**Needs**: 9 Apples Base Game and 9 Apples Booster Pack

**Age Level**: Grade 6

**Learning Objectives**: Understand that integers on a number line may be less than zero; demonstrate how negative integers are created by subtracting a larger number from a smaller number, or by multiplying or dividing a negative number with a positive number.

Experts in the field of education, as well as common core standards, state that students should be introduced to negative numbers in the sixth grade (Ryan). By this time, they should have a thorough understanding of the positive number line, how numbers change when added, subtracted, multiplied, or divided with each other. Once they comprehend this, they may be introduced to numbers less than zero, a more abstract concept. With standards in some states becoming stricter, this skill may soon be taught in fifth grade (Ryan).

Whether they realize it or not, most children do have experience with negative numbers. One excellent way to introduce your students to the idea of negative numbers is using the thermometer. Children living in colder climates will recognize the idea of negative temperatures, and based on experience they will understand that a temperature below zero is colder than zero, and thus lower. The thermometer on the right clearly shows temperatures above and below zero. |

Negative numbers may also be illustrated using images of large buildings. The floors of a building that are above ground are counted up as on the positive number line (the first floor is floor 1, the second floor is floor 2, etc). If the building has multiple levels below ground, these are denoted with negative numbers (the first floor below ground is -1, the second floor below ground is -2, etc.). The ground may be denoted as zero.

We can use the 9 Apples Base Game to illustrate how negative numbers are formed. One way they may be formed is by subtracting a larger number from a smaller number. (Many children may have been told this is not possible. You may need to clarify that this is not possible only if you wish the answer to the problem to be a positive number, which is what was meant in the previous situation.) For example, let’s take the example of a farmer’s market:

Mathematically, this story has the following formula: 5 - 7 = -2

You have five apples, but Mrs. Johnson wants to take away 7. This means that you are two apples short for Mrs. Johnson.

We may begin the illustration of this problem using a number line. Create a number line using the playing cards numbered -5 through 5, using the back of a card for zero (there are no zero cards in the deck). Alternatively, you may ask the student to draw the number line on paper.

*You are running the apple stand at the farmer’s market, and you have 5 apples left. Mrs. Johnson comes to the stand, and says she wants to buy seven apples. How many more apples would you need to give Mrs. Johnson all the apples she wants?*

Mathematically, this story has the following formula: 5 - 7 = -2

You have five apples, but Mrs. Johnson wants to take away 7. This means that you are two apples short for Mrs. Johnson.

We may begin the illustration of this problem using a number line. Create a number line using the playing cards numbered -5 through 5, using the back of a card for zero (there are no zero cards in the deck). Alternatively, you may ask the student to draw the number line on paper.

Remind the student that we have five apples, and seven should be taken away. Begin at the number five, and count out seven cards going down the number line. The student should land on -2, therefore we are two apples short.

For more advanced testing, we may present the student with an equation, and ask them to find the answer. For example, if we present the equation 6 - 9 = ?, we may ask the students to construct a number line to find the answer, or we may offer a few cards as possible solutions and ask them to choose the correct one.

We must also address the way negative numbers affect multiplication and division. One of the most difficult things to grasp is why multiplying a negative number and a positive number should equal a negative number. For an excellent explanation of why this principle makes sense, please watch this video from Khan Academy.

We may present students with equations using the cards, as well as presenting them with possible answers. For example, we may present the equations 3 x -2 = ? or -8 ÷ 4 = ?.

We may present students with equations using the cards, as well as presenting them with possible answers. For example, we may present the equations 3 x -2 = ? or -8 ÷ 4 = ?.

For additional practice, play the game of 9 Apples (with or without addition of the booster pack, depending on whether you wish to exercise multiplication and division skills) and require that all the numbers formed be negative! Instead of starting at +9, going to +8, and so forth, begin at -9, then -8, etc. Please see our tutorial on playing 9 Apples, or see the game rules for more information.

Citations:

Ryan, A.J. “When do kids learn negative numbers?” Global Post. http://everydaylife.globalpost.com/kids-learn-negative-numbers-3458.html

Citations:

Ryan, A.J. “When do kids learn negative numbers?” Global Post. http://everydaylife.globalpost.com/kids-learn-negative-numbers-3458.html