WARDEN AVE P.S.

Adding & Subtracting Integers

Number Sense & Numeration Unit #1

Grade 7 Math

2014-2015 School Year

This mini-unit will run from September 15-26 and must be handed in on Friday Sept. 26th by 3:45 pm

PART A: INTEGERS

What is an Integer?

An integer is a number that has no fractional part, and no digits after the decimal point. We sometimes call them WHOLE NUMBERS. An integer can be positive, negative or zero. (Compare this to real numbers than can have digits after the point and can have fractional parts)

Example integers: +12 , +34 , -4 , 0

The following are real numbers and are not integers:

1.23 (cannot have decimal places) 12½ (cannot have a fractional part)

Helpful ways to remember how Integers work:

The Number Line

Negative Numbers (-) Positive Numbers (+)

(The line continues left and right forever.)

Numbers on the left are smaller than numbers on the right.

Examples:

5 is smaller than 8 −1 is smaller than +1 −8 is smaller than −5

Now its your turn to place numbers along a number line. Remember to use the guide above to help you if you are stuck

or confused.

SKILL BUILDER

Please place the following numbers on the number line in their correct place.

-6 +12 -3 -12 +8 +7 0

END OF LESSON

Adding and Subtracting Integers

Numbers Can be Positive or Negative:

Negative Numbers (−) Positive Numbers (+)

"−" is the negative sign. "+" is the positive sign

No Sign Means Positive

If a number has no sign it usually means that it is a positive number.

Example: 5 is really +5

Adding Positive Numbers

Adding positive numbers is just simple addition.

Example: 2 + 3 = 5 is really saying

"Positive 2 plus Positive 3 equals Positive 5" OR You could write it as (+2) + (+3) = (+5)

Subtracting Positive Numbers

Subtracting positive numbers is just simple subtraction.

Example: 6 − 3 = 3 is really saying

"Positive 6 minus Positive 3 equals Positive 3" OR You could write it as (+6) − (+3) = (+3)

Now for something a little different…

Subtracting a Negative is the same as Adding

Example: What is 6 − (−3) ?

6−(−3) = 6 + 3 = 9

Example: What is 14 − (−4) ?

14−(−4) = 14 + 4 = 18

RULE OF THUMB

If the operational sign (what it’s asking you to do) matches the number’s integer sign, then you are ADDING.

And Positive and Negative Together ...

Subtracting a Positive

or

Adding a Negative

is

Subtraction

Example: What is 6 − (+3) ?

6−(+3) = 6 − 3 = 3

Example: What is 5 + (−7) ?

5+(−7) = 5 − 7 = −2

RULE OF THUMB

If the operational sign (what it’s asking you to do) does not match the number’s integer sign, then you are

SUBTRACTING.

QUICK REFERENCE

OPERATION RESULT

+ + +

+ − -

− + - − − +

Now you get to try out your new skills with some practice sheets. Ready to do it? Go!!!

Name: Date:

Add and Subtract Integers

3. Fill, and observe the patterns.

4. Match the equations with the situations, and complete the missing parts.

1. Temperature is rising so we add a positive number. Addition sentence:

a. Temperature was - 3°C. Then it rose 4 degrees. Now it is ______. −3 + 4 = 1

b. Temperature was -5°C. Then it rose 2 degrees. Now it is ______.

c. Temperature was -9°C. Then it rose 4 degrees. Now it is ______.

d. Temperature was -1°C. Then it rose 7 degrees. Now it is ______.

e. Temperature was -2°C. Then it rose 5 degrees. Now it is ______.

f. Temperature was -10°C. Then it rose 3 degrees. Now it is ______.

2. Temperature is dropping so we subtract a positive number. Subtraction sentence:

a. Temperature was 3°C. Then it dropped 4 degrees. Now it is ______.

b. Temperature was 7°C. Then it dropped 10 degrees. Now it is ______.

c. Temperature was 5°C. Then it dropped 8 degrees. Now it is ______.

d. Temperature was -1°C. Then it dropped 5 degrees. Now it is ______.

e. Temperature was -7°C. Then it dropped 7 degrees. Now it is ______.

f. Temperature was -10°C. Then it dropped 2 degrees. Now it is ______.

a.5 −4 =

5 −5 =

5 −6 =

5 −7 =

5 −8 =

b.−4 −0 =−4 −1 =−4 −2 =−4 −3 =−4 −4 =

c.−3 + 0 =−3 + 1 =−3 + 2 =−3 + 3 =−3 + 4 =

d.−2 + 2 =−2 + 3 =−2 + 4 =−2 + 5 =−2 + 6 =

a. A diver was the depth of 20 ft. Then he rose 15 ft. Now he is at _________ ft.

b. John had $15. He had to pay his dad $20. Now he ________________.

c. John had a $15 debt. He earned $20. Now he __________________.

d. A ball was dropped from 15 ft above the sea; it fell 20 ft. Now the ball is at_________ ft.

e. Temperature was 20°C and fell 15°. Now the temperature is ____ °C.

15 −20 =

-15 + 20 =

-20 + 15 =

20 −15 =

15 −20 =

Math Mammoth Grade 6 Worksheets Collection. Copyright SpiderSmart, Inc. and Taina Maria Miller

Two Ways to Solve a Word Problem

Here are two quick methods to help you solve a word problem (hint of what’s coming next). The two (2)

approaches are called the C.U.B.E. method and the U.P.S. check method. Let’s break them down.

C.U.B.E.

CUBE stands for:

Circle the numbers.

Underline important words.

Box the question.

Eliminate unnecessary information

This is how it works:

PROBLEM: Mr. Johnson's class has 21 students. If the seven of his students are absent due to heavy

rainfall on a particular day, how many students does he have in his class on that day?

CUBE APPROACH:

Mr. Johnson's class has 21 students. If the seven of his students are absent due to heavy rainfall on a

particular day, how many students does he have left in his class on that day?

I underlined the word "left" because it helps us understand what type of problem we'll be doing. I

realize you could classify other words in this word problem as "important," but the students I

know only underline the important math words. They might also underline words such as remain, divide,

in all, altogether, take away, etc. These are the "telling words" that tell students what kind of action they

should perform to those numbers. Lots of teachers post these "key math words" on giant keys (aren't

we clever?) on a math bulletin board somewhere in the room.

I boxed the question so that we could focus on what answer we're supposed to find.

I crossed out unnecessary information about the teacher's name and why the students were absent so

that we could concentrate more easily on important info.

You could do this to any word problem!

The other method mentioned above is the U.P.S. check

Understand the problem.

Plan how to solve the problem.

Solve the problem.

Check your answer

Let’s use the same problem as before but apply this method to it:

PROBLEM: Mr. Johnson's class has 21 students. If the seven of his students are absent due to heavy

rainfall on a particular day, how many students does he have in his class on that day?

UPS APPROACH:

Either way can work, you just need to find which one works for you. Here’s a quick reference card to

help you.

Practice – Integer Word Problems

1. A submarine was situated 800 feet below sea level. If it ascends 250 feet, what is its new position?

2. Mt. Everest, the highest elevation in Asia, is 29,028 feet above sea level. The Dead Sea, the lowest elevation, is 1,312 feet below sea level. What is the difference between these two elevations?

3. In golf, the average score a good player should be able to achieve is called "par." Par for a whole course is calculated by adding up the par scores for each hole. Scores in golf are often expressed at some number either greater than or less than par. Ms. Floop is having a pretty good day at the City Golf Club. Her score so far after 15 holes is -5. If par for 15 holes is 62, what is her score?

4. Dylan plays in the backfield of the Big Town football team. Last week he ran four plays from the running back position. He made "gains" measured in yards of 0, -5, 1, and -3. What were his average yards per gain? Round your answer to the nearest tenth of a yard.

5. There was a 100-mile race at the Toronto Race Track. The winning driver had a time of 57 minutes. The next four drivers in order of finish had times (relative to the winning time) of +2, +3.2, +3.8, and +4.5 minutes. The sixth place driver had a time that was 3 minutes slower than the driver ahead of him. What was the sixth place driver's time? Express your answer in hours, minutes, and seconds.

6. In 2011, Belter Books reported a net loss of $43.9 million. In 2012, the company had a net income of $33 million. How much more money did the company make in 2012 than in 2011?

PROJECT TIME

Now that we’ve learned all about how to add and subtract integers, it’s time to show your understanding and share your

newly acquired knowledge. That’s right, its project time!

For your project, you will be asked to explain the rules of adding and subtracting integers by creating a poster. Your

poster must have the following elements:

A clear explanation of the rules (in your own words)

Visual demonstrations to help explain

An example for each rule (create your own questions and answers)

A catchy title

A clear sense of organization

This is an individual project, but you can always have a partner look over your draft work. Below if your rough work

space. You MUST complete your work here before moving on to the good copy.

Good luck.

The rules for Adding and Subtracting Integers (in my own words) are:

Adding:

Subtracting:

Examples:

1)

2)

3)

4)

DRAFT OF POSTER (pencil sketch and layout)

Teacher Name:

Student Name:     ________________________________________

CATEGORY 4 3 2 1 0

Graphics -Clarity Graphics are all in

focus and the content

easily viewed and

identified from 6 ft.

away.

Most graphics are in

focus and the content

easily viewed and

identified from 6 ft.

away.

Most graphics are in

focus and the content

is easily viewed and

identified from 4 ft.

away.

Many graphics are not

clear or are too small.

None graphics are

clear or are too

small.

Content - Accuracy At least 7 accurate

facts (rules and

examples) are

displayed on the

poster.

5-6 accurate facts

(rules and examples)

are displayed on the

poster.

3-4 accurate facts

(rules and

examples)are

displayed on the

poster.

Less than 1-2 accurate

facts (rules and

examples) are

displayed on the

poster.

No accurate facts

(rules and

examples) are

displayed on the

poster.

Required Elements The poster includes all

required elements as

well as additional

information.

All required elements

are included on the

poster.

All but 1 of the

required elements are

included on the

poster.

Several required

elements were

missing.

All required

elements were

missing.

Attractiveness The poster is

exceptionally

attractive in terms of

design, layout, and

neatness.

The poster is

attractive in terms of

design, layout and

neatness.

The poster is

acceptably attractive

though it may be a bit

messy.

The poster is

distractingly messy or

very poorly designed.

It is not attractive.

The poster is not

presentable.

Title Title can be read from

6 ft. away and is quite

creative.

Title can be read from

6 ft. away and

describes content

well.

Title can be read from

4 ft. away and

describes the content

well.

The title is too small

and/or does not

describe the content

of the poster well.

There is no title on

the poster

Integers Rules Poster