Herd immunity math
Do now
Calculate a herd immunity threshold from a reproduction number and explain who it protects.
- Hand in
- Two herd immunity threshold calculations with work shown, and one sentence explaining who herd immunity protects.
- Where
- Turn this in at the drop folder with your district Microsoft sign-in, or hand it to Mr. Mendoza in class. Both count as submitted. Doing the activity in myPLTW does not.
You get two school days for every day you were absent, so this deadline moves with you.
Calculate a threshold from a reproduction number and explain who it protects.
Calculate a threshold from a reproduction number and explain who it protects.
- • You'll be able to compute a threshold from R-zero.
- • You'll be able to explain who protects and why.
- What do you already know about math?
- What would you need to find out to answer today's question?
- 1Write the threshold formula, 1 minus 1 over R-zero, in your notebook.
- 2Using two R-zero values from the case, calculate the threshold percentage for each disease.
- 3Explain in one sentence why a higher R-zero requires a higher vaccination rate.
- 4Identify one group that protects who cannot be vaccinated themselves.
- 5Submit your two calculations and your explanation as your daily evidence.
What did this day actually feel like?
Herd immunity math
The threshold depends on how contagious the disease is. More contagious means a higher fraction needed, and for the most contagious diseases the number is uncomfortably close to everyone.
It is not a slogan, it is a calculation.
AT HOME, THE WEEKEND BEFORE MON OCT 12 Unit 1 tracker check Portfolio audit against the rubric. Two items were missing labels. Two minutes to fix once found.
Turned in: tracker → recorded in Class Records
Fiction. There is no such student. The lessons, labs and dates are the real planned course; the student, the classmates and the conversations are invented.
The same day, drawn.
The threshold depends on how contagious the disease is. More contagious means a higher fraction needed, and for the most contagious diseases the number is uncomfortably close to everyone.
ME
The model stopped spreading before everyone was vaccinated. The unvaccinated are protected by the vaccinated.
Fiction. There is no such student. The lessons, labs and dates are the real planned course; the student, the classmates and the conversations are invented.
🛠 Get unstuck · pick your level
🔑 Today's words · 5
Tap a word in the lesson for a plain meaning and one example. Recycled into next week's Do-Now.
Do the work · 80-minute blockfirst 5 min = hook▸
💡 Big idea: At what vaccination coverage does a community protect its most vulnerable members?
- 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.
Auditory anatomy, audiograms, cochlear implants, immune response, vaccine design, herd immunity. · math
Day 4 of this lesson. Open this exact section in myPLTW (find it in Clever, Microsoft sign-in), then do the work below.
Do this: Open Activity 1.4.1 Disease Prevention Through Vaccination in myPLTW and use the threshold formula with your case R-zero values.
Mark the math activity complete after your calculations and explanation are submitted.
Immunity diagram and should be saved (Wednesday); calculations due today.
Two worked threshold calculations with explanation sentence submitted on the class site.
The official PLTW activity stays inside myPLTW. If myPLTW will not open, use F1 and E1-E3 on this page to complete today's local evidence decision, then make up the official activity when access returns. Turn this in at the drop folder with your district Microsoft sign-in, or hand it to Mr. Mendoza in class. Both count as submitted. Doing the activity in myPLTW does not.
Check things off as you work, then submit. This tells Mr. Mendoza how you're doing so he can help the class. It does not replace turning in your producible through the submission route shown below.
Use the code Mr. Mendoza gave you, not your name. Saved on this device.
Auditory anatomy, audiograms, cochlear implants, immune response, vaccine design, herd immunity. · Herd immunity math
Open Activity 1.4.1 Disease Prevention Through Vaccination in myPLTW and use the threshold formula with your case R-zero values.
Immunity diagram and should be saved (Wednesday); calculations due today.
This is how Mr. Mendoza sees the class keeping pace with PLTW. Be honest, it only helps if it is accurate.
🎯 Calculate a threshold from a reproduction number and explain who it protects.
- Write the 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 protects who cannot be vaccinated themselves.
- Submit your two calculations and your explanation as your daily evidence.
Exit ticket: Two threshold calculations with work shown, and one sentence explaining who herd immunity protects.
Turn this in at the drop folder with your district Microsoft sign-in, or hand it to Mr. Mendoza in class. Both count as submitted. Doing the activity in myPLTW does not. Use the checklist just below and upload by 11:29 PM for full credit. Absent with an excused absence? You get two school days for every day you were absent, so this deadline moves with you.
| Task | Who |
|---|---|
| Write the 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 protects who cannot be vaccinated themselves. | _______ |
| Submit your two calculations and your explanation as your daily evidence. | _______ |
Working solo? Put your own name in "Who" for every row.
- You'll be able to compute a threshold from R-zero.
- You'll be able to explain who protects and why.
- 1Do thisCalculate a herd immunity threshold from a reproduction number and explain who it protects.
- 2Use this resource
- 3Submit thisExit ticket: Two herd immunity threshold calculations with work shown, and one sentence explaining who herd immunity protects.
- 4Submit it here
- 1Open the drop folder.
- 2Sign in with your district Microsoft account, not a personal one.
- 3Upload the file, named Lastname_Firstname__Assignment Title.
- 4Your own upload panel says Uploaded with a green check: that is your receipt.
Turn this in at the drop folder with your district Microsoft sign-in, or hand it to Mr. Mendoza in class. Both count as submitted. Doing the activity in myPLTW does not. Genetics of Disease (Medical Interventions) › Auditory anatomy, audiograms, cochlear implants, immune response, vaccine design, herd immunity. › Exit ticketOpen the drop folder
Learn it · deck, reading, 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.
A builds memory cells before the real arrives, so the secondary is fast enough to stop infection in one person and, when enough people are covered, to break the chain of spread across a population.
At what vaccination coverage does a community protect its most vulnerable members?
An airport checkpoint uses several imperfect checks before deciding what action to take.
- What can each check detect?
- What might create a false alarm?
- Why is one result not always enough?
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.
- • Checkpoint evidence maps to E1-E3.
- • False alarms map to test limitations.
- • The response maps to the justified next intervention or test.
Driving question: Calculate a threshold from a reproduction number and explain who it protects.
What you already know: A builds memory cells before the real arrives, so the secondary is fast enough to stop infection in one person and, when enough people are covered, to break the chain of spread across a population.
New idea: At what vaccination coverage does a community protect its most vulnerable members?
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: Calculate a threshold from a reproduction number and explain who it protects.
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 trains the immune system to recognize a specific , building protection so the body can fight it off faster 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.
threshold = 1 - (1/R0); a disease with R0=10 needs 90% coverage to stop spread.
Limit: E1 supplies context or an observation; it does not by itself establish the explanation.
At what vaccination coverage does a community protect its most vulnerable members?
Limit: E2 is a teaching statement or comparison and must be checked against the task evidence.
You'll be able to compute a threshold from R-zero.
Limit: E3 supports only the result or product criterion named here; it cannot justify a broader clinical or causal claim.
PLTW-GEND-2026-10-08 · 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 the lesson page.
- • Select the option best supported by E1-E3.
- • Select a reasonable alternative and name the evidence it would require.
- • Delay the claim because the evidence does not distinguish the options.
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: The supplied lesson evidence can support an observation, pattern, classroom mechanism, or next-step decision about math. It cannot by itself prove causation, establish a real clinical diagnosis, or justify action outside this classroom task.
Reason for review: Your team must decide what the evidence from math supports before submitting the exit response named on the lesson page.
Context: Calculate a threshold from a reproduction number and explain who it protects.
- • 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: threshold = 1 - (1/R0); a disease with R0=10 needs 90% coverage to stop spread.
- • E2: At what vaccination coverage does a community protect its most vulnerable members?
- • E3: You'll be able to 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.
Rate or percent = part / comparison total x 100%. Percent change = (new - comparison) / comparison x 100%.
If 18 of 60 records meet a condition, the frequency is 18 / 60 x 100% = 30%.
Name the comparison total. A percent describes the supplied group and does not automatically predict an individual's outcome.
Use today's supplied counts to calculate one rate, risk, frequency, or percent change. Show the denominator and interpretation.
- 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).
How to get there: open Clever and sign in with your Microsoft (district) account. Both myPLTW and Schoology are in Clever. Do the activity in myPLTW. Turn the work in on this site or hand it to Mr. Mendoza, because that is the step that counts as submitted. Schoology only shows your report-card grade later.
Check yourself · commit, then reveal▸
Claim ceiling for this check: The supplied lesson evidence can support an observation, pattern, classroom mechanism, or next-step decision about math. It cannot by itself prove causation, establish a real clinical diagnosis, or justify action outside this classroom task.
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.
Go further and get help▸
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.
Open the drop folderTurn this in at the drop folder with your district Microsoft sign-in, or hand it to Mr. Mendoza in class. Both count as submitted. Doing the activity in myPLTW does not.
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.
- SubmittedTurned in the right way, on the class site or handed to Mr. Mendoza in class, and confirmed. Not in Schoology: that is where the report-card grade appears later.