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Expressions and Equations 6-8 / Week 06 / Friday
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Week 06 · Two-Step Equations

Friday

Two steps all around
// Undo in reverse order, rewrite to see the puzzle, estimate to check
⏱ about 20 min

Friday: Two Steps All Around

Rocket sets the kitchen timer. "Puzzle Night prep. I need 3 trays of cards, each with the same number, plus 4 spares. 25 cards in all."

"3x + 4 = 25," Raven says. "What do you notice about the spares?"

"Added last, so off first," Rocket says. "21 left. Share by 3. Seven a tray."

Nova glides past the bench, her light on the timer. "Two steps hide everywhere," she says. "Trays, timers, jugs, walks."

"A walk of 2 laps plus 150 meters home is 950 meters," Raven says. "2L + 150 = 950."

"Four hundred a lap," Rocket says, then stops and checks. "2 × 400 + 150. 950. Yes."

Nova hums. "Checked before shouted, again."

Two-step equations in everyday life

Trays: 3 trays of x cards plus 4 spares make 25 cards. 3x + 4 = 25, so x = 7.

Walks: 2 laps of L meters plus 150 meters home is 950 meters. 2L + 150 = 950, so L = 400.

Jugs: 4 equal pours of p cups fill a 10-cup jug that already held 2 cups. 4p + 2 = 10, so p = 2.

Timers: 5 rounds of t minutes each, plus a 2.5 minute break, take 20 minutes. 5t + 2.5 = 20, so t = 3.5.

The week in one line

Write the equation. Undo the added number, then the multiplied number, on both sides. Estimate to check. Then substitute to prove it.

For a group multiplied, p(x + q) = r, divide first or distribute first. Both roads meet.

EVERYDAY TWO-STEP EQUATIONS
  • Read the question.
  • Tap your answer.
Three trays of x cards plus 4 spares make 25 cards. 3x + 4 = 25. How many cards on each tray?
Two laps of L meters plus 150 meters home is 950 meters. 2L + 150 = 950. How long is a lap?
Four pours of p cups fill a 10-cup jug that already held 2 cups. 4p + 2 = 10. What is p?
Five rounds of t minutes plus a 2.5 minute break take 20 minutes. 5t + 2.5 = 20. What is t?
WEEK REVIEW
  • Read the question.
  • Tap your answer.
Undo the first step of 2x + 7 = 19. What does the equation become?
What is x if 3(x + 4) = 27?
Which expression is equivalent to b + 0.5b?
About what is 3.9 × 5.1, to the nearest whole number?
Week reviewTrue or false?
In 2x + 3 = 11, divide by 2 before subtracting 3 to keep the numbers whole.?
x = 7 is a solution of 3x + 4 = 25.?
a + 0.5a is the same as 1.5a.?
3(x + 2) and 3x + 6 give different answers for x = 5.?
1.5 × 24 = 36?
WHY THIS EXERCISE3(5 + 2) and 3 × 5 + 6 are both 21. Equivalent expressions match for every value.
OUR WEEK, IN ORDER
  • ?We undid 2x + 3 = 11 in reverse order on the balance.
  • ?We solved p(x + q) = r by two roads, dividing first or distributing first.
  • ?We built two-envelope puzzles and logged both undo steps.
  • ?We rewrote a + 0.5a as 1.5a and estimated before solving exactly.
WHY THIS EXERCISEEach day built on the last: reverse order, then groups, then building, then rewriting.
Try it
Find one two-step situation at home: trays plus spares, laps plus the walk home, pours into a jug.
Write it as px + q = r, estimate, solve, and check.
Draw the three trays of cards and the 4 spares as a bar labeled 3x + 4 = 25.

A whole week in two steps. Tomorrow is Puzzle Day: a two-envelope challenge for your family.

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