← Back to course
Expressions and Equations 6-8 / Week 04 / Friday
5/6
Week 04 · The Balance: One-Step Equations

Friday

Equations all around
// An equation is a level balance, and a solution keeps it level
⏱ about 20 min

Friday: Equations All Around

Rocket counts the steps from the garage door to the mailbox. "Forty-two steps, and I have taken 18. How many left?"

"That is an equation," Raven says. "18 plus the steps left equals 42. What do you notice?"

"The steps left are the envelope," Rocket says. "18 + x = 42. Take 18 from both sides. 24."

Nova glides beside them along the path. "Equations hide everywhere," she says. "Minutes, pages, cups of water, steps."

"Three equal jugs fill a 12-liter tub," Raven says. "3x = 12."

"Four liters each," Rocket says, before she finishes. Then he stops. "Let me check. Three times 4 is 12. Yes."

Nova hums. "Checked before shouted. That is new."

One-step equations in everyday life

Steps: 18 steps done plus x steps left is 42 steps. 18 + x = 42, so x = 24.

Minutes: a timer ran x minutes and 4.5 minutes more, 10 minutes in all. The equation x + 4.5 = 10 gives x = 5.5.

Pages: 6 equal chapters make 90 pages. 6x = 90, so x = 15.

Water: half a jug is 3 cups. 0.5x = 3, so x = 6 cups.

What the letter stands for

In each puzzle the letter stands for one unknown number, the number that makes the sentence true.

Write the equation first. Then undo on both sides. Then put the answer back in and check. Every time.

EVERYDAY EQUATIONS
  • Read the question.
  • Tap your answer.
Rocket has taken 18 of 42 steps to the mailbox. 18 + x = 42. How many steps are left?
A timer ran x minutes, then 4.5 more, 10 minutes in all. What is x?
Six equal chapters make 90 pages. 6x = 90. How many pages is one chapter?
Half a jug of water is 3 cups. 0.5x = 3. How many cups fill the jug?
WEEK REVIEW
  • Read the question.
  • Tap your answer.
Which value of x makes x + 8 = 20 true: 10, 12, 28?
What is x if x - 3.5 = 6?
What is x if 2/3x = 4?
Three equal envelopes balance 24 beans. Which equation fits?
Week reviewTrue or false?
An equation is like a level balance: both sides name the same number.?
To solve x + 5 = 12, add 5 to both sides.?
x = 7 is a solution of x + 5 = 12.?
Taking beans from one cup only keeps the balance level.?
3 × 4 = 12?
WHY THIS EXERCISEAdding 5 to both sides of x + 5 = 12 gives x + 10 = 17, still not solved. Subtracting 5 finds x = 7.
OUR WEEK, IN ORDER
  • ?We built the balance and logged six envelope rounds.
  • ?We hung the balance and tested solutions by substitution.
  • ?We undid an operation on both sides to solve x + p = q and px = q.
  • ?We turned the crew's puzzle cards into equations and solved them.
WHY THIS EXERCISEEach day built on the last: test, then undo, then build, then write your own.
Try it
Find one unknown number at home today: minutes left on a timer, pages left in a chapter, steps to the door.
Write it as a one-step equation, solve it, and check by substitution.
Draw the walk to the mailbox as a bar: 18 steps done, x steps left, 42 steps in all.

A whole week level. Tomorrow is Puzzle Day: a balance puzzle for your family to solve.

← Thursday