NCEA Level 1 Pāngarau study plan

NCEA Level 1 Pāngarau · Give each week a clear focus.

8 weeks · About 6 hours per week

Week 1

Pāngarau

Solve 20 number problems involving integers, fractions, decimals, and percentages without a calculator, showing each step.
Convert fluently between fractions, decimals, and percentages across 15 mixed items and explain the method for each conversion.
Apply order of operations (including brackets and exponents) to 15 expressions and identify the errors in 5 deliberately flawed worked examples.
Set up and solve 10 word problems on ratio, proportion, and rates (e.g., unit pricing, scale, speed) with units stated correctly.

A marked 50-question number skills test scored at 80% or higher, with a written correction log for every wrong item.

Week 2

Calculate with powers, roots, and standard form (scientific notation), including multiplying and dividing numbers in standard form.
Round numbers to a given number of decimal places or significant figures and judge when rounding is appropriate in a practical context.
Solve linear equations and simple inequalities, including those with variables on both sides, and check solutions by substitution.
Interpret and use formulas by rearranging them to make a specified variable the subject.

A one-page formula sheet you can rearrange from memory, plus 20 solved equation and inequality problems with substitution checks shown.

Week 3

Expand and factorise simple algebraic expressions, including common factors and difference of two squares.
Plot and interpret straight-line graphs from equations, and find gradient and intercepts from both graphs and equations.
Generate and describe patterns and sequences, including finding the nth term of a linear sequence.
Translate a real-life situation into an algebraic expression or equation and justify each term you use.

A portfolio of 6 graphs on grid paper with gradients, intercepts, and equations labelled, plus a table of 3 sequences with nth-term rules.

Week 4

Measure and calculate perimeter, area, and volume of rectangles, triangles, circles, prisms, and cylinders, keeping units consistent.
Apply Pythagoras' theorem to find missing sides in right-angled triangles, including in real-world contexts.
Use trigonometric ratios (sin, cos, tan) to find missing sides and angles in right-angled triangles.
Convert between metric units of length, area, and volume and explain why area and volume conversions use squared and cubed factors.

A timed 45-minute measurement and trigonometry practice paper completed at 75% or higher, with a list of the 3 error types you made.

Week 5

Calculate mean, median, mode, and range from raw data sets and from frequency tables.
Construct and read bar graphs, histograms, stem-and-leaf plots, and box plots, and describe the shape of a distribution.
Interpret scatter plots by describing correlation and drawing a line of best fit to make a prediction.
Identify misleading graphs and statistical claims and write a short critique of each.

A 2-page statistical report on a data set you collect or find, including summary statistics, one graph, and a 150-word interpretation.

Week 6

List outcomes of simple and combined events using tables and tree diagrams and calculate probabilities as fractions, decimals, and percentages.
Apply the addition and multiplication rules for probability to independent and mutually exclusive events.
Compare experimental relative frequency with theoretical probability and explain the role of sample size.
Solve 10 probability problems drawn from games, weather, and everyday risk contexts.

A set of 10 fully worked probability problems, each with a tree diagram or outcome table and a one-sentence justification of the rule used.

Week 7

Complete a full-length practice paper under timed conditions and record your score by question type.
Classify every error as conceptual, procedural, or careless and rank the topics by lost marks.
Re-teach yourself the two weakest topics by writing a worked example set for each from scratch.
Practise reading questions carefully by underlining the command word and the required answer form before solving.

A timed practice paper with an error analysis table listing topic, error type, and the corrected working for each lost mark.

Week 8

Redo every previously incorrect question from weeks 1-7 until each is solved correctly without notes.
Complete two short mixed-topic quizzes at 85% or higher to confirm retention.
Build a one-page summary sheet of formulas, rules, and common traps and recite it from memory.
Simulate exam conditions once more and practise allocating time across questions before starting.

A corrected error log with all items re-solved and two mixed quizzes scored at 85% or higher, plus your final one-page summary sheet.

Week 2: Score 80% or higher on a self-marked number and algebra test and explain every correction in your own words.

Week 4: Complete the timed measurement and trigonometry paper at 75% or higher with units correct on every answer.

Week 6: Produce a statistical report and 10 probability solutions that a peer can follow without asking you questions.

Week 8: Score 85% or higher on both mixed quizzes and show a fully corrected error log covering all eight weeks.