Input-Output Tables

Organizing Data, Drawing Graphs, and Deriving Formulas

CAPS Grade 10 Mathematical Literacy

This document serves as a comprehensive guide to mastering Input-Output Tables, a fundamental concept in Grade 10 Mathematical Literacy. These tables are essential for organizing data, drawing graphs, and deriving formulas, illustrating the cause-and-effect relationship between two quantities.

1. Identifying the Variables

Every Input-Output Table consists of two primary components that represent the relationship between two quantities:

Input (Independent Variable)

This is the value you start with. It typically represents the independent variable, such as the number of hours worked or litres bought. In a horizontal table, the Input is always located in the top row.

Output (Dependent Variable)

This value changes based on the Input and represents the dependent variable, such as total pay or total cost. In a horizontal table, the Output is always found in the bottom row.

Input (x)	1	2	3	4	5
Output (y)	5	10	15	20	25

Example: Input (hours worked) → Output (money earned at R5 per hour)

Test Yourself: Identifying Variables

3 Questions

1 In a table showing "number of litres of petrol" and "total cost", which is the input?

Number of litres

Total cost

Both

Neither

2 In a horizontal input-output table, where is the output located?

Top row

Bottom row

Left column

Right column

3 A table shows "hours worked" (top row) and "wages earned" (bottom row). The dependent variable is:

Hours worked

Wages earned

Both

Neither

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2. Completing Gaps in the Table

In exam scenarios, you may encounter partially completed tables where you need to find missing values.

Finding an Output

Use the given rule or formula to calculate the Output based on the Input.

Example: If the rule is y = 3x and Input = 4, then Output = 12.

Finding an Input

If you need to determine the Input from a given Output, work backwards using the inverse operation.

Example: If Output = 15 and rule is y = 3x, then x = 5.

Input (x)	2	4	?	8	10
Output (y)	6	12	18	?	30

Practice: Find the missing input and output values (rule: y = 3x)

Complete the Table Challenge

Find the missing values in the input-output table.

Hint: Find the rule first (output ÷ input = constant)

3. Calculating the Constant Difference

In linear relationships, particularly those involving direct proportion, you can find the "rule" by examining the differences between Output values.

Example:

Input	1	2	3
Output	12	24	36

Constant difference: 24 - 12 = 12, 36 - 24 = 12 → Rule: y = 12x

Test Yourself: Constant Difference

3 Questions

1 Input: 1,2,3,4 | Output: 7,14,21,28. What is the rule?

Add 7

Multiply by 7

Add 6

Multiply by 6

2 Find the constant difference: Output: 5,9,13,17

3 If Input=3 gives Output=15, and Input=4 gives Output=20, what is the rule?

Add 12

Multiply by 5

Add 5

Multiply by 4

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4. Direct vs. Inverse Tables

Direct Proportion Table

Multiplying the Input by a specific number yields the Output.

Input	1	2	3	4
Output	5	10	15	20

Rule: y = 5x

Inverse Proportion Table

The product of the Input and Output remains constant.

Workers	2	4	5	10
Hours	10	5	4	2

Constant product: 2×10=20, 4×5=20

Test Yourself: Direct vs Inverse

3 Questions

1 Input: 1,2,3,4 | Output: 8,16,24,32. Is this direct or inverse?

Direct

Inverse

Neither

2 Workers: 3,6,9 | Days: 12,6,4. Is this direct or inverse?

Direct

Inverse

Neither

3 In an inverse table, what remains constant?

Difference

Product

Sum

Quotient

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5. Practical Contexts

Electricity Tariffs

Input: Units used → Output: Cost (R)

Units	100	200	300
Cost (R)	220	440	660

Taxi Fares

Input: km → Output: Fare (R)

km	5	10	15
Fare (R)	35	60	85

Catering

Input: Guests → Output: Rice (g)

Guests	10	20	30
Rice (g)	500	1000	1500

Study Tip: Always check the first column of the table. If the Input is a fixed value while the Output is a variable, this indicates a Fixed Cost, such as a monthly rental fee or a call-out charge.

Final Assessment: Input-Output Tables

8 Questions

1 Input: 2,4,6,8 | Output: 10,20,30,40. What is the rule?

Add 8

Multiply by 5

Multiply by 4

Add 5

2 Workers: 2 take 12 days, 4 take 6 days. This is:

Direct proportion

Inverse proportion

Fixed relationship

No relationship

3 Rule: y = 4x, Input = 7. Output?

4 Missing Output: Input: 3,6,9,12 | Output: 15,30,?,60

5 In a table showing litres of petrol and cost, the independent variable is:

Litres of petrol

Cost

Both

Neither

6 Constant difference in Output: 3,7,11,15

7 Output=24 when Input=6, Output=32 when Input=8. Rule?

Add 18

Multiply by 4

Multiply by 3

Add 4

8 In an inverse table, if Input doubles, Output:

Doubles

Halves

Stays the same

Quadruples

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Conclusion

Mastering Input-Output Tables is essential for Grade 10 learners in Mathematical Literacy. By understanding how to identify variables, complete gaps, calculate constant differences, and distinguish between direct and inverse relationships, students can effectively analyze data and apply these concepts to practical scenarios.