Numbers, Operations & Algebra
Numeric and Geometric Patterns
Grade 4 · Grade 5 · Grade 6
- ✓By the end of this lesson students will be able to identify and describe numeric patterns by finding the rule.
- ✓By the end of this lesson students will be able to identify and describe geometric patterns by observing changes.
- ✓By the end of this lesson students will be able to extend both numeric and geometric patterns based on their rules.
- ✓By the end of this lesson students will be able to formulate number sentences to represent pattern rules.
Key concepts
A numeric pattern is a sequence of numbers that follows a specific rule. To find the rule, we look at how each number (or term) changes to become the next number in the sequence. This change can be adding, subtracting, multiplying, or dividing by a constant number.
A geometric pattern is a sequence of shapes or objects that follows a specific rule. The rule describes how the shapes change from one term to the next in terms of their number, size, orientation, or arrangement.
The pattern rule is the instruction that tells you how to get from one term in a pattern to the next term. It is important to check if the rule works for all the given terms in the pattern to ensure it is correct.
A number sentence is a mathematical statement that uses numbers, operation symbols (+, -, ×, ÷), and relation symbols (=, <, >) to show a relationship or describe a pattern. For patterns, a number sentence can be used to describe the rule or to find a specific term.
Key facts to remember
- 1Patterns can be found in numbers (numeric patterns) or shapes (geometric patterns).
- 2A pattern rule describes how to get from one term to the next term in a sequence.
- 3For numeric patterns, look for constant addition, subtraction, multiplication, or division between terms.
- 4For geometric patterns, observe changes in the number, size, position, or orientation of shapes.
- 5Always check your rule against all given terms in the pattern to ensure it is correct.
- 6Number sentences use mathematical symbols to express relationships or rules in patterns.
- 7Understanding patterns helps us to predict what comes next in a sequence.
Worked examples
Example 1
Find the rule and the next two terms in the numeric pattern: 7, 10, 13, 16, ...
Answer
The rule is 'Add 3'. The next two terms are 19 and 22.
Always check the difference or ratio between at least three terms to confirm the rule.
Example 2
Describe the geometric pattern and draw the next term:\nTerm 1: One square.\nTerm 2: Two squares in a horizontal row.\nTerm 3: Three squares in a horizontal row.
Answer
The pattern is a sequence of horizontal rows of squares, where each term has one more square than the previous term. The next term (Term 4) will be a row of four squares.
When describing geometric patterns, be specific about how the shapes change (e.g., number, arrangement, orientation).
Example 3
Consider the pattern: 2, 4, 8, 16, ...\na) Find the rule for the pattern.\nb) Write a number sentence to find the 5th term.\nc) Find the 5th term.
Answer
a) The rule is 'Multiply by 2'.\nb) Number sentence: 16 × 2 = ?\nc) The 5th term is 32.
A number sentence clearly shows the operation used to find the next term.
Common mistakes
- ✗Only checking the rule for the first two terms and assuming it applies to the entire pattern.
- ✗Confusing additive rules with multiplicative rules (e.g., seeing 2, 4, 6 and thinking 'multiply by 2' instead of 'add 2').
- ✗Incorrectly extending geometric patterns by not following the observed changes precisely.
- ✗Not writing a clear and complete rule for the pattern, or just stating the next term without the rule.
- ✗Making calculation errors when extending numeric patterns.
Exam tips
- ★Show all your working when finding a rule for numeric patterns.
- ★For geometric patterns, describe the changes clearly or draw the next terms accurately.
- ★Always double-check your rule by applying it to at least three terms in the pattern.
- ★Read the question carefully to ensure you answer all parts, e.g., finding the rule AND extending the pattern AND writing a number sentence.
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