Formalizing Upper and Lower Bounds: Rules and Operations Walkthrough

Section role: supports the 'Formalizing the Limits of Accuracy' section while the teacher synthesizes findings from the engineering challenge into formal mathematical rules. Slides: (1) Title — 'Formalizing Limits of Accuracy'; (2) The Half the Unit Rule — bullets: definition of degree of accuracy, formula for upper and lower bounds (+/- 0.5 * accuracy); (3) Inequality Notation — bullets: standard form LB <= x < UB, handling strict versus inclusive inequalities for continuous data; (4) Visualizing Error Intervals — bullets: number line representation showing boundaries for a measurement of 12.4m; (5) Operations with Bounds: Addition and Subtraction — bullets: combining maximums and minimums, why subtraction requires crossing values (Max - Min); (6) Operations with Bounds: Multiplication and Division — bullets: rules for compound measures, maximizing a quotient by taking Max distance and Min time; (7) Worked Example: Speed Calculation — bullets: distance = 100m (nearest 10m), time = 9.6s (1 d.p.), step-by-step substitution into Max speed = Upper Distance / Lower Time; (8) Video Integration — prompt to play FuseSchool video on bounds; Closing slide: 'Why must we divide the maximum distance by the minimum time to find the fastest possible speed?' — hands control back to the teacher for discussion.

Lara from Teachy