Herd immunity math
Open your materials, follow the steps, then turn in your work.
Calculate a herd immunity threshold from a reproduction number and explain who it protects.
1. Open your materials
Use the materials named in the first step below. Open lesson resources.
2. Start the work
Write the herd immunity threshold formula, 1 minus 1 over R-zero, in your notebook.
Show all 5 required steps
- Write the herd immunity threshold formula, 1 minus 1 over R-zero, in your notebook.
- Using two R-zero values from the case, calculate the threshold percentage for each disease.
- Explain in one sentence why a higher R-zero requires a higher vaccination rate.
- Identify one group that herd immunity protects who cannot be vaccinated themselves.
- Submit your two calculations and your explanation as your daily evidence.
Lost your place? Lost your place? You need two numbers: an R-zero and the threshold you calculated from it. If you have both, move to the sentence explaining who that threshold protects.
Check your work before submitting
- You'll be able to compute a herd immunity threshold from R-zero.
- You'll be able to explain who herd immunity protects and why.
3. Turn in your work
DueCheck Schoology- Hand in
- Two herd immunity threshold calculations with work shown, and one sentence explaining who herd immunity protects.
How to submit and name your file
Use the submission route shown on today's today's page.
In Schoology, open your course and the assignment for this lesson. Attach your file, select Submit, and check that it appears in the submission.
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How this lesson connects
Keep using what you learned last class: Innate and adaptive defenses interact, and vaccination can prepare antigen-specific immune memory that changes the probability or severity of later disease without guaranteeing protection for every person. Today: How contagious a disease is determines what share of a community must be immune, which is why the same coverage figure can be safe for one disease and dangerous for another.
Optional: listen or watch a unit review▸
Need help? Warm-up, timing, and directions▸
💡 Big idea: How contagious a disease is determines what share of a community must be immune, which is why the same coverage figure can be safe for one disease and dangerous for another.
- 0-8Hook: compare R-zero values; derive threshold formula together
- 8-25Guided calculation for R-zero value 1 from the case; check units and percent conversion
- 25-40Independent calculation for R-zero value 2; check against neighbor
- 40-55Write explanation sentence: why higher R-zero demands higher coverage
- 55-70Identify and justify one group protected by but unable to receive the
- 70-80Submit calculations and explanation; preview Friday tracker audit
- • Hook: Post two R-zero values (measles ~15, flu ~1.3) and ask students which disease is harder to stop.
- • Why it matters: This single formula determines vaccination targets that agencies use globally.
- • Today's work: Apply the formula to two real diseases, then explain the human impact of crossing the threshold.
- • Exit goal: Two worked calculations and an explanation submitted by block end.
- • threshold = 1 - (1/R0); a disease with R0=10 needs 90% coverage to stop spread.
- • R-zero is the average number of people one infectious person infects in a fully susceptible population.
- • Infants, immunocompromised individuals, and those with certain allergies depend on because they cannot receive some vaccines.
PLTW connection and today's work
Open Activity 1.4.1 Disease Prevention Through Vaccination in Lesson 1.4 of myPLTW. Use the herd immunity threshold formula with your case R-zero values.
Today's stopping point: Immunity diagram and data table should be saved (Wednesday); herd immunity calculations due today.
PLTW activity titles identify the course connection. If your account will not open, use the posted materials for today and tell Mr. Mendoza. Do not mark an online activity complete unless you completed it.
Course connection
- Activity 1.4.1 Disease Prevention Through Vaccination
Use the turn-in directions at the top of this page. Do not create a second submission unless your teacher asks for one.
Show another explanation or a smaller first step
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Lesson resources: reading, slides, and vocabulary▸
The deck carries the prior idea forward, lets you inspect an analogy, maps the rule to biology, and ends with the same evidence decision and exit ticket used on this page.
Generated from this lesson's canonical data with a red-team citation check.
and adaptive defenses interact, and vaccination can prepare -specific immune memory that changes the probability or severity of later disease without guaranteeing protection for every person.
How contagious a disease is determines what share of a community must be immune, which is why the same coverage figure can be safe for one disease and dangerous for another.
An airport checkpoint uses an ID check, a metal detector, and an X-ray scanner.
- What can the ID check detect?
- What might set off the metal detector by mistake?
- Why do we need the X-ray if we already checked their ID?
A decision is stronger when the test fits the question and its limits are known.
Medical decisions also depend on biology, patient context, ethics, and professional judgment.
- • The ID check maps to confirming patient identity.
- • The metal detector maps to a rapid, non-specific screening test.
- • The X-ray scanner maps to a detailed, specific diagnostic test.
Driving question: Measles spreads far faster than seasonal flu. Should both require the same vaccination rate to keep a school safe?
What you already know: and adaptive defenses interact, and vaccination can prepare -specific immune memory that changes the probability or severity of later disease without guaranteeing protection for every person.
New idea: How contagious a disease is determines what share of a community must be immune, which is why the same coverage figure can be safe for one disease and dangerous for another.
Visual or model: F1. F1. A lesson illustration or teaching diagram for Herd immunity math. Use it with E1-E3; it is a model or context image, not experimental or patient data. What to notice: Trace the labeled testing, treatment, or biological process and identify where evidence limits the decision.
- Observe or measure the relevant feature in math.
- Organize the observation with a stable evidence ID.
- Apply this rule: A decision is stronger when the test fits the question and its limits are known.
- Choose the option the evidence supports and state the limit of the conclusion.
Real biomedical example: Measles spreads far faster than seasonal flu. Should both require the same vaccination rate to keep a school safe?
What the evidence supports: E1-E3 and F1 support the daily take-home when the response meets the stated success criteria.
What it cannot prove: The package does not support claims beyond this lesson's or any real patient diagnosis.
- • : The spiral, snail-shaped part of the inner ear that turns sound vibrations into nerve signals the brain reads as hearing.
- • : A sensory cell in the inner ear with tiny hair-like bundles that convert sound vibrations or movement into nerve signals the brain can read.
- • : A graph from a hearing test that plots the softest sounds a person can hear at different pitches, showing the type and degree of any hearing loss.
- • : A preparation that delivers an (or the instructions to make one) so the immune system learns to recognize the real later.
- • : Protection that arises when enough people in a community are immune to a disease that its spread slows and shields those who are not immune.
- • : The part of the immune system that learns a specific , builds targeted antibodies and memory cells, and responds faster the next time it appears.
Use it now: Choose one decision option. Cite E1 and E3, then explain how the rule connects the evidence to your choice.
Go further, optional: The source links below are optional enrichment. Every fact required for today's local evidence decision appears in this lesson package.
and adaptive defenses interact, and vaccination can prepare -specific immune memory that changes the probability or severity of later disease without guaranteeing protection for every person.
Limit: A teaching model simplifies interacting cells, signals, timing, types, and population differences.
A decision is stronger when the test fits the question and its limits are known.
Limit: Medical decisions also depend on biology, patient context, ethics, and professional judgment.
You can compute a threshold from R-zero.
Limit: E3 defines the classroom product or success criterion. It is not independent scientific evidence and cannot justify a clinical or causal claim.
PLTW-GEND-2026-10-13 · Simulated classroom evidence scenario
Your role: medical interventions team member
Decision: Your team must decide what the evidence from math supports before submitting the exit response named on today's page.
- • Close the debate by citing GINA, because that law already makes genetic discrimination illegal in every kind of insurance.
- • Check which insurers GINA actually covers before claiming a spit tube result cannot cost someone a policy.
- • Argue that access rules must cover relatives too, since your genome carries information about people who never got tested.
Response: State one choice, cite at least two evidence IDs, explain the rule that connects them, and add one limitation. Submit it as the exit response.
Claim ceiling: Today's evidence supports a classroom claim about math. It cannot prove causation, diagnose a real patient, or justify action outside this room.
Reason for review: Your team must decide what the evidence from math supports before submitting the exit response named on today's page.
Context: is arithmetic, not goodwill: the threshold is set by how contagious the disease is, so a disease that spreads faster demands a higher share of the community and leaves less room for opting out.
- • T1: Write the threshold formula, 1 minus 1 over R-zero, in your notebook.
- • T2: Using two R-zero values from the case, calculate the threshold percentage for each disease.
- • T3: Explain in one sentence why a higher R-zero requires a higher vaccination rate.
- • T4: Identify one group that protects who cannot be vaccinated themselves.
- • T5: Submit your two calculations and your explanation as your daily evidence.
- • E1: and adaptive defenses interact, and vaccination can prepare -specific immune memory that changes the probability or severity of later disease without guaranteeing protection for every person.
- • E2: A decision is stronger when the test fits the question and its limits are known.
- • E3: You can compute a threshold from R-zero.
Measurements: Use only the measurements, units, graph, or counts supplied in today's task. No additional patient measurement is implied.
Figure finding: Teaching diagram for math. Trace the labeled testing, treatment, or biological process and identify where evidence limits the decision. This is a teaching model, not patient or experimental data.
Uncertainty: This is a composite classroom scenario. Missing history, measurements, or confirmation tests remain unknown and limit the conclusion.
Mean = sum of values / number of values. Median = middle ordered value. Range = maximum - minimum.
For 2, 4, 4, and 10: mean = 20 / 4 = 5, median = 4, and range = 10 - 2 = 8.
Mean, median, and range keep the measurement unit. Order the values before finding the median.
Calculate the requested summary for today's supplied values, then write what it reveals and what it hides.
Students often think Students think means most people are vaccinated, so roughly a majority is enough.. The trap: The threshold is not a majority, it is set by R-zero and can sit above 90 percent. Treating 60 or 70 percent as safe is exactly how a community with good intentions still gets an outbreak, because the last few percent are doing the load-bearing work.
Herd immunity threshold work (sample)
Formula: HIT = 1 minus (1 divided by R-zero)
Disease A, measles, R-zero of 12
HIT = 1 minus (1 divided by 12) = 1 minus 0.083 = 0.917
So about 92 percent of the community has to be immune.
Disease B, seasonal influenza, R-zero of 1.3
HIT = 1 minus (1 divided by 1.3) = 1 minus 0.77 = 0.23
So about 23 percent has to be immune.
Why a higher R-zero needs a higher rate: one infectious person with measles infects about 12 others in a fully susceptible group, so nearly every route out of that person has to be blocked before the chain dies out. A disease whose average case infects only slightly more than one other person needs far fewer of those routes blocked, which is why the same 60 percent coverage can be comfortable for one disease and dangerous for another.
One group this protects who cannot be vaccinated: infants who are too young for the first MMR dose. They cannot be vaccinated yet, so the only thing between them and measles is that the people around them are immune. People receiving chemotherapy are in the same position, because their immune systems cannot mount a response to a live vaccine.
The ceiling on this calculation: the formula assumes a vaccine that works every time and a community that mixes at random. Neither is true for influenza, where the vaccine is partly effective and changes year to year, so 23 percent is the floor this model gives and not a public health target anyone would set.
What surprised me: 92 percent leaves very little room. A school at 85 percent coverage sounds high and is still under the measles threshold.
This model shows the level of evidence and organization needed to complete: Completes the herd immunity task: two threshold calculations with the formula and the work shown, one sentence on why a higher R-zero demands higher coverage, and one group that depends on herd immunity.
- Name the prompt or task.
- Answer it directly with the key evidence.
- Check that the response matches the requested format.
Keep the structure. Replace the question, facts, measurements, and evidence. Then recheck units, vocabulary, and whether the conclusion goes beyond the evidence.
Also due today: Submit both calculations and your explanation on Schoology before you leave.
- CER:
- Claim, Evidence, Reasoning: make a claim, back it with evidence, explain your reasoning.
- SOP:
- Standard Operating Procedure, the exact steps to follow (especially in a lab).
- Tracker:
- Your PLTW progress log where you record completed evidence.
- myPLTW:
- The PLTW course site where you do the online activities. Find it in Clever with your Microsoft sign-in, right next to Schoology.
Tap the speaker to hear a term. Add two of these to your notebook glossary with a definition and an example in your own words.
Pick just 2 or 3 words from today and make them yours: write what each one means in your own words, name the context clue or evidence that helped, then give one example from what you actually did in Herd immunity math. Try your own words first; the glossary is there if you get stuck. This is voluntary and counts as extra credit, so keep it short.
Saved on this device. Show Mr. Mendoza or add these to your notebook glossary to claim the extra credit.
Classroom documents for this lesson are posted in Schoology. Open Clever, then Schoology, and find each one by the name shown on its card.
Use this with the vaccination lesson to connect development to a real example.
Placement rationale
Relocated to the vaccination lesson (Unit 1.4), where the COVID activity supports the day. Visibility: student-schoology.
Use this if you were absent, got stuck, or need another pass before you submit the lesson artifact.
Placement rationale
Matched Hearing loss, cochlear implants, vaccines by path:Medical-Interventions/Unit-1_How-to-Fight-Infection/1.3_Hearing-Loss; keywords:hearing, , cochlear. Score 142. Visibility: student-schoology (student-facing resource; link through Schoology rather than local path).
Use this if you were absent, got stuck, or need another pass before you submit the lesson artifact.
Placement rationale
Matched Hearing loss, cochlear implants, vaccines by path:Medical-Interventions/Unit-1_How-to-Fight-Infection/1.4_Vaccination; keywords:, vaccination. Score 142. Visibility: student-schoology (student-facing resource; link through Schoology rather than local path).
Open this when the class reaches this activity and use it to complete the required lesson artifact.
Placement rationale
Matched Hearing loss, cochlear implants, vaccines by path:Medical-Interventions/Unit-1_How-to-Fight-Infection/1.4_Vaccination; keywords:, vaccination. Score 142. Visibility: student-schoology (student-facing resource; link through Schoology rather than local path).
Sign in to Clever with your district Microsoft account to open Schoology or myPLTW. Follow today's posted steps. If myPLTW will not open, use the posted alternative and tell Mr. Mendoza. Turn in your completed work through the Schoology assignment.
Practice: try a question, then check your answer▸
Claim ceiling for this check: Today's evidence supports a classroom claim about math. It cannot prove causation, diagnose a real patient, or justify action outside this room.
A disease has an R-zero of 4. What vaccination coverage stops sustained spread, and who does that coverage protect that it does not immunise?
Write an answer and pick a confidence to unlock the key.
Fast retrieval with instant answers, not the commit-then-reveal check above. Try each from memory first: write what you remember about the earlier units, then check yourself here.
Missed class or ready for more?▸
Run this before you touch the bench. It is built from the real lab procedure, so the decisions you make here are the ones you will make with the equipment in your hands.
What today's skills lead to. These are real health-science careers this course builds toward. Tap one to see, on the US Department of Labor's O*NET site, what the job actually involves, what it pays, and how fast it is growing.
Today is individual work you can do from home: complete the same target above, then submit your Exit ticket.
Go to Schoology to turn this in. Submit one PDF. Put your first and last name in the document header. Name the file: FirstName LastName - Assignment Title - YYYY-MM-DD.pdf. If you cannot get in, see Mr. Mendoza. Do not skip the work.
Class still runs. Complete the online activity above (it's self-guided). Need the concept taught without a teacher? Use this authoritative explainer:
NIH MedlinePlus- CompleteEvery required part of the artifact is present, nothing left blank.
- AccurateThe science and the data are correct and match the evidence.
- Scientific reasoningYou explain your claim with evidence and reasoning (CER), not just an answer.
- Professional communicationClear, organized, labeled, and written the way a clinician or scientist would.
- SubmittedGo to Schoology to turn this in. Submit one PDF. Put your first and last name in the document header. Name the file: FirstName LastName - Assignment Title - YYYY-MM-DD.pdf. If you cannot get in, see Mr. Mendoza. Do not skip the work.
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