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Extended Understanding on Numbers Facts & Worksheets

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.

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Worksheets /Math /Grade 6 (ages 11-12) /Extended Understanding on Numbers Facts & Worksheets

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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

INTRODUCTION

  • 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?
  • QUESTION
    • Is -5 greater than -3?
  • ANSWER
    • NO
  • 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.
  • Why?
  • 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.
  • Temperature
    • 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.
  • Money
    • 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.
  • Elevator/lift
    • 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)
  • Games
    • 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.
  • Sports
    • 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
  • Identify
  • Absolute
  • L or R?
  • Plot
  • Compare
  • Greatest
  • Lesser
  • Travel
  • P vs N
  • Problems

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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.

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