3A · Chapter 2 · Lesson 5
Making 100 and Making 1,000
Find the missing part of 100 or 1,000 using benchmarks.
Today's challenge
What must be added to 170 to make 1,000? Try your own method, then compare it with a model.
What you'll learn
- Find the missing part of 100 or 1,000 using benchmarks.
- 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 subtraction.
Prerequisite competency: 3A-C02-L03
Entry · 2 questions
Warm-up: prerequisite check
Try on paper before continuing. If the questions are hard, review the prerequisite concepts.
- E1
Find 366 − 133 by breaking apart the amount subtracted.
Show answer and reasoning
Answer: 233
Decompose 133 into tens and ones, subtract each part from 366, and check the difference 233.
- E2
Find 426 − 156 by breaking apart the amount subtracted.
Show answer and reasoning
Answer: 270
Decompose 156 into tens and ones, subtract each part from 426, and check the difference 270.
Learn the concept
Words to know
- complement
- the amount needed to reach a target total
Find the missing part of 100 or 1,000 using benchmarks.
Represent the target as one whole bar. Mark the known part and label the unknown complement. Count up to the next ten/hundred, then on to the target.
Why this works
A missing part can be found by counting upward to a friendly target. From 786 to 800 is 14; from 800 to 1,000 is 200. Together 14 + 200 = 214, and 786 + 214 = 1,000. A part-whole bar helps show that the starting amount and the missing part make one whole.
Check the meaning
Verify that known part plus missing part equals the target. Counting up is often more reliable than a long subtraction.
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
What must be added to 170 to make 1,000?
- Represent the target as one whole bar. Mark the known part and label the unknown complement. Count up to the next ten/hundred, then on to the target.
- The missing part is 1,000 − 170 = 830; check 170 + 830 = 1,000.
- Verify that known part plus missing part equals the target. Counting up is often more reliable than a long subtraction.
Result: 830
Understanding check 1 — your turn
What must be added to 50 to make 100?
Reveal reasoning
Answer: 50 — The missing part is 100 − 50 = 50; check 50 + 50 = 100.
Worked example 2
Reason and verify
What must be added to 32 to make 100?
- Represent the target as one whole bar. Mark the known part and label the unknown complement. Count up to the next ten/hundred, then on to the target.
- The missing part is 100 − 32 = 68; check 32 + 68 = 100.
- Verify that known part plus missing part equals the target. Counting up is often more reliable than a long subtraction.
Result: 68
Understanding check 2 — your turn
What must be added to 102 to make 1,000?
Reveal reasoning
Answer: 898 — The missing part is 1,000 − 102 = 898; check 102 + 898 = 1,000.
Worked example 3
Reason and verify
What must be added to 244 to make 1,000?
- Represent the target as one whole bar. Mark the known part and label the unknown complement. Count up to the next ten/hundred, then on to the target.
- The missing part is 1,000 − 244 = 756; check 244 + 756 = 1,000.
- Verify that known part plus missing part equals the target. Counting up is often more reliable than a long subtraction.
Result: 756
Understanding check 3 — your turn
What must be added to 54 to make 100?
Reveal reasoning
Answer: 46 — The missing part is 100 − 54 = 46; check 54 + 46 = 100.
Guided · 4 questions
Guided practice
Practice with the model visible. Explain the units at each step.
- G1
What must be added to 58 to make 100?
Show answer and reasoning
Answer: 42
The missing part is 100 − 58 = 42; check 58 + 42 = 100.
- G2
What must be added to 270 to make 1,000?
Show answer and reasoning
Answer: 730
The missing part is 1,000 − 270 = 730; check 270 + 730 = 1,000.
- G3
What must be added to 42 to make 100?
Show answer and reasoning
Answer: 58
The missing part is 100 − 42 = 58; check 42 + 58 = 100.
- G4
What must be added to 94 to make 1,000?
Show answer and reasoning
Answer: 906
The missing part is 1,000 − 94 = 906; check 94 + 906 = 1,000.
Independent · 8 questions
Independent practice
Work without relying on the model or checking answers prematurely.
- I1
What must be added to 38 to make 100?
Show answer and reasoning
Answer: 62
The missing part is 100 − 38 = 62; check 38 + 62 = 100.
- I2
What must be added to 959 to make 1,000?
Show answer and reasoning
Answer: 41
The missing part is 1,000 − 959 = 41; check 959 + 41 = 1,000.
- I3
What must be added to 20 to make 100?
Show answer and reasoning
Answer: 80
The missing part is 100 − 20 = 80; check 20 + 80 = 100.
- I4
What must be added to 961 to make 1,000?
Show answer and reasoning
Answer: 39
The missing part is 1,000 − 961 = 39; check 961 + 39 = 1,000.
- I5
What must be added to 22 to make 100?
Show answer and reasoning
Answer: 78
The missing part is 100 − 22 = 78; check 22 + 78 = 100.
- I6
What must be added to 213 to make 1,000?
Show answer and reasoning
Answer: 787
The missing part is 1,000 − 213 = 787; check 213 + 787 = 1,000.
- I7
What must be added to 94 to make 100?
Show answer and reasoning
Answer: 6
The missing part is 100 − 94 = 6; check 94 + 6 = 100.
- I8
What must be added to 665 to make 1,000?
Show answer and reasoning
Answer: 335
The missing part is 1,000 − 665 = 335; check 665 + 335 = 1,000.
Challenge · 2 questions
Challenge practice
Solve original application and explanation problems. Draw and defend a useful model.
- C1
Use two jumps to explain the missing amount from 786 to 1,000.
Show answer and reasoning
Answer: 214
786→800 is 14 and 800→1,000 is 200. Together 214.
- C2
A ribbon must be 1,000 cm long. It currently measures 687 cm. Find the missing length in TWO jumps.
Show answer and reasoning
Answer: 313 cm
687→700 uses 13 cm, then 700→1,000 uses 300 cm, totaling 313 cm.
Exit · 3 questions
Exit check
Solve independently; revisit the skill if an important explanation is missing.
- E1
What must be added to 88 to make 100?
Show answer and reasoning
Answer: 12
The missing part is 100 − 88 = 12; check 88 + 12 = 100.
- E2
What must be added to 559 to make 1,000?
Show answer and reasoning
Answer: 441
The missing part is 1,000 − 559 = 441; check 559 + 441 = 1,000.
- E3
What must be added to 70 to make 100?
Show answer and reasoning
Answer: 30
The missing part is 100 − 70 = 30; check 70 + 30 = 100.