GEMS: A Better Way to Remember Order of Operations

Mathematics Grades 4th Grade 4:00 Video
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Lesson Description

Learn why GEMS is a helpful way to remember the order of operations in math, and understand why PEMDAS can be confusing.

Video Resource

This Order of Operations Mnemonic is Better Than PEMDAS Rule!

Mashup Math

Duration: 4:00
Watch on YouTube

Key Concepts

  • Order of Operations
  • Grouping Symbols
  • Exponents
  • Multiplication and Division (left to right)
  • Addition and Subtraction (left to right)
  • GEMS mnemonic

Learning Objectives

  • Students will be able to explain what GEMS stands for.
  • Students will be able to apply the GEMS method to solve mathematical expressions.
  • Students will be able to explain why GEMS is a more effective mnemonic than PEMDAS.

Educator Instructions

  • Introduction (5 mins)
    Begin by asking students what they already know about order of operations. Discuss the PEMDAS mnemonic and potential challenges students might have faced with it. Introduce the concept that there might be a better way to remember the order.
  • Video Viewing (7 mins)
    Play the Mashup Math video 'This Order of Operations Mnemonic is Better Than PEMDAS Rule!'. Encourage students to take notes on what GEMS stands for and the explanations given in the video.
  • Discussion and Explanation (8 mins)
    After the video, discuss what GEMS stands for: Grouping Symbols, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). Emphasize that multiplication and division are on the same level, as are addition and subtraction, and that they are performed from left to right.
  • Practice Problems (10 mins)
    Work through several example problems using the GEMS method. Start with simpler problems and gradually increase the complexity. For example: 1. 2 + 3 x 4 2. (5 + 2) x 3 3. 10 - 2 + 5 4. 12 ÷ 3 x 2
  • Independent Practice (10 mins)
    Provide students with a worksheet containing various order of operations problems to solve independently. Encourage them to use the GEMS method and show their work. You can use the free worksheet from Mashup Math's website.

Interactive Exercises

  • Group Problem Solving
    Divide students into small groups and give each group a complex order of operations problem. Have them work together to solve the problem using GEMS, explaining each step to one another.
  • Online Order of Operations Game
    Use an online game or interactive tool to provide students with additional practice in a fun and engaging way. Many free order of operations games are available online.

Discussion Questions

  • What does each letter in GEMS stand for?
  • Why is it important to follow the order of operations?
  • How is GEMS different from PEMDAS?
  • Can you give an example of a math problem where following the wrong order of operations would lead to an incorrect answer?

Skills Developed

  • Problem-solving
  • Critical thinking
  • Attention to detail
  • Mathematical reasoning
  • Collaboration

Multiple Choice Questions

Question 1:

What does the 'G' in GEMS stand for?

Correct Answer: Groups

Question 2:

What does the 'E' in GEMS stand for?

Correct Answer: Exponents

Question 3:

In GEMS, what should you do *after* you solve what's in the Grouping Symbols?

Correct Answer: Exponents

Question 4:

Which operation comes first: Multiplication or Addition?

Correct Answer: Multiplication

Question 5:

According to GEMS, which do you do first: Multiplication or Division?

Correct Answer: Whichever comes first from left to right

Question 6:

What is the correct answer to 2 + 3 x 4 using GEMS?

Correct Answer: 14

Question 7:

What is the correct answer to (5 + 2) x 3 using GEMS?

Correct Answer: 21

Question 8:

What is the correct answer to 10 - 2 + 5 using GEMS?

Correct Answer: 7

Question 9:

What is the correct answer to 12 ÷ 3 x 2 using GEMS?

Correct Answer: 8

Question 10:

Why is GEMS better than PEMDAS?

Correct Answer: It helps you remember that Multiplication and Division are equal

Fill in the Blank Questions

Question 1:

The 'G' in GEMS stands for ___________ Symbols.

Correct Answer: Grouping

Question 2:

The 'E' in GEMS stands for ___________.

Correct Answer: Exponents

Question 3:

In GEMS, you do Multiplication and ___________ from left to right.

Correct Answer: Division

Question 4:

In GEMS, you do Addition and ___________ from left to right.

Correct Answer: Subtraction

Question 5:

___________ tells us the order to solve math problems.

Correct Answer: GEMS

Question 6:

If a problem has parentheses, you solve what's inside them ___________.

Correct Answer: first

Question 7:

2 + 3 x 5 = ___________

Correct Answer: 17

Question 8:

(4 + 1) x 2 = ___________

Correct Answer: 10

Question 9:

10 - 5 + 2 = ___________

Correct Answer: 7

Question 10:

12 ÷ 2 x 3 = ___________

Correct Answer: 18

Educational Standards

4.N.2.4:Apply and analyze models to solve multi-step problems requiring the use of addition, subtraction, and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results. 4.A.2.2:Solve for a variable in an equation involving addition, subtraction, multiplication, or division with whole numbers. Analyze models to represent number sentences and vice versa.

Teaching Materials

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