Mathematics
Grade 5
15 min
Multiplication input/output tables: find the rule
Multiplication input/output tables: find the rule
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1
Introduction & Learning Objectives
Learning Objectives
Identify input and output values in a multiplication table.
Recognize patterns between input and output numbers in a multiplication table.
Determine the multiplication rule (factor) that connects input to output.
Express the multiplication rule using mathematical notation.
Use the identified rule to predict missing output or input values.
Apply inverse operations (division) to find the multiplication factor.
Verify a proposed rule by checking it against all given input/output pairs.
Have you ever seen a secret code where one number changes into another? 🕵️♀️ In this lesson, we'll become detectives to crack the code in number tables!
You'll learn how to find the hidden multiplication rule that transforms an 'input' number into an &#...
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Key Concepts & Vocabulary
TermDefinitionExample
InputThe starting number in an input/output table. It's the number that goes 'into' the rule.In a table where 2 becomes 6, '2' is the input.
OutputThe ending number in an input/output table. It's the number that comes 'out' after the rule is applied.In a table where 2 becomes 6, '6' is the output.
RuleThe mathematical operation (like multiplication by a specific number) that transforms the input into the output.If 2 becomes 6, and 3 becomes 9, the rule is 'multiply by 3'.
FactorThe specific number by which the input is multiplied to get the output. This is the 'secret number' in our multiplication rule.If the rule is 'multiply by 3', then '3' is the factor.
Input/Output TableA t...
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Core Formulas
General Multiplication Rule
$\text{Input} \times \text{Factor} = \text{Output}$
This rule shows how an input number is transformed into an output number using a constant multiplication factor. We are looking for this 'Factor'.
Finding the Factor (Inverse Operation)
$\text{Factor} = \text{Output} \div \text{Input}$
To find the unknown multiplication factor, you can use the inverse operation of multiplication, which is division. Divide any output by its corresponding input.
4 more steps in this tutorial
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Challenging
The table below is supposed to follow one multiplication rule, but one output is incorrect. Which row contains the error?
| Row | Input | Output |
|---|---|---|
| 1 | 3 | 24 |
| 2 | 5 | 40 |
| 3 | 7 | 54 |
| 4 | 9 | 72 |
A.Row 1
B.Row 3
C.Row 2
D.Row 4
Challenging
Table 1 follows the rule 'Multiply by Factor A'. Table 2 follows the rule 'Multiply by Factor B'. What is the value of Factor A multiplied by Factor B?
Table 1:
| Input | Output |
|---|---|
| 4 | 24 |
| 6 | 36 |
Table 2:
| Input | Output |
|---|---|
| 5 | 45 |
| 8 | 72 |
A.48
B.63
C.54
D.15
Challenging
A scientist observes that a plant grows a certain number of centimeters each day. On day 2, it was 10 cm tall. On day 5, it was 25 cm tall. On day 10, it was 50 cm tall. If 'Day' is the input and 'Height' is the output, what is the multiplication rule, and how tall will the plant be on day 15?
A.Rule: Multiply by 5. Height: 75 cm.
B.Rule: Add 8. Height: 23 cm.
C.Rule: Multiply by 10. Height: 150 cm.
D.Rule: Multiply by 2. Height: 30 cm.
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