019. Rules and Input-Output Tables

Learning Intentions

• To understand that a rule connects two varying quantities
• complete an input-output table given a rule
• Solve a rule in the form output input for an input-output table

Pre-requisite Summary

• Understand that a quantity can change and that two quantities can be related
• Be able to Substitute a number into a simple numerical rule
• Recall multiplication facts and basic addition facts
• Understand the meaning of input and output in a table
• Be able to follow a two-step process such as multiply, then add
• Recognise that the same rule must work for every row in a table

Worked Examples

Worked Example 1

A rule connects two varying quantities.

a) Complete the input-output table for the rule output input when the inputs are .

b) Describe in words how the rule connects input and output.

Worked Example 2

Complete the input-output table for the rule output input .

a) Find the outputs for inputs .

b) State the rule in words.

Worked Example 3

Find the rule in the form output input for the table:

a) input:

b) output:

Worked Example 4

Find the rule in the form output input for the table:

a) input:

b) output:

Worked Example 5

Use the rule output input .

a) Find the output when the input is .

b) Find the output when the input is .

c) Complete the table for inputs .

Worked Example 6

A table has:

a) input:

b) output:

Find the rule in the form output input and use it to find the output when the input is .

Problems

Problem 1

A rule connects two varying quantities.

a) Complete the input-output table for the rule output input when the inputs are .

b) Describe in words how the rule connects input and output.

Problem 2

Complete the input-output table for the rule output input .

a) Find the outputs for inputs .

b) State the rule in words.

Problem 3

Find the rule in the form output input for the table:

a) input:

b) output:

Problem 4

Find the rule in the form output input for the table:

a) input:

b) output:

Problem 5

Use the rule output input .

a) Find the output when the input is .

b) Find the output when the input is .

c) Complete the table for inputs .

Problem 6

A table has:

a) input:

b) output:

Find the rule in the form output input and use it to find the output when the input is .

Exercises

Understanding and Fluency

Exercise 1.

Complete each table Use the rule output input :

a) input:

b) input:

Exercise 2.

Complete each table using the rule output input :

a) input:

b) input:

Exercise 3.

Complete each table using the rule output input :

a) input:

b) input:

Exercise 4.

Find the rule in the form output input :

a) input: ; output:

b) input: ; output:

Exercise 5.

Find the rule in the form output input :

a) input: ; output:

b) input: ; output:

Exercise 6.

Use the rule output input :

a) find the output for input

b) find the output for input

c) find the output for input

Exercise 7.

Use the rule output input :

a) find the output for input

b) find the output for input

c) find the output for input

Exercise 8.

Complete the table and then state the rule:

a) input: ; output:

b) input: ; output:

Reasoning

Exercise 9.

Explain why a rule must work for every row in an input-output table.

Exercise 10.

A student says the rule for input-output pairs is output input. Explain the mistake.

Exercise 11.

Explain how the number added in a rule output input can be found from the row where the input is .

Exercise 12.

A student finds the rule output input for the table input: and output: . Explain whether the rule is correct.

Problem-solving

Exercise 13.

A machine uses the rule output input . How many items does it produce when the input is ?

Exercise 14.

A taxi fare table follows a rule of the form output input . If the inputs are and the outputs are , find the rule.

Exercise 15.

A pattern table has inputs and outputs . Find the rule and then find the output for input .

Exercise 16.

A factory packs items using the rule output input . How many items are packed for input ?

Exercise 17.

A student finds that input gives output and input gives output . The rule is of the form output input . Find the rule.

Exercise 18.

A table follows the rule output input . Find the outputs for inputs .

Potential Misunderstandings

• Students may think a rule only needs to work for one row instead of every row
• Students may reverse the order of operations and add before multiplying
• Students may confuse the input column with the output column
• Students may use a different rule for different rows in the same table
• Students may think the number added is the same as the common increase in the outputs
• Students may forget that the value of the output when the input is gives the constant term in rules of the form output input
• Students may Identify the multiplier incorrectly by looking only at one pair of numbers without checking the whole table
• Students may substitute the input incorrectly when completing the table

Next: 020. Coordinates on the Number Plane