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Algebra 1
Visualizing Number Sequence Relationships

Visualizing Number Sequence Relationships

Algebra 1 Grades High School 2:28 Video

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Lesson Description

Explore number patterns, ordered pairs, and how to plot them on a graph to understand sequence relationships.

Video Resource

Number patterns: visualizing sequence relationships | Algebric thinking | 5th grade | Khan Academy

Khan Academy

Duration: 2:28

Watch on YouTube

Key Concepts

Number Sequences
Ordered Pairs
Graphing
Linear Relationships

Learning Objectives

Students will be able to generate number sequences based on given rules.
Students will be able to represent number sequences as ordered pairs.
Students will be able to plot ordered pairs on a coordinate plane.
Students will be able to identify relationships between sequences using visual representations.

Educator Instructions

Introduction (5 mins)
Begin by reviewing the concept of number sequences and ordered pairs. Briefly discuss how ordered pairs can be used to represent relationships between two sets of numbers. Ask students for examples of sequences they have seen before.
Video Viewing (7 mins)
Play the Khan Academy video "Number patterns: visualizing sequence relationships | Algebric thinking | 5th grade | Khan Academy". Instruct students to pay attention to how the sequences are generated, how ordered pairs are formed, and how they are plotted on the graph.
Guided Practice (10 mins)
Work through a similar example on the board. Start with two new sequences with different rules (e.g., Sequence A: start at 2, add 2; Sequence B: start at 3, add 3). Guide students through filling out a table with the first three terms of each sequence, creating ordered pairs, and plotting them on a coordinate plane.
Independent Practice (10 mins)
Provide students with a worksheet containing similar problems. They should work independently to generate sequences, create ordered pairs, and plot them on a graph. Circulate to provide assistance as needed.
Wrap-up & Discussion (3 mins)
Review the key concepts of the lesson. Facilitate a brief discussion on the patterns observed in the graphs and how they relate to the rules of the sequences.

Interactive Exercises

Online Graphing Tool
Use an online graphing tool (e.g., Desmos, GeoGebra) to allow students to plot the ordered pairs and visualize the sequences. They can experiment with different sequence rules and observe how the graph changes.
Sequence Matching Game
Create a matching game where students match sequence rules with their corresponding graphs.

Discussion Questions

How does the rule of a sequence affect its graph?
What patterns do you notice when you plot ordered pairs from related sequences?
How can graphs help us understand the relationship between two sequences?

Skills Developed

Pattern Recognition
Analytical Thinking
Graphing Skills
Algebraic Thinking

Multiple Choice Questions

Question 1:

Sequence X starts at 3 and the rule is 'add 2'. What is the third term in the sequence?

Correct Answer: 7

Question 2:

If x=4 and y=12, what is the ordered pair?

(12,4)

(4,12)

(0,0)

(4,4)

Correct Answer: (4,12)

Question 3:

Sequence A starts at 1, add 3. Sequence B starts at 2, add 6. What is the ordered pair (x,y) for the second term of each sequence?

(2,8)

(4,14)

(4,8)

(1,2)

Correct Answer: (4,8)

Question 4:

If a graph shows a straight line, what does this tell you about the relationship between x and y?

It is a random relationship

There is no relationship

The relationship is linear

It is a non-linear relationship

Correct Answer: The relationship is linear

Question 5:

Sequence M starts at 2 and the rule is 'multiply by 2'. What is the fourth term in the sequence?

Correct Answer: 16

Question 6:

Which of the following ordered pairs represents a point on the y-axis?

(0, 5)

(5, 0)

(5, 5)

(1, 1)

Correct Answer: (0, 5)

Question 7:

If sequence A is defined by x and sequence B is defined by y and y = 3x, what is the relationship between the two sequences?

Sequence B is 3 times Sequence A

Sequence A is 3 times Sequence B

Sequence A and Sequence B are identical

There is no relationship between Sequence A and Sequence B

Correct Answer: Sequence B is 3 times Sequence A

Question 8:

Which of the following is NOT needed to define a number sequence?

A starting number

A rule for generating the next number

The color of the graph

A direction to generate the sequence

Correct Answer: The color of the graph

Question 9:

The terms in Sequence Y are blank, times the terms in Sequence X. If x = 2 and y = 8, what is the value in blank?

Correct Answer: 4

Question 10:

What is the first step for graphing a number sequence?

Identifying the independent variable as 'y'.

Creating ordered pairs (x, y) using the terms of the sequences.

Choosing your favourite colored pencil.

Throwing darts at a graph.

Correct Answer: Creating ordered pairs (x, y) using the terms of the sequences.

Fill in the Blank Questions

Question 1:

A set of numbers that follow a specific pattern is called a number ________.

Correct Answer: sequence

Question 2:

In an ordered pair (x, y), x represents the _________ variable.

Correct Answer: independent

Question 3:

To plot an ordered pair on a graph, you move horizontally based on the x-value and vertically based on the ________-value.

Correct Answer: y

Question 4:

A relationship where the ratio between two variables is constant is called a _________ relationship.

Correct Answer: linear

Question 5:

If Sequence A has the rule 'add 4' and Sequence B has the rule 'add 8', Sequence B increases _____ times as fast as Sequence A.

Correct Answer: two

Question 6:

The coordinate plane is formed by two perpendicular number lines called the x-axis and the _________-axis.

Correct Answer: y

Question 7:

The point where the x-axis and y-axis intersect is called the _________.

Correct Answer: origin

Question 8:

Given sequence X has the rule 'start at 2 and add 3' and sequence Y has the rule 'start at 1 and add 2'. The ordered pair of the second term of each sequence is (____, ____).

Correct Answer: 5, 3