🏰 Number Kingdom · Bounds
Find and use the highest possible value before rounding would change. In this lesson, focus on a rounded value represents an interval of possible originals.
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Find and use the highest possible value before rounding would change. In this lesson, focus on a rounded value represents an interval of possible originals.
A rounded value represents an interval of possible originals. Subtract half the rounding unit for the included lower bound and add half the unit for the excluded upper bound. For upper bounds, the final written answer should make that exact relationship visible rather than hiding it inside an unexplained result.
Upper bounds: A rounded value represents an interval of possible originals. Test the lower endpoint, a value just below the upper endpoint, and the upper endpoint itself by rounding them. Keep the upper bounds representation visible until the final line.
Drag interval gates around the rounded value and test values just inside and just outside the interval. Use the model to explain one change you notice while working on upper bounds.
Test the lower endpoint, a value just below the upper endpoint, and the upper endpoint itself by rounding them. Write that check beside the final upper bounds answer.
Lower bound = rounded value − half unit; upper bound = rounded value + half unit.
Visual / interactive
Drag interval gates around the rounded value and test values just inside and just outside the interval. Use the model to explain one change you notice while working on upper bounds.
Worked examples
Understand the idea with small numbers, one representation and one clear step.
Use the standard Year 8 method with mixed examples and normal wording.
Handle multi-step or less familiar questions and explain choices.
Solve a worded question, show reasoning, check accuracy and write a final sentence.
Given information: Upper bounds — A value rounds to 13 to the nearest 1. Write its strict upper bound. Method choice: use the upper bounds method and show each step with the stated values. Calculation or reasoning: A value rounds to 13 to the nearest 1. Write its strict upper bound.5. Final answer: 13.5. Check: substitute or compare with the original information to confirm the result fits the question.
Given information: Upper bounds — A value rounds to 1300 to the nearest 100. Write its strict upper bound. Method choice: use the upper bounds method and show each step with the stated values. Calculation or reasoning: A value rounds to 1300 to the nearest 100. Write its strict upper bound. Final answer: 1350. Check: substitute or compare with the original information to confirm the result fits the question.
Check: Add half for the upper bound and use a strict upper limit.
Given information: Upper bounds — A value rounds to 130 to the nearest 10. Write its strict upper bound. Method choice: use the upper bounds method and show each step with the stated values. Calculation or reasoning: A value rounds to 130 to the nearest 10. Write its strict upper bound. Final answer: 135. Check: substitute or compare with the original information to confirm the result fits the question.
Try explaining why each step works before checking the answer.
Given information: Upper bounds — A value rounds to 13 to the nearest 1. Write its strict upper bound. Method choice: use the upper bounds method and show each step with the stated values. Calculation or reasoning: A value rounds to 13 to the nearest 1. Write its strict upper bound.5. Final answer: 13.5. Check: substitute or compare with the original information to confirm the result fits the question.
Test the lower endpoint, a value just below the upper endpoint, and the upper endpoint itself by rounding them. Write that check beside the final upper bounds answer.
Create a upper bounds problem with a tempting incorrect answer. Solve it, apply the check, and explain exactly where the incorrect method breaks down.
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Use interval sort controls to solve three checked upper bounds rounds. Solve at least two of three marked rounds and use feedback to correct any error.
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Upper bounds: A rounded value represents an interval of possible originals. Test the lower endpoint, a value just below the upper endpoint, and the upper endpoint itself by rounding them. Keep the upper bounds representation visible until the final line.
Tap to mark reviewedlower bound · upper bound · error interval · inclusive · strict upper limit · upper · bounds
Tap to mark reviewedIdentify the rounding unit. Halve the unit. Subtract half for the included lower endpoint. Add half for the strict upper endpoint and write the interval carefully. Record the check explicitly for upper bounds.
Tap to mark reviewedLower bound = rounded value − half unit; upper bound = rounded value + half unit.
Tap to mark reviewedGiven information: Upper bounds — A value rounds to 13 to the nearest 1. Write its strict upper bound. Method choice: use the upper bounds method and show each step with the stated values. Calculation or reasoning: A value rounds to 13 to the nearest 1. Write its strict upper bound.5. Final answer: 13.5. Check: substitute or compare with the original information to confirm the result fits the question.
Tap to mark reviewedGiven information: Upper bounds — A value rounds to 1300 to the nearest 100. Write its strict upper bound. Method choice: use the upper bounds method and show each step with the stated values. Calculation or reasoning: A value rounds to 1300 to the nearest 100. Write its strict upper bound. Final answer: 1350. Check: substitute or compare with the original information to confirm the result fits the question.
Tap to mark reviewedGiven information: Upper bounds — A value rounds to 130 to the nearest 10. Write its strict upper bound. Method choice: use the upper bounds method and show each step with the stated values. Calculation or reasoning: A value rounds to 130 to the nearest 10. Write its strict upper bound. Final answer: 135. Check: substitute or compare with the original information to confirm the result fits the question.
Tap to mark reviewedGiven information: Upper bounds — A value rounds to 13 to the nearest 1. Write its strict upper bound. Method choice: use the upper bounds method and show each step with the stated values. Calculation or reasoning: A value rounds to 13 to the nearest 1. Write its strict upper bound.5. Final answer: 13.5. Check: substitute or compare with the original information to confirm the result fits the question.
Tap to mark reviewedIncluding the upper endpoint. This is a key trap when answering upper bounds questions.
Tap to mark reviewedFor upper bounds, show the key representation before the final calculation. Use this final check: Test the lower endpoint, a value just below the upper endpoint, and the upper endpoint itself by rounding them.
Tap to mark reviewedManufacturing tolerances, Measured dimensions
Tap to mark reviewedI can explain upper bounds, use the method, check for mistakes, and answer an exam-style question.
Tap to mark reviewedI’m Stuck
Use this whenever a question feels confusing. Nothing here is locked.
Upper bounds: A rounded value represents an interval of possible originals. Test the lower endpoint, a value just below the upper endpoint, and the upper endpoint itself by rounding them. Keep the upper bounds representation visible until the final line.
Think of upper bounds as a careful model: make the important values visible, change one thing at a time, and use the check to prove the answer fits.
Start by naming the given information and the exact result required for upper bounds.
Identify the rounding unit.
Given information: Upper bounds — A value rounds to 13 to the nearest 1. Write its strict upper bound. Method choice: use the upper bounds method and show each step with the stated values. Calculation or reasoning: A value rounds to 13 to the nearest 1. Write its strict upper bound.5. Final answer: 13.5. Check: substitute or compare with the original information to confirm the result fits the question.
Method: Identify the rounding unit. → Halve the unit. → Subtract half for the included lower endpoint. → Add half for the strict upper endpoint and write the interval carefully. Record the check explicitly for upper bounds.
Including the upper endpoint. This is a key trap when answering upper bounds questions.
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