3A · Chapter 2 · Lesson 1
Mental Addition — Part 1
Group by place value, then recombine. Addition can be rearranged without changing the total.
Today's challenge
Add 190 + 88. Show a place-value breakdown. Try your own method, then compare it with a model.
What you'll learn
- Group by place value, then recombine. Addition can be rearranged without changing the total.
- Explain the connection between a diagram and a number sentence.
- Solve a fresh application without step-by-step hints.
Before this lesson
Place value and expanded form.
Prerequisite competency: MATH-3A-C01-PV-03
Entry · 2 questions
Warm-up: prerequisite check
Try on paper before continuing. If the questions are hard, review the prerequisite concepts.
- E1
Write 5,735 as thousands + hundreds + tens + ones.
Show answer and reasoning
Answer: 5000 + 700 + 30 + 5
Break the number into the value of each nonzero place. This is a Chapter 1 decomposition skill.
- E2
In 5,976, what is the value of the hundreds digit?
Show answer and reasoning
Answer: 900
The hundreds digit is 9; it represents 9 hundreds, or 900 ones. This is a Chapter 1 place-value skill.
Learn the concept
Words to know
- addend
- a number being added
- sum
- the result of addition
Group by place value, then recombine. Addition can be rearranged without changing the total.
Break each number into hundreds, tens, and ones. Combine like units, then recompose the quantity. If you use a number line, make the large jump first.
Why this works
A number can be split into hundreds, tens, and ones without changing its value. For 235 + 142, combine 200 + 100, then 30 + 40, then 5 + 2. You get 300 + 70 + 7 = 377. The parts can be combined in a different order because no quantity has been added or removed.
Check the meaning
Check the result by subtracting one addend. A reliable strategy works for unfamiliar numbers, not just friendly examples.
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
Add 190 + 88. Show a place-value breakdown.
- Break each number into hundreds, tens, and ones. Combine like units, then recompose the quantity. If you use a number line, make the large jump first.
- 190 is 100 + 90; add the two parts to 88. The sum is 278.
- Check the result by subtracting one addend. A reliable strategy works for unfamiliar numbers, not just friendly examples.
Result: 278
Understanding check 1 — your turn
Add 319 + 163. Show a place-value breakdown.
Reveal reasoning
Answer: 482 — 319 is 300 + 19; add the two parts to 163. The sum is 482.
Worked example 2
Reason and verify
Add 227 + 111. Show a place-value breakdown.
- Break each number into hundreds, tens, and ones. Combine like units, then recompose the quantity. If you use a number line, make the large jump first.
- 227 is 200 + 27; add the two parts to 111. The sum is 338.
- Check the result by subtracting one addend. A reliable strategy works for unfamiliar numbers, not just friendly examples.
Result: 338
Understanding check 2 — your turn
Add 106 + 186. Show a place-value breakdown.
Reveal reasoning
Answer: 292 — 106 is 100 + 6; add the two parts to 186. The sum is 292.
Worked example 3
Reason and verify
Add 264 + 134. Show a place-value breakdown.
- Break each number into hundreds, tens, and ones. Combine like units, then recompose the quantity. If you use a number line, make the large jump first.
- 264 is 200 + 64; add the two parts to 134. The sum is 398.
- Check the result by subtracting one addend. A reliable strategy works for unfamiliar numbers, not just friendly examples.
Result: 398
Understanding check 3 — your turn
Add 143 + 31. Show a place-value breakdown.
Reveal reasoning
Answer: 174 — 143 is 100 + 43; add the two parts to 31. The sum is 174.
Guided · 4 questions
Guided practice
Practice with the model visible. Explain the units at each step.
- G1
Add 273 + 193. Show a place-value breakdown.
Show answer and reasoning
Answer: 466
273 is 200 + 73; add the two parts to 193. The sum is 466.
- G2
Add 310 + 38. Show a place-value breakdown.
Show answer and reasoning
Answer: 348
310 is 300 + 10; add the two parts to 38. The sum is 348.
- G3
Add 97 + 61. Show a place-value breakdown.
Show answer and reasoning
Answer: 158
97 is 0 + 97; add the two parts to 61. The sum is 158.
- G4
Add 134 + 84. Show a place-value breakdown.
Show answer and reasoning
Answer: 218
134 is 100 + 34; add the two parts to 84. The sum is 218.
Independent · 8 questions
Independent practice
Work without relying on the model or checking answers prematurely.
- I1
Add 1,953 + 471. Show a place-value breakdown.
Show answer and reasoning
Answer: 2424
1,953 is 1,900 + 53; add the two parts to 471. The sum is 2,424.
- I2
Add 2,079 + 523. Show a place-value breakdown.
Show answer and reasoning
Answer: 2602
2,079 is 2,000 + 79; add the two parts to 523. The sum is 2,602.
- I3
Add 1,955 + 575. Show a place-value breakdown.
Show answer and reasoning
Answer: 2530
1,955 is 1,900 + 55; add the two parts to 575. The sum is 2,530.
- I4
Add 2,081 + 627. Show a place-value breakdown.
Show answer and reasoning
Answer: 2708
2,081 is 2,000 + 81; add the two parts to 627. The sum is 2,708.
- I5
Add 2,207 + 679. Show a place-value breakdown.
Show answer and reasoning
Answer: 2886
2,207 is 2,200 + 7; add the two parts to 679. The sum is 2,886.
- I6
Add 2,333 + 553. Show a place-value breakdown.
Show answer and reasoning
Answer: 2886
2,333 is 2,300 + 33; add the two parts to 553. The sum is 2,886.
- I7
Add 659 + 605. Show a place-value breakdown.
Show answer and reasoning
Answer: 1264
659 is 600 + 59; add the two parts to 605. The sum is 1,264.
- I8
Add 785 + 657. Show a place-value breakdown.
Show answer and reasoning
Answer: 1442
785 is 700 + 85; add the two parts to 657. The sum is 1,442.
Challenge · 2 questions
Challenge practice
Solve original application and explanation problems. Draw and defend a useful model.
- C1
A student adds 235 + 142 by adding hundreds, tens and ones separately. Explain why regrouping the addends does not change the sum.
Show answer and reasoning
Answer: Adding by place value partitions the same two quantities into parts. The sum of the parts remains 377.
235 = 200+30+5 and 142 = 100+40+2. Combining matching units gives 300+70+7 = 377.
- C2
A student adds 246 + 137 using 200+100, 40+30 and 6+7. Where must a ten be renamed, and what is the final total?
Show answer and reasoning
Answer: 383
Hundreds: 300; tens: 70; ones: 13. Exchange 13 ones as 1 ten and 3 ones, giving 300+80+3=383.
Exit · 3 questions
Exit check
Solve independently; revisit the skill if an important explanation is missing.
- E1
Add 1,553 + 345. Show a place-value breakdown.
Show answer and reasoning
Answer: 1898
1,553 is 1,500 + 53; add the two parts to 345. The sum is 1,898.
- E2
Add 1,679 + 397. Show a place-value breakdown.
Show answer and reasoning
Answer: 2076
1,679 is 1,600 + 79; add the two parts to 397. The sum is 2,076.
- E3
Add 1,555 + 449. Show a place-value breakdown.
Show answer and reasoning
Answer: 2004
1,555 is 1,500 + 55; add the two parts to 449. The sum is 2,004.