1. negative numbers are an advanced math tool
Level 6 Module 2
Introduction to Negative Numbers

3. © Professor Pete's Classroom. All rights reserved.
Index
Think Bubble Mathematics: Level 6
Module 2
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4. Think Bubble Math: Level 6 Overview
Module 1:
244825_TBM601_xdiv _10_100_1000_.pptx
Module 2:
240903_TBM602_Integers .pptx
Module 3:
244832_TBM603_xdiv_ by_2_3-digit_nos.pptx
Module 4:
241750_TBM604_Fractions _convert_compare.pptx
Module 5:
242003_TBM605_Percent .pptx
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5. Think Bubble Math Worksheets:
Many lessons are supported by corresponding worksheets
Purchasers:
Included in zip file for download
Members:
Access via profpete.com in TBM section
Some lessons recommend that students use hands-on materials
243504_TBM102_WS_Counting_on_back_1_2_3
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6. Navigating in Think Bubble Math on a Computer
Return to Index
Go to other slide:
Right-click screen, click “See All Slides”
Navigate forward & back: click right & left arrows
Start presentation:
Double-click file name or icon
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7. Using Think Bubble Math on a Tablet or Phone
Download free PowerPoint app in iTunes or Google Play:
iPhone or iPad:
Android:
Save Think Bubble file to your device
You may find it helps to install Microsoft OneDrive, to save and find files
If you see a warning about “unsupported content”, you can safely ignore it
We include special fonts to improve the presentation’s appearance
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8. Navigating in Think Bubble Math on a Tablet or Phone
Start presentation:
click “play” button in top bar
Navigate to other slide:
rotate device to portrait, click slide thumbnail at bottom of screen
Navigate forward & back: swipe left & right
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9. Integers: Positive and Negative
ACMNA124
Investigate everyday situations that use integers. Locate and represent these numbers on a number line
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10. Assumed Prior Knowledge
Students should already be able to:
Count forwards and backwards on a number line
Add and subtract large numbers
Work with money and change money
Express familiarity with everyday contexts involving negative integers, such as temperatures and financial transactions
Draw and interpret open number lines
(c) Professor Pete's Classroom, All rights reserved.

11. Contexts for Negative Numbers
Temperatures below zero:
Many Australian students will not have experienced “below zero” temperatures outdoors
Most homes have a freezer which provides the context we need
As when teaching any topic for the first time, we want to connect the topic with students’ experiences
This topic introduces students to the “second half” of the set of integers (whole numbers), used extensively in more advanced topics including algebra
The goal is to help students to connect with experiences of negative numbers and their contexts, before attempting to manipulate the symbols which represent the numbers
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12. Contexts for Negative Numbers
Money:
Owing money is effectively the same as having a negative balance, or of having “less than zero”
As when teaching any topic for the first time, we want to connect the topic with students’ experiences
This topic introduces students to the “second half” of the set of integers (whole numbers), used extensively in more advanced topics including algebra
The goal is to help students to connect with the concept of negative numbers, before attempting to manipulate the symbols which represent the numbers
$ 5
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13. Contexts for Negative Numbers
Elevations below sea level:
Certain well-known locations around the world are below sea level
They are said to be a negative distance above sea level
e.g. The Dead Sea has an elevation of -413 m
As when teaching any topic for the first time, we want to connect the topic with students’ experiences
This topic introduces students to the “second half” of the set of integers (whole numbers), used extensively in more advanced topics including algebra
The goal is to help students to connect with the concept of negative numbers, before attempting to manipulate the symbols which represent the numbers
Photo: Flickr/Phil Norton
CC BY-ND 2.0
© Professor Pete's Classroom. All rights reserved.

14. Accompanying Master and worksheet for Printing
Lesson 1, 2 and 3
Duplicate one per 2 students
Cut in half
Laminate (optional)
Lesson 1 and 2
Duplicate one per student (both lessons are on the one sheet)
printing this sheet is optional
students could use the printed number line master and write questions and answers in their books
240904_TBM602_T_NL_integers
240904_TBM602_T_NL_integers
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15. Supporting Resources:
Resources at profpete.com
Number Lines with Integers
Integers: Positive and Negative
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16. Lesson 1: Negative Numbers - thermometer
ACMNA124
Investigate everyday situations that use integers. Locate and represent these numbers on a number line
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17. Fridge and Freezer Temperatures°C
Thermometers show temperatures above and below freezing
Water freezes at 0°C
The recommended freezer temperature is -18°C
The recommended fridge temperature is 5°C
Any number below zero is a negative number
freezing point
-18°C
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18. Fridge and Freezer Temperatures
Look at the thermometer sideways
The numbers to the left of zero are the negative numbers
The numbers to the right (regular numbers) are referred to as positive numbers
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19. Counting with Negative Numbers
The number line does not stop at 0. It actually goes below zero.
These are the negative numbers
Count backwards through the negative numbers. Notice they increase in size.
Negative numbers can be read as “negative 3” or “minus 3”
Count backwards from zero
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20. Counting with Negative Numbers
Count forwards again and the negative numbers get smaller towards zero
Whether the start number is positive or negative, we move to the right on a number line to “count up”, add or increment a number
Count up, towards zero
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21. Counting with Negative Numbers
Count backwards again:
start at 4
stop at -8
Count backwards over the zero from positive to negative numbers
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22. Counting with Negative Numbers
Now count forwards:
start at -6
stop at 6
Have students practice on their own number lines (printed number line master)
Count to and from -20 to 20
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23. Working with Negative Numbers
Start at -3, count on by 5
When adding a (positive) number, counting always moves to the right, even if starting on a negative number
When counting on, always count the hops = 2
Have students work with these questions on their worksheet Or
Have them write the questions in their books and count one their printed number line
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24. Working with Negative Numbers
Work out this question: count on 7, starting at -4 = 3
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25. Working with Negative Numbers
Work out this question
This time you can see that the answer is still below zero; it is a smaller negative number = -1
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26. Working with Negative Numbers
Work out this question = -2
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27. Working with Negative Numbers
Work out this question =
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28. Working with Negative Numbers
When subtracting, we always count to the left
It doesn’t matter where you start it is the number of hops to the left that are counted
1 – 4 = -3
When taking away numbers we always move to the left
It doesn’t make any difference whether we start on a positive number or a negative one, the hop count is the same
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29. Working with Negative Numbers
Try this one
-2 – 6 = -8
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30. Working with Negative Numbers
Try this one
0 – 3 = -3
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31. Working with Negative Numbers
Try this one
-3 – 3 = -6
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32. Working with Negative Numbers
Try this one
2 – 6 = -4
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33. Lesson 2: Negative numbers -Money, sea level
ACMNA124
Investigate everyday situations that use integers. Locate and represent these numbers on a number line
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34. © Professor Pete's Classroom. All rights reserved.
Money Owed
If you owe more money than you possess, you have less than zero, a negative balance
Owing money is like having negative money.
You borrowed $ 5 off your brother
You receive $ 7 on pocket money day
How much money will you have once you have paid your brother back?
I get $7
$5 is for Bro’
pocket money day
$ 5
$ 7
$-5
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35. Working with Negative Numbers
You borrow $4
You get $6
What is your account balance now? = 2
Owing money means that you have a negative balance
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36. Working with Negative Numbers
You borrow $10
You get $8
What is your account balance now? = -2
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37. Working with Negative Numbers
You borrow $9
You get $5
What is your account balance now? = -4
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38. Working with Negative Numbers
You borrow $2
You borrow another $3
What is your account balance now?
-2 – 3 = -5
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39. Working with Negative Numbers
You borrow $4
You borrow another $6
What is your account balance now?
-4 – 6 =
-10
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40. © Professor Pete's Classroom. All rights reserved.
Land Below Sea Level
Nearly half of Holland lies below sea level
Sea level is at 0 metres
Many houses are built below sea level. The house below is at - 4 m.
A system of seawalls and sand dunes keep the sea out
We say that the land is at - 4 m
4 m
seawall
sea level 0 m
0 m
sea level
- 4 m
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41. © Professor Pete's Classroom. All rights reserved.
Land Below Sea Level
Elevations below sea level:
Certain well-known locations around the world are below sea level
They are said to have a negative elevation above sea level
e.g. The Dead Sea has an elevation of -413 m
Photo: Flickr/Phil Norton
CC BY-ND 2.0
© Professor Pete's Classroom. All rights reserved.

42. Land Below Sea Level
Below sea level: some of the lowest points around the world
The Fens, UK
- 4 m
Lake Eyre,
Australia
-15 m
sea level 0 m
sea level 0 m
Holland
- 6 m
Lowest land point on earth
Death Valley, USA
-86 m
Dead Sea,
Israel/Jordan
- 413 m
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43. Comparing Negative Numbers
Compare the Fens (-4 m) with the lowest point in Holland (-6 m)
The difference between
- 6 m and - 4 m is
How many hops between them?
2 m
When comparing two numbers it does not matter which number is first. It is the gap between them that is counted. The answer is positive even though both numbers are negative
Land which is below sea level can be said to have a negative elevation
e.g. The Fens have an elevation of -4 metres (above sea level)
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44. Comparing Negative Numbers
Compare the elevations of the lowest point in Holland with Lake Eyre
The difference between
- 6 m and - 15 m is
9 m
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45. Comparing Negative and Positive Numbers
Compare these elevations
The difference between
3 m and - 5 m is
8 m
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46. Comparing Negative and Positive Numbers
Compare these elevations
The difference between
-14 m and -8 m is
6 m
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47. Comparing Negative and Positive Numbers
Compare these elevations
The difference between
4 m and - 4 m is
8 m
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48. Lesson 3: open number lines - Negative numbers
ACMNA124
Investigate everyday situations that use integers. Locate and represent these numbers on a number line
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49. Working with Negative Numbers
Work out this question
Counting on 9 is a rather slow process
By using an open number line we can work it out faster
One of the best ways to understand negative numbers is to use a number line = 3
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50. Bridging Zero on an Open Number Line
= ?
Think how many makes 0
-6 + __ = 0
= __ 6 9 3 6 3 -6 3
Have students draw their own blank number line
Repeat the same question
Write the starting number and 0, then the hop to zero
Draw the total hop to be added
Work out the remaining hop to complete the addition
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51. Bridging Zero on an Open Number Line
= ?
Think how many makes 0
-4 + __ = 0
= __ 4 7 3 4 3 -4 3
A question like this could be solved by rearranging the terms to 7 – 4 = ?
However, at this stage we want to emphasise the idea that adding a positive number always increments to the right, even when starting from a negative number
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52. Bridging Zero on an Open Number Line
= ?
Think how many makes 0
-2 + __ = 0
= __ 2 6 4 2 4 -2 4
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53. Bridging Zero on an Open Number Line
= ?
Think how many makes 0
-12 + __ = 0
= __ 12 15 3 12 3
-12 3
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54. Open Number Lines with Negative Numbers
Subtraction requires counting backwards.
Within negative numbers it is the same
-3 – 4 = -7
Introduce the idea of counting to the left to subtract a number, even when starting at a negative number
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55. Open Number Lines with Negative Numbers
-3 – 4 = __ -7 -4 -7 -3
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56. Open Number Lines with Negative Numbers
Try this one
1 – 6 = -5
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57. Open Number Lines with Negative Numbers
1 – 6 = __ -5 -6 -5 -1 -5 6
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58. Open Number Lines with Negative Numbers
-4 – 5 = __ -9 -5 -9 -4
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59. Open Number Lines with Negative Numbers
3 – 8 = __ -5 -8 -5 -3 -5 3
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60. Open Number Lines with Negative Numbers
-1 – 7 = __ -8 -7 -8 -1
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61. Open Number Lines with Negative Numbers
4 – 6 = __ -2 -6 -2 -4 4 -4
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62. Open Number Lines with Negative Numbers
-2 – 9 = __
-11 -9
-11 -2
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63. Lesson 4: Dates – open number lines
ACMNA124
Investigate everyday situations that use integers. Locate and represent these numbers on a number line
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64. Important Dates: BC and AD
A timeline of history is a special number line. Dates BC are numbered backwards, like negative numbers
AD 1 Birth of Christ
What! No year zero?
2560 BC Great Pyramid
55 BC Caesar invades Britain
AD 79 Vesuvius erupts
AD 900 Vikings invade Greenland
776 BC first Olympics
AD 1770 Cook charts east coast of Australia
509 BC Roman Empire begins
221 BC Great Wall of China begins
AD 455 Vandals destroy Rome
2033 BC Abraham
1200 BC Fall of Troy
AD 1492 Columbus reaches New World
AD 2000 New millennium
2500 BC
2000 BC
1500 BC
1000 BC
500 BC
AD 500
AD 1000
AD 1500
AD 2000
AD 2500 BC AD
Years BC are numbered backwards from 1 BC
Some of these dates are disputed
Discuss your own important dates such as this current year
Timelines spanning BC and AD work in similar ways to integers
Years BC (Before Christ) date backwards from the birth of Christ
Years AD (Anno Domini - in the Year of our Lord) date forwards
There is no year zero
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65. BC and AD Years and Dates
Using approximate dates, the Roman empire began in 509 BC and fell in AD 455
How long was the reign of the Roman Empire?
950 yrs
500
450
500 BC
AD 1
AD 450
In order to handle questions mentally, in this lesson dates should be rounded to a suitable number
In this question: round each date to the nearest 50 years
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66. BC and AD Years and Dates
Make your own open number line for dates from the first Olympics (776 BC) to the current Olympics (remember to round the years)
2800 yrs
2000
800
800 BC
AD 1
AD 2000
Round to the nearest 100 years
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67. BC and AD Years and Dates
Make your own open number line for dates from Abraham (2033 BC) to the current date (remember to round the years)
4000 yrs
2000
2000
2000 BC
AD 1
AD 2000
Round to the nearest 100 years
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68. BC and AD Years and Dates
Make your own open number line for dates from the birth of the Roman Empire (509 BC) to Pompeii being buried by Vesuvius eruption (AD 79). Remember to round the years.
600 yrs
500
100
500 BC
AD 1
AD 100
These dates have been rounded to the nearest 100 years; to increase accuracy, they could be rounded to the nearest 10
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69. BC and AD Years and Dates
How long has the Great Wall of China (221 BC) been standing?
2200 yrs
200
2000
200 BC
AD 1
AD 2000
These dates have been rounded to the nearest 100 years, but they could be rounded to the nearest 10.
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