- This topic has 5 replies, 4 voices, and was last updated 8 years, 7 months ago by
.
-
Posts
-
In this standard, apply the properties of operations to generate equivalent expressions, two examples are distributive, the third says apply properties of operations to y + y + y. For the third, I am thinking multiplicative identity and commutative?
Should we expect to review all mathematical properties that could ever be used to generate equivalent expressions, or just focus on these examples at the sixth grade level?
Formally, this is the existence of a multiplicative identity and the distributive law,
$$
y + y + y = 1\cdot y + 1 \cdot y + 1 \cdot y = (1 + 1 + 1) y = 3y.
$$
But in this example I think it would be fine if students also saw this informally as 3 $y$s. And it’s important to remember the footnote on page 23: students need not remember the formal names for the properties. The main point is that they should use them. Thinking of seeing $y$ as $1 \cdot y$ is useful in many manipulations, for example $xy + y = (x+1)y$.Thank you for clarifying.
Would we also review all other properties of operations with this standard or will those be picked up in other standards with Expressions and Equations? We were discussing this at a meeting with some disagreement. Should we include the inverse operation standards here? Zero property? Associative and commutative?
The concern for us is that PARCC may interpret the standard differently and we don’t want our students unprepared.
Hi Bill – in response to your comment that it would be ok if students saw y + y + y informally as 3 y’s…do you see that happening after a good amount of formal work actually using the properties? The reason I ask is because I rarely see any work with the properties and work with “like terms” generally boils down to some analogy like “3 apples and 5 apples is 8 apples, so 3x + 5x = 8x”. I’m not convinced that type of argument actually counts as mathematics. I’d like to see my teachers treating 3x + 5x as x(3 + 5). Is that what the standard is expecting?
What about an expression like 6x + 7y – 2x? I am looking at a book that uses the commutative property as justification for rewriting this as 6x – 2x + 7y and then the distributive property to go from there to (6 – 2)x + 7y and then 4x + 7y. I don’t think the commutative property should be used in this case because the expression involves subtraction, and students do not yet know that subtracting 2x is the same as adding –2x. Do you agree? If so, how should students reason about simplifying this expression?
I’m going to leave the question of whether this is an appropriate 6th grade task for someone else, but what about this for writing the equivalent expressions?
Use the commutative property of addition to rewrite the expression as 7y + 6x – 2x. Then proceed with the distributive property: 7y + x(6 – 2). Yeah?
- You must be logged in to reply to this topic.