Discovering Patterns: From Tables to Algebra

Algebra 1 Grades High School 3:38 Video
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Lesson Description

Explore mathematical patterns using a real-world scenario involving arranging tables and people. Learn to identify, extend, and generalize patterns, setting the stage for algebraic thinking.

Video Resource

Math patterns example 1 | Applying mathematical reasoning | Pre-Algebra | Khan Academy

Khan Academy

Duration: 3:38
Watch on YouTube

Key Concepts

  • Pattern Recognition
  • Linear Growth
  • Mathematical Modeling

Learning Objectives

  • Students will be able to identify and extend a numerical pattern based on a real-world scenario.
  • Students will be able to describe the pattern verbally and predict future terms.
  • Students will be able to relate the pattern to a linear relationship and recognize the constant rate of change.

Educator Instructions

  • Introduction (5 mins)
    Begin by posing the problem: 'Imagine you are setting up tables for a banquet. How many people can you seat depending on how many tables you join together?' Briefly discuss real-world examples where patterns are important (e.g., architecture, music).
  • Video Viewing (7 mins)
    Play the Khan Academy video 'Math patterns example 1'. Instruct students to pay attention to how the pattern is visually represented and how the number of people seated changes with each additional table.
  • Guided Discussion (8 mins)
    After the video, lead a class discussion using the discussion questions below. Focus on understanding the logic behind the pattern and the constant addition of 4 people.
  • Interactive Exercise (10 mins)
    Divide students into small groups and have them complete the 'Table Arrangement Challenge' interactive exercise.
  • Wrap-up (5 mins)
    Summarize the key concepts learned during the lesson. Preview how these pattern-recognition skills are fundamental to understanding algebraic functions and equations.

Interactive Exercises

  • Table Arrangement Challenge
    Provide students with a worksheet containing variations of the table arrangement problem (e.g., different seating arrangements per table). Students work in groups to identify the pattern and predict the number of people that can be seated with a given number of tables. Have students justify their answers.

Discussion Questions

  • What is the pattern in the number of people that can be seated as you add more tables?
  • Why does the number of people increase by 4 each time a table is added?
  • Can you predict how many people could be seated with 10 tables? 20 tables?
  • How can we represent this pattern in a table or an equation?

Skills Developed

  • Pattern Recognition
  • Problem Solving
  • Logical Reasoning

Multiple Choice Questions

Question 1:

In the table arrangement problem, how many people can be seated with one table?

Correct Answer: 6

Question 2:

What is the constant number of people added for each additional table in the pattern?

Correct Answer: 4

Question 3:

If 3 tables can seat 14 people, how many people can 4 tables seat, following the same pattern?

Correct Answer: 18

Question 4:

Which of the following best describes the type of pattern observed in the table arrangement problem?

Correct Answer: Linear

Question 5:

Why does the number of people seated increase by 4, and not some other number, for each added table?

Correct Answer: Because one person from the previous table moves and 3 new people can sit

Question 6:

If you had 7 tables, how many people could you seat?

Correct Answer: 26

Question 7:

A pattern starts with 3 and increases by 5 each time. What are the first three numbers in the sequence?

Correct Answer: 3, 8, 13

Question 8:

What is the main idea behind recognizing patterns in math?

Correct Answer: To predict future values

Question 9:

Which real world situation is most like the table problem?

Correct Answer: The number of seats in a movie theatre as more rows are added

Question 10:

If you can seat 38 people using some number of tables, how many tables are you using?

Correct Answer: 9

Fill in the Blank Questions

Question 1:

The process of identifying a consistent set of numbers is called _______ recognition.

Correct Answer: pattern

Question 2:

In the table problem, with each additional table, the number of seats increases by a constant amount of _______.

Correct Answer: 4

Question 3:

If 5 tables can seat 22 people, then 6 tables can seat _______ people.

Correct Answer: 26

Question 4:

A sequence of numbers that increases by the same amount each time is called a(n) _______ sequence.

Correct Answer: arithmetic

Question 5:

The number of people at the end of the table had to move when you added a table. The four new seats from the new table are the ones that ______ the number of people seated.

Correct Answer: increased

Question 6:

A pattern that increases by a fixed amount each time is said to have a constant ______.

Correct Answer: rate

Question 7:

Recognizing patterns is an important skill because it helps you make ______ about future events.

Correct Answer: predictions

Question 8:

If the first number in a pattern is 7 and the pattern grows by 2 each time, the next number is ______.

Correct Answer: 9

Question 9:

A line graph is an example of a ______ representation of a mathematical model.

Correct Answer: visual

Question 10:

If a mathematical problem involves real world data, it can also be called a _________.

Correct Answer: scenario

Educational Standards

A1.F.2.1:Distinguish between linear and nonlinear (including exponential) functions. Understand that linear functions grow by equal intervals (arithmetic) and that exponential functions grow by equal factors over equal intervals (geometric). A1.F.3.1:Identify and generate equivalent representations of linear functions, graphs, tables, and real-world situations. A1.A.4.1:Analyze, use and apply mathematical models and other data sets (e.g., graphs, equations, two points, a set of data points) to calculate and interpret slope and the x- and y-intercepts of a line.

Teaching Materials

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