Cracking Consecutive Integers: A Sum-Solving Adventure

Algebra 2 Grades High School 1:36 Video
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Lesson Description

Unlock the secrets to solving consecutive integer problems using algebraic equations. Learn how to define variables, set up equations, and find those elusive numbers that add up just right!

Video Resource

Find 3 Consecutive Even Integers with a Sum of 72

Mario's Math Tutoring

Duration: 1:36
Watch on YouTube

Key Concepts

  • Consecutive Even Integers
  • Algebraic Representation
  • Solving Linear Equations
  • Combining Like Terms

Learning Objectives

  • Students will be able to define consecutive even integers algebraically.
  • Students will be able to set up and solve a linear equation to find consecutive even integers given their sum.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the definition of consecutive even integers. Discuss how each integer relates to the previous one (adding 2). Present the problem: Find three consecutive even integers that sum to 72.
  • Video Presentation (7 mins)
    Watch the video 'Find 3 Consecutive Even Integers with a Sum of 72' by Mario's Math Tutoring. Pay attention to how the variable expressions are set up and how the equation is solved.
  • Guided Practice (10 mins)
    Work through the example problem from the video step-by-step on the board. Emphasize the process of defining the variables (x, x+2, x+4), setting up the equation (x + x+2 + x+4 = 72), combining like terms, and solving for x. Show how to find the actual integers after solving for x.
  • Independent Practice (10 mins)
    Present students with similar problems to solve independently. For example: 'Find three consecutive even integers that sum to 48' or 'Find three consecutive even integers that sum to 96'. Circulate to provide assistance as needed.
  • Review and Wrap-up (3 mins)
    Review the solutions to the independent practice problems. Address any remaining questions. Summarize the key steps in solving consecutive integer problems.

Interactive Exercises

  • Consecutive Integer Challenge
    Divide the class into groups. Each group creates their own consecutive integer problem and challenges another group to solve it. Ensure that all problems are solvable and that students can verify the solutions.

Discussion Questions

  • Why do we add 2 to represent the next consecutive even integer?
  • How would the equation change if we were looking for consecutive odd integers instead of even integers?
  • Can you think of real-world scenarios where you might need to solve this type of problem?

Skills Developed

  • Algebraic Reasoning
  • Problem-Solving
  • Equation Solving

Multiple Choice Questions

Question 1:

Which of the following represents three consecutive even integers?

Correct Answer: x, x+2, x+4

Question 2:

If 'x' represents the first of three consecutive even integers, and their sum is 60, which equation correctly represents this scenario?

Correct Answer: x + x + 2 + x + 4 = 60

Question 3:

What is the next consecutive even integer after 24?

Correct Answer: 26

Question 4:

What operation is used to find the sum?

Correct Answer: Addition

Question 5:

If the first of three consecutive even integers is 10, what are the other two?

Correct Answer: 12 and 14

Question 6:

What is the correct first step to solving the equation x + x + 2 + x + 4 = 72?

Correct Answer: Combine like terms

Question 7:

What does 'x' represent in the equation x + x + 2 + x + 4 = 72?

Correct Answer: The smallest integer

Question 8:

Which of the following is NOT a consecutive even integer?

Correct Answer: 5

Question 9:

After solving for x in the equation, what must you do to find the other consecutive integers?

Correct Answer: Add 2 and 4 to x

Question 10:

Why do we use 'x+2' and 'x+4' to represent consecutive even integers?

Correct Answer: Because each even integer is 2 more than the previous one

Fill in the Blank Questions

Question 1:

________ even integers follow each other in order, each differing by 2.

Correct Answer: Consecutive

Question 2:

If 'x' is the first even integer, the next consecutive even integer is represented by x + ________.

Correct Answer: 2

Question 3:

In the problem x + x + 2 + x + 4 = 72, the goal is to solve for ________.

Correct Answer: x

Question 4:

The first step in solving x + x + 2 + x + 4 = 72 is to ________ like terms.

Correct Answer: combine

Question 5:

After finding the value of 'x', you must ________ to find the other consecutive even integers.

Correct Answer: substitute

Question 6:

Adding all the numbers together is known as finding the ________.

Correct Answer: sum

Question 7:

If x = 10, then x+4 = ________.

Correct Answer: 14

Question 8:

An ________ is a statement that two expressions are equal.

Correct Answer: equation

Question 9:

Consecutive even numbers are always ________ apart.

Correct Answer: 2

Question 10:

If the sum of three consecutive even integers is 30, and the first integer is x, the equation is x + (x+2) + (x+4) = ________.

Correct Answer: 30

Educational Standards

A2.A.1:Represent and solve mathematical and real-world problems using nonlinear equations, systems of linear equations, and systems of linear inequalities; interpret the solutions in the original context. A2.A.2:Generate and evaluate equivalent algebraic expressions and equations using various strategies.

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