Maryland Math 6.AT.C.10

6.AT.C.10 is a cluster heading. These are the individual standards under it.

• 6.AT.C.10.a

  Explain that a variable can represent an unknown number in a set and use substitution to determine whether a given number in a set makes an inequality true.

• 6.AT.C.10.b

  Write and solve one-step inequalities of the form x + p > q, x − p > q, px > q and x/p > q (using ≥, >, ≤, <) where p and q are nonnegative rational numbers.

• 6.AT.C.10.c

  Represent solutions of such inequalities on a number line.

01

What Students Need to Do

Students turn a word problem into a one-step inequality and solve it. They test possible values by substitution, including fractions and decimals. They graph all values that work on a number line and explain which make sense in the problem.

02

What Mastery Looks Like

Given a goal of at least 12 miles and 3 miles already walked, a student writes x + 3 ≥ 12 and finds x ≥ 9. They test a value by substitution and mark 9 with a closed circle on a number line. They explain that any additional distance of 9 miles or more reaches the goal.

03

Common Misconceptions

Some students write an equation when a limit calls for an inequality. Others use a closed circle for a strict inequality or shade the wrong side of the number line. They may treat the variable as one answer rather than a set of values.

04

How to Assess It

Exit ticket: You have $12 for lunch and pay $3.50 for a drink. Write and solve an inequality for sandwich cost, graph affordable prices, and substitute $8.75 to check whether it works.

1. 01

   Lay a tape number line on the floor, place an open circle at 4 for 3x > 12, and mark values that work.

2. 02

   Have partners explain why 4 fails and 4.5 works for x > 4 using substitution and an open circle at 4.

3. 03

   Match four inequality cards, x + 2 > 5, x − 1 ≤ 4, 2x ≥ 6, x/2 < 3, to graphed solutions.

4. 04

   With a $10 lunch budget and a $2.50 drink, write and solve an inequality for sandwich cost, then mark affordable prices.

• 7.AT.C.8.c

  Solve word problems leading to equations of these forms and interpret the solution in terms of the context.

• 7.AT.C.9

  Use variables to represent quantities and write and solve inequalities to model and reason about constraints and conditions in context.

• 6.AT.C.8

  Solve problems in context by writing and solving equations and interpreting the solutions in context.

• 7.AT.C.9.c

  Interpret the solution set in terms of the context by describing what values are possible or reasonable in the given situation.