until they gain a better understanding of the number system.

Next I modeled rounding the number to the nearest 100; 1,000; 10,000; and 100,000. After demonstrating with a few more numbers, they worked some problems with me, and finally they set off on their own.

This year we'll use rounding a lot! As students review longer addition and subtraction problems then learn long multiplication and division, I will require them to estimate. In fourth grade, students will estimate on paper, but in subsequent grades they should be able to estimate mentally. This arms them with a powerful tool! Estimation (which is addressed in 4.OA.A.3) allows students to know if the answer to a complex problem is reasonable (or if a red flag is being waved), and it allows them to go to the store with $50 and figure out if they have enough money to buy a series of objects. 

Practicing Multi-Digit Numbers in Standard Form, Words, and Expanded Form

The time has come to practice writing multi-digit numbers in standard form, words, and expanded form (4.NBT.A.2). Why not have some fun? We began today's lesson with a game and an activity involving students' birthdays.

"I Have, Who Has?" - This game switched between place value, words, expanded form, and numerals. Students received number recording sheets (shown below) and were required to write each number presented, keeping everyone on task.

How does "I Have, Who Has?" work? Each student receives a card like those shown below. The first person says, "I have..." and the person with the answer has to respond, "I have..." then pose the next question. 

Click here to try it in your classroom.

The second activity involved students' personal numbers. They entered their dates of birth then translated each to standard form, words, and expanded form. These fold-overs are perfect for hanging on the classroom wall!

Finally, each student demonstrated their competency in transferring numbers between standard form, words, and expanded form on tables like this:

Yes, students need to practice writing numbers in various forms. But why not make it fun?

Introducing Multi-Digit Whole Numbers in Standard Form, Words, and Expanded Form

Fourth graders usually have some background with writing numbers in standard form, words, and expanded form. To continue toward mastery of 4.NBT.A.2, I like to use dry-erase boards like this one from Really Good Stuff:

When we used these boards today, my students told me they'd used them in second and third grades too. Numbers they had experienced looked similar to the one shown above. Today we moved into the millions (and on their request, the billions!) Later this year we'll use these same boards for decimals.

After a review of how to write numbers in words and expanded form, I had students build numbers as I called out the value of each place. Here's an example:

• nine hundreds
• three ten thousands
• five ones
• six tens

This left some places blank, and students were again required to hold the place value with a zero. After this, they wrote the number in standard form, words, and expanded form. As students finished each step, they flashed their boards at me for approval. Great formative assessment. What problem areas did we experience?

1. A few children had difficulty moving the number straight down to the standard form lines. This showed me that these students were not grasping the concept of place value.
2. Many children forgot to put commas after the period names or hyphens between the tens and ones places. It's typical, and I filed this knowledge away to review over and over this year.
3. Some students kept the tens and ones places (in one or more periods) together when writing expanded form. I had to remind them that EVERY non-zero digit is translated to a separate number when writing expanded form.

After this activity, each child practiced with traditional worksheets. Although this lesson is procedural, it's also conceptual. Don't underestimate its importance! When students understand and can manipulate place value for multi-digit numbers, they possess a sturdy foundation for the study of mathematics.