Open any fitness app and you will see coloured bands: green, amber, red. Behind every band is a short formula. Today you learn two of the most common ones — BMI and the Karvonen target heart rate — by plugging worked figures into the formula and reading where the answer lands. You will not use your own body measurements; every example uses fixed worked numbers so the maths stays on the page.
Two formulae, one shared method: substitute the values, work the arithmetic in order, then read the answer against a band.
BMI = weight (kg) ÷ height² (m)
Karvonen target = resting + intensity × (maximum − resting)
| Concept | Why it matters | Example |
|---|---|---|
| BMI — weight (kg) ÷ height² (m). Convert cm to m first (÷ 100). | If height stays in cm, the answer is wildly wrong. Gyms and apps use the bands as a quick screen. | 70 kg at 175 cm → 1.75 m → BMI ≈ 22.9 (band 18.5–24.9). |
| Karvonen target — resting + intensity × (maximum − resting). | Training plans talk about Zone 2 or Zone 3. The zone is just a target bpm from this formula. | Resting 62, max 190, 60% → ≈ 139 bpm → Zone 3. |
Watch the gauge for a worked BMI: weight 70 kg, height 175 cm. The working line shows the cm-to-m conversion and the division; the marker shows which band the result falls in.
Order rule for both formulae: finish what is inside first (height², or maximum − resting), then multiply or divide, then add. The band name on the gauge is the interpretation — a bare number is not finished.
We work the two formulae with the class, one at a time. Before each reveal, write or say your prediction for the next number — then check it on the board. Keep the units on every line.
Order rule first: in both formulae something inside must be finished first — height² for BMI, (maximum − resting) for Karvonen — then multiply or divide, then add.
Example 1 — BMI (height in centimetres). We finish this fully, including the band, before we open Example 2.
Example 2 — Karvonen at 60% intensity. Same method, formula already on the board. We pause for a short check-in after BMI so nobody is still copying when Karvonen starts.
Now drive the Karvonen gauge yourself. The resting rate is 62 bpm and the maximum is 190 bpm. Change the intensity slider and watch three things update together: the working line, the target bpm, and the zone the marker lands in.
Try these three intensities and write the target and zone for each: 40%, 60%, and 80%.
Then use the slider to hunt for the intensity that lands nearest 130 bpm (the Zone 2 / Zone 3 boundary). No algebra needed — trial values on the slider until the target reads about 130.
The structure on the board is your guide for MA3 KA1 portfolio evidence. No printed handout ships with this lesson. Open a fresh page in your Maths Portfolio (exercise book or portfolio folder paper) and copy the rows shown on the board onto it. Pick one of the two formulae — BMI or Karvonen — and work it end-to-end using the worked figures given. Show every line of working, keep the units on, and finish with one sentence that names the band or zone.
Figures you may use (do not use your own body data):
On your portfolio page: copy every row shown on the board. Show the working, not just the final number. End with the interpretation sentence — a bare number without a band is not finished.
Work each row in order onto a fresh page in your Maths Portfolio. Show the working, not just the answer.
Write these down the page, leaving room under each for your answer:
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