Grade 7 expressions, equations and inequalities: what it is and what to check

What it is

The domain has two clusters. The first is using properties of operations to write equivalent expressions; the second is solving real-life and mathematical problems with expressions, equations and inequalities.

• Adding, subtracting, factoring and expanding linear expressions with rational coefficients (NY-7.EE.1), like rewriting 3(x + 4) as 3x + 12.
• Seeing that different forms of an expression can show how quantities are related (NY-7.EE.2).
• Multistep problems with positive and negative numbers in any form, using estimation to check the answer is reasonable (NY-7.EE.3).
• Solving equations of the form px + q = r and p(x + q) = r, and writing them from word problems; students are expected to be fluent (NY-7.EE.4a).
• Word problems that lead to inequalities, graphed on a number line (NY-7.EE.4b).

Five things to check

1. One step: solve x + 9 = 15 and 4x = 28. Quick and without a calculator?
2. Two steps: solve 2x + 5 = 17, and say what they did first and why.
3. Distributing: expand 3(x + 4). Many children write 3x + 4.
4. From a story: "A gym charges a $20 sign-up fee plus $15 a month. Total so far is $95." Can they write the equation before solving it?
5. Checking: after solving, do they put the answer back in the equation to see if it works?

Sample questions, with answers

Each question was checked by two separate programs. The other answers are the ones a child gets from a typical slip.

1. Find the value of $x$ that makes this equation true.

   $2(x - 5) = \dfrac{22}{-0.25}$

   • A. $-39$Answer
   • B. $-41.5$
   • C. $-78$
   • D. $-83$
   What the other answers come from

   • $-41.5$: Out of Order. Divide by the number outside the parentheses first, then undo what is inside.
   • $-78$: Stopped Early. There is still a number next to x. Divide both sides by it.
   • $-83$: Outside Number Left. The number outside the parentheses multiplies everything inside. Divide by it.

2. Find the value of $x$ that makes this equation true.

   $2(x - 3) = \dfrac{12}{-0.75}$

   • A. $-5$Answer
   • B. $-6.5$
   • C. $-10$
   • D. $-13$
   What the other answers come from

   • $-6.5$: Out of Order. Divide by the number outside the parentheses first, then undo what is inside.
   • $-10$: Stopped Early. There is still a number next to x. Divide both sides by it.
   • $-13$: Outside Number Left. The number outside the parentheses multiplies everything inside. Divide by it.

3. Solve for $x$: $3x + 9 = 42$

   • A. $x = 33$
   • B. $x = 11$Answer
   • C. $x = 17$
   • D. $x = 5$
   What the other answers come from

   • $x = 33$: Half Done. After you undo the plus or minus, divide by the number next to x.
   • $x = 17$: Sign Slip. Undo with the opposite: take away what was added, add back what was taken.
   • $x = 5$: Divided One Part. Divide every term on a side by the number next to x, not just one.

4. Solve for $x$: $2x - 2 = 14$

   • A. $x = 16$
   • B. $x = 8$Answer
   • C. $x = 6$
   • D. $x = 9$
   What the other answers come from

   • $x = 16$: Half Done. After you undo the plus or minus, divide by the number next to x.
   • $x = 6$: Sign Slip. Undo with the opposite: take away what was added, add back what was taken.
   • $x = 9$: Divided One Part. Divide every term on a side by the number next to x, not just one.

What a gap looks like

• Multiplying only the first term when expanding: 3(x + 4) becomes 3x + 4.
• Undoing the operations in the reverse order, or doing the same thing to only one side.
• Dropping the number that was added or subtracted after the first step.
• Not knowing what the letter stands for, so a word problem cannot be set up.

Because this domain is so large and uses fractions and negative numbers, a gap in either one costs points here too. If your child is stuck, check the Number System guide next.

Keep reading

• Grade 7 negative numbers and fractions: what to check
• How to find math gaps in a 7th grader