Review the key concepts, formulae, and examples before starting your quiz.
đConcepts
A number pattern is a sequence of numbers that follow a specific rule to find the next numbers. Imagine a row of blocks where each block has a number written on it, like ; these blocks follow a predictable path.
The 'Rule' of a pattern is the mathematical operation (addition or subtraction) applied to one number to get the next. For example, if we have , the rule is to 'Add ' to the previous number.
Growing patterns are sequences where the numbers increase. Visually, this looks like a staircase going up, where each step is higher than the last, such as .
Shrinking or decreasing patterns are sequences where the numbers get smaller. Imagine a countdown for a rocket launch or walking down a ladder, such as .
Skip counting is a common way to form patterns. When you skip count by , you jump over one number to land on the next, creating a sequence like on a number line.
Even and Odd number patterns follow specific sequences. Even numbers always end in , while odd numbers always end in . On a number grid, these often form vertical stripes of color.
Number patterns can also be found in Grids or Tables. In a square, moving down a column usually increases the number by (e.g., ), while moving across a row increases it by .
đFormulae
đĄExamples
Problem 1:
Identify the rule and find the next two numbers in the pattern:
Solution:
Step 1: Find the difference between the first two numbers: . \ Step 2: Check if the same difference applies to the next pair: . \ Step 3: The rule is 'Add '. \ Step 4: Add to the last number: . \ Step 5: Add to that result: . \ The next two numbers are and .
Explanation:
To solve an increasing pattern, find the 'gap' by subtracting a number from the one following it, then use that gap to continue the sequence.
Problem 2:
Complete the decreasing pattern:
Solution:
Step 1: Observe the change: becomes , which is a decrease of (). \ Step 2: The rule is 'Subtract '. \ Step 3: Apply the rule to : . \ Step 4: Apply the rule to : . \ Step 5: Verify the last step: . \ The missing numbers are and .
Explanation:
In a shrinking pattern, the numbers go down by a fixed amount. We subtract the rule value from the previous number to find the next one.