Lung Volume Math

Overview

Today students use a balloon lab to collect measurements of tidal volume and vital capacity, then convert those measurements into rational-number calculations. The lesson builds number-system thinking by connecting real-world contexts (breathing and lung capacity) to operations with integers and rational numbers.

Learning intentions

• Students will measure balloon diameters for tidal volume and vital capacity trials and record data accurately.
• Students will convert balloon measurements into volume values using the class method (graph or teacher-provided conversion key).
• Students will calculate an estimated vital capacity using the given formulas and compare it to measured vital capacity.
• Students will interpret sums, products, and quotients of rational numbers in a real-world context (breathing).

Success criteria

• I can record three trials for tidal volume and three trials for vital capacity and compute an average.
• I can compute estimated vital capacity using the correct formula and substitute age and height.
• I can use rational-number operations (including negatives) correctly when evaluating expressions.
• I can explain in complete sentences which value (measured vs. estimated) seems more accurate and why.

Curriculum links

• The Number System — add and subtract rational numbers using representations (aligned to 7.NS.A.1).
• The Number System — interpret rational-number sums and contexts (aligned to 7.NS.A.1b).
• The Number System — multiply signed numbers and interpret products in context (aligned to 7.NS.A.2a).
• The Number System — divide integers with nonzero divisors and interpret quotients in context (aligned to 7.NS.A.2b).
• The Number System — solve real-world problems with four operations using rational numbers (aligned to 7.NS.A.3).

Lesson structure (50 minutes)

1. 0–5 min · Launch & safety. Teacher reviews lab purpose (measure tidal volume and vital capacity with balloon diameters) and reminds students: if breathing difficulties (asthma or other condition), they may observe or collect data for a partner. Students preview the calculations section and write a one-sentence goal for their data.

2. 5–12 min · Materials + procedure walkthrough. Teacher demonstrates Part A and Part B:

• Stretch balloon several times.
• Normal breath exhale into balloon (tidal volume), pinch, measure diameter across top to a metric ruler.
• Repeat 3 trials.
• Then deep breath and exhale ALL air into balloon (vital capacity), repeat 3 trials. Students practice labeling their data table columns and record baseline measurement notes (not full trials yet).

3. 12–26 min · Lab Part A (tidal volume). Teacher circulates in groups of 2–3, checking measurement technique (no forcing breathing; balloon fully pinched before measuring). Students collect three tidal-volume balloon diameters and record each in centimeters, then compute a quick average at the end of Part A.

4. 26–36 min · Lab Part B (vital capacity). Teacher reminds: breathe in as deep as possible and exhale ALL air; measure immediately before the balloon changes shape. Students collect three vital-capacity balloon diameters and record each; compute average vital-capacity diameter.

5. 36–44 min · Convert to volumes + rational-number mini-lesson. Teacher provides the class conversion method (example: “Volume (cm³) comes from our predetermined balloon-diameter-to-volume graph/key”). Teacher then models one estimated-vital-capacity calculation step-by-step, highlighting rational operations that may include negative results inside parentheses:

• For boys: VC = (27.63 – 0.112a) × h
• For girls: VC = (21.78 – 0.101a) × h Students complete their estimated VC calculation and compute measured VC from their recorded data using the provided conversion key/graph.

6. 44–49 min · Compare + written explanation. Teacher gives sentence starters and expects complete sentences for: which is more accurate (measured vs. calculated) and why (real measurements include individual factors and error; model is theoretical). Students write two responses: (a) measured vs. calculated accuracy and (b) athlete vs. non-athlete claim.

7. 49–50 min · Exit ticket. Students answer: “If one trial diameter is smaller than another, what happens to the measured volume? Explain using words and one rational-number operation (addition, subtraction, multiplication, or division).”

Resources

• Balloon(s) per lab pair/group (latex considerations below)
• Metric ruler (cm)
• Ribbon or marker to stabilize balloon pinch point
• Student lab handout (includes data table and questions)
• Calculator or phone calculator for estimation steps (teacher-approved)
• Conversion graph/key from balloon diameter to volume (teacher-prepared)
• PPE if required by school policy (e.g., gloves optional)
• Timer for “measure quickly after exhale” (projected or visible)

Assessment

• Formative: teacher checks during trials for correct procedure (normal vs. deep inhale; exhale into balloon; measuring across top to ruler).
• Formative: students must show estimated VC work for at least one formula step (substitute age and height; compute parentheses).
• Exit ticket: rational-number explanation using correct operation language tied to measured volume change.

Differentiation

• Support for measurement: provide a small checklist at each station (stretch balloon; normal breath exhale; pinch; measure across top). Pair students strategically (one recorder, one measurer).
• Support for calculations: offer a worked example on the board and provide a “math steps” template: (1) compute parentheses value, (2) multiply by height, (3) write units cm³.
• EAL/SEN scaffolds: sentence starters for writing (“I think the measured value is more accurate because…”; “The athlete likely has a larger lung capacity since…”). Allow use of graph/key instead of recreating it.
• Accommodation for breathing difficulties: students who cannot safely participate may record partner data and complete all calculations using provided data.
• Latex allergy modification: if any student has a latex allergy, replace standard balloons with latex-free balloons in advance and confirm materials early with the nurse; ensure the same measurement steps work with the alternative balloons.