# Estimations and Limits of Accuracy

Scheme of work: GCSE Higher: Year 10: Term 2: Estimations and Limits of Accuracy

#### Prerequisite Knowledge

• Recognise the value of a digit using the place value table.
• Round numbers to the nearest integer or given degree of accuracy not including decimal place or significant figure
• Calculate square numbers up to 12 x 12.

#### Success Criteria

• Use standard units of mass, length, time, money and other measures (including standard compound measures) using decimal quantities where appropriate.
• Round numbers and measures to an appropriate degree of accuracy (e.g. to a specified number of decimal places or significant figures
• Estimate answers; check calculations using approximation and estimation, including answers obtained using technology
• Use inequality notation to specify simple error intervals due to truncation or rounding
• Apply and interpret limits of accuracy, including upper and lower bounds

#### Key Concepts

• When rounding to the nearest ten, decimal place or significant figure students need to visualise the value at a position along the number line. For instance, 37 to the nearest 10 rounds to 40 and 5.62 to 1 decimal place rounds to 5.6.
• When a value is exactly halfway, for instance 15 to the nearest 10, by definition it is rounded up to 20.
• To estimate a solution it is necessary to round values to 1 significant figure in the first instance. However, students need to apply their knowledge of square numbers when estimating roots.

#### Common Misconceptions

• When rounding to a significant figure the values that are less significant become zero rather than being omitted. For instance, 435 to 1 s.f. becomes 400 rather than 4.
• Students often have difficulty calculating the upper bound of a rounded value. For instance the upper bound for a number rounded to the nearest 10 as 20 is 25 not 24.999.
• When using inequality notation to describe the limits of accuracy there can be confusion with the direction of the symbols.
• Students often have difficulty knowing which bound to use when calculating the limits of accuracy for division and subtraction problems.

## Estimations and Limits of Accuracy Resources

### Mr Mathematics Blog

#### Planes of Symmetry in 3D Shapes

Planes of Symmetry in 3D Shapes for Key Stage 3/GCSE students.

Use isometric paper for hands-on learning and enhanced understanding.

#### GCSE Trigonometry Skills & SOH CAH TOA Techniques

Master GCSE Math: Get key SOH-CAH-TOA tips, solve triangles accurately, and tackle area tasks. Ideal for students targeting grades 4-5.

#### Regions in the Complex Plane

Explore Regions in the Complex Plane with A-Level Further Maths: inequalities, Argand diagrams, and geometric interpretations.