Algebra, Lines and Data

Overview

This 60-minute integrated Year 9 mathematics lesson revises key Stage 5 ideas across algebraic techniques, linear relationships, surds and data analysis. The student rotates through short, connected tasks using algebra to model a situation, coordinates to investigate a line, surds to simplify a result, and summary statistics to compare data.

Learning intentions

• WALT simplify algebraic fractions with numerical and algebraic denominators.
• WALT expand expressions and use equations of straight lines.
• WALT apply surds and fractional indices in exact calculations.
• WALT compare datasets using quartiles, interquartile range and box plots.

Success criteria

• I can simplify an algebraic fraction and expand brackets, showing each step.
• I can find gradient, midpoint and distance from coordinates and use a line equation.
• I can simplify a surd or rewrite a fractional index.
• I can calculate the five-number summary and explain which dataset is more consistent.

Curriculum links

• Algebraic techniques A: operations with algebraic fractions, distributive law and collecting like terms.
• Algebraic techniques B: algebraic fractions involving pronumerals, expansion and factorisation.
• Linear relationships C: gradient, midpoint, distance, transformations and equations of lines.
• Indices C and Data analysis A: surds, fractional indices, quartiles, interquartile range and box plots.

Lesson structure (60 minutes)

1. 0–5 min · Hook and diagnostic. Open with the integrated challenge introduction and ask: “How can one mathematical model describe movement, measurement and variation?” The student completes three quick prompts aloud or on paper: expand (3(x+4)), find the gradient between ((1,2)) and ((3,8)), and simplify (\sqrt{18}). Note misconceptions without correcting every answer immediately.

2. 5–15 min · Algebra mini-lesson. Use the algebra teaching slides to model the distributive law, collecting like terms, and simplifying fractions such as (\frac{6x+12}{6}=x+2) and (\frac{3}{4}+\frac{x}{4}=\frac{x+3}{4}). The student completes the first examples on the integrated practice worksheet, explaining why each operation is valid. Briefly demonstrate taking out a common factor, for example (6x+9=3(2x+3)).

3. 15–27 min · Coordinate geometry investigation. Display the gradient and intercept reference mat and revisit the meanings of (m) and (c) in (y=mx+c). The student uses the worksheet to find the gradient, midpoint and distance between two points, then writes the equation of the line through ((2,3)) and ((6,11)). Ask the student to check the equation by substituting both points. If time permits, discuss how reflecting a point in the (x)-axis changes its coordinates.

4. 27–37 min · Surds and fractional indices. Use the surds and indices teaching slides to connect square roots with exact values. Model (\sqrt{18}=3\sqrt2), (\sqrt8+\sqrt{18}=5\sqrt2), and (16^{1/2}=4). The student completes three worksheet questions, including one requiring a choice between index notation and surd notation. Emphasise that exact answers should remain in surd form unless a decimal approximation is requested.

5. 37–52 min · Data comparison task. Introduce two small datasets on the data investigation slides: weekly practice minutes for two athletes, for example A: (20, 25, 25, 30, 35, 40, 45); B: (10, 20, 30, 30, 30, 40, 50). The student orders each dataset, determines the minimum, lower quartile, median, upper quartile and maximum, and calculates each interquartile range. Using the box plot and five-number summary mat, the student constructs both box plots on the provided number line and explains which athlete has the more consistent practice pattern. Discuss how the median and spread support the conclusion.

6. 52–60 min · Consolidation and exit check. Return to the plenary and exit-question slides. The student completes the final worksheet questions independently: simplify (\frac{8x+16}{8}), expand (2(x+3)+x), find the gradient of a line through ((0,4)) and ((3,10)), simplify (\sqrt{50}), and state what the IQR measures. Review answers together, requiring the student to correct one error and explain the correction.

Resources

• the integrated mathematics slide deck
• the integrated practice worksheet
• the box plot and five-number summary mat
• the gradient and intercept reference mat
• Graph paper
• Ruler and pencil
• Calculator for checking, not replacing, exact working

Assessment

• Listen for accurate mathematical vocabulary and require the student to justify each algebraic or statistical step.
• Use the diagnostic prompts, worksheet responses and completed box plots to identify gaps in algebra, coordinate geometry, surds or data analysis.
• Use the final five-question check to decide whether the next lesson should reteach one strand or progress to mixed problem-solving.

Differentiation

• For support, provide one worked example beside each new question, use graph paper and colour-code numerator/denominator, gradient changes and quartile positions.
• Offer dyslexia-friendly access: read questions aloud, use a clear sans-serif font, short lines, generous spacing, uncluttered pages and avoid requiring the student to copy large amounts of text.
• Allow oral explanations, a calculator for checking arithmetic, and manipulable written steps before expecting independent notation.
• For extension, ask the student to create a line whose gradient is (-2), simplify an expression involving algebraic denominators such as (\frac{x}{3}+\frac{2}{x}), or design a third dataset with the same median but a different IQR, then justify the result.