3A · Chapter 4 · Lesson 9
2-Step Word Problems
Solve group problems with one additional quantity change or comparison.
Today's challenge
A store has 6 packs of 11 markers, then sells 19 markers. How many remain? Try your own method, then compare it with a model.
What you'll learn
- Solve group problems with one additional quantity change or comparison.
- Explain the connection between a diagram and a number sentence.
- Solve a fresh application without step-by-step hints.
Before this lesson
One-step multiplicative stories.
Prerequisite competency: 3A-C04-L07
Entry · 2 questions
Warm-up: prerequisite check
Try on paper before continuing. If the questions are hard, review the prerequisite concepts.
- E1
Each of 9 shelves holds 21 equally sized boxes. How many boxes altogether?
Show answer and reasoning
Answer: 189
The total is 9 equal groups of 21: 9 × 21 = 189.
- E2
Each of 11 shelves holds 5 equally sized boxes. How many boxes altogether?
Show answer and reasoning
Answer: 55
The total is 11 equal groups of 5: 11 × 5 = 55.
Learn the concept
Words to know
- multistep problem
- a problem that needs more than one operation
Solve group problems with one additional quantity change or comparison.
Find the total in equal groups, then apply the addition or subtraction described afterward. A before/after bar can keep these steps distinct.
Why this works
Solve the equal-group situation before making a later change. Five cartons of 12 pencils hold 60 pencils. If 17 remain loose, the original total was 60 + 17 = 77. A labeled before-and-after bar helps distinguish the cartons’ contents from the leftover pencils.
Check the meaning
Do not subtract the changed number from the number of groups rather than the total objects.
Concrete → Pictorial → Abstract
- Build: Use counters, grid paper, or labeled bundles to represent the story or quantity.
- Draw: Sketch an array, place-value exchange, or equal-unit bar; label what is known.
- Calculate: Write an equation matching the representation and solve.
- Verify: Use an inverse operation or a second strategy to check.
For advanced students: if you can already explain this concept, start with the independent or challenge set.
Worked examples and immediate checks
Explain each step aloud or in writing. Work the fresh question before revealing its solution.
Worked example 1
Reason and verify
A store has 6 packs of 11 markers, then sells 19 markers. How many remain?
- Find the total in equal groups, then apply the addition or subtraction described afterward. A before/after bar can keep these steps distinct.
- First find total 6×11=66, then subtract 19 to get 47.
- Do not subtract the changed number from the number of groups rather than the total objects.
Result: 47
Understanding check 1 — your turn
A store has 7 packs of 18 markers, then sells 24 markers. How many remain?
Reveal reasoning
Answer: 102 — First find total 7×18=126, then subtract 24 to get 102.
Worked example 2
Reason and verify
A store has 7 packs of 14 markers, then sells 24 markers. How many remain?
- Find the total in equal groups, then apply the addition or subtraction described afterward. A before/after bar can keep these steps distinct.
- First find total 7×14=98, then subtract 24 to get 74.
- Do not subtract the changed number from the number of groups rather than the total objects.
Result: 74
Understanding check 2 — your turn
A store has 8 packs of 7 markers, then sells 29 markers. How many remain?
Reveal reasoning
Answer: 27 — First find total 8×7=56, then subtract 29 to get 27.
Worked example 3
Reason and verify
A store has 8 packs of 17 markers, then sells 29 markers. How many remain?
- Find the total in equal groups, then apply the addition or subtraction described afterward. A before/after bar can keep these steps distinct.
- First find total 8×17=136, then subtract 29 to get 107.
- Do not subtract the changed number from the number of groups rather than the total objects.
Result: 107
Understanding check 3 — your turn
A store has 9 packs of 10 markers, then sells 4 markers. How many remain?
Reveal reasoning
Answer: 86 — First find total 9×10=90, then subtract 4 to get 86.
Guided · 4 questions
Guided practice
Practice with the model visible. Explain the units at each step.
- G1
A store has 7 packs of 6 markers, then sells 24 markers. How many remain?
Show answer and reasoning
Answer: 18
First find total 7×6=42, then subtract 24 to get 18.
- G2
A store has 8 packs of 9 markers, then sells 29 markers. How many remain?
Show answer and reasoning
Answer: 43
First find total 8×9=72, then subtract 29 to get 43.
- G3
A store has 9 packs of 12 markers, then sells 4 markers. How many remain?
Show answer and reasoning
Answer: 104
First find total 9×12=108, then subtract 4 to get 104.
- G4
A store has 10 packs of 15 markers, then sells 9 markers. How many remain?
Show answer and reasoning
Answer: 141
First find total 10×15=150, then subtract 9 to get 141.
Independent · 8 questions
Independent practice
Work without relying on the model or checking answers prematurely.
- I1
A store has 7 packs of 14 markers, then sells 4 markers. How many remain?
Show answer and reasoning
Answer: 94
First find total 7×14=98, then subtract 4 to get 94.
- I2
A store has 8 packs of 17 markers, then sells 9 markers. How many remain?
Show answer and reasoning
Answer: 127
First find total 8×17=136, then subtract 9 to get 127.
- I3
A store has 9 packs of 6 markers, then sells 14 markers. How many remain?
Show answer and reasoning
Answer: 40
First find total 9×6=54, then subtract 14 to get 40.
- I4
A store has 10 packs of 9 markers, then sells 19 markers. How many remain?
Show answer and reasoning
Answer: 71
First find total 10×9=90, then subtract 19 to get 71.
- I5
A store has 3 packs of 12 markers, then sells 24 markers. How many remain?
Show answer and reasoning
Answer: 12
First find total 3×12=36, then subtract 24 to get 12.
- I6
A store has 4 packs of 15 markers, then sells 29 markers. How many remain?
Show answer and reasoning
Answer: 31
First find total 4×15=60, then subtract 29 to get 31.
- I7
A store has 5 packs of 18 markers, then sells 4 markers. How many remain?
Show answer and reasoning
Answer: 86
First find total 5×18=90, then subtract 4 to get 86.
- I8
A store has 6 packs of 7 markers, then sells 9 markers. How many remain?
Show answer and reasoning
Answer: 33
First find total 6×7=42, then subtract 9 to get 33.
Challenge · 2 questions
Challenge practice
Solve original application and explanation problems. Draw and defend a useful model.
- C1
A shop sold 12 pens from three equal packs and now has 33 pens. How many pens were in each original pack?
Show answer and reasoning
Answer: 15 pens
Before selling there were 33+12=45 pens. Three equal packs held 45÷3=15 each.
- C2
After 5 cartons of 12 pencils are filled, 17 loose pencils remain. How many pencils were available before filling?
Show answer and reasoning
Answer: 77 pencils
Filled pencils: 5×12=60. Add 17 leftovers to obtain 77.
Exit · 3 questions
Exit check
Solve independently; revisit the skill if an important explanation is missing.
- E1
A store has 7 packs of 16 markers, then sells 24 markers. How many remain?
Show answer and reasoning
Answer: 88
First find total 7×16=112, then subtract 24 to get 88.
- E2
A store has 8 packs of 19 markers, then sells 29 markers. How many remain?
Show answer and reasoning
Answer: 123
First find total 8×19=152, then subtract 29 to get 123.
- E3
A store has 9 packs of 8 markers, then sells 4 markers. How many remain?
Show answer and reasoning
Answer: 68
First find total 9×8=72, then subtract 4 to get 68.