CCSS.Math.Content.7.EE.B.4.a

[SurretteH]

In this standard:

CCSS.Math.Content.7.EE.B.4.a
Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

Should 7th grade students solve problems following structures like:

(x + 7) /3 = 28 and x/2 + 5 = 51 ?

or are these forms not introduced because they do not follow the px + q = r or p(x +q) = r structure strictly?

I have been researching and have found many different interpretations of this standard. Some curriculum include the various forms and others stick strictly to the px + q = r or p(x +q) = r structure.

The 8th grade teacher in my district feels that the 7th grade should be covering all the different forms but the 7th is trying to use algebra tiles to demonstrate the strict interpretation of the standard (showing the other two structures above using algebra tiles is not optimal).

Any clarification would be greatly appreciated,
Holly

[Bill McCallum]

I think this is a case where you have to distinguish between what is assessed and what is in the curriculum. I don’t think you could have anything other than the exact forms given on an assessment aligned to the standards. On the other hand, I can see having a word problem that leads to one of your forms and then has a discussion about x/2 = 1/2 x or (x + 7)/3 = 1/3(x + 7) would be o.k. Both of these are facts the students know from their work with rational numbers. To my mind, there’s a distinction between what you expect students to do routinely and what can come up in a discussion. Full-blown fluency with linear equations in any form doesn’t happen until Grade 8.

[Cathy Kessel]

This is related to use of different forms mentioned in 7.EE.1, 7.EE.2, and 7.EE.3 as well as:

6.EE. 4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.

Understanding equivalences such as (x + 7)/3 equivalent to (x + 7) times 1/3, (x + 7) times 1/3 equivalent to 1/3 times x + 7/3 (which is in the form px + q where p and q are rational), or x/2 equivalent to 1/2 times x relies on properties of operations as well as:

6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.

The latter builds on

5.NF.3 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b).

and

4.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

a. Understand a fraction a/b as a multiple of 1/b.

In grade 7, px + q and p(x + q) may include rational p and q (as opposed to nonnegative rational p and q in grade 6 expressions) and equivalences may need to rely on:

7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

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