Values Ratio 4B

Overview

This Phlow develops proportional thinking through visual and numerical scaling. Using a scalene triangle and a fixed ratio (1 cm = 2.5 m), students convert diagram dimensions into actual lengths and calculate the triangle’s real-world perimeter. The sequence reinforces how all dimensions in a scaled figure change proportionally.

Worked Example

Scale: 1 cm = 2.5 m
Diagram sides: 3 cm, 4 cm, 5 cm
Actual sides:
3 × 2.5 = 7.5 m
4 × 2.5 = 10 m
5 × 2.5 = 12.5 m
Perimeter = 7.5 + 10 + 12.5 = 30 m

Step Sequence

Identify the scale ratio (1 cm = 2.5 m).
Multiply each diagram length by 2.5 to find the real measurement.
List all actual side lengths in the table.
Add the three sides to calculate the perimeter.

Sample Prompts

“Which side represents the real length of 4 cm?”
“What operation do you use to move from diagram to actual?”
“What is the total perimeter in metres?”

Why This Matters

Scale drawings appear everywhere — from maps to blueprints. By practising proportional reasoning in this geometric context, students learn that ratios preserve shape while changing size. This understanding prepares them for advanced geometry, trigonometry, and design applications.

Step 1 / 8

Prerequisite Knowledge Required

Understanding of ratio and proportion.
Ability to multiply and divide by a constant factor.
Values Ratio 4A – Finding scale factors and converting between units.
Triangle 4C – Constructing and measuring triangles.

Main Category

Measurement and Geometry

Estimated Completion Time

Approx. 10–14 seconds per question.
40 questions total → Total time: 7–10 minutes.

Cognitive Load / Step Size

Moderate. Each question introduces one new calculation with the same scale, helping students reinforce proportional reasoning fluently. The repetition and consistent layout maintain smooth cognitive flow.

Language & Literacy Demand

Low–moderate. Visual tables and labelled triangles support comprehension. Short instructions and colour-coded mathematical terms (diagram, actual, perimeter, scale) reduce reliance on text and support all literacy levels.

Clarity & Design

Triangle diagram paired with a clear data table for side lengths.
Consistent colour coding: purple for knowns, pink for unknowns.
Tables align vertically to highlight proportional correspondence.
Design focuses on reasoning flow, not decoration.

Curriculum Alignment (ROI – Measurement Strand)

Interpret and construct scale drawings using proportional reasoning.
Convert between metric units using ratios and scale factors.
Calculate perimeter and side lengths from scale representations.

Engagement & Motivation

The use of a familiar geometric figure keeps focus on logic and method. Learners build mastery through repetition and immediate feedback — the process encourages a flow state where success reinforces motivation.

Error Opportunities & Misconceptions

Reversing scale direction (dividing instead of multiplying).
Forgetting to convert cm to m when interpreting results.
Adding before scaling when calculating the perimeter.
Treating scale as additive instead of multiplicative.

Transferability / Real-World Anchoring

Highly transferable. The same proportional reasoning applies to maps, models, blueprints, and technical drawings. It also underpins conversions in geography, architecture, and science.

Conceptual vs Procedural Balance

Balanced. While the task is procedural (multiply by scale factor), the reasoning behind proportionality is constantly reinforced — building a conceptual understanding of similarity and scale.

Learning Objectives Addressed

Relate diagram and actual measurements using fixed ratios.
Convert scaled lengths between centimetres and metres.
Calculate perimeters from scaled side lengths.
Recognise and explain proportional relationships in shapes.

What Your Score Says About You

Less than 20: You’re reversing or misapplying the scale — review direction of multiplication/division.
21–29: You understand scaling but need to double-check unit conversions.
31–39: You’re confident with proportional reasoning — only small arithmetic slips remain.
40 / 40: Excellent! You’ve mastered scale drawings and are ready for map ratios, model design, and composite scaling.