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Table of Contents
In this lesson, we will try to have a deeper understanding of numbers: negative numbers, the relationship between negative numbers and positive numbers, their relation to the number line, and how we can use them in real-world situations.
See the fact file below for more information on the extended understanding on numbers or alternatively, you can download our 28-page Extended Understanding on Numbers worksheet pack to utilise within the classroom or home environment.
Key Facts & Information
- In previous lessons, we have already learned about positive numbers and how they are related to the number line.
- If the numbers found on the right side of zero on a number line are positive numbers, the numbers found on the left side of zero are negative numbers.
- Negative numbers are numbers less than zero, they are on the left side of zero, and have the minus sign (-) in front to indicate that they are less than zero.
- -10 = 0 – 10 OR MINUS TEN
RELATIONSHIP BETWEEN POSITIVE AND NEGATIVE NUMBERS
- The best way to visualize negative and positive numbers is through a number line.
- Using zero as the base, you can visualize negative numbers as zero minus the number, and you can visualize positive numbers as zero plus the number.
- Although positive numbers do not have the plus sign before the number itself, the plus sign is an invisible indicator.
- Despite the difference in their signs, both negative numbers and positive numbers indicate distance.
- The distance of -3 from 0 is 3 places or movements to the left, which is indicated by the red arrow.
- On the other hand, the distance of 3 from 0 is 3 places or movements to the right, which is also indicated by the blue arrow.
- Therefore, the distance from the zero of a negative number is the same as the positive counterpart of it, or the absolute value.
- -(-3) = |-3| = 3
- The absolute value of a number is the distance of the number from the 0 on a number line without taking into consideration the direction where it is located, whether right or left.
- On a number line, negative numbers are on the left side of zero, while positive numbers are on the right side.
- On the other hand, on a plane, negative numbers can either be on the left or below.
- Looking at the plane above and using your past knowledge about planes and coordinates, quadrants II, III, and IV are the quadrants with negative numbers.
- Quadrant II has a (negative, positive) coordinate, while quadrant III has a (negative, negative) coordinate, and quadrant IV has a (positive, negative) coordinate.
- Despite the differences in their coordinate signs, the location of the coordinates just mirror each other; take a look at the example on the left.
- Coordinate (-1,-3) is a mirror of coordinate (1,-3). The red point is the horizontal flip of the blue point.
COMPARING NEGATIVE NUMBERS
- Remember that when we compare positive numbers, we look at their distance from the zero on a number line.
- For example, we know that 5 is greater than 3 and 2 is less than 3.
- Now, how do we compare negative numbers?
- Is -5 greater than -3?
- Why no? We know that 5 is greater than 3, but why is -5 not greater than -3?
- We have to look back at the number line.
- From our previous knowledge, we know that the number closer to zero is lesser than the number farther from zero.
- Taking the distance into account, we know that 5 is 5 places from zero while 3 is 3 places from zero, therefore we know that 5 is greater than 3.
- This is correct for positive numbers, but is different for negative numbers.
- For negative numbers, the closer the number is to zero, the larger it is.
- Therefore, on the number line presented above, the largest negative number is -1.
- Taking that into account, -3 is therefore greater than -5.
- Negative numbers indicate zero minus the number, therefore the farther it is from zero, the lesser the value.
NEGATIVE NUMBERS IN REAL WORLD
- Listed below are some of the common uses of negative numbers in the real world.
- In temperatures, we can have positive numbers indicating hot or warm weather or temperature.
- On the other hand, we can also have negative numbers to indicate cold temperature.
- -15°C is a negative temperature, which means that the temperature is 15 degrees below 0.
- For banking systems, negative numbers are often used to indicate negative balance.
- In addition, borrowed money can also be considered as a negative quantity of money.
- Sea level
- Sea level can also be measured using negative quantities.
- If the measurement is below the fixed reference point, it is indicated as a negative measurement.
- In some infrastructures or buildings, the ground floor is considered as level 0 or floor 0; thus, the basement or any other floors below the ground floor are signified using negative numbers (e.g. -1, -2)
- In games, numbers usually stand for the scores or points of the player.
- Losing a round or the game could make the player lose some points, which can be indicated by a negative number.
- There are some sports that use negative numbers for calculation of scores (e.g. golf).
Extended Understanding on Numbers Worksheets
This is a fantastic bundle which includes everything you need to know about the extended understanding on numbers across 28 in-depth pages. These are ready-to-use Extended Understanding on Numbers worksheets that are perfect for teaching students about the deeper understanding of numbers: negative numbers, the relationship between negative numbers and positive numbers, their relation to the number line, and how we can use them in real-world situations.
Complete List Of Included Worksheets
- Lesson Plan
- Extended Understanding on Numbers
- L or R?
- P vs N
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Link will appear as Extended Understanding on Numbers Facts & Worksheets: https://kidskonnect.com - KidsKonnect, December 3, 2020
Use With Any Curriculum
These worksheets have been specifically designed for use with any international curriculum. You can use these worksheets as-is, or edit them using Google Slides to make them more specific to your own student ability levels and curriculum standards.