One-Step Inequalities

[Lynda]

 

In a previous response, you indicated that you could foresee a curriculum being developed for Grade 6 that included solving 1-step inequalities. If so, how would students check negative solutions for an inequality such as x + 2 < 5? Is the expectation that they would only check positive solutions and 0? Additionally, are students expected to know other inequality symbols, such as greater than or equal to?

[Bill McCallum]

[corrected 2013/2/2]

The relevant standard here is

6.EE.8. Write an inequality of the form $x<c$ or $x>c$ to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form $x<c$ or $x>c$ have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

On the one hand, there is no restriction on the sign of the solution; on the other hand, the inequalities are simpler than the ones you describe. In Grade 7, students solve more complicated inequalities, of the form $px+q<r$ or $px+q>r$, so I think I was thinking of preparing for that in my earlier comments. But note that $x+p<q$ is not required by the standards in Grade 6. My feeling is that if you are going to do these, it makes sense to include negative solutions. But the standards don’t really offer any guidance here.

As for the question about inequality symbols, the key point in Grade 6 is to understand what an inequality is and to visualize solutions, not to learn a lot of notation. The standard is intentionally sparse to focus on that. At some point in their careers students will have to learn the meaning of ≤ and ≥, but it doesn’t seem important right off the bat.

[Lynda]

” But the standards don’t really offer any guidance here.”

As a standards writer, is it your guidance that a teacher should mention the negative solutions but not ask students to “check” any of them in the original inequality, or that all solving of inequalities should wait unti Grade 7?

[Jim]

The relevant standard here is:
6.EE.8. Write an inequality of the form x<c or x>c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x<c or x>c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

[Bill McCallum]

Thanks for pointing that out, original now corrected.

[nancymclaughlin]

Hello All,

 

To the CCSS-M folks, Are there future plans to include a standard for learning the meaning of ≤ and ≥, in a subsequent grade level?

[Bill McCallum]

There is no intention to exclude these symbols from the curriculum. There is a discussion of this point here. In general, some confusion has resulted from the avoidance of specifying vocabulary and specific symbol usage in the standards. A lot of those decisions are up to curriculum writers.

[Author]

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