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September 19, 2012

A Positive Approach to Teaching Negative Numbers

How many of us have heard (or said), “It’s not seven minus ten — you can’t subtract the bigger number from the smaller number”? Mea culpa: for a while I was also guilty of that sort of mathematical hogwash. While the “bigger number on top” blanket rule for subtraction may make life easier for a bit, I now realize that that sort of thinking is a roadblock to students because it simplifies their understanding of addition, subtraction, and how numbers work. Negative numbers pop up naturally: just look at my checkbook. So, rather than ignoring negative numbers, here are five fun activities for introducing integers.

Why Bother With Integers?

Heading south on the number line may not be in your curriculum. Negative numbers often aren’t introduced until much later in the mathematical sequence. However, some children are clearly ready to tackle integers much earlier, and shying away from negative numbers will hamper their mathematical development. As with a whole-language approach to literacy instruction — in which students are exposed to a wide range of concepts in context, prior to formal instruction on a specific concept — immerse students in contextual explorations of numbers at work. That means letting negative numbers out of the closet.

With the strong emphasis on conceptual understanding in the Common Core Learning Standards for Mathematics, it feels right to allow my students to playfully experience both sides of the number line. Instead of telling students to always subtract the smaller number from the larger number, I’d rather ask my students if their answer makes sense. This asserts that my students are the bosses of the numbers, rather than subject to an arbitrary set of rules.

Integers in Their Natural Habitat

Teaching about negative numbers only makes sense in the appropriate contexts. Throughout the year, we keep a running list of real-world instances in which negative numbers make sense.

Brrr! Negative Numbers Are Freezing

Our first discussions of negative numbers happen in the context of temperature. This is where children will most likely encounter negative numbers in their daily life.

Hark, the Class Meteorologist Speaks!

As part of our daily math routines in my class, we review the weather report every day. Each week, a student is assigned the job of class meteorologist. Every morning, the meteorologist looks up the high and low forecasted temperatures and the percent chance of precipitation on a weather website. He or she records the data on the board.

I ask the students to mentally calculate the difference between the high and low temperatures, and we discuss several mental math strategies. Come winter, when the temperatures dip below freezing, this is a natural way to talk about negative values. (Are you so lucky as to live somewhere that is warm year round? You can record temperatures of other cities that your students may find interesting, in addition to your local weather.)

Temperature Bingo

If your students are excited when negative numbers show up in the daily weather forecast, you can extend the learning with this version of bingo. To prepare for the game, cut apart the bingo clue cards and copy the three sets of bingo cards for your students.

To play, the teacher (or a student leader) calls out the clues. Students search for the temperature on their bingo boards. If they find the temperature, they color in the thermometer to show the correct value.

Integer Tug-of-War

Exploring the number line becomes a game when you call it “tug-of-war.” It’s even more fun when you play with a life-sized number line. I simply use a long piece of masking tape on the floor in the hallway. The students mark off the numbers at appropriate intervals, using the floor tiles as a guide for spacing the numbers.

The students love tossing beanbags onto the giant number line. After the students are comfortable locating integers on the number line, I divide the class into two teams, the Powerful Positives and the Negative Ninjas. As I call out positive and negative values using a set of dice, one with numbers 1–6 and one marked with positive and negative signs, the students move their team’s beanbag.

When the classroom isn't big enough, I take my math lessons out into the hallway. Here, a student places a beanbag on our integer number line.

After we play several rounds of tug-of-war as a class, the students play the game in pairs using smaller game boards. To make positive and negative dice, I use a permanent marker on blank cubes.

For another variation with a sports theme, you can use Scholastic’s integer football game.

Integer Kakooma

Math educator extraordinaire Greg Tang has teamed up with Scholastic to bring his clever math games to life online. A fun puzzle-game, Kakooma helps students work towards automaticity with math facts. To solve one puzzle, students have to do dozens of calculations in their heads. Over time, students begin to recognize patterns automatically, and they are “rewarded” with more questions to solve.

When my students were comfortable with regular addition Kakooma and wanted a bit more of a challenge, they were excited to give Negatives Kakooma a try. At the moment, you can sign up for a free one-month trial of the Greg Tang's World of Math website (until October 15, 2012). In addition to the games on the website, you can also download printable workbooks of Kakooma and other games, such as this sample of a Kakooma Negatives puzzle.

Game Time: First Connect Three

I discovered this game from the amazing NRICH Project, a math education initiative by the University of Cambridge. Students roll two dice and can add or subtract the dice in any order to obtain a sum. They cover the sum on the game board, aiming to get three in a row.

We first played the online version of the game on my SMART Board so my students could learn the game. Then I handed out paper game boards and game kits: Ziploc bags with two dice, and about a dozen counters in each of two colors. Not only does this game reinforce addition and subtraction going into the negatives, but it also builds strategic thinking as students notice that certain numbers are easier to obtain than others.

Games are a great way for students to engage in mathematical thinking!

For more integer activities, check out Scholastic's StudyJams! about integers and an integer lesson and game based on the idea of traveling up and down a building on an elevator from NCTM's Illuminations. You might also download and print a mini math poster about comparing integers from DynaMath.

How many of us have heard (or said), “It’s not seven minus ten — you can’t subtract the bigger number from the smaller number”? Mea culpa: for a while I was also guilty of that sort of mathematical hogwash. While the “bigger number on top” blanket rule for subtraction may make life easier for a bit, I now realize that that sort of thinking is a roadblock to students because it simplifies their understanding of addition, subtraction, and how numbers work. Negative numbers pop up naturally: just look at my checkbook. So, rather than ignoring negative numbers, here are five fun activities for introducing integers.

Why Bother With Integers?

Heading south on the number line may not be in your curriculum. Negative numbers often aren’t introduced until much later in the mathematical sequence. However, some children are clearly ready to tackle integers much earlier, and shying away from negative numbers will hamper their mathematical development. As with a whole-language approach to literacy instruction — in which students are exposed to a wide range of concepts in context, prior to formal instruction on a specific concept — immerse students in contextual explorations of numbers at work. That means letting negative numbers out of the closet.

With the strong emphasis on conceptual understanding in the Common Core Learning Standards for Mathematics, it feels right to allow my students to playfully experience both sides of the number line. Instead of telling students to always subtract the smaller number from the larger number, I’d rather ask my students if their answer makes sense. This asserts that my students are the bosses of the numbers, rather than subject to an arbitrary set of rules.

Integers in Their Natural Habitat

Teaching about negative numbers only makes sense in the appropriate contexts. Throughout the year, we keep a running list of real-world instances in which negative numbers make sense.

Brrr! Negative Numbers Are Freezing

Our first discussions of negative numbers happen in the context of temperature. This is where children will most likely encounter negative numbers in their daily life.

Hark, the Class Meteorologist Speaks!

As part of our daily math routines in my class, we review the weather report every day. Each week, a student is assigned the job of class meteorologist. Every morning, the meteorologist looks up the high and low forecasted temperatures and the percent chance of precipitation on a weather website. He or she records the data on the board.

I ask the students to mentally calculate the difference between the high and low temperatures, and we discuss several mental math strategies. Come winter, when the temperatures dip below freezing, this is a natural way to talk about negative values. (Are you so lucky as to live somewhere that is warm year round? You can record temperatures of other cities that your students may find interesting, in addition to your local weather.)

Temperature Bingo

If your students are excited when negative numbers show up in the daily weather forecast, you can extend the learning with this version of bingo. To prepare for the game, cut apart the bingo clue cards and copy the three sets of bingo cards for your students.

To play, the teacher (or a student leader) calls out the clues. Students search for the temperature on their bingo boards. If they find the temperature, they color in the thermometer to show the correct value.

Integer Tug-of-War

Exploring the number line becomes a game when you call it “tug-of-war.” It’s even more fun when you play with a life-sized number line. I simply use a long piece of masking tape on the floor in the hallway. The students mark off the numbers at appropriate intervals, using the floor tiles as a guide for spacing the numbers.

The students love tossing beanbags onto the giant number line. After the students are comfortable locating integers on the number line, I divide the class into two teams, the Powerful Positives and the Negative Ninjas. As I call out positive and negative values using a set of dice, one with numbers 1–6 and one marked with positive and negative signs, the students move their team’s beanbag.

When the classroom isn't big enough, I take my math lessons out into the hallway. Here, a student places a beanbag on our integer number line.

After we play several rounds of tug-of-war as a class, the students play the game in pairs using smaller game boards. To make positive and negative dice, I use a permanent marker on blank cubes.

For another variation with a sports theme, you can use Scholastic’s integer football game.

Integer Kakooma

Math educator extraordinaire Greg Tang has teamed up with Scholastic to bring his clever math games to life online. A fun puzzle-game, Kakooma helps students work towards automaticity with math facts. To solve one puzzle, students have to do dozens of calculations in their heads. Over time, students begin to recognize patterns automatically, and they are “rewarded” with more questions to solve.

When my students were comfortable with regular addition Kakooma and wanted a bit more of a challenge, they were excited to give Negatives Kakooma a try. At the moment, you can sign up for a free one-month trial of the Greg Tang's World of Math website (until October 15, 2012). In addition to the games on the website, you can also download printable workbooks of Kakooma and other games, such as this sample of a Kakooma Negatives puzzle.

Game Time: First Connect Three

I discovered this game from the amazing NRICH Project, a math education initiative by the University of Cambridge. Students roll two dice and can add or subtract the dice in any order to obtain a sum. They cover the sum on the game board, aiming to get three in a row.

We first played the online version of the game on my SMART Board so my students could learn the game. Then I handed out paper game boards and game kits: Ziploc bags with two dice, and about a dozen counters in each of two colors. Not only does this game reinforce addition and subtraction going into the negatives, but it also builds strategic thinking as students notice that certain numbers are easier to obtain than others.

Games are a great way for students to engage in mathematical thinking!

For more integer activities, check out Scholastic's StudyJams! about integers and an integer lesson and game based on the idea of traveling up and down a building on an elevator from NCTM's Illuminations. You might also download and print a mini math poster about comparing integers from DynaMath.

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