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Videos, examples, solutions and lessons to help Grade 5 students learn to generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane.

For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

Common Core: 5.OA.3

### Suggested Learning Targets

• I can make 2 numerical patterns with the same starting number for 2 different given rules.
• I can explain the relationship between each of the corresponding terms from a pattern.
• I can make ordered pairs with the corresponding terms in a pattern.
• I can graph ordered pairs on a coordinate plane.

Activities:

1) The output of a function table is 4 less than each input.   Angela says the function rule is x - 4 = y. Kara says the rule is 4 - x = y.  Who is correct? Use what you know about patterns and functions to explain your answer.

2) Given the rule add 3 and starting at 0 complete the table below.

 0

Given the rule add 6 and starting at 0 complete the table below.

 0

Look at both of the tables once they are complete and explain the relationship between the two tables using the rules to help you.

Function Machines - Input & Output Boxes 5-OA-3
This lesson takes a look at function machines, rules, inverse rules and missing values.
Function Machines - Input & Output Boxes Finding the Missing Output Value 5-OA-3
This lesson explains how to find missing output values when given a rule and input values.
One Step Function Machine
Find the rules of the function machines.
Examples:
1) Frank is a number crunching machine with a unique function. Each time you drop a number into Frank he will do the exact same operation to it and spit out the result.
Drop a few numbers into Frank and try to determine Frank's function.
Describe the function.

2) Felix is a number crunching machine with a unique function. Each time you drop a number into Frank he will do the exact same operation to it and spit out the result.
Drop a few numbers into Felix and try to determine Felix's function.
Express Felix's function using a sentence, an equation relating input to output, or using function notation.

What's my rule?
Using In/out machines

Two Step Function Machine
Find the rules of the function machines.
Examples:
1) Fabiola is a number crunching machine with a unique function. Each time you drop a number into Fabiola he will do the exact same operation to it and spit out the result.
Drop a few numbers into Fabiola and try to determine Fabiola's function.
Describe the function.

2) Write a sentence describing the table below.
3) Write an equation that represents the table below.
Interpreting relationships between patterns Example:
The following graph represents the first five terms of two given patterns.
Choose all correct statements.

### Coordinate Plane

Plotting Points in the First Quadrant - 5.OA.3
In this video, students learn how to plot points in the first quadrant of the coordinate plane. This video relates to Common Core Standard 5.OA.3. Students learn to inspect both the x and y coordinates and how to graph them accordingly. Create and Label a Coordinate Plane in the First Quadrant

Plot Points on a Coordinate Plane
An ordered pair is a pair of numbers used to locate a point on a plane.
The x-coordinate is the first number in an ordered pair; tells how many units to the left or right.
The y-coordinate is the second number in an ordered pair; tells how many units to the up or down.
Interpreting and graphing relationships between patterns
Example:
Below are ordered pairs that represent the first six terms of two given patterns. The first value in each pair is a term from Pattern A and the second value is a term from Pattern B.
Choose all correct statements.

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