Exponents, Integers, and Real Numbers by Kaley Mcglawn https://padlet.com/kmcglawn/4ae4djcta5w5oh35 Resource Board en-us 2022-10-12 20:52:30 UTC 2026-03-04 21:17:15 UTC hello@padlet.com Exponents kmcglawn https://padlet.com/kmcglawn/4ae4djcta5w5oh35/wish/2347395593
  • Definition: An exponent indicates the number of times the base is used as a factor, so it indicates repeated multiplication and it precedes other multiplication and division, as well as addition and subtraction.
  • Exponents are first introduced in 5th grade in terms of powers of 10 and place value

  • In 6th grade students learn to write and evaluate numerical expressions involving whole number exponents

    • ]]>     2022-10-19 16:39:58 UTC https://padlet.com/kmcglawn/4ae4djcta5w5oh35/wish/2347395593     Exponents Confusion kmcglawn https://padlet.com/kmcglawn/4ae4djcta5w5oh35/wish/2347398266
  • The rules are what confuse students because they might not remember whether to add or multiply the exponents when they raise a number to a given power.

  • This shows lack of understanding of operations and notation therefore, students need to explore exponents with whole numbers before they use exponents with variables.

    • ]]>     2022-10-19 16:41:14 UTC https://padlet.com/kmcglawn/4ae4djcta5w5oh35/wish/2347398266     Order of Operations kmcglawn https://padlet.com/kmcglawn/4ae4djcta5w5oh35/wish/2347403419
  • Working with exponents extends to order of operations
  • Definition:  is the rule that tells us the sequence in which we should solve an expression with multiple operations
  • As early as 3rd grade students need to know the order of operations for addition, subtraction, multiplication and division 

  • By 6th grade, exponents are added to the order of operations 

    • ]]>     2022-10-19 16:43:53 UTC https://padlet.com/kmcglawn/4ae4djcta5w5oh35/wish/2347403419     PEMDAS kmcglawn https://padlet.com/kmcglawn/4ae4djcta5w5oh35/wish/2347403919
  • We are taught to work through an expression left to right, AKA PEMDAS, but this rule misleads students into thinking "multiplication precedes division and addition precedes subtraction".
  • Instead students should use:

    • P =parenthesis

    E =exponents

    MD =multiplication and division (whichever is first from left to right)

    AS =addition and subtraction (whichever is first from left to right)



    ]]>     2022-10-19 16:44:10 UTC https://padlet.com/kmcglawn/4ae4djcta5w5oh35/wish/2347403919     Exponents with 0 or Negatives kmcglawn https://padlet.com/kmcglawn/4ae4djcta5w5oh35/wish/2347576157
    • Any number to the 0 power is always 1 for example 10^0= 1
    • So what about negative exponents such as 10 ^ (-2) ? 
    • Well… you change the number to the reciprocal and the base does not change ! but the exponent becomes positive so it would become 1/10^2.

    ]]>     2022-10-19 18:11:17 UTC https://padlet.com/kmcglawn/4ae4djcta5w5oh35/wish/2347576157     Scientific Notation kmcglawn https://padlet.com/kmcglawn/4ae4djcta5w5oh35/wish/2347579212
  • Definition: "a number is changed to be the product of a number greater than or equal to 1 and less than 10 multiplied by a power of 10. For example, 3,414,000,000 can also be written as " 3.414 x 10^9


    • Different notations have different purposes and values. For example, the population of the world on 6/24/17 was estimated to be 7,513,768,345 (U.S. Census Bureau, n.d.) This number can be written in the following ways depending on the purpose: "7,513 million, 7.5×10 ^ 9 and about 7.5 billion.


    ]]>     2022-10-19 18:13:03 UTC https://padlet.com/kmcglawn/4ae4djcta5w5oh35/wish/2347579212     Examples of Extremes: Large and Small Numbers kmcglawn https://padlet.com/kmcglawn/4ae4djcta5w5oh35/wish/2347581304
  • The human body which has about 100 billion cells
  • Exploring lottery combinations 
  • The estimated size of the universe is 40 billion light-years etc..
    The chance of winning the lottery
  • "The length of a DNA strand in a cell is about 10^7 m. This is also measured as 1000 angstroms."
  • "Human hair grows at the rate of 10^8 miles per hour."


    • ]]>     2022-10-19 18:14:10 UTC https://padlet.com/kmcglawn/4ae4djcta5w5oh35/wish/2347581304     Positive and Negative Numbers kmcglawn https://padlet.com/kmcglawn/4ae4djcta5w5oh35/wish/2347584417 Students must… Understand that positive and negative numbers are used together to describe quantities having opposite directions or values, use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.]]> 2022-10-19 18:15:51 UTC https://padlet.com/kmcglawn/4ae4djcta5w5oh35/wish/2347584417 Tools for Teaching Positive and Negative Numbers kmcglawn https://padlet.com/kmcglawn/4ae4djcta5w5oh35/wish/2347594117 Using two different colored counters, one (yellow) for positive and one (red) for negative helps students illustrate they are opposite values.

    Yellow= +1

    Red= -1

    Number Lines are a great tool to represent the operation conceptually 

    Shows the distance from 0 or absolute value from a number 

    Arrows can be used to represent positive and negative numbers by showing the distance and direction they are going



    ]]>     2022-10-19 18:21:05 UTC https://padlet.com/kmcglawn/4ae4djcta5w5oh35/wish/2347594117     Real Numbers kmcglawn https://padlet.com/kmcglawn/4ae4djcta5w5oh35/wish/2347623342 “Whole numbers, fractions and decimals, and integers are all rational numbers because they can all be written as a fraction with an integer over a nonzero integer”

    "Irrational numbers are numbers such as 2—numbers whose value cannot be written as a fraction and whose exact value can only be estimated"

    ]]>     2022-10-19 18:37:20 UTC https://padlet.com/kmcglawn/4ae4djcta5w5oh35/wish/2347623342