Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
Sixth graders write and solve equations of exactly two shapes: x + p = q and px = q, where every number involved, including the solution, is zero or positive. That restriction is deliberate. It lets students concentrate on what solving means, undoing an operation to find the unknown, before negative numbers and two-step equations arrive in seventh grade.
For x + p = q, subtracting p from both sides isolates x: if x + 4.5 = 11, then x = 6.5. For px = q, dividing both sides by p isolates x: if 3x = 7, then x = 7/3. The numbers can be fractions and decimals, so (2/3)x = 10 is fair game, and its solution is 15. Writing the equation from a word problem is half the task. A student who reads 'after spending $18 Ana has $27 left' should be able to write x - 18 = 27, or think of it as 27 + 18 = x, and explain why both describe the same situation.
For x + 8 = 20 some students add 8 to both sides. Ask what undoes adding 8: subtracting 8.
For 4x = 10 students write x = 4/10. The x is multiplied by 4, so divide 10 by 4: x = 10/4 = 2.5.
Subtracting from the left side and not the right breaks the balance. A hanger or scale model shows why both sides must change.
Two thirds of a number of tickets have been sold, which is 10 tickets. Write and solve an equation for the total number of tickets.
Answer: There are 15 tickets in total.
Balance pictures and tape diagrams help students see why the same operation is done to both sides. Encourage students to check every solution by substitution, which also links back to 6.EE.B.5.
Assessments pair equation-writing with solving, often in money, measurement and sharing contexts with decimal or fraction values. Students should be able to explain each step in words.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 6.5 (also accepted: x = 6.5)
Subtract 4.5 from both sides: x = 11 - 4.5 = 6.5. Check: 6.5 + 4.5 = 11.
Answer: 6.5 (also accepted: y = 6.5, 13/2)
Divide both sides by 8: y = 52 ÷ 8 = 6.5. Check: 8 × 6.5 = 52.
Answer: B) 16
Divide by 3/4, which means multiplying by 4/3: 12 × 4/3 = 16. Check: 3/4 of 16 is 12.
Answer: C) x - 18 = 27
Starting amount minus what she spent equals what is left: x - 18 = 27, so x = 45.
Answer: 0.70 (also accepted: 0.7)
Divide both sides by 6: c = 4.20 ÷ 6 = 0.70. Each box costs $0.70.
Answer: 3/5 (also accepted: 0.6, n = 3/5)
Subtract 2/5 from both sides: n = 1 - 2/5 = 3/5.
A full lesson with slides, activities and an exit ticket on solving one-step equations, pitched to grade 6 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 6.EE.B.7 with an answer key, ready in about a minute.
Make a worksheet →Turn solving one-step equations into a quiz students answer online that marks itself, with a class summary for you.
Build a test →Only one-step equations of the forms x + p = q and px = q, where p, q and x are nonnegative rational numbers. Two-step equations come in grade 7.
Yes. Nonnegative rational numbers include fractions and decimals, so solutions like 7/3 or 6.5 are expected.