Maryland Math 6.AT.C.8

6.AT.C.8 is a cluster heading. These are the individual standards under it.

• 6.AT.C.8.a

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

• 6.AT.C.8.b

  Write and solve one-step equations of the form x + p = q, x − p = q, px = q and x/p = q for cases in which p, q and x are all nonnegative rational numbers.

• 6.AT.C.8.c

  Represent solutions of such equations on a number line.

01

What Students Need to Do

Students use a letter for an unknown amount in a word problem. They write and solve one-step equations using addition, subtraction, multiplication, or division with nonnegative fractions and decimals. They check answers by substitution and mark solutions on a number line.

02

What Mastery Looks Like

Given a word problem, a student writes an equation that matches the story and solves it. They replace the letter in the original equation with their answer to check it. They give the answer with units and locate it on a number line.

03

Common Misconceptions

Students may subtract again in x − 1/2 = 2 and get x = 1 1/2. They may read x/4 = 3 as x = 3/4. They may put 1.5 between 0 and 1 on a number line.

04

How to Assess It

Exit ticket: Three equal bags hold 0.75 kg of rice altogether. Write and solve an equation for the amount in one bag, check by substitution, and mark the answer on a number line from 0 to 1.

1. 01

   Use paper strips marked in fourths to build x + 0.5 = 1.25, then mark x on a taped number line.

2. 02

   Post: “Four equal cups hold 1.5 liters altogether.” Ask what x means in 4x = 1.5 and why x = 1.5 is wrong.

3. 03

   Deal pairs equation cards: x − 0.25 = 1, 3x = 1.5, x/2 = 0.75; partners solve and check by substitution.

4. 04

   Show a $7.50 receipt for three identical notebooks; students write an equation, find one notebook's price, and check against the receipt.

• 7.AT.C.8.c

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

• 6.AT.C.10

  Solve problems in context by writing and solving inequalities and interpreting solution sets in context.

• 7.AT.C.8

  Use variables to represent quantities and write and solve equations to model and reason about relationships in context.