Estimating: Challenge & Extension
Mathematics
Grade 6
13 questions
~26 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on estimating square roots with various question types, including practice, problem-solving, real-world applications, and extension challenges.
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Estimating: Challenge & Extension
Subject: MathematicsGrade: Grade 6
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Untitled Worksheet
Grade Grade 6
A
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
Estimate the value of √50. Round to the nearest whole number and explain your reasoning.
[2 marks]2.
Estimate the square root of 200 using nearby perfect squares. Show your work.
[2 marks]3.
Calculate an approximate value for √18. Round to the nearest whole number.
[2 marks]4.
Estimate √125 and justify your answer by referencing perfect squares.
[2 marks]B
Targeted Practice & Reasoning
Complete the following questions that require multi-step reasoning and explanation.
1.
A square has an area of approximately 150 square units. Estimate the length of one side. Show your working and reasoning.
[3 marks]2.
A ladder reaches a height of approximately 24 meters. Estimate the length of the ladder if it forms a right triangle with the ground. Assume the height is close to the hypotenuse of a right-angled triangle.
[3 marks]3.
If √80 is approximately 9 while √81 is exactly 9, explain why your estimate for √80 is reasonable. Include your reasoning.
[3 marks]C
Real-world Applications
Solve these word problems related to estimation in real-world contexts.
1.
A garden has an area of approximately 300 square meters. Estimate the length of one side if it is a square-shaped garden. Show your calculations.
[3 marks]2.
A rectangular room is 12 meters long and has an estimated width so that its area is about 144 square meters. Estimate the width of the room.
[2 marks]D
Challenge & Extension
Attempt these more difficult problems to extend your understanding of estimating square roots.
1.
Estimate √450. Justify why your estimate is reasonable using perfect squares.
[3 marks]2.
Construct a triangle on the grid with sides approximately 5, 7, and 9 units. Clearly show your construction process.
[4 marks]E
Mixed Review & Error Analysis
Answer these questions to review estimation techniques and identify common mistakes.
1.
Estimate √200 as 14. Show the calculation and reasoning behind your estimate.
[2 marks]2.
Identify and fix the mistake: A student estimates √85 as 10 because 85 is close to 100, which has a square root of 10. What is wrong with this reasoning?
[3 marks]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
- • Change grade level (Grade 6 → Grade 7)
- • Swap topics (Harry Potter → Macbeth)
- • Add more questions (10 → 15)
- • Adjust difficulty
Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet