krit.club logo

Patterns and Function - Identifying and Extending Number Patterns

Grade 4IB

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

•

Number Patterns: A sequence of numbers that follows a specific mathematical rule. Imagine a row of stepping stones where the distance between each stone represents the constant change, such as 5,10,15,205, 10, 15, 20 where each step adds 55.

•

Identifying the Pattern Rule: To find the rule, compare two numbers that are next to each other. If the sequence is 3,7,113, 7, 11, calculate the difference: 7−3=47 - 3 = 4. This shows the rule is 'Add 44'. Visually, this is like adding 44 more dots to a pattern at every step.

•

Increasing (Growing) Patterns: A pattern where numbers get larger through addition or multiplication. On a bar graph, this looks like a staircase moving upwards, such as 2,4,8,162, 4, 8, 16 where each value is multiplied by 22 to reach the next height.

•

Decreasing (Shrinking) Patterns: A pattern where numbers get smaller through subtraction or division. Imagine a countdown or a stack of blocks being removed; for example, 50,45,40,3550, 45, 40, 35 represents a shrinking pattern where the rule is 'Subtract 55'.

•

Input-Output Tables: Often called a 'Function Machine', this table shows a relationship between two sets of numbers. An 'Input' number enters the machine, a rule is applied, and an 'Output' number is produced. Visually, it is represented as a T-chart with InputInput on the left and OutputOutput on the right.

•

Extending the Sequence: Once a rule is found, it can be used to predict future numbers. If the pattern is 12,15,1812, 15, 18 (Rule: +3+3), the next term is found by calculating 18+3=2118 + 3 = 21. This allows you to continue the line of numbers indefinitely.

•

Repeating Patterns: A sequence that repeats the same core group of numbers or shapes over and over. A visual example is a bead string with colors 1,2,3,1,2,31, 2, 3, 1, 2, 3, where the pattern unit 1,2,31, 2, 3 repeats.

📐Formulae

Next Term=Previous Term±Change\text{Next Term} = \text{Previous Term} \pm \text{Change}

Output=Input+n\text{Output} = \text{Input} + n

Output=Input×n\text{Output} = \text{Input} \times n

Difference=Term2−Term1\text{Difference} = \text{Term}_{2} - \text{Term}_{1}

💡Examples

Problem 1:

Identify the rule and find the next two terms in the sequence: 14,21,28,35,…14, 21, 28, 35, \dots

Solution:

Step 1: Find the difference between the first two terms: 21−14=721 - 14 = 7. \ Step 2: Check if this works for the next pair: 28−21=728 - 21 = 7. The rule is 'Add 77'. \ Step 3: Add 77 to the last known term: 35+7=4235 + 7 = 42. \ Step 4: Add 77 to that result: 42+7=4942 + 7 = 49.

Explanation:

By subtracting consecutive terms, we determine the constant additive rule. We then apply this rule repeatedly to extend the sequence.

Problem 2:

Complete the Input-Output table if the rule is Output=Input×4\text{Output} = \text{Input} \times 4. Input values are 2,5,102, 5, 10.

Solution:

Step 1: For Input 22, calculate 2×4=82 \times 4 = 8. \ Step 2: For Input 55, calculate 5×4=205 \times 4 = 20. \ Step 3: For Input 1010, calculate 10×4=4010 \times 4 = 40. \ The outputs are 8,20,408, 20, 40.

Explanation:

This example uses a multiplicative function rule. Each input is multiplied by the same constant (44) to find its corresponding output.