Multiplicative Relationships Between Patterns
Multiplicative relationships between patterns is a Grade 5 math skill in enVision Mathematics, Chapter 15: Algebra: Analyze Patterns and Relationships. When every term in Pattern B equals the corresponding term in Pattern A multiplied by a constant k, the relationship is multiplicative: B = k x A. Students identify this constant multiplier and use it to extend and describe paired patterns.
Key Concepts
Property When comparing two numerical patterns, a multiplicative relationship exists if each term in one pattern can be found by multiplying the corresponding term in the other pattern by a constant number. If Pattern A has terms $a$ and Pattern B has terms $b$, the relationship is $b = k \times a$ for a constant number $k$.
Examples Pattern A: 1, 2, 3, 4 Pattern B: 4, 8, 12, 16 The relationship is that each term in Pattern B is 4 times the corresponding term in Pattern A. ($B = 4 \times A$) Pattern A: Start at 2, add 2 (2, 4, 6, 8) Pattern B: Start at 10, add 10 (10, 20, 30, 40) The relationship is that each term in Pattern B is 5 times the corresponding term in Pattern A. ($B = 5 \times A$).
Explanation A multiplicative relationship occurs when two patterns are connected by a consistent multiplication rule. To identify this relationship, compare the corresponding terms from each pattern. You can check for this relationship by dividing a term from the second pattern by its corresponding term in the first pattern. If this operation yields the same number for all pairs of terms, you have found the multiplicative rule.
Common Questions
What is a multiplicative relationship between two patterns?
When every term in one pattern is a constant multiple of the corresponding term in the other pattern: B = k x A for the same k throughout.
How do you find the constant multiplier between two patterns?
Divide a term in Pattern B by the corresponding term in Pattern A. If the result is the same for all corresponding pairs, that is the constant multiplier k.
If Pattern A is 2, 4, 6, 8 and Pattern B is 6, 12, 18, 24, what is the relationship?
B = 3 x A. Every term in Pattern B is 3 times the corresponding term in Pattern A.
Where are multiplicative relationships between patterns taught in enVision Grade 5?
Chapter 15: Algebra: Analyze Patterns and Relationships in enVision Mathematics, Grade 5.
How is a multiplicative pattern different from an additive one?
In an additive pattern, corresponding terms differ by a constant amount (B = A + c). In a multiplicative pattern, one is always a constant multiple of the other (B = k x A).