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Integers

- Mathematical Systems
- 7th grade Pre-Algebra

Teacher Page

- Content Mathematical Systems Integers
- Grade Level 7th grade
- Creator Mary Anne Burton
- Objective Students will compute the sums,

differences, products or quotients using integers

in equation format. - Process MA-1 1.6, 1.8 2.2, 3.3

Addition of Integers

- You are probably familiar with a number line.

Traditionally, zero is placed in the center.

Positive numbers extend to the right of zero and

negative numbers extend to the left of zero. In

order to add positive and negative integers, we

will imagine that we are moving along a number

line. - Draw a number line on your paper.

Adding Integers on a Number Line

- If asked to add 8 and -2, we would start by

moving eight units to the right of zero. Then we

would move two units left from there because

negative numbers make us move to the left side of

the number line. Since our last position is six

units to the right of zero, the answer is 6.

Adding Integers on a Number Line

- If asked to add -13 and 4, we start by moving

thirteen units to the left of zero. Then we move

four units to the right. Since we land up nine

units to the left of zero, the answer is -9.

Adding Integers on a Number Line

- If asked to add -6 and -5, first move six units

to the left of zero. Then move five units further

left. Since we are a total of eleven units left

of zero, the answer is -11.

Rules for Addition

- Positive Positive Positive
- Positive Negative Depends
- Negative Positive Depends
- Negative Negative Negative

How to solve positive negative or negative

positive

- Absolute Value This is the number of spaces from

zero on the number line. - Example the absolute value of 10 is 10
- the absolute value of -10 is

10 - Once you find the absolute value of each number

you subtract and take the sign of the greater

number.

Subtraction with Integers

- The technique for changing subtraction problems

into addition problems is extremely mechanical.

There are two steps - Change the subtraction sign into an addition

sign. - Take the opposite of the number that immediately

follows the newly placed addition sign.

Subtraction with Integers

- Let's take a look at the problem 3 4 x
- According to step 1, we have to change the

subtraction sign to an addition sign. - According to step 2, we have to take the

opposite of 4, which is -4. - Therefore the problem becomes
- 3 (-4) x
- Using the rules for addition, the answer is -1.

Subtraction with Integers

- Here is another problem -2 8 x
- Switching the problem to an addition problem, it

becomes -2 (-8) x, which is equal to -10. - 6 - (-20) x is equal to 6 20, which is 26.
- -7 - (-1) x is the same as -7 1, which is -6.

Rules for Multiplication

- Positive x Positive Positive
- Positive x Negative Negative
- Negative x Positive Negative
- Negative x Negative Positive

Understanding Multiplication Rules

- The first rule is the easiest to remember because

we learned it so long ago. Working with positive

numbers under multiplication always yields

positive answers. However, the last three rules

are a bit more challenging to understand.

Multiplication with Integers

- The second and third rules can be explained

simultaneously. This is because numbers can be

multiplied in any order. -3 x 7 has the same

answer as 7 x -3, which is always true for all

integers. This example demonstrated the

commutative property.

Multiplication with Integers

- The fourth rules follows the pattern that when

two numbers of the same sign are multiplied the

answer is always positive. - -8 x 3 -24
- -8 x 2 -16
- -8 x 1 -8
- -8 x 0 0
- -8 x -1 8
- -8 x -2 16
- -8 x -3 24

Here are some examples

- 5 x -10 ?
- 0 x 8 ?
- -10 x 9 ?
- 6 x 6 ?
- 7 x -6 ?

Division with Integers

- The rules for division are exactly the same as

those for multiplication. If we were to take the

rules for multiplication and change the

multiplication signs to division signs, we would

have an accurate set of rules for division.

Rules for Division with Integers

- Positive Positive Positive
- Positive Negative Negative
- Negative Positive Negative
- Negative Negative Positive

Division with Integers

- -9 3 -320 (-4) -5
- -18 (-3) 6 Now you try the ones

below - 36 (6) ?
- 8 (-7) ?
- -63 (-9) ?
- 18 (-2) ?
- -70 (-10) ?

Now You Are the Teachers

- Group Presentation demonstrating your knowledge

of the rules of Integers. - 2-3 students per group
- Choose one of the following presentations
- Cartoon Creations
- Demonstration Dilemma
- Sing Us A Song
- Thriving Thespians

Cartoon Creations

- This project must contain a comic strip that

demonstrates your understanding of Integers. It

should consist of eight panels, minimum. Elements

such as artistic quality and mathematical

accuracy will be checked. Cartoons that contain

those items as well as a creative component will

receive more points.

Demonstration Dilemma

- This project is appropriate for students who

enjoy showing people how to do new things and/or

creating models. - It may also include a physical explanation on

how to solve problems with Integers using

mathematical tools. Students may also explain how

and where Integers are used in our everyday

world. This project, although open-ended, must

involve student acquired props and models. The

more involved the class gets, the more points

will be awarded. It must involve at least a five

minute presentation to the class.

Sing Us A Song

- This project is appropriate for those who enjoy

using their voice, It involves creating lyrics,

possibly an original work or a parody of

something already in existence (like the theme to

a television program), that demonstrates your

understanding of Integers. The song must be

presented to the teacher as a hardcopy and must

be at least a page in length. The actual song

will be sung in class. The singer may choose to

supplement this presentation with recorded music

or a played instrument, which may be a team

effort -- two people maximum. Part of this grade

will be based on the emotional delivery of the

piece.

Thriving Thespian

- A skit will be produced and it involves creating

a script, possibly an original work or a play on

something already in existence pun intended,

that demonstrates your understanding of Integers.

The script must be presented to the teacher as a

hardcopy and must be at least four pages in

length. The actual presentation must be at

least five to ten minutes. This project can

involve a team effort, up to three people

maximum. The team may choose to supplement this

presentation with props and music. Part of this

grade will be based on the emotional delivery of

the skit.

Scoring GuideProjects will be worth a maximum of

100 points!

- Factor Weak ----Strong
- Creativity

0 1 2 3 4 5 - Math 0 1 2 3

4 5 - Content 0 1 2 3 4 5
- Neatness

0 1 2 3 4 5 - Presentation 0 1 2 3 4

5 - Once the factors are determined they will be

added together and then multiplied by 5 to

generate the points for the project

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