Grade 2 · Operations · MAT-02-OPS-007
Add and Subtract Within 1000 Using Place-Value Strategies
Add and subtract within 1000 using hundreds, tens, and ones strategies.
Learning objectives
What you should be able to do
- Add and subtract within 1000 using hundreds, tens, and ones strategies.
- Regroup across ones/tens and tens/hundreds as needed.
- Use estimation and inverse operations to check results.
Prerequisite check
Make sure the foundation is ready.
Checks the place-value and regrouping skills extended here.
Learn
Build the idea from meaning, not memorization.
Three-digit operations extend the same base-ten logic
Hundreds, tens, and ones are combined or separated by place. The process is not a new rule; it is the same place-value reasoning applied to one more position.
Regroup wherever a place exceeds or lacks ten units
In addition, 10 ones become 1 ten and 10 tens become 1 hundred. In subtraction, 1 hundred can become 10 tens and 1 ten can become 10 ones.
Partial sums and differences expose structure
For 326+241, combine hundreds 300+200, tens20+40, and ones6+1. For more complex cases, regroup after combining each place.
Reasonableness checks grow more important
Estimate hundreds and tens before calculating. After subtracting, add the difference back; after adding, subtract an addend when practical.
Interactive math lab
Change it. See what stays true.
Base-Ten Lab
Change hundreds, tens, and ones and watch the total rebuild from place value.
- add three digit
- subtract three digit
- multi place regroup
- estimate check
Worked examples
Twenty different ways to see the concept work.
326+241
567300+200,20+40,6+1.
452+136
588400+100,50+30,2+6.
278+145
4238+5=13 regroup;7T+4T+1T=12T regroup.
367+258
625Regroup ones and tens.
489+123
6129+3=12;8T+2T+1T=11T.
615−203
412Subtract by place no regroup.
748−326
422Subtract by place.
532−117
415Regroup ones.
604−278
326Regroup across zero tens using hundreds.
700−356
344Regroup hundred to tens, then ten to ones.
250+375
62550+70=120 triggers hundred regroup.
999−456
543Subtract each place.
125+875
1000Place-value sum reaches one thousand.
1000−250
750Subtract 2 hundreds5 tens.
430−185
245Regroup through zero ones.
Estimate326+241.
About600300+200 plus tens suggests mid-500s.
Estimate604−278.
About300600−300≈300.
Check423−145=278.
278+145=423Inverse operation confirms.
Explain278+145.
200+100=300;70+40=110;8+5=13;300+110+13=423.Partial sums regroup naturally.
Explain604−278.
604 can regroup to5H9T14O before subtracting2H7T8O.Result326.
Practice
Guided practice with hints
01315+242
Hint: Add by place.
Answer: 557
02268+157
Hint: Regroup ones/tens.
Answer: 425
03754−321
Hint: Subtract by place.
Answer: 433
04602−185
Hint: Regroup across zero.
Answer: 417
05Estimate489+123.
Hint: Round mentally.
Answer: About600
06Check417+185.
Hint: Should return602.
Answer: 602
Practice
Independent practice
01342+215
Answer: 557
02476+189
Answer: 665
03825−413
Answer: 412
04703−286
Answer: 417
05599+201
Answer: 800
06900−457
Answer: 443
07275+325
Answer: 600
081000−625
Answer: 375
Common mistakes
Learn to catch the error, not just the answer.
Record each trade explicitly in place-value terms.
Regroup across places step by step; zero is a real place holder.
Estimate before calculating and compare the exact result to the estimate.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Combine or compare three-digit inventory, attendance, or distance quantities.
- Track changes in totals that involve hundreds, tens, and ones.
Challenge problems
Explain700−356 using trades.
700=6H10T0O=6H9T10O; then subtract3H5T6O to get344.
Find two three-digit addends totaling1000.
Example 425+575.
Why does278+145 create a new hundred?
Tens total12 tens, which regroup as1 hundred2 tens.
Check604−278=326 two ways.
326+278=604 and estimate600−300≈300.
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 6
Game mode
Base-Ten Builder 1000
Solve three-digit addition/subtraction by making correct place-value trades.
Practice
Mastery check
01324+231
Answer: 555
02278+146
Answer: 424
03754−321
Answer: 433
04602−184
Answer: 418
05What is10 tens?
Answer: 1 hundred
06How can subtraction be checked?
Answer: Add the difference and subtrahend.
07Estimate468+219.
Answer: About700
08Explain why zeros can require multiple regrouping steps.
Answer: A needed smaller unit may have to be created by trading from a farther-left nonzero place.
Terminology
Words to know
- partial sum
- A subtotal from adding matching place-value parts.
- partial difference
- A difference obtained from place-value parts.
- regroup
- Exchange equivalent base-ten units.
- estimate
- A close approximation used to check reasonableness.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Common Core State Standards for Mathematics — 2.NBT.B.7–9
Addition and subtraction within 1000 using place-value understanding.