Negative Numbers (Negativa tal)

Ämne / Topic

Review of negative numbers (what is a negative number etc.) and operations (includes order of operations) with negative numbers.

Inlärningsmål / Learning Goals

After this lesson you should know / understand....

Whiteboard: I know... I understand...I can do...

Understand what negative numbers are and how to represent them.

Be able to complete calculations, which includes addition, subtraction, multiplication and division, involving negative numbers.

Google Slides & Videos

Lektionssteg / Steps in the lesson: 

1. Lektionsuppvärmning / Lesson warm up / Hook / Review from previous lesson

Lesson 1:

Material: Two dice

Number of participants: 2 - 3

Instructions:

• Everyone should roll the two dice six times. After each roll, the player chooses if the dice should show positive or negative numbers.

• The following options are available for the players:

• Once die shows a positive number and the other a negative number.

• Both dice show negative numbers.

• Player 1 rolls the dice one time and selects one of the options. The player then multiplies the two numbers and writes down the answer.

• Each player has a chance to throw the dice and write down their answers, until all players have had six turns.

• After six throws each player should have six numbers written down e.g. 10; -15, 16, -6, -9, 20.

• When all players have thrown the dice six times, they add their results together.

• The player with the biggest result wins.

Lesson 2: Warm-up: come up with a real life math question using negative numbers.

2. Introduktion till lektionen / Introduction to the lesson content 

• Lesson 1: Adding and subtracting using negative numbers

• Lesson 2: multiplying and dividing using negative numbers.

3. Aktiviteter / Key Activities 

Negative Numbers

Negative numbers (or minus numbers), denoted by a minus sign (−), are what we use to count below zero. For example, counting backwards from 3 looks like 3, 2, 1, 0, −1, −2, −3, −4,...

 Lesson 1: How to Add and Subtract Negatives

• Build and solve equations using props (i.e. counters)

Using a Number Line

1

Draw your number line. Draw a long, horizontal line. Mark a short vertical line in the middle and label it "0." 

Make more marks to the right of 0 and label them 1, 2, 3, and so on in that order. 

Those are the positive numbers. Negative numbers go the opposite direction. Starting at 0 and moving left, draw more marks and label them -1, -2, -3, and so on.

2

Start with the first number in your problem. 

Let's say you want to solve the problem -8 + 3. Find the first number, -8, on the number line. Draw a thick dot at that number.

3

Review how to add positive numbers. 

On the number line, adding a positive number moves you to the right. For example, if you start at -8 and add 3, you move 3 marks to the right. The answer is where you end up: -5. 

This works no matter which number we start with.[1]

4

Subtract positive numbers by moving left. 

Subtracting a positive number moves you to the left of the number line. For example, you know that -8 - 3 = -11, because -11 is three marks left of -8.[2]

5

Add a negative number. 

Now let's try the other way around. 

This time, start at +5 on the number line and solve the problem 5 + (-2). Because the second number is negative, we change the direction we move on the number line. 

Adding normally moves to the right, but adding a negative number moves to the left instead. 

Start at +5, move 2 spaces to the left, and you end up at +3. So 5 + (-2) = 3.[3]

• Here's another way to think of it: adding a negative number is the same as subtracting a positive number. 5 + (-2) = 5 - 2.

6

Subtract a negative number. Now try subtracting a negative number: 5 - (-2). 

Again, we're going to switch the normal direction, and move right instead of left. 

Start at +5, move two spaces to the right, and you end up at 7.[4]

• Subtracting a negative number is the same as adding a positive number. 5 - (-2) = 5 + 2.

7

Add two negative numbers. Let's solve -6 + (-4). 

Start at -6 on the number line. 

Addition moves to the right, but the negative sign in front of the 4 changes our direction, so we move to the left instead. 

Move four spaces left of -6 and you'll land on -10, so -6 + (-4) = -10.

• Don't get confused by where you start on the number line. The first number only tells you where to begin on the number line. You'll always move right or left based on the type of problem and the second number.

8 Subtract two negative numbers. Now let's solve -10 - (-3). 

Start at -10. 

Subtraction moves to the left but the negative in front of the 3 changes direction to the right instead. 

Move 3 places to the right and land on -3. The solution is -10 - (-3) = -7.

• Here's a memory aid: it takes two lines to draw the two negative signs. It also takes two lines to draw a plus sign, so - - is the same as +, moving to the right.

Without a Number Line

1 Add two negative numbers. Adding negative numbers together is just like adding positive numbers together, except that the answer has a "negative" sign in front of it. For instance, (-2) + (-4) = -6.

2

Add a positive and a negative number. For a problem like 2 + (-4), you might not know whether the answer will be positive or negative. If the number line doesn't help you figure it out, here's another way to solve it:

• Rearrange it so you're subtracting the smaller absolute value from the larger one. Ignore the negative sign for now. For our example, write 4 - 2 instead.

• Solve that problem: 4 - 2 = 2. This isn't the answer yet!

• Look at the original problem and check the sign (+ or -) of the number with the largest absolute value number. 4 has a higher value than 2, so we look at that in the problem 2 + (-4). There's a negative sign in front of the 4, so our final answer will also have a negative sign. The answer is -2.

3

Subtract a negative number. Subtracting the negative is the same as adding a positive. For instance, 4 - (-6) = 4 + 6. This gets a little harder when you start with a negative number as well. Once it's an addition problem, you can switch the order of the two numbers and turn it into an ordinary subtraction problem. Here are a few examples:

• 3 - (-1) = 3 + 1 = 4

• (-2) - (-5) = (-2) + 5 = 5 - 2 = 3

• (-4) - (-3) = (-4) + 3 = 3 - 4 = -1

4 Solve problems with more than two numbers. If you have a long chain of numbers, just use these steps to solve them two at a time. Here's an example:

• (-7) - (-3) - 2 + 1

• =(-7) + 3 - 2 + 1

• =3 - 7 - 2 + 1

• =(-4) - 2 + 1

• =-6 + 1

• =-5

• Relating practical work examples to mathematical problems.

• Review operations with negative numbers

• Differentiated worksheets on adding and subtracting using negative numbers.

Lesson 2: 

How to Divide and Multiply by Negative Numbers

• Reviewing fundamentals and rules with regards to multiplying and dividing with negative numbers.

• Relating fundamentals and rules to worked examples.

Example of work to be done:

Dividing with Negative Numbers

1

Divide a positive number by a negative number. To do this, divide the integers as usual, then place a negative sign in front of the quotient. 

A positive number divided by a negative number is always negative. This also is the rule when dividing a negative number by a positive number.[1]

• For example

3

Divide a positive fraction by a negative number. 

To do this, divide the numbers as usual, then add a negative sign to the quotient.

 A positive number divided by a negative number will always be negative, regardless of whether the number is a whole number or a fraction. 

The same is true when dividing a negative number by a positive number. Remember that dividing by a number is the same as multiplying by its reciprocal.[3]

• For example:

4

Divide a negative fraction by a negative number. 

To do this, divide the numbers as usual, and ignore the negative signs. 

A negative number divided by a negative number will always be positive, regardless of whether the number is a whole number or a fraction. 

Remember that dividing is the same as multiplying by the reciprocal.

• For example:

Solving Word Problems

1

A peregrine falcon can dive (lose height) at a rate of 320 km/hr. Assuming it can sustain this rate indefinitely, how long would it take a peregrine to reach a height of -240 km?

• Differentiated worksheets on multiplying and dividing using negative numbers.

• Differentiated worksheets using mixed operations, with regards to adding, subtracting, multiplying and dividing using negative numbers.

4. Kolla vad eleverna kan / Check for understanding / Exit ticket

Lesson 1: Adding and subtracting using negative numbers

Exit ticket - what have you learned about negative numbers (students will share what they have learned with the rest of the class and teachers).

Lesson 2: Multiplying and dividing using negative numbers

Exit ticket - answering your partners real life math problem on negative numbers.

5.  Avslutning / Closure / Summary of lesson

• Students will be selected at random to answer a question based on the work done in class (adding, subtracting, multiplying or dividing using negative numbers). If they are not sure, they can ask a member of the class to assist them, this will encourage peer and collaborative learning. 

Resurser & Materiel / Resources & Materials

Textbook:

ETT pg. 19. no. 1029 abc, 1030 abc, 1031 abc, 1035 abc.

TVA pg.19 no. 1038 ab, 1040 abc, 1041, 1043 abc.

TRE pg. 20/21 no. 1046 ab, 1047 abc, 1048 abc, 1051 abc.

FYRA pg. 21/22 no. 1054, 1056, 1057 abc, 1058, 1059.

negative numbers answers.pdf

negative numbers worksheet.pdf