š° Number Kingdom Ā· Bounds
Write the range of possible original values for a rounded number. In this lesson, focus on a rounded value represents an interval of possible originals.
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Write the range of possible original values for a rounded number. 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 error intervals, the final written answer should make that exact relationship visible rather than hiding it inside an unexplained result.
Error intervals: 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 error intervals 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 error intervals.
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 error intervals answer.
Lower bound = rounded value ā 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 error intervals.
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: Error intervals ā 2.3 was rounded to 1 decimal place. Write the error interval. Method choice: use the error intervals method and show each step with the stated values. Calculation or reasoning: 2.3 was rounded to 1 decimal place. Write the error interval.25 ā¤ x < 2.35. Final answer: 2.25 ā¤ x < 2.35. Check: substitute or compare with the original information to confirm the result fits the question.
Given information: Error intervals ā 2.3 was rounded to 1 decimal place. Write the error interval. Method choice: use the error intervals method and show each step with the stated values. Calculation or reasoning: 2.3 was rounded to 1 decimal place. Write the error interval.25 ā¤ x < 2.35. Final answer: 2.25 ā¤ x < 2.35. 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: Error intervals ā 2.3 was rounded to 1 decimal place. Write the error interval. Method choice: use the error intervals method and show each step with the stated values. Calculation or reasoning: 2.3 was rounded to 1 decimal place. Write the error interval.25 ā¤ x < 2.35. Final answer: 2.25 ā¤ x < 2.35. 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: Error intervals ā 2.3 was rounded to 1 decimal place. Write the error interval. Method choice: use the error intervals method and show each step with the stated values. Calculation or reasoning: 2.3 was rounded to 1 decimal place. Write the error interval.25 ā¤ x < 2.35. Final answer: 2.25 ā¤ x < 2.35. 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 error intervals answer.
Create a error intervals 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 error intervals rounds. Solve at least two of three marked rounds and use feedback to correct any error.
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Error intervals: 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 error intervals representation visible until the final line.
Tap to mark reviewedlower bound Ā· upper bound Ā· error interval Ā· inclusive Ā· strict upper limit Ā· error Ā· intervals
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 error intervals.
Tap to mark reviewedLower bound = rounded value ā half unit; upper bound = rounded value + half unit.
Tap to mark reviewedGiven information: Error intervals ā 2.3 was rounded to 1 decimal place. Write the error interval. Method choice: use the error intervals method and show each step with the stated values. Calculation or reasoning: 2.3 was rounded to 1 decimal place. Write the error interval.25 ā¤ x < 2.35. Final answer: 2.25 ā¤ x < 2.35. Check: substitute or compare with the original information to confirm the result fits the question.
Tap to mark reviewedGiven information: Error intervals ā 2.3 was rounded to 1 decimal place. Write the error interval. Method choice: use the error intervals method and show each step with the stated values. Calculation or reasoning: 2.3 was rounded to 1 decimal place. Write the error interval.25 ā¤ x < 2.35. Final answer: 2.25 ā¤ x < 2.35. Check: substitute or compare with the original information to confirm the result fits the question.
Tap to mark reviewedGiven information: Error intervals ā 2.3 was rounded to 1 decimal place. Write the error interval. Method choice: use the error intervals method and show each step with the stated values. Calculation or reasoning: 2.3 was rounded to 1 decimal place. Write the error interval.25 ā¤ x < 2.35. Final answer: 2.25 ā¤ x < 2.35. Check: substitute or compare with the original information to confirm the result fits the question.
Tap to mark reviewedGiven information: Error intervals ā 2.3 was rounded to 1 decimal place. Write the error interval. Method choice: use the error intervals method and show each step with the stated values. Calculation or reasoning: 2.3 was rounded to 1 decimal place. Write the error interval.25 ā¤ x < 2.35. Final answer: 2.25 ā¤ x < 2.35. 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 error intervals questions.
Tap to mark reviewedFor error intervals, 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 error intervals, use the method, check for mistakes, and answer an exam-style question.
Tap to mark reviewedIām Stuck
Use this whenever a question feels confusing. Nothing here is locked.
Error intervals: 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 error intervals representation visible until the final line.
Think of error intervals 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 error intervals.
Identify the rounding unit.
Given information: Error intervals ā 2.3 was rounded to 1 decimal place. Write the error interval. Method choice: use the error intervals method and show each step with the stated values. Calculation or reasoning: 2.3 was rounded to 1 decimal place. Write the error interval.25 ā¤ x < 2.35. Final answer: 2.25 ā¤ x < 2.35. Check: substitute or compare with the original information to confirm the result fits the question.
Method: Identify the rounding unit. ā Halve the unit. ā Subtract half for the included lower endpoint. ā Add half for the strict upper endpoint and write the interval carefully. Record the check explicitly for error intervals.
Including the upper endpoint. This is a key trap when answering error intervals questions.
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