Mathematics
Grade 5
15 min
Multiplication input/output tables
Multiplication input/output tables
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1
Introduction & Learning Objectives
Learning Objectives
Define and identify the components of a multiplication input/output table.
Determine the multiplication rule given a set of input and output values.
Complete a multiplication input/output table by applying a given rule.
Find missing input values when given the output and the multiplication rule.
Find missing output values when given the input and the multiplication rule.
Create their own multiplication input/output tables based on a given rule or pattern.
Have you ever noticed how some things always change in a predictable way? 📈 Like how many wheels are on a certain number of cars? Let's discover the hidden rules!
In this lesson, you'll learn all about multiplication input/output tables. These tables help us see patterns and relationships bet...
2
Key Concepts & Vocabulary
TermDefinitionExample
InputThe starting number or value that goes into a rule or operation. It's what you begin with.In a table where you multiply by 3, if the input is 5, you start with 5.
OutputThe ending number or value that comes out after applying a rule or operation to the input. It's the result.If the input is 5 and the rule is 'multiply by 3', the output is 15.
RuleThe mathematical operation (in this case, multiplication) that transforms the input into the output. It's the consistent pattern.The rule could be 'multiply by 4' or '$ imes$ 7'.
Input/Output TableA structured way to organize pairs of input and output values, showing how a specific rule connects them.A table with columns for 'Input' and 'Output' and rows s...
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Core Formulas
Finding the Output
$\text{Output} = \text{Input} \times \text{Rule}$
Use this rule when you know the starting input number and the multiplication rule, and you want to find the resulting output number.
Finding the Rule (Multiplier)
$\text{Rule} = \text{Output} \div \text{Input}$
Use this rule when you have at least one complete input/output pair and need to figure out what number the input is being multiplied by to get the output.
Finding the Input
$\text{Input} = \text{Output} \div \text{Rule}$
Use this rule when you know the output number and the multiplication rule, and you need to find the original input number.
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Challenging
Which of the following tables is correctly completed for the rule 'Multiply by 11'?
A.| Input: 3, Output: 33 |, | Input: 7, Output: 77 |, | Input: 9, Output: 90 |
B.| Input: 4, Output: 44 |, | Input: 6, Output: 66 |, | Input: 8, Output: 88 |
C.| Input: 2, Output: 22 |, | Input: 5, Output: 50 |, | Input: 10, Output: 111 |
D.| Input: 5, Output: 55 |, | Input: 11, Output: 121|, | Input: 12, Output: 131 |
Challenging
An input/output table's rule is a whole number. If an input of 6 gives an output of 108, and an input of 10 gives an output of 180, what would be the input for an output of 216?
A.18
B.14
C.12
D.16
Challenging
A student was given the table below and said the rule was 'Multiply by 3'. What was their most likely mistake?
| Input | Output |
|---|---|
| 6 | 24 |
| 9 | 36 |
A.They divided the input by the output.
B.They subtracted the input from the output.
C.They divided the output by the input, but made a calculation error.
D.They confused the rule with the rule from a different problem.
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