Lesson Plan

• Order integers, fractions, decimals and surds accurately.
• Convert numbers between ordinary notation and standard (scientific) form.
• Estimate calculations and determine appropriate upper and lower bounds.
• Apply the laws of indices to simplify and manipulate expressions.
• Simplify surds, rationalise denominators and use bounds for irrational numbers.

• Projector/interactive whiteboard
• Printed worksheets with ordering, standard‑form and surd tasks
• Scientific calculators
• Number‑line posters for bounds activity
• Handout of index and surd formulas
• Whiteboard markers and sticky notes for exit tickets

Begin with a quick real‑world scenario: “You need to compare a mix of whole numbers, fractions and square‑root values to decide which product is cheapest.” Recall that students already know basic operations with integers and fractions. State the success criteria: by the end of the lesson they will be able to order any set of numbers, write numbers in standard form, estimate with bounds, apply index laws and simplify surds.

1. Do‑now (5'): Students order a mixed list of integers, fractions, decimals and a surd on the board; quick peer check.
2. Mini‑lecture (10'): Explain standard (scientific) form, show conversion table and multiplication/division rules.
3. Guided practice (15'): Convert a set of numbers between ordinary notation and standard form; teacher models, then students work in pairs.
4. Estimation & bounds activity (10'): Round numbers, estimate sums/products, then determine upper and lower bounds using number‑line visuals.
5. Indices & surds workshop (20'): Review index laws, simplify expressions, then move to surd operations (simplify, multiply/divide, rationalise denominators) with worked examples.
6. Exit ticket (5'): Students write one example of each skill learned on a sticky note and hand it in.

Summarise how the five strands—ordering, standard form, estimation, indices and surds—interconnect to check and simplify results. Collect exit tickets as a quick retrieval check and assign homework: a worksheet requiring conversion to standard form, estimation with bounds, and surd simplification.