Standard: 1.OA.B3 – Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)
Grade level: Grade 1
Subject: Mathematics
Domain: Operations & Algebraic Thinking
Teacher Overview
This standard focuses on teaching students the properties of addition and subtraction, specifically the commutative and associative properties. These properties are fundamental as they help students understand that numbers can be manipulated in various ways to simplify calculations, which is a critical skill in all areas of mathematics. Students should be comfortable with basic addition and subtraction facts within 10 and understand simple number sentences. They should also be familiar with the concept of grouping numbers.
After mastering this standard, students will be able to apply these properties to more complex mathematical operations, including multiplication and division, and will have a stronger foundation for algebraic thinking.
Common Misconception 1
A common misconception is that students may think the order in which numbers are added or subtracted does not matter. This is incorrect for subtraction because the order of numbers affects the outcome.
Intervention 1
To address this misconception, use visual aids such as number lines and manipulatives to demonstrate how changing the order in subtraction changes the result.
Common Misconception 2
Another misconception is that the associative property can be applied to subtraction in the same way it is applied to addition. This is incorrect because grouping numbers differently in subtraction can lead to different results.
Intervention 2
Provide concrete examples and counterexamples to illustrate how the associative property works for addition but not for subtraction. Use manipulatives to physically group and regroup numbers.
Prerequisite Knowledge
Students should have a basic understanding of addition and subtraction within 10 and be familiar with simple number sentences.
Subsequent Knowledge
Students will develop the ability to solve more complex addition and subtraction problems and will be able to use these properties in multiplication and division.
Instructional Activities
- Create number sentences using manipulatives to demonstrate the commutative property.
- Group numbers in different ways to show the associative property with visual aids.
- Use real-world scenarios, such as shopping or game scoring, to practice applying these properties.
