RockLicker · Grade 8 · Lesson 4 of 5

A Half-Life Clock with Assumptions

Calculate elapsed half-lives in a simplified model and state the assumptions needed for a numerical age.

Grade 8
60 minutes
Worksheet + teacher guidance

What you will learn

A half-life is the time for half the parent atoms in a large population to decay. Radiometric dating uses measured isotope relationships and geological assumptions; not every rock or isotope system records the same event.

Words to use

parent isotope: radioactive starting isotope
daughter: decay product
closed system: no relevant parent or daughter gained or lost

Evidence for this lesson

Idealized fictional system: initially 800 parent atoms, no initial daughter; 100 parent atoms remain; half-life 10 million years; closed system throughout. Treat counts as expected values, not an actual laboratory sample.

Use the supplied record as written; do not invent missing results.

Work through the activity

10 min · Build the sequenceStart with 800 parent atoms and halve the expected remaining number at each step. Write four rows from zero to three half-lives.
20 min · Calculate timeUse the fictional isotope’s 10-million-year half-life and 100 remaining parent atoms. Determine elapsed half-lives, then modeled age.
20 min · Examine assumptionsState the known starting amount, no initial daughter assumption and closed-system condition. Discuss why a natural sample needs appropriate calibration and geological interpretation.
10 min · Distinguish agesExplain why dating a crystal’s formation is not automatically the deposition age of a sedimentary rock containing that crystal.

GRADE 8 · LESSON 4

A Half-Life Clock with Assumptions

Learner / team

Date

1. List expected parent counts at 0, 1, 2 and 3 half-lives.Draw on the printed sheet or write, type or dictate your response.

2. How many half-lives leave 100 from 800?Draw on the printed sheet or write, type or dictate your response.

3. What modeled elapsed time does that represent?Draw on the printed sheet or write, type or dictate your response.

4. Name two assumptions and one limit of applying it to a rock.Draw on the printed sheet or write, type or dictate your response.

Responses stay in this open page only. Print before closing or changing pages; no student record is stored online.

Check your understanding

100 remains from an initial 800 after …

Choose an answer. You can revise after reading the explanation.

Teacher & family guide · answers and assessment

Grade 8 · A Half-Life Clock with Assumptions

Learning goal: Calculate elapsed half-lives in a simplified model and state the assumptions needed for a numerical age.

Expected responses

800, 400, 200, 100.
Three half-lives; 100/800 = 12.5%.
30 million years for the fictional 10-million-year half-life.
Known starting conditions, no initial daughter and a closed system are assumptions; a mineral date can record crystallization rather than later sediment deposition.

Understanding check: three half-lives. 800→400→200→100 is three halvings. Multiply three by the stated half-life.

Watch for this misconception

The halving sequence is an expected large-population model; individual atoms decay probabilistically. The isotope is fictional.

Assess the evidence

Look for the observations, calculation or explanation named in the learning goal. Accept accurate drawings and dictated responses. Use the expected responses to discuss reasoning; a correct guess without explanation is a starting point for another conversation.

Adapt and extend

Read prompts aloud, enlarge print or let a partner record the learner’s explanation. Calculate the model age for 200 remaining parent atoms and compare the result.