Number & Algebra
Number Patterns and Equivalence
Year 5 · Year 6
- ✓By the end of this lesson students will be able to identify and describe rules for number patterns.
- ✓By the end of this lesson students will be able to extend number patterns based on a given rule.
- ✓By the end of this lesson students will be able to create number patterns given a starting point and a rule.
- ✓By the end of this lesson students will be able to understand and apply the concept of equivalence using the equals sign.
- ✓By the end of this lesson students will be able to determine if two expressions are equivalent.
Key concepts
A number pattern is a sequence of numbers that follows a specific rule. This rule tells you how to get from one number to the next in the sequence. The rule can involve adding, subtracting, multiplying, or dividing by a constant number, or sometimes a combination. Identifying the rule helps us predict the next numbers in the pattern.
Equivalence means 'having the same value'. When we use the equals sign (=), it means that the expression or number on one side of the sign has exactly the same value as the expression or number on the other side. It's like a balanced scale – both sides must weigh the same. Understanding equivalence is crucial for solving equations and comparing mathematical statements.
Key facts to remember
- 1A number pattern is an ordered list of numbers that follows a specific rule.
- 2The rule for a pattern can involve addition, subtraction, multiplication, or division.
- 3To find the rule, look for the relationship between consecutive numbers in the sequence.
- 4Equivalence means that two mathematical expressions or quantities have the exact same value.
- 5The equals sign (=) is used to show that two expressions are equivalent.
- 6To check for equivalence, calculate the value of each side of the equals sign separately.
- 7Patterns can be extended by repeatedly applying the identified rule.
Worked examples
Example 1
Identify the rule for the following number pattern and write the next two terms: 3, 7, 11, 15, __, __
Answer
Rule: Add 4. Next two terms: 19, 23.
Always check the rule across several pairs of numbers to ensure it is consistent.
Example 2
Create a number pattern that starts at 50 and subtracts 7 each time. Write the first five terms of the pattern.
Answer
The first five terms are: 50, 43, 36, 29, 22.
Example 3
Determine if the following statement is true or false: 12 + 8 = 5 × 4
Answer
True.
The equals sign means 'is the same value as', not 'the answer is'.
Common mistakes
- ✗Only checking the pattern rule for the first two numbers instead of the entire sequence.
- ✗Confusing the equals sign (=) with 'the answer is' rather than 'is the same value as'.
- ✗Incorrectly applying the pattern rule (e.g., adding instead of subtracting, or using the wrong number).
- ✗Not calculating both sides of an equivalence statement before making a comparison.
Exam tips
- ★Always write down the rule you have identified for a number pattern.
- ★For equivalence questions, show your working for both sides of the equals sign clearly.
- ★Read the question carefully to determine if you need to find the rule, extend a pattern, create a pattern, or check for equivalence.
- ★If a pattern involves multiplication or division, it often grows or shrinks much faster than patterns involving addition or subtraction.
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