Unlocking Patterns: Building Townhouses with Math

Algebra 1 Grades High School 5:41 Video
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Lesson Description

Explore number patterns by analyzing toothpick townhouse constructions. Use tables and equations to predict values and extend patterns.

Video Resource

Math patterns example 2 | Applying mathematical reasoning | Pre-Algebra | Khan Academy

Khan Academy

Duration: 5:41
Watch on YouTube

Key Concepts

  • Identifying patterns
  • Creating a table to represent data
  • Developing an equation from a pattern
  • Linear functions

Learning Objectives

  • Students will be able to identify and extend a number pattern.
  • Students will be able to represent a pattern using a table and an equation.
  • Students will be able to use an equation to predict values in a pattern.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the concept of number patterns and their importance in mathematics. Briefly discuss how patterns can be represented in different ways (e.g., sequences, tables, equations).
  • Video Viewing (10 mins)
    Watch the Khan Academy video 'Math patterns example 2'. Encourage students to take notes on the pattern identified in the video, the table created, and the equation derived.
  • Discussion (10 mins)
    Lead a class discussion about the video. Focus on how the pattern was identified, how the table helped to organize the data, and how the equation was derived. Discuss the meaning of each part of the equation in relation to the townhouse construction.
  • Interactive Exercise (15 mins)
    Provide students with a similar pattern-based problem (e.g., building a fence with posts and rails). Have them work individually or in pairs to create a table, derive an equation, and predict the number of materials needed for a larger structure. Example: 'You are building a row of connected square gardens. Each garden shares a side with the one next to it. The first garden requires 4 fence posts. Each additional garden requires 3 more fence posts. Create a table, write an equation, and predict the number of fence posts needed for 10 gardens.'
  • Wrap-up (5 mins)
    Summarize the key concepts learned in the lesson. Emphasize the importance of identifying patterns, organizing data, and representing relationships with equations. Assign practice problems for homework.

Interactive Exercises

  • Fence Post Pattern
    You are building a row of connected square gardens. Each garden shares a side with the one next to it. The first garden requires 4 fence posts. Each additional garden requires 3 more fence posts. Create a table, write an equation, and predict the number of fence posts needed for 10 gardens.

Discussion Questions

  • How does a table help in identifying a pattern?
  • How can you use an equation to predict values in a pattern?
  • What are some other real-world examples where patterns can be used to solve problems?

Skills Developed

  • Pattern recognition
  • Algebraic reasoning
  • Problem-solving
  • Representing data with tables and equations

Multiple Choice Questions

Question 1:

What is the first step in finding a pattern?

Correct Answer: Observing the numbers and looking for a relationship

Question 2:

In the townhouse example, how many toothpicks are added for each additional house?

Correct Answer: 5

Question 3:

What does the table help you do when finding patterns?

Correct Answer: Organize the data

Question 4:

If the equation for a pattern is T = 6 + 5(H - 1), where T is the number of toothpicks and H is the number of houses, how many toothpicks are needed for 10 houses?

Correct Answer: 51

Question 5:

What type of function is the townhouse pattern an example of?

Correct Answer: Linear

Question 6:

Which of the following is NOT a way to represent functions?

Correct Answer: Stories

Question 7:

What is another name for equal intervals?

Correct Answer: arithmetic

Question 8:

What is the range?

Correct Answer: y-values

Question 9:

What is the domain?

Correct Answer: x-values

Question 10:

What happens to the line as the slope increases?

Correct Answer: becomes steeper

Fill in the Blank Questions

Question 1:

A list of numbers that follow a certain rule is called a __________.

Correct Answer: pattern

Question 2:

The first step to solving word problems is to _________ the problem.

Correct Answer: understand

Question 3:

In an equation, a __________ represents an unknown value.

Correct Answer: variable

Question 4:

The y-intercept of a line is where the line crosses the __________ axis.

Correct Answer: y

Question 5:

The x-intercept of a line is where the line crosses the __________ axis.

Correct Answer: x

Question 6:

The dependent variable is another name for _________.

Correct Answer: range

Question 7:

The independent variable is another name for _________.

Correct Answer: domain

Question 8:

A line that is perfectly horizontal has a slope of _________.

Correct Answer: zero

Question 9:

What tool might you use to collect data?

Correct Answer: spreadsheet

Question 10:

A line that goes up to the right has a ___________ slope.

Correct Answer: positive

Educational Standards

A1.A.4:Analyze real-world and mathematical problems involving linear equations. A1.F.3:Represent functions in multiple ways and use the representation to interpret real-world and mathematical problems. 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).

Teaching Materials

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