Estimating: Problem Solving & Reasoning with Cube Roots
Mathematics
Grade 7
15 questions
~30 mins
1 views0 downloads
About This Worksheet
This worksheet focuses on estimating cube roots through problem solving and reasoning activities, helping students develop intuitive understanding and practical skills.
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Estimating: Problem Solving & Reasoning with Cube Roots
Subject: MathematicsGrade: Grade 7
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Untitled Worksheet
Grade Grade 7
A
Introduction
Read the key concept below before attempting the questions.
1.
Estimating cube roots involves finding a rough value of the cube root of a number by identifying nearby perfect cubes and interpolating.
[2 marks]B
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
Estimate the cube root of 64.
[2 marks]2.
Estimate the cube root of 125.
[2 marks]3.
Estimate the cube root of 50.
[2 marks]4.
Estimate the cube root of 200.
[2 marks]C
Targeted Estimation & Reasoning
Solve the following multi-step problems involving estimation of cube roots. Show detailed reasoning.
1.
A box contains approximately 150 cubic centimeters of material. Estimate the side length of a cube with this volume by estimating the cube root.
[3 marks]2.
A sculpture is estimated to have a volume close to 4000 cubic inches. Estimate the length of one side of the cube assuming the volume is a perfect cube.
[3 marks]3.
Estimate the cube root of 500, then explain how you determined your answer.
[3 marks]D
Real-world Applications
Use estimation skills to solve these contextual word problems.
1.
A water tank has about 27,000 liters of water. If the tank is shaped as a cube, estimate the length of one side of the tank in meters.
[3 marks]2.
A large storage container's volume is roughly 1,000,000 cubic centimeters. Estimate the length of its sides in centimeters assuming it is cubic.
[3 marks]E
Challenge & Extension
Tackle these more complex estimation problems to extend your understanding.
1.
Estimate the cube root of 1728 without calculating the exact value. Explain your reasoning.
[3 marks]2.
If a cube’s volume is 8000 cubic units, estimate the side length and justify your estimate.
[3 marks]F
Mixed Review
Answer these questions to review your estimation skills across different contexts.
1.
Estimate the cube root of 1000.
[2 marks]2.
Estimate the cube root of 343.
[2 marks]G
Error Analysis
Identify and correct the common mistake in estimating the cube root of 125 as 3.5.
1.
A student estimates √125 ≈ 3.5. Is this correct for cube roots? If not, what is the mistake and the correct estimate?
[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)
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet