Distinguishing Between One-Time and Repeated Additions
Distinguishing Between One-Time and Repeated Additions is a Grade 7 math skill in Illustrative Mathematics, Chapter 6: Expressions, Equations, and Inequalities. Students learn to represent one-time changes with addition/subtraction and recurring additions with multiplication in algebraic expressions.
Key Concepts
To model a situation, choose the equation form that matches how a quantity is added: One Time Addition/Subtraction: Use $px + q = r$ when a single quantity $q$ is added or subtracted once from a total of $p$ groups. Repeated Addition/Subtraction: Use $p(x + q) = r$ when a quantity $q$ is added or subtracted from each of the $p$ groups.
Common Questions
What is the difference between a one-time addition and a repeated addition?
A one-time addition adds a fixed amount once to a starting value. A repeated addition adds the same amount multiple times, which is more efficiently expressed as multiplication.
How do you write an expression for a one-time addition?
Use addition with a constant. For example, if a price increases by $5 once, write the expression as p plus 5.
How do you write an expression for repeated additions?
Use multiplication. For example, if you earn $12 per hour for h hours, write 12h instead of adding $12 over and over.
Why is it important to distinguish these in 7th grade algebra?
Correctly identifying whether an amount occurs once or repeatedly determines whether to use addition or multiplication in your expression, leading to the right equation or model.
What chapter covers one-time vs repeated additions in Illustrative Mathematics Grade 7?
This skill is covered in Chapter 6: Expressions, Equations, and Inequalities in Illustrative Mathematics Grade 7.