Unlocking Number Patterns: Predicting and Graphing Relationships

Algebra 1 Grades High School 2:36 Video
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Lesson Description

Explore number patterns, learn to identify relationships between them, and visualize these relationships through graphing. This lesson lays the groundwork for algebraic thinking by connecting patterns to visual representations.

Video Resource

Number patterns: Seeing relationships | Applying mathematical reasoning | Pre-Algebra | Khan Academy

Khan Academy

Duration: 2:36
Watch on YouTube

Key Concepts

  • Number patterns and sequences
  • Identifying relationships between patterns
  • Graphing ordered pairs
  • Linear relationships

Learning Objectives

  • Students will be able to generate a number pattern based on a given rule.
  • Students will be able to identify the relationship between two different number patterns.
  • Students will be able to graph ordered pairs representing corresponding terms in two number patterns.
  • Students will be able to interpret the graph and relate it to the rule that generates the pattern.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing what a number pattern or sequence is. Ask students for examples of patterns they've seen before (e.g., even numbers, multiples of 5). Briefly discuss the importance of finding relationships within patterns.
  • Video Viewing and Guided Practice (15 mins)
    Play the Khan Academy video 'Number patterns: Seeing relationships'. Pause at key points to ask clarifying questions and ensure understanding. Work through the example problem presented in the video together as a class. Emphasize how to create Pattern B from Pattern A, how to derive ordered pairs, and how to plot them on a graph.
  • Independent Practice (15 mins)
    Provide students with a worksheet containing similar problems to the one in the video. For example, provide a table with Pattern A and a rule to generate Pattern B. Students should complete the table, write the ordered pairs, and graph them. Encourage them to observe the relationship between the patterns and the resulting graph.
  • Discussion and Wrap-up (5 mins)
    Bring the class back together to discuss their findings. What patterns did they observe in the graphs? How did the rule for generating Pattern B affect the graph? Briefly introduce the concept of a linear relationship and how it connects to these types of patterns. Preview the next lesson on interpreting relationships between patterns.

Interactive Exercises

  • Pattern Generator
    Use an online pattern generator (or create a simple one in a spreadsheet) where students can input a rule (e.g., multiply by 2, add 3) and see the resulting pattern and graph. This allows for experimentation and visual reinforcement.

Discussion Questions

  • How does changing the rule for generating Pattern B affect the graph?
  • What are some real-world examples where understanding number patterns might be useful?

Skills Developed

  • Identifying patterns
  • Applying mathematical rules
  • Graphing ordered pairs
  • Analyzing relationships between variables

Multiple Choice Questions

Question 1:

Pattern A is: 2, 4, 6, 8. Pattern B is created by multiplying each term in Pattern A by 2. What is the fourth term in Pattern B?

Correct Answer: 16

Question 2:

If Pattern A increases by 1 each time, and Pattern B increases by 5 each time, what can you say about the distance between the points when you graph them?

Correct Answer: The distance will be the same.

Question 3:

You have Pattern A and you generate Pattern B by multiplying each term in Pattern A by a number and adding 3. What will always be true?

Correct Answer: The first term of Pattern B will be 3 when Pattern A is 0.

Question 4:

Pattern A: 1, 2, 3, 4. Pattern B: 3, 5, 7, 9. What rule was used to create Pattern B from Pattern A?

Correct Answer: Multiply each term by 2 and add 1.

Question 5:

When graphing patterns, which pattern's values are typically on the horizontal axis?

Correct Answer: Pattern A

Question 6:

If Pattern A is 0, 1, 2, 3 and Pattern B is 5, 6, 7, 8, what ordered pair represents the first terms of both patterns?

Correct Answer: (0,5)

Question 7:

What does graphing the relationship between two patterns help us visualize?

Correct Answer: How the patterns change together

Question 8:

What type of relationship do the graphs represent when Pattern B is generated by multiplying Pattern A by a constant and adding another constant?

Correct Answer: Linear

Question 9:

Pattern A is 5, 10, 15, 20. Pattern B is Pattern A times 2. What is the third term of Pattern B?

Correct Answer: 30

Question 10:

Why is understanding number patterns important in algebra?

Correct Answer: It builds a foundation for understanding functions and relationships.

Fill in the Blank Questions

Question 1:

When graphing two related number patterns, the values of Pattern A are usually plotted on the _________ axis.

Correct Answer: horizontal

Question 2:

If Pattern B is created by adding 5 to each term of Pattern A, the difference between corresponding terms will always be _________.

Correct Answer: 5

Question 3:

The visual representation of the relationship between two patterns is called a _________.

Correct Answer: graph

Question 4:

If the graph of two related patterns forms a straight line, it indicates a _________ relationship.

Correct Answer: linear

Question 5:

In the video, the rule to create Pattern B was to multiply by 3 and add _________.

Correct Answer: 1

Question 6:

The pairs of corresponding terms from Pattern A and Pattern B are written as _________ pairs.

Correct Answer: ordered

Question 7:

Understanding number patterns is a foundation for understanding _________ in algebra.

Correct Answer: functions

Question 8:

If Pattern A is 1, 2, 3, 4 and Pattern B is Pattern A times 4, the second term of Pattern B is _________.

Correct Answer: 8

Question 9:

The distance between the points of Pattern B on a graph being 3 means Pattern B is increasing by _________.

Correct Answer: 3

Question 10:

In order to generate Pattern B, you must have a _________ for Pattern A.

Correct Answer: rule

Educational Standards

A1.F.1:[Standard] Understand functions as descriptions of covariation (how related quantities vary together) in real-world and mathematical problems. A1.F.3:[Standard] Represent functions in multiple ways and use the representation to interpret real-world and mathematical problems. A1.A.4:[Standard] Analyze real-world and mathematical problems involving linear equations.

Teaching Materials

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