Math Is Like a Video Game

Math is like a video game.

In a video game, you learn skills and strategies to move you to the next level, right? It's the same in math.

At the intermediate level (grades 3-5), students learn skills such as adding, subtracting, multiplying and dividing. They lay foundations for algebra and geometry too. Knowing these things allows a student to move along in the video game we call math.

How can a child become an expert at this game? That's more difficult. He or she must really understand what the game is about, which translates to deep understanding of the place value system and how it's manipulated for each operation. Learning strategies, such as properties of addition and multiplication and decomposition of numbers, takes each student one notch closer to becoming a math whiz.

Even with these phenomenal skills, a student cannot master the game. He or she needs to learn (and have permission) to look at problems from different angles, solve them in a variety of ways, and apply skills and strategies in new and different scenarios. With this, the player has mastered the game.

Math is like a video game. Let's help our students conquer it.

Vocabulary in Informational Text

Every morning, before I crawl out of bed, I consider challenges that await me in my classroom. Today, for some reason, vocabulary was on my mind. How can I encourage my students to pay attention to new vocabulary in informational text?

Kids must learn vocabulary associated with so many subjects each day. For example, in math, we're using words like factor, product, dividend, divisor, and quotient. Today's geology lesson requires them to discriminate between humus, silt, clay, and sand. Social studies vocabulary of the day includes marsh, moraine, till, and cavern. If you're a teacher, you'll understand that's just the tip of the iceberg!

I want my students to be detectives as they read informational text, looking for clues to vocabulary meaning in visual aids, definitions, appositional phrases, context clues, word parts, and glossaries. My newest tool can be found below. I'll be trying it out in my classroom today. Feel free to snatch it so your students, too, can become great deTEXTives!

P.S. This addresses Standard 4 for Reading: Informational Text in the Common Core State Standards.

Latitude's Like a Tomato, Longitude's Like an Orange

Latitude, Flatitude; Longitude, Long-itude. There are many different tricks and sayings for teaching this tricky grid-work to children, but I have my own. I think latitude is just like a tomato, while longitude's like an orange.

I reinforce this using my arm while saying, "Latitude tells how far north or south of the equator, and longitude tells how far west or east of the Prime Meridian."

If you're new to teaching this set of concepts (or just need a refresher course), head to Latitude 34 North for concise yet thorough discussions of latitude and longitude, as well as important named circles of latitude (equator, Tropic of Cancer, Tropic of Capricorn, Arctic Circle, and Antarctic Circle), the Prime Meridian and International Date Line. In my experience, it's important to bone up on specific information before teaching so you can answer questions like this one that popped up in my class: "Is it named Topic of Cancer because you're more likely to get cancer when you cross it?" (Great thinking, but no.)

I like linking the reason for seasons to this discussion. My decrepit globe comes out of the closet, and the path around my room becomes the path of Earth around the sun each year. The lucky student in the center of the room becomes the sun. This 30-second You Tube video is a shortened version of the movement and discussion that then transpire in my classroom. We review this three times during our school year: at autumnal equinox, winter solstice, and vernal equinox. Repetition helps students to remember and conceptualize how Earth's tilted axis causes seasons.

Now's the perfect time to explore patterns of sunshine at daylightmap.com. How cool! My class likes to display this all day long. It's interesting and thought-provoking. You can manipulate the calendar to show the equinoxes, solstices, and everything in between.

Teaching latitude and longitude can't be rushed. The preliminary conceptual background discussed above generally takes one full period or longer. Then we move on to locating specific places using latitude and longitude. Each student needs only one resource: an atlas, which can usually be found in his/her social studies book. 

The pointer finger on the right hand scans up and down along the labels for latitude, and the left pointer scans across on the labels for longitude. The teacher calls out the latitude and longitude; students locate them with their pointers and slide along the lines until their fingers come together.

My students respond best when starting with a map of our state. Since we're in the western hemisphere, I have to explain how and why the lines of longitude increase from right to left (instead of from left to right as we normally read a page). We find the latitude and longitude of our city then discuss the range of latitudes and longitudes for our state. Finally, we locate the closest crosshairs for our capital city. 

After exploring our state, we move to a map of our country, the USA. I call out latitudes and longitudes, wait until everyone's hand is in the air, and ask them to shout out the name of the state.

Finally, we work on latitude and longitude in all four quadrants using the world map. In years when I tried teaching with a world map first, my students were confused. This year, however, after using state and country maps first, they were ready to take on the world!

To ensure mastery, several days of full-class practice are necessary. Then students can hone their skills using games like these:

• Latitude and Longitude Map Match Game, KidsGeo.com
• Treasure Hunt, ABCYa.com
• Latitude and Longitude, Purpose Games

This site from the Oswego City School District also provides a great student-centered review of latitude and longitude.

My social studies book provides one page of text, one map, and one worksheet for teaching latitude and longitude. That's just not enough! Do you have a clever way to teach this skill? If so, please share!

Subtracting Across Zeros

The words "subtracting across zeros" can make a third or fourth grade teacher's hair stand on end. All of that crossing out and mess of nines and tens. How can we teach this skill (and the underlying concept) so that our students will truly understand?

Yesterday I tried something new. Each of my students was given four sheets of Kovich Class Cash (thousands, hundreds, tens, and ones), each with ten bills.

As they cut out their funny money, excitement grew. Comments like, "The bigger the bill, the more Mrs. Koviches you get," and "Can we keep it?" and "I'm rich!" could be heard.

Each child organized his/her money on the top of the desk to represent a place value chart.

Then the subtracting began. I explained that the money at the top of the desk was the bank. In the first problem, we began with the number 1000. Each child put a $1000 bill in the middle of his or her desk.

The problem was revealed on the screen in front of the class.

We discussed the fact that taking two hundred dollar bills, seven ten dollar bills, and six one dollar bills away from a single one thousand dollar bill would be impossible. Instead, we would need to go to the bank.

Each child exchanged one thousand dollar bill for ten hundred dollar bills. On the screen I showed how this appears in the common algorithm.

We established that we still had $1000. Ten hundreds equals one thousand. But could we take two hundreds, seven tens, and six ones away from ten hundreds? No. We had to go back to the bank.

The students took one hundred to the bank and exchanged it for ten tens. Then we looked at our algorithm again. 

Now we had nine hundreds and ten tens. Did this still equal 1000? Yes! Could we subtract two hundreds, seven tens, and six ones? No. Back to the bank.

One ten was exchanged for ten ones. Now we had nine hundreds, nine tens, and ten ones. Did this still equal 1000? Yes! And here's how our algorithm looked:

Could we subtract two hundreds, seven tens, and six ones? Yes! Yay! The students busily arranged their bills on their desks, taking 276 away from 1000.

When the flurry of activity was over, seven hundreds, two tens, and four ones were left. We again looked at the algorithm. Yep! 724. That's the same as seven hundreds, two tens, and four ones.

After this, we worked a half a dozen or so more problems, moving faster and faster. Eventually we moved to working the problems without the funny money. When the time came for each student to subtract using paper and pencil on their own, a few used their funny money to get started.

P.S. Due to popular demand, I have created a PowerPoint presentation and class cash templates that you can use in your classroom. Subtracting Across Zeros with Class Cash is now available in my Teachers pay Teachers store.

Estimating Subtraction Problems

Today I will teach my fourth grade students how to estimate when subtracting. Some of them already understand how to estimate, but most have no clue (as their pretests have shown). And most of those who know to round then compute clearly don't understand the purpose of estimation.

Here's what I've been getting:

Now what's wrong with this picture? (After all, it's the way our textbook teaches it. Shhh! Don't tell, but haven't opened that text yet this year.) The trouble is that the problem is no easier to solve, and that, my friends, is why we estimate. Estimation should make the problem easy enough to do in your head, which will allow you to check if an actual answer is correct or make some other decision in everyday life.

There's no best way to estimate, but some strategies are better than others.  Here are the steps I will take with my students:

1. When estimating with whole numbers, always round each number to the biggest digit possible then compute. This way we can estimate using mental math. (This is today's lesson, which we will practice, practice, practice.)
2. When estimating numbers that include decimals, do the same.
3. Think! If a problem is easy to compute in your head, why estimate? (For example, the answer to 2060 - 1060 is clearly 1000.) If both numbers round to the same number, go to a lower digit. (For example, if we round the problem 7132 - 6854 to the highest digit, we would come up with 7000 - 7000, and our estimate would be zero. That clearly does not make sense, so in this case, we could round to 7100 - 6900 and see that the answer will be around 200.)
4. Continue building strategies, such as using compatible numbers. I found this set of activities online to use with students who already have a decent grasp of estimating.

Good mathematicians can and do estimate every day. It's a skill worth teaching and honing throughout the year.

Assessing Addition & Subtracting for Middle Grade Students

Now that my class has wrapped up numeration, it's time to move on to computation. The first order of business is adding and subtracting. Since I teach fourth grade, our guiding standard is 4.NBT.B.4: "Fluently add and subtract multi-digit whole numbers using the standard algorithm."

Neither adding nor subtracting whole numbers appears in the fifth grade standards, so you know what they say: The buck stops here. I am responsible for mastery of addition and subtraction of any number with and without regrouping. 

Even though I feel that my students should have a good grasp of this concept already, I must pretest to make sure. (And fifth grade teachers should probably do this as well.)

This simple test would show if my students could (1) add without regrouping, (2) add with regrouping, (3) subtract without regrouping, (4) subtract with regrouping, (5) subtract across zeros, and (6) appropriately use estimation as a tool for checking accuracy.

My results? All of my students showed mastery of addition (with and without regrouping) and subtraction without regrouping. About half of the class needs remediation on subtraction with regrouping and/or across zeros. More than three-fourths could not estimate (or estimated in an inappropriate manner). The most common error students made was rounding the answer to their problems in an attempt to estimate.

I've decided to place them in two groups. Those who mastered addition and subtraction (even if they're not too hot on estimation yet) and those who mastered everything will have a quick lesson on the purpose of estimation then move on to adding, subtracting, and estimating decimals. (We reviewed tenths and hundredths last week, so it will segue well.) Students who need help with subtracting with regrouping will get it - - - as well as a lot of practice with estimation.

If you think I'm a bit obsessed with estimation, you are correct. Even though it isn't in the standard, I believe a good mathematician uses estimation to judge an answer's reasonableness all the time. While my fourth graders will be writing their estimates, the ultimate goal is rapid mental calculation. Therefore, except in rare cases, students should round each number to the largest place value when estimating.

Those who peek in my classroom this week will see kids subtracting with regrouping, asking themselves, "Is my answer reasonable?" and estimating like crazy!

P.S. If you're creating computation worksheets for your students, try the font called Courier. All letters, numbers, and spaces are equally justified; therefore, everything stays lined up from row to row.

Look! I Can Work with Large Numbers!

My class wrapped up their study of multi-digit numbers this week. To show off their skills, each student completed this page and hung it on the wall. Now anyone who enters our room knows that all students have mastered 4.NBT.A.2 and 4.NBT.A.3. Yay!

You can use it too. Simply click on the image to download the sheet.