MS-LS4-6: Using Math to Show Natural Selection Changing Traits Over Time
In plain English: MS-LS4-6 is the NGSS middle school performance expectation that asks students to use mathematical representations, such as tables, graphs, probabilities and percents, to support explanations of how natural selection can make specific traits more common or less common in a population over many generations. It is usually taught in grade 7 or 8 life science.
Use mathematical representations to support explanations of how natural selection may lead to increases and decreases of specific traits in populations over time.
Clarification Statement: Emphasis is on using mathematical models, probability statements, and proportional reasoning to support explanations of trends in changes to populations over time.
Assessment Boundary: Assessment does not include Hardy Weinberg calculations.
Next Generation Science Standards · Disciplinary Core Idea: Biological Evolution: Unity and Diversity · Official standard
Students use mathematical representations to support explanations of natural selection: the process in which individuals with inherited traits that help them survive and reproduce in their environment leave more offspring, so those traits become more common over generations and others become less common. Students build generation-by-generation tables from survival probabilities, graph percents over time, compute rates of change, and use the numbers to explain both increases and decreases of specific traits. Cases include a model of long and short wings in salt-marsh planthoppers, cliff swallows near roads, Colorado potato beetles, wild rabbits and a hands-on bean simulation. All numbers are invented for teaching; where a pattern comes from a real study, the page says so.
The NGSS Clarification Statement says: "Emphasis is on using mathematical models, probability statements, and proportional reasoning to support explanations of trends in changes to populations over time." The Assessment Boundary says: "Assessment does not include Hardy Weinberg calculations." So the models on this page count individuals with each form of a trait and assume that offspring have the same form as their parent; they never use gene-frequency equations. Students do the practice of using mathematics: they calculate, graph and interpret numbers, and then use those numbers as evidence in written explanations.
Learning Objectives
By the end of this lesson, students will be able to:
Use survival probabilities to build a generation-by-generation table of the percent of a population with a trait
Graph the percent of a trait over time and describe the shape and rate of the change
Use mathematical representations to explain how natural selection increases some traits and decreases others
Critique a model or claim by checking its numbers against the rules of natural selection
Prior Knowledge Required
Students should already be comfortable with:
Inherited variations can raise an individual's probability of surviving and reproducing in a specific environment MS-LS4-4
A probability is a number from 0 to 1 that describes how likely an event is 7.SP.C.5
Solving multistep ratio and percent problems 7.RP.A.3
Plotting and reading data on graphs and number lines 6.SP.B.4
Write on the board: "In a population of 100 beetles, 20 are brown and 80 are green. Birds find green beetles more easily on the brown ground."
Warm-Up Prompt
"Predict the percent of brown beetles after one generation, after five, and after twenty. Sketch a graph of your prediction. Will the percent ever go above 100%? Could it ever go down?"
Collect sketches. Many students draw a straight line that shoots past 100%. Keep the sketches: by the end of the lesson students will have numbers that show the real shape of the curve and when a trait can fall.
Direct Instruction15-20 minutes
Key words. A population is a group of one species in one area, and a generation is one round of parents and their offspring. A trait is a feature such as wing length; here each individual has one of two inherited forms of it. Natural selection is the process in which individuals with inherited traits that help them survive and reproduce in their environment leave more offspring, so over generations those traits become more common. A mathematical representation is a table, graph, probability or percent that shows a pattern with numbers. The probability of surviving is the number that survive ÷ the number at the start.
The model used on this page. (1) Multiply the number with each form by its probability of surviving to reproduce. (2) Offspring have the same form as their parent. (3) The environment supports the same total number each generation, so the new percent with a form = its survivors ÷ all survivors. All numbers on this page are invented.
A model of an increase: long wings after storms
Planthoppers are tiny insects that suck sap from salt-marsh grass. In this model, some inherit long wings and can fly to fresh grass; others inherit short wings. (In real planthoppers, crowding also affects which wing form an insect develops; the model keeps only the inherited part.) In years of storms, the grass grows in scattered patches. Of 100 planthoppers, 10 have long wings; a long-winged one has a 0.9 probability of reaching fresh grass and reproducing, a short-winged one 0.3.
Result: Generation 1: 10 × 0.9 = 9 and 90 × 0.3 = 27, so 9 ÷ 36 = 25% long-winged. Repeating the step: 25% → 50% → 75% → 90%. Long wings rise from 10% to 90% in 4 generations (Diagram 1).
A model of a decrease: the same trait when the environment changes
Then calm years come, and the grass grows evenly, so flying is no longer needed. Short-winged females lay more eggs, so now a long-winged planthopper has a 0.6 probability of reproducing and a short-winged one 0.9. Start from 90 long-winged and 10 short-winged.
Result: 90 × 0.6 = 54 and 10 × 0.9 = 9, so 54 ÷ 63 ≈ 85.7% long-winged. Repeating: 85.7% → 80% → 72.7% → 64%. The trait decreases, more slowly than it rose, because the advantage is smaller (0.9 ÷ 0.6 = 1.5 against 0.9 ÷ 0.3 = 3).
Field data: a decrease in long wings near roads
In a real study in southwestern Nebraska, cliff swallows nest under highway bridges, and scientists counted swallows killed by cars over about 30 years. Fewer were killed as time went on, and the birds' wings got shorter on average. Shorter wings let a bird take off more steeply and turn faster. Invented numbers that follow this pattern are in Diagram 2.
Result: Long-winged birds: 50% in 1984 and 26% in 2008, a drop of 24 percentage points in 24 years, about 1 point per year. Road-killed swallows found: 20 down to 4, so 4 ÷ 20 = 1/5 as many.
Field data: an increase in insecticide resistance
Colorado potato beetles eat potato leaves, and in many places they have evolved resistance (an inherited ability to survive) to insecticides, chemicals that once killed them. Invented lab tests from one farm that sprayed the same insecticide every year: the percent of beetles that survived a standard dose was 2% in year 1, 6% in year 2, 25% in year 3, 60% in year 4 and 85% in year 5.
Result: From year 1 to year 5 the percent rose by 85 - 2 = 83 percentage points. The biggest one-year jump was from year 3 to year 4, 35 points. Resistant beetles survived the spray and reproduced, so each year more beetles inherited resistance.
Compare Diagram 1 with the warm-up sketches. The curve rises slowly at first (few long-winged individuals), fastest near 50%, and slowly again near 100% (few short-winged ones are left to replace). The same trait falls when the environment changes, so natural selection can increase or decrease a trait.
Guided Practice10-15 minutes
Pairs complete a model table. A weed grows in a hay field that the farmer mows every July. Some plants inherit early seeding (they drop seeds before July), and the rest seed late. An early-seeding plant has a 0.8 probability of making seeds before mowing and a late-seeding plant 0.4. The field holds 100 plants each year, and 20 seed early at the start. Round each percent to the nearest whole number before the next step.
Guided practice model (invented): fill in the blanks
Generation
Early seeders at start
Early survivors (× 0.8)
Late seeders at start
Late survivors (× 0.4)
Percent early in next generation
0
20
16
80
32
?
1
?
?
?
?
?
2
?
?
?
?
?
3
?
?
?
?
?
Find the percent early in generation 1 from the first row: early survivors ÷ all survivors.
Use that percent as the number of early seeders out of 100 for the next row, and repeat until generation 4.
Graph percent early against generation. Describe the shape.
Explain with your numbers why early seeding increased, and predict what would happen to it if the farmer stopped mowing for many years.
Independent Practice10-15 minutes
Each student analyzes data on wild rabbits in Australia. In 1950 a rabbit disease, myxomatosis, was released there to control rabbits, and at first it killed more than 99% of infected rabbits. Over the next years, rabbits that survived passed on their resistance. The numbers below are invented for teaching and follow that pattern.
Independent practice data (invented): rabbits that survived a standard test infection
Year
Rabbits tested
Survived
1951
50
1
1955
50
9
1959
50
19
1963
50
26
Students turn each row into a percent, graph percent against year, compute the change in percentage points for each 4-year period and write an explanation that uses at least three numbers. Ask: "Which trait increased, which decreased, and what about the environment caused it?"
Closure5 minutes
Exit ticket: "A trait has a probability of 0.5 of surviving and the other form 0.5. What happens to its percent over generations, and why? Then change one number so the trait decreases." Return to the warm-up graphs and ask which ones went above 100%, and why the model curve cannot.
Differentiation Strategies
For Struggling Students
Give the model table with the multiplication column already filled for the first row
Let students work with counts out of 100 so a count and a percent are the same number
Provide the frame: "The percent with ___ went from ___ to ___ because individuals with ___ had a probability of ___ compared with ___."
For Advanced Students
Ask students to find, by trying numbers, how many generations long wings need to go from 10% to 90% if the advantage is 1.5 instead of 3
Have students explain why the curve in Diagram 1 is steepest near 50%
Ask students to compare the bean simulation with the model and explain why small populations wobble
Assessment Guidance
What to Look For
Check that students divide by the total number of survivors, not by the starting number, and that their percents never go above 100% or below 0%. Look for explanations that cite numbers from tables or graphs and name both the trait and the environment. Listen for students who think individuals change their own traits, or who expect a trait to keep rising when the environment changes. Gene-frequency (Hardy-Weinberg) calculations are not part of this standard.
02
Classroom Activities
3 Activities
1
Bean Bag Generations: A Survival Simulation
25 minutesGroups of 3
Groups model a population of 20 seeds with two inherited colors. Red kidney beans are the form that hides better on dark soil, and white navy beans are easier for birds to find. A number cube decides which beans survive.
Procedure
Put 4 red and 16 white beans in a paper bag (20% red). Keep spare beans in two cups.
Draw the beans one at a time and roll the number cube for each: a red bean survives on 1-5, a white bean survives on 1-3. Set dead beans aside.
Reproduce: refill the bag to 20 beans so that the percent red equals the percent red among the survivors (round to a whole bean).
Record the percent red for 5 generations, then pool the class results and find the class mean for each generation.
Safety: do not eat the beans, and pick up any dropped beans so no one slips.
Sample Data (invented)
Red beans out of 20 at the start of generations 0 to 5: 4, 6, 8, 11, 13, 15.
Discussion Questions
Turn the sample counts into percents. By how many percentage points did red rise from generation 0 to generation 5?
What is the probability of surviving for each color? How many times as likely is a red bean to survive?
Your group's numbers may differ from another group's, and the model's. Why does chance matter more with 20 beans than with 2,000?
Modification for a Decrease
For a second round, the soil turns pale: white beans now survive on 1-5 and red on 1-3. Start from your last generation and record 3 more generations to show red decreasing.
2
Graph It: Two Real Patterns, Two Directions
20 minutesPairs
Pairs graph two data sets on one set of axes. Both follow patterns reported in real studies, with invented numbers for teaching. Then they compute rates and write one explanation for each line.
Data (invented, following real patterns)
Two-spot ladybugs in the Netherlands. Some inherit dark wing covers, which absorb more sunlight and help in cool weather. As springs became warmer, the dark form became less common. Percent dark: 1980, 45%; 1988, 33%; 1996, 22%; 2004, 14%.
Brown rats and the poison warfarin. Warfarin was used against rats from the early 1950s, and rats with inherited resistance were first found in Scotland in 1958. Percent resistant in one farm region: 1960, 5%; 1965, 15%; 1970, 35%; 1975, 55%.
Procedure
Draw a graph with year on the horizontal axis (1950 to 2010) and percent on the vertical axis (0% to 100%). Plot both data sets in different colors.
For each data set, find the total change and the average change per year.
Label each line "increase" or "decrease" and name the trait and the environmental change.
Discussion Questions
The ladybug line falls and the rat line rises. Is natural selection at work in both? Explain using your numbers.
Which data set changed faster per year? Show the calculation.
The rat percent cannot keep rising at the same rate forever. Why not?
3
Model Critique Cards
15 minutesPairs
Each pair gets 4 cards, each with a short model and a student claim. Pairs decide whether the math supports the claim and fix any errors.
The Four Cards
Card A: Both forms have a 0.5 probability of surviving. Claim: "The spotted form will rise from 20% to 60% because spots are better."
Card B: 50 dark and 50 pale snails; dark survive with probability 0.8, pale 0.4. Claim: "The next generation will be 80% dark."
Card C: 40 striped and 60 plain fish; striped survive with probability 0.6, plain 0.3. Claim: "About 57% of the next generation will be striped."
Card D: A graph shows a trait falling 15 percentage points each generation from 40%. Claim: "After 3 generations, -5% of the population will have it."
Discussion Questions
Which card is correct? Show the calculation that proves it.
On Card B, what number did the student mistake for the percent? Find the right percent.
What is wrong with Card A's reasoning, and what would really happen?
Why can no population have -5% of a trait, and what shape should the curve on Card D have instead?
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: A Model of Long Wings Rising, Then Falling
Invented model from the worked examples, drawn to scale. In stormy years long-winged planthoppers are 3 times as likely to reproduce and the trait rises from 10% to 90% in 4 generations. When calm years return, long wings lose their advantage and fall to 64% in 4 more generations.
Diagram 2: Cliff Swallows Near Roads
Invented numbers following the pattern of a real Nebraska study, drawn to scale. Below each bar is the number of road-killed swallows found on the study roads that summer. As the percent of long-winged swallows fell, fewer swallows were found killed: birds with shorter wings escaped cars more often and left more offspring.
04
Homework Assignment
~30 min
MS-LS4-6 Homework: Natural Selection in Tables and Graphs
Directions: All numbers are invented for practice. Use the model from class: survivors = number × probability, and new percent = survivors with the trait ÷ all survivors. Round each percent to the nearest whole number before the next step.
Part 1: Building Models (Problems 1-3)
A meadow holds 100 plants of one species, and 30 have hairy leaves. Caterpillars avoid hairy leaves, so a hairy plant has a 0.9 probability of surviving to make seeds and a smooth plant 0.6. (a) Find the percent hairy in generations 1, 2 and 3. (b) Graph your results. (c) Explain the trend with two of your numbers.
In a pond, 80 of 100 male damselflies have bright wing spots, which attract females. Then a spider that hunts by color moves in: a bright male now has a 0.3 probability of surviving to mate and a dull male 0.6. (a) Find the percent bright in generations 1, 2 and 3. (b) Which trait decreased, and by how many percentage points in all? (c) Explain why the trait that helped before now decreases.
Bed bugs in many cities have become resistant to a common group of insecticides. Invented test data from one city, percent that survived a standard spray: 2004, 20%; 2008, 44%; 2012, 68%; 2016, 86%. (a) Find the change in each 4-year period. (b) Did the rate of change stay the same? (c) Predict whether the percent in 2020 was closer to 92% or 110%, and explain.
Part 2: Explaining With Math (Problems 4-6)
A student modeled 40 striped and 60 plain beach crabs. Striped crabs survive with probability 0.5 and plain crabs 0.3. The student wrote: "Striped crabs will be 50% of the next generation, because 0.5 = 50%." (a) Find the correct percent. (b) Explain the student's error. (c) Write a correct sentence that uses your result to explain the change.
Invented data, a desert plant whose seeds have thick or thin coats. Thick coats protect seeds in long dry spells; thin-coated seeds sprout faster in wet years. Percent thick-coated: year 1 (wet), 40%; year 2 (drought), 55%; year 3 (drought), 68%; year 4 (wet), 61%; year 5 (wet), 52%. (a) Find the change each year. (b) Explain both the increase and the decrease, using at least four numbers. (c) What does this show about whether a trait is simply "good"?
Design your own model that shows a trait decreasing. (a) Describe the organism, the two forms of the trait and the environment. (b) Choose a starting percent and two survival probabilities, and explain why you chose them. (c) Make a table for 3 generations. (d) Write two sentences that use your table to explain the decrease.
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
Model Calculations
Survivors and new percents correct for every generation, dividing by all survivors
Most steps correct, or one division by the wrong total
Graphs and Rates
Graphs labeled and to scale; changes given in percentage points with the right sign
Graph present but missing labels, or rates without units
Explanation
Names the trait, the environment and the direction of change, and cites at least two numbers as evidence
Explanation without numbers, or numbers without an explanation
Reasoning About Natural Selection
Explains that inherited traits change in frequency because of who survives and reproduces, not because individuals change
Mostly correct, but says individuals change or need the trait
05
Quiz: 20 Questions
Interactive, with answers
Instructions
All numbers are invented. In model questions, multiply each group by its probability of surviving, then divide by all survivors. Your score updates as you answer, and Reset quiz clears everything so you or your students can try again.
Multiple choice: pick an option to check it. Short answer: write your answer, then reveal the model answer.
0 of 20 answered · 0 correct
Question 1 of 20 · Multiple Choice
Which statement describes natural selection?
Answer: C
In natural selection, individuals with helpful inherited traits leave more offspring, so the traits become more common over generations. Choice A describes changes during one life, which are not inherited. Choice B is artificial selection. Choice D describes a case with no selection at all.
Question 2 of 20 · Multiple Choice
In a model, 50 dark and 50 light frogs start a generation. Dark frogs survive with probability 0.8 and light frogs with probability 0.5. About what percent of the next generation is dark?
Answer: B
Survivors: 50 × 0.8 = 40 dark and 50 × 0.5 = 25 light, so 40 ÷ 65 ≈ 62%. Choice A uses the survival probability as if it were the percent. Choice C is the number of dark survivors, 40, not a percent of the survivors. Choice D assumes nothing changes.
Question 3 of 20 · Multiple Choice
A graph shows the percent of spiny sea urchins in a bay: 70%, 60%, 50% and 40% in four generations. What does it show?
Answer: D
Each generation the percent drops by 10 points (70 - 60 = 10), a decrease of 10 percentage points per generation. Choice A reads the graph backward. Choice C uses the last value, 40, as the change per generation. Choice B ignores the trend.
Question 4 of 20 · Multiple Choice
In a model, both forms of a trait have the same probability of surviving and reproducing. What happens to the percent with each form over many generations?
Answer: A
With equal probabilities, survivors keep the same proportions, so selection does not change the percent; only chance changes it a little. Choice B and choice C both need one form to have an advantage. Choice D is impossible: the two percents always add up to 100%.
Question 5 of 20 · Multiple Choice
In a model population, the percent of long-legged ground beetles fell from 64% to 40% over 6 generations. What was the average change per generation?
Answer: C
(64 - 40) ÷ 6 = 24 ÷ 6 = 4 percentage points per generation. Choice A is the total change, not the change per generation. Choice B divides 64 by 6, and choice D divides 40 by 6; both use one value instead of the change.
Question 6 of 20 · Multiple Choice
In a model, a helpful trait rose from 10% to 95% and then barely changed for many generations. Why does the rise slow down near 100%?
Answer: D
Near 100%, almost everyone already has the trait, so each generation only a few individuals without it are left to be replaced, and the percent changes very little. Choice A and choice C would make the trait fall, not level off. Choice B is invented: selection continues as long as the advantage does.
Question 7 of 20 · Multiple Choice
A trait helps in dry years and hurts in wet years. Ten dry years are followed by ten wet years. Which graph of the percent with the trait fits natural selection?
Answer: A
In dry years individuals with the trait leave more offspring, so the percent rises; in wet years they leave fewer, so it falls. Choice B ignores the wet years. Choice C assumes the effects cancel, but the order of the years matters. Choice D reverses the advantage.
Question 8 of 20 · Multiple Choice
Which representation best supports an explanation that a trait increased by natural selection?
Answer: D
A table of the percent across generations shows the trend that the explanation must account for. Choice A shows one individual, not a population over time. Choice B is not evidence about the trait. Choice C gives one number with nothing to compare it with.
Question 9 of 20 · Multiple Choice
In a model, 30% of a population has a trait. The trait gives a 0.9 probability of surviving, and the other form gives 0.45. About what percent has the trait in the next generation?
Answer: B
Out of 100: 30 × 0.9 = 27 and 70 × 0.45 = 31.5, so 27 ÷ 58.5 ≈ 46%. Choice A doubles 30% because the probability is twice as large, but the other form still survives too. Choice C uses the 27 survivors as the percent. Choice D assumes no change.
Question 10 of 20 · Multiple Choice
In a model, form A survives with probability 0.4 and form B with probability 0.8, and A starts at 60%. What happens to form A?
Answer: D
Out of 100: 60 × 0.4 = 24 and 40 × 0.8 = 32, so A drops to 24 ÷ 56 ≈ 43% and keeps falling while B has the advantage. Choice A ignores the probabilities. Choice B confuses a fixed total with fixed percents. Choice C is too fast: A does fall, but to about 43% in the first generation, not 20%.
Question 11 of 20 · Multiple Choice
In the bean simulation, one group's favored red beans dropped from 55% to 50% in one generation, while the class mean rose. What is the best explanation?
Answer: B
In a small population, chance events (unlucky rolls) can move the percent the "wrong" way for a generation even when one form has an advantage. Choice A is contradicted by the class mean. Choice C assumes a mistake without evidence. Choice D overstates it: selection works in small populations too, but chance has a bigger effect there.
Question 12 of 20 · Multiple Choice
The percent of a population with a trait rose from 20% to 30%. Which statement is correct?
Answer: A
30 - 20 = 10 percentage points, and 10 ÷ 20 = 0.5, so the percent itself grew by 50%. Choice B confuses percentage points with percent increase. Choice C uses the 50% growth as points. Choice D uses the ratio 30 ÷ 20 = 1.5 as points.
Question 13 of 20 · Multiple Choice
Invented data: after crabs became common on a rocky shore, the percent of thick-shelled mussels rose 30%, 45%, 60% over three generations. Which claim do the data NOT support?
Answer: C
The data describe the population, not individuals, and natural selection works by who survives and reproduces, not by individuals changing. Choice A and choice B are read directly from the numbers (45 - 30 = 15). Choice D is the selection explanation the rising percent supports.
Question 14 of 20 · Multiple Choice
A model graph of a trait rises from 30% to 95% and levels off. Then the environment changes, and the other form now has the higher probability of surviving. What should the graph show next?
Answer: B
Once the other form has the advantage, the trait decreases. At first only a few individuals have the other form, so the percent falls slowly; as that form becomes more common, the fall speeds up, as in the calm-year part of Diagram 1 (drops of about 4, 6, 7 and 9 points). Choice A forgets that selection depends on the current environment, not on how common a trait is. Choice C is too fast: one generation moves the percent only part of the way. Choice D ignores the change in which form has the advantage.
Question 15 of 20 · Short Answer
Model: 40 of 100 snails have dark shells. Dark snails survive with probability 0.75 and light snails 0.5. Find the percent dark in generations 1 and 2, showing each step.
Generation 1: 40 × 0.75 = 30 and 60 × 0.5 = 30, so 30 ÷ 60 = 50%. Generation 2: 50 × 0.75 = 37.5 and 50 × 0.5 = 25, so 37.5 ÷ 62.5 = 60%. Dark shells increase because dark snails are 1.5 times as likely to survive.
Question 16 of 20 · Short Answer
Most birds avoid hairy caterpillars, but cuckoos eat them. Invented data: after cuckoos arrived in a forest, the percent of hairy caterpillars of one moth species went 60%, 55%, 50%, 45%, 40% over five generations. Use the numbers to explain the change.
The hairy form decreased by 20 percentage points in all, 5 points each generation. Cuckoos ate hairy caterpillars, so hairy individuals had a lower probability of surviving and reproducing than smooth ones, and each generation fewer offspring inherited hairiness. The trait that protected caterpillars from other birds became a disadvantage once cuckoos were in the environment.
Question 17 of 20 · Short Answer
Invented data: the percent of river salmon that migrate early went 30%, 38%, 46%, 54% in four decades after a dam warmed the river in late summer. Find the rate of change, predict the next decade, and give one reason the prediction might be wrong.
The percent rose 8 percentage points per decade (38 - 30 = 8), so the next decade would be about 62% if the trend continued. The prediction might be wrong because the environment could change again (for example, the dam could change how it releases water), or the rise could slow down as the percent gets high.
Question 18 of 20 · Short Answer
A student says: "Cliff swallows grew shorter wings so they could dodge cars." Use Diagram 2 to rewrite the explanation correctly.
Swallows inherit their wing length and cannot grow shorter wings on purpose. Diagram 2 shows long-winged birds falling from 50% to 26% while road kills fell from 20 to 4. Birds with shorter wings were more likely to escape cars and survive to reproduce, so each generation a larger share of young swallows inherited shorter wings.
Question 19 of 20 · Short Answer
Without using the numbers from this lesson, choose a starting percent and two survival probabilities that would make a trait decrease. Show one generation of your model.
Any choice works if the trait's probability is lower than the other form's. Example: start at 70%, trait 0.4 and other form 0.8. Out of 100: 70 × 0.4 = 28 and 30 × 0.8 = 24, so 28 ÷ 52 ≈ 54%, a decrease from 70%.
Question 20 of 20 · Short Answer
Two models start at 20%. In Model 1 the trait survives with probability 0.9 and the other form 0.3. In Model 2, 0.9 and 0.6. Find the percent after 2 generations in each model and explain what the comparison shows.
Model 1: 20 × 0.9 = 18 and 80 × 0.3 = 24, so about 43%; then 43 × 0.9 = 38.7 and 57 × 0.3 = 17.1, so about 69%. Model 2: 18 and 80 × 0.6 = 48, so about 27%; then 27 × 0.9 = 24.3 and 73 × 0.6 = 43.8, so about 36%. A bigger survival advantage (3 times as likely compared with 1.5 times) makes a trait spread much faster.
0 of 20 answered · 0 correct
06
Frequently Asked Questions
10 Questions
What does MS-LS4-6 mean?
MS-LS4-6 asks students to use math, such as tables, graphs, probabilities and percents, to support explanations of how natural selection makes traits more or less common in a population over time. The code means Middle School, Life Science, core idea 4 (Biological Evolution: Unity and Diversity), performance expectation 6.
Does MS-LS4-6 include Hardy-Weinberg calculations?
No: the official Assessment Boundary says "Assessment does not include Hardy Weinberg calculations." Students work with counts, probabilities, percents and graphs of individuals with each form of a trait. Gene-frequency equations come later, in some high school biology courses.
What grade is MS-LS4-6 taught in?
It is a middle school standard for grades 6-8, usually taught in grade 7 or 8 life science. It fits after MS-LS4-4, which looks at one generation, because it follows the same idea over many generations.
Can natural selection make a trait decrease?
Yes: a trait decreases when its owners have a lower probability of surviving and reproducing than others. Long wings in the planthopper model rise in stormy years and fall in calm years. The standard asks for both directions, "increases and decreases", so students should see examples of each.
What math do students need for MS-LS4-6?
Students need multiplication by a probability, percents, percentage-point changes and simple graphs. The Clarification Statement names "mathematical models, probability statements, and proportional reasoning". A calculator helps, and keeping populations at 100 makes counts and percents the same number.
Why does a trait's curve level off instead of going past 100%?
Because a percent of a population can never go above 100%. As a helpful trait gets common, fewer individuals without it are left to be replaced, so each generation the percent rises less. Many students first draw a straight line that runs past 100%, and building the table corrects that.
Is evolution by natural selection a theory or a fact?
It is a scientific theory, which in science means a well-tested explanation supported by many lines of evidence. Natural selection has been observed directly in living populations, such as insects becoming resistant to insecticides and swallows changing near roads.
What are common mistakes students make on MS-LS4-6?
Frequent mistakes are dividing survivors by the starting number instead of by all survivors, using a survival probability as the new percent, and mixing up percentage points with percent change. In explanations, students often say individuals changed their traits because they needed to.
How can a class simulate natural selection without a computer?
A bag of two colors of dried beans and a number cube work well. Each color survives on different rolls, survivors "reproduce" by refilling the bag in the same proportion, and students graph the percent of each color over 5 or more generations. Pooling class data shows the trend more clearly than one group's data.
How does MS-LS4-6 connect to high school biology?
It prepares students for HS-LS4-3, which uses statistics and probability to show that advantageous traits increase in proportion, and for HS-LS4-4, which explains how natural selection leads to adaptation. The same table-and-graph reasoning carries over with larger data sets.
07
Related Standards
5 standards
These standards connect to MS-LS4-6: prerequisites to review first, parallel standards at the same level, and next steps that build on it.
Before this lesson
MS-LS4-4Prerequisite
Explain how inherited variations raise some individuals' odds of surviving and reproducing
NGSS is a registered trademark of WestEd. Neither WestEd nor the lead states and partners that developed the Next Generation Science Standards were involved in the production of this product, and do not endorse it.
