MS-ETS1-4: Using Models to Test, Improve and Optimize a Design
In plain English: MS-ETS1-4 is the NGSS middle school engineering performance expectation that asks students to develop a model that generates data for testing and changing a proposed object, tool or process over and over, until an optimal design is reached. Students use physical, mathematical and process models, change one variable at a time and decide when to stop. It is usually taught inside grades 6-8 science.
Develop a model to generate data for iterative testing and modification of a proposed object, tool, or process such that an optimal design can be achieved.
Next Generation Science Standards · Disciplinary Core Idea: Engineering Design · Official standard
An engineer rarely gets a design right on the first try. Instead, the engineer builds a model, a simpler version of the design that can be tested, and uses it to generate data. There are several kinds: a physical model (a scale model or a working prototype, an early version of the real thing), a mathematical model (a rule, table or graph that predicts results), a computer model (a simulation or spreadsheet) and a process model (a step-by-step map or role-play of how something is done). Iterative testing means testing, studying the results, changing the design and testing again, in rounds. Each round changes one variable (one thing that can be changed, such as sail size) so the data show what the change did. The goal is an optimal design: the best design the team can find that meets the criteria within the constraints. A team can stop when changes no longer improve the results by more than the normal spread between trials.
NGSS gives no Clarification Statement and no Assessment Boundary for MS-ETS1-4, so this lesson follows the wording of the performance expectation. Students develop and use models of an object (a sail cart and a cardboard box), a tool (a cup water timer) and a process (a car wash fundraiser), as the standard names all three. All test data and times are invented for teaching and labeled as invented. The water timer lab uses cups, water and pushpins only; the box fan in the sail cart example runs on low behind its grille.
Learning Objectives
By the end of this lesson, students will be able to:
Develop a physical, mathematical or process model that generates data about a proposed object, tool or process
Plan rounds of testing that change one variable at a time and keep everything else the same
Analyze model data to choose the next change, narrowing in on the best value
Decide when a design is optimal, using the criteria, the constraints and the spread between trials
Explain what a model leaves out and why the final design still needs testing
Prior Knowledge Required
Students should already be comfortable with:
Writing precise criteria and constraints for a design problem MS-ETS1-1
Analyzing test data to combine the best features of several designs MS-ETS1-3
"You are making a paper airplane fly as far as possible. You can change the wing size, the nose weight and the throw. You get 10 throws. How would you use them to find the best plane?"
Collect plans. Some students will change everything at once; others will change one thing at a time. Ask which plan lets you tell what made the plane better. Tell students that engineers use models to do exactly this kind of test-and-change, and that today they will decide when the design is as good as it is going to get.
Direct Instruction15-20 minutes
Models generate data; data guide the next change. Define model (physical, mathematical, computer and process), prototype, iterative testing, variable and optimal design (see the overview). Show Diagram 2, the iteration cycle, and then work through the sail cart example round by round with Diagram 1.
Develop the model and choose what to measure
A class is designing a wind-powered cart to carry supplies across a field. To test ideas cheaply, it builds a scale model: a 100 g toy cart with a cardstock sail, pushed by a box fan on low, 1 m away. Criteria: the cart reaches at least 0.5 m/s (timed over 2 m) and does not tip over in 3 runs. Constraint: the sail is cut from one sheet of cardstock (22 × 28 cm).
Result: The model turns the design question into data: change the sail, time the cart over 2 m, and compute speed = 2 m ÷ time. One sheet gives at most 22 × 28 = 616 cm² of sail. Every trial keeps the same fan setting, distance, cart and floor, so only the sail changes.
Round 1: test a wide range
Flat square sails of 100, 200, 300, 400 and 500 cm², 3 runs each (invented means): 0.30, 0.46, 0.55, 0.53 and 0.44 m/s. The 500 cm² sail tipped the cart once.
Result: Speed rises from 100 to 300 cm², then falls: a bigger sail catches more air, but past a point it adds weight and drag and makes the cart top-heavy. The best value lies near 300 cm², somewhere between 200 and 400 cm². The 500 cm² sail fails the no-tipping criterion.
Round 2: narrow in on the best value
The class tests between 200 and 400 cm²: a 250 cm² sail gives 0.52 m/s, a 300 cm² sail is retested at 0.55 m/s again, and a 350 cm² sail gives 0.56 m/s. The 3 runs of each sail spread over about 0.04 m/s.
Result: 350 cm² beats 300 cm² by only 0.56 - 0.55 = 0.01 m/s, less than the 0.04 m/s spread between runs, so the two sizes are a tie. Testing sizes even closer together will not help. To improve further, the class changes a different variable.
Round 3: modify a second variable
The class curves the sail into a shallow scoop, keeping the area the same. Curved 350 cm² sail: 0.61 m/s. Curved 400 cm² sail: 0.60 m/s. Neither tipped.
Result: Curving the 350 cm² sail added 0.61 - 0.56 = 0.05 m/s, more than the 0.04 m/s spread, so the change is real. The curved 400 cm² sail is no better (0.60 m/s, within the spread). The curved 350 cm² sail is the optimal design so far: it meets both criteria and uses 350 of the 616 cm² allowed.
Decide when to stop, and check what the model leaves out
The class compares the last round with the first and asks what a scale model cannot show about a full-size cart.
Result: From round 1 to round 3 the best speed rose from 0.55 to 0.61 m/s, about 11% faster, and the latest changes are within the trial spread, so the class stops. The model does not include real wind gusts, grass instead of a smooth floor, or the weight of real supplies, so the full-size design needs its own tests before anyone builds it.
After each round, ask: "What did this round tell us? What is the one change we will make next, and why? Is the improvement bigger than the spread between runs?" Stress that an optimal design is the best one found within the criteria and constraints, not a perfect one, and that a model is useful only for the questions it was built to answer.
Guided Practice15 minutes
A mathematical model. A company wants a closed cardboard box with a square base that holds 2,744 cm³ of cereal, using as little cardboard as possible. For a base side of s cm, the height must be h = 2,744 ÷ (s × s) cm, and the cardboard needed is 2 × s × s (top and bottom) + 4 × s × h (four sides). Pairs use the model to generate data instead of building eight boxes.
Model output: boxes that hold 2,744 cm³ (values rounded to 0.1)
Base side s (cm)
Height h (cm)
Cardboard (cm²)
10
27.4
1,297.6
11
22.7
1,239.8
12
19.1
1,202.7
13
16.2
1,182.3
14
14.0
1,176.0
15
12.2
1,181.7
16
10.7
1,198.0
17
9.5
1,223.6
Check one row yourself: for s = 16, find h and the cardboard needed.
Which base side uses the least cardboard? Describe the shape of that box.
New constraint: the box must be no taller than 10 cm so it fits on the store shelf. Which base sides in the table are allowed now, and which allowed one uses the least cardboard?
The team tries s = 16.6 cm with the model. Find h and the cardboard needed, and say whether this finer step was worth testing.
Independent Practice10-15 minutes
Each student writes a short memo to the company that wants to build the full-size wind-powered supply cart from the Direct Instruction example. The memo (1) states the optimal sail that the model found and the data that support it, (2) lists three things the scale model leaves out, and (3) proposes the next model or prototype test, naming the one variable it would change, what it would measure, how many trials it would run and the rule for when to stop.
Closure5 minutes
Exit ticket: "Name a kind of model, the data it can generate and one thing it cannot tell you. Then write a stopping rule for an iterative test." Return to the warm-up: the 10 throws are a model test, and the best plan changes one thing per round.
Teacher note: MS-ETS1-3 combines the best features of several designs; MS-ETS1-4 then refines one design through rounds of model testing. In high school, HS-ETS1-4 uses computer simulations of more complex problems.
Differentiation Strategies
For Struggling Students
Give an iteration log with columns: round, the one thing changed, the value, trial results, mean, meets criteria (yes or no), next step
Start the box model with s = 10, 14 and 17 only, then fill in the rest
Use a stopping rule card: "Stop when it meets the criteria AND the last change helped less than the spread"
For Advanced Students
Ask students to put the box model in a spreadsheet and test base sides in steps of 0.1 cm
Have students add a second criterion to the car wash model, such as no volunteer working more than 2 hours, and find the new optimum
Ask students to graph the water timer data and use the pattern to predict the drain time for 5 holes before testing it
Assessment Guidance
What to Look For
Check that students state which variable they change, keep the others fixed, and use the data from each round to choose the next test, narrowing in rather than guessing. Strong work compares each improvement with the spread between trials, checks the criteria and constraints before calling a design optimal, and names what the model leaves out. Watch for changing several variables in one round, stopping at the first design that passes, and treating a model result as proof that the full-size design will work.
02
Classroom Activities
3 Activities
1
Cup Water Timer: Test, Change, Retest
35 minGroups of 3
Groups build a water timer (a tool) from a plastic cup with pushpin holes in the bottom, and change it round by round until 100 mL of water drains in 2.0-2.5 minutes, the time needed for a quick quiz review. The cup is a physical model that generates data on every run.
Procedure
Safety: push pins through the cup bottom only while the cup sits on a foam block or folded towel, with the point aimed down and away from fingers; the teacher can pre-punch holes for students who prefer it. Work over a tub and wipe spills right away.
Round 1: make 1 hole in the center of the cup bottom. Hold the cup over the tub, pour in 100 mL of water and time how long it takes to empty. Run 3 trials and find the mean.
Each new round: add one hole (same pin, same spacing) and repeat. Change nothing else: same cup, same water amount, same height above the tub.
Stop when the mean time falls in the 2.0-2.5 minute range and the trials agree within about 0.2 minutes.
Sample Data (invented)
Mean drain times: 1 hole 6.4 min, 2 holes 3.3 min, 3 holes 2.2 min, 4 holes 1.6 min.
Discussion Questions
Which number of holes gives an optimal timer? How do you know it is optimal and not just "good enough"?
What pattern do you see when the number of holes doubles? Use it to predict the time for 6 holes.
The criterion changes to 3.0-3.5 minutes. Which design from your data meets it, and what would you test if none did?
Modification for Distance Learning
Students use a disposable cup at home with an adult's help, or use the sample data and a class video, and post their round-by-round log to a shared document.
2
Car Wash Fundraiser: A Process Model
25 minGroups of 4
Groups model a process: a student car wash with four stations in a row and 8 volunteers. Station cards show how long one volunteer needs for one car at each station (invented): rinse 2 minutes, soap 3 minutes, scrub 6 minutes, dry 4 minutes. Groups move counters (volunteers) between stations, use the model to predict cars washed per hour, and iterate until no move helps.
Model Rules
With k volunteers at a station, each car takes (time for one volunteer) ÷ k minutes there.
Cars move down the line together, so the slowest station sets the pace: cars per hour = 60 ÷ (time at the slowest station).
Every station needs at least 1 volunteer, and all 8 volunteers must be placed.
Procedure
Round 1: put 2 volunteers at every station. Find each station's time per car and the cars per hour.
Each new round: move one volunteer from one station to another. Record the new times and cars per hour in an iteration log.
Stop when no single move raises the cars per hour.
Discussion Questions
Which station is the slowest in Round 1, and how many cars per hour does the model predict?
What arrangement gave the most cars per hour, and why does moving any one more volunteer not help?
Name two things the model leaves out (for example, breaks, or cars arriving in bunches). How could the class test the model on the day of the fundraiser?
Challenge Variation
A ninth volunteer joins. Use the model to find where to place the ninth volunteer and the new cars per hour, then find how many volunteers the line needs to reach 40 cars per hour.
3
Iteration Log Detective
20 minPairs
Four invented teams kept logs while improving a rubber-band paddle boat that must cross a 2 m tub of water in under 8 seconds. Pairs judge each log, name any mistake and rewrite the next step.
The 4 Logs (invented)
Team 1: Round 1: 10 s. Round 2: bigger paddle, more rubber-band twists and a longer hull, all at once: 7 s. "The bigger paddle worked!"
Team 2: Round 1: 7.8 s, under 8 s. "Done." They never tried another change.
Team 3: 30 twists: 7.2 s; 40 twists: 6.4 s; 45 twists: 6.3 s; 50 twists: 6.3 s, with trials spreading over 0.4 s. They then tested 41, 42, 43 and 44 twists.
Team 4: 3 trials per round, one change per round: paddle 4 cm wide 9.1 s, 6 cm 7.4 s, 8 cm 7.5 s; then, with the 6 cm paddle, 40 twists 6.6 s and 50 twists 6.5 s, with trials spreading over 0.3 s. "Stop: 6.5 s meets the criterion, and our last change helped by only 0.1 s, less than our 0.3 s spread."
Discussion Questions
Only one team changed one variable at a time, ran repeat trials and used a stopping rule. Which team?
Why can't Team 1 say that the paddle made the difference?
Was Team 2 wrong to stop? What might it have missed?
From 45 twists on, Team 3's times change by less than the spread between trials. What should Team 3 have done instead of testing 41-44 twists?
Modification for Distance Learning
Post the logs on slides. Pairs comment on each log in a shared document and vote on the strongest one.
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: Sail Cart Speed by Sail Area, Three Rounds of Model Testing (Invented Data, to Scale)
Invented data from the Direct Instruction example, drawn to scale. Navy dots are round 1 (flat sails), blue squares are round 2 (flat sails between 200 and 400 cm²), green triangles are round 3 (curved sails). The dashed red line is the 0.5 m/s criterion. Each point is the mean of 3 runs.
Diagram 2: The Model, Test, Analyze and Modify Cycle
Iterative testing repeats the cycle, changing one variable per round, until the design meets the criteria within the constraints and further changes no longer improve the results by more than the spread between trials. The box on the right traces the sail cart example.
04
Homework Assignment
~30 min
MS-ETS1-4 Homework: Models, Iteration and Optimal Designs
Directions: All data are invented for practice. Show your work for every calculation, and for every round you plan, say which one variable changes and what stays the same.
Part 1: Mathematical and Process Models (Problems 1-2)
A class has 40 m of rope to mark out a rectangular play area for field day. (a) Make a table of the length, width and area for lengths of 4, 8, 10, 12, 16 and 18 m (the width is 20 - length). (b) Which rectangle gives the most area? (c) New constraint: the area must be at least 12 m wide for one of the games. Which rectangle in your table is now optimal, and how much area does the constraint cost?
A bake sale checkout has three stations. One volunteer needs 1.0 minute per customer to take the order, 1.5 minutes to bag the items and 2.0 minutes to take payment. With k volunteers at a station, the time per customer there is divided by k, and the slowest station sets the pace. (a) With 6 volunteers placed 2-2-2, how many customers per hour can the line serve? (b) Try at least two other arrangements of the 6 volunteers. What is the most customers per hour the model allows? (c) How many volunteers would the line need to serve 80 customers per hour?
Part 2: Analyzing Rounds of Testing (Problems 3-4)
A team builds a ramp model for a mini-golf hole: a toy car rolls down a ramp and must stop in a target zone 150-170 cm from the bottom. Round 1: ramp height 10 cm, car stopped at 95 cm; height 20 cm, 185 cm. Round 2: height 15 cm, 140 cm. (a) About how many centimeters farther does the car roll for each extra centimeter of ramp height? (b) Use that pattern to choose the next height to test and predict where the car will stop. (c) Another team tests 18 cm and the car stops at a mean of 167 cm, with trials spreading over 6 cm. Should that team keep iterating? Explain.
A team uses a spreadsheet model to find the number of solar panels for a school garden shed that must store enough energy for 3 cloudy days. The model's output: 2 panels, 1.5 days of storage; 3 panels, 2.3 days; 4 panels, 3.1 days; 5 panels, 3.8 days. Each panel costs $180, and the budget is $800. (a) Which numbers of panels meet the 3-day criterion? (b) Which meet the budget? (c) Which is optimal, and why might the team still test a real prototype before buying panels?
Part 3: Planning and Judging Iterations (Problems 5-6)
A team's log for a paper "marble catcher" cup (it must catch a marble rolling off a table edge): Round 1, 6 cm cup at 10 cm from the table: caught 3 of 10. Round 2, a 9 cm cup at 15 cm from the table, with a cardboard backstop added: caught 8 of 10. The team writes, "The wider cup is the key." (a) What is wrong with this conclusion? (b) Plan the next three rounds so the team can tell which change mattered. (c) Write a stopping rule for the team.
Plan your own model test: a pleated paper fan should move as much air as possible, measured by how far a paper strip hung 30 cm away swings. (a) Describe the model and the one variable you will change first (for example, the number of pleats). (b) List what you will keep the same. (c) Describe your first two rounds, including how many trials per test and how you will choose the values for round 2. (d) State how you will know you have reached an optimal design.
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
Using the Model
Model outputs computed correctly and used to compare designs
One calculation error or a missing comparison
Iteration Plan
One variable changed per round, others fixed, next values chosen from the data
Several variables changed at once, or next values guessed
Optimal Design
Criteria, constraints and trial spread used to decide when to stop
Stops at the first design that passes, or never stops
Model Limits
Names what the model leaves out and how to check it
Treats the model result as proof
05
Quiz: 20 Questions
Interactive, with answers
Instructions
All test results, times and model outputs are invented. Your score updates as you answer, and Reset quiz clears everything so you or your students can try again. Short-answer questions show a model answer.
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 of these is a model that engineers could use to generate data about a footbridge design?
Answer: C
A scale model can be loaded and measured, so it generates data about the design. Choice A shows a different bridge and cannot be tested. Choices B and D are words and opinions, not data.
Question 2 of 20 · Multiple Choice
Why do engineers test a design in several rounds instead of once?
Answer: A
Iterative testing uses each round's results to choose the next change, moving step by step toward an optimal design. Choice C overstates it: a first design may work, but iteration can still improve it. Choices B and D are not reasons to iterate.
Question 3 of 20 · Multiple Choice
A team's cart model went 0.42 m/s. For the next round, which plan will best show the effect of the wheels?
Answer: B
Changing one variable at a time lets the team link any change in speed to that variable. Choices A and C change several things together, so the cause of a change would be unclear. Choice D does not change the wheels at all.
Question 4 of 20 · Multiple Choice
A model of a kite tail gave these means: 40 cm tail, 6 s of steady flight; 60 cm, 14 s; 80 cm, 19 s; 100 cm, 15 s; 120 cm, 9 s. Between which two lengths does the best tail length lie?
Answer: D
The flight time rises to 19 s at 80 cm and falls on both sides, so the best length lies between its neighbors, 60 and 100 cm. Choices A and B are where the results are worst, and choice C ignores that the times are already falling at 100 and 120 cm.
Question 5 of 20 · Multiple Choice
In a ramp model, a 10 cm ramp sent a ball 80 cm and a 14 cm ramp sent it 112 cm. The target is 100 cm. Which height is the best next test?
Answer: C
Distance grows about 8 cm per cm of height (32 cm more for 4 cm more), so 100 cm needs about 100 ÷ 8 = 12.5 cm. Choice A repeats the first test. Choice B goes beyond the 14 cm ramp, which already overshoots. Choice D adds the two heights (10 + 14).
Question 6 of 20 · Multiple Choice
A team's last three changes improved its design by 0.3, 0.2 and 0.1 s. Its trials spread over about 0.5 s, and the design meets every criterion. What should the team do?
Answer: A
When improvements are smaller than the normal spread between trials, the team cannot tell them from chance, and the design already meets the criteria, so it has reached an optimal design. Choice B never stops, choice C throws away what the team learned, and choice D bends the criteria.
Question 7 of 20 · Multiple Choice
A math model says the cardboard needed for a closed box that holds 2,744 cm³ is 2 × s × s + 10,976 ÷ s, for base side s cm. How much cardboard does it give for s = 28?
Answer: D
2 × 28 × 28 + 10,976 ÷ 28 = 1,568 + 392 = 1,960 cm². Choice A keeps only the 10,976 ÷ s part (the four sides). Choice B is the least cardboard, at s = 14, not the amount at s = 28. Choice C keeps only the 2 × s × s part (the top and bottom) and leaves out the sides.
Question 8 of 20 · Multiple Choice
In a process model of a lunch fundraiser, the stations take 2 minutes (order), 5 minutes (cook) and 3 minutes (pack) per meal, one meal at a time, and the slowest station sets the pace. How many meals per hour can the line serve?
Answer: B
The slowest station, cooking, takes 5 minutes per meal, so the line serves 60 ÷ 5 = 12 meals an hour. Choice A adds all three times (60 ÷ 10). Choice C uses the pack station (60 ÷ 3), and choice D uses the fastest station (60 ÷ 2).
Question 9 of 20 · Multiple Choice
What does an optimal design mean in MS-ETS1-4?
Answer: B
An optimal design is the best the team can find that meets the criteria within the constraints. It is not perfect (choice A) and not simply the first to pass (choice C). Cost is a constraint, not a goal (choice D).
Question 10 of 20 · Multiple Choice
A team's scale model of a delivery cart works well on a smooth classroom floor. Why does the full-size cart still need testing?
Answer: C
A model is simpler than the real thing: it may leave out gusty wind, rough ground or heavy loads, so its results must be checked at full size. Choices A and D reject models that are useful, and choice B is false.
Question 11 of 20 · Multiple Choice
A box model shows that a 14 cm cube uses the least cardboard, but a new constraint says the box can be no taller than 10 cm. What happens to the optimal design?
Answer: A
The cube is 14 cm tall, so it breaks the new constraint; the best allowed box has a wider base and is shorter. Choice B ignores the constraint, choice C makes the box taller, and choice D is false, since wide, short boxes still hold 2,744 cm³.
Question 12 of 20 · Multiple Choice
A larger water timer drains in 6.8 minutes with 1 hole and 3.4 minutes with 2 holes. If the pattern holds, about how long will it take with 4 holes?
Answer: D
Doubling the holes halved the time, so doubling again from 2 to 4 holes halves 3.4 to 1.7 minutes. Choice A is about the time for 3 holes (6.8 ÷ 3 ≈ 2.3). Choice B halves the time three times, and choice C averages the two times.
Question 13 of 20 · Multiple Choice
Why might a team use a computer model before building physical prototypes?
Answer: C
A computer model can run many versions of a design fast and at low cost, so the team builds only the most promising ones. Choice A is false, since models simplify reality, and choices B and D skip steps every design needs.
Question 14 of 20 · Multiple Choice
A log reads: "Round 1: 9 s. Round 2: new paddle, more twists, longer hull: 6 s. The new paddle fixed it." What is the main problem?
Answer: B
Three things changed at once, so the log cannot show which one made the boat faster. Choice D misreads the data (6 s is faster), and choices A and C do not affect what the data can show.
Question 15 of 20 · Short Answer
A model of a shoe-box guitar (rubber bands stretched over a box) tested sound-hole sizes. Loudness heard 2 m away, in a class rating from 1 to 10: 2 cm hole, 4; 4 cm, 6; 6 cm, 8; 8 cm, 7; 10 cm, 5. Describe the next two tests you would run and why.
The best result is at 6 cm, with lower scores on both sides, so the best size lies between 4 and 8 cm. Next tests: 5 cm and 7 cm holes, with several listeners or trials each, changing only the hole size. If both score below 8, 6 cm is optimal; if one scores higher, test halfway between it and 6 cm next. Stop when differences are smaller than the spread of the ratings.
Question 16 of 20 · Short Answer
A recycling-drive process model has three stations: one volunteer needs 2 minutes to weigh a bag, 4 minutes to sort it and 1 minute to log it. With k volunteers at a station, divide its time by k; the slowest station sets the pace. Place 5 volunteers to process the most bags per hour, and give the number of bags per hour.
Each station needs at least 1 volunteer. Placing 1 to weigh, 3 to sort, 1 to log gives times of 2, 4 ÷ 3 ≈ 1.3 and 1 minutes, so weighing (2 minutes) sets the pace: 60 ÷ 2 = 30 bags per hour. Placing 2 to weigh, 2 to sort, 1 to log gives 1, 2 and 1 minutes, also 30 bags per hour. No placement does better: 1-3-1 is limited by weighing and 2-2-1 by sorting, and any other placement leaves a station at 2 minutes or more (for example 1-2-2 gives 2, 2 and 0.5 minutes). So the model's maximum with 5 volunteers is 30 bags per hour.
Question 17 of 20 · Short Answer
A pencil-box model holds 600 cm³ with a base 15 cm long and w cm wide, so its height is 600 ÷ (15 × w) cm. Find the height for w = 4, 5 and 8 cm. Which width gives a box no taller than 6 cm?
w = 4: 600 ÷ 60 = 10 cm tall. w = 5: 600 ÷ 75 = 8 cm. w = 8: 600 ÷ 120 = 5 cm. Only w = 8 cm keeps the box no taller than 6 cm. The model lets the team check all three widths without building any of them.
Question 18 of 20 · Short Answer
A 500 mL water timer must drain in 2.0-2.5 minutes. Invented means of 3 trials, with trials spreading over about 0.2 minutes: 5 holes 2.9 minutes, 6 holes 2.4 minutes, 7 holes 2.1 minutes. The team wants to try 8 holes "to be sure." Which design is optimal, and should the team keep testing? Explain.
Both 6 holes (2.4 minutes) and 7 holes (2.1 minutes) meet the criterion. With trials spreading over about 0.2 minutes, single runs of the 7-hole timer may dip below 2.0 minutes, while the 6-hole timer (about 2.3-2.5 minutes) stays inside the range, so 6 holes is the safer optimal choice. The pattern (5 holes × 2.9 minutes ≈ 14.5, so time ≈ 14.5 ÷ holes) predicts about 14.5 ÷ 8 ≈ 1.8 minutes for 8 holes, outside the range, so the team should stop testing.
Question 19 of 20 · Short Answer
A class used a 1:20 scale model of a classroom to test where to put a new air vent, using a small fan and a ribbon that shows air movement. Name two things this model can show and two things it might get wrong about the real room.
It can show which vent positions move air across the whole room and where dead spots are (places where the ribbon barely moves). It might get wrong how strong the airflow is (a small fan in a small box does not behave exactly like a full-size vent) and the effect of people, desks and open doors, which the model leaves out. The best vent position should be checked in the real room before it is installed.
Question 20 of 20 · Short Answer
Write a short iteration plan for a tool: a cardboard dustpan that should pick up as many dried beans as possible in one sweep. Name the model, the one variable for the first round, what stays the same, how many trials, and your stopping rule.
Sample: Model: a cardboard dustpan prototype tested on 50 dried beans spread in a 30 × 30 cm square. Variable: the angle of the front lip (for example 10°, 20° and 30°). Same: the beans, the floor, the broom, the sweeper and the dustpan width. 3 trials per angle, using the mean count picked up. Next round: test angles between the two best. Stop when it picks up at least the target number (say 45 of 50) and the next change helps by less than the spread between trials.
0 of 20 answered · 0 correct
06
Frequently Asked Questions
10 Questions
What does MS-ETS1-4 mean?
MS-ETS1-4 asks students to develop a model that generates data for testing and changing a proposed object, tool or process over and over, until an optimal design is reached. The code means Middle School, Engineering, Technology and Applications of Science, core idea 1 (Engineering Design), performance expectation 4.
What grade is MS-ETS1-4 taught in?
It is a grades 6-8 standard, usually taught inside a science unit with a design project, often as the last step after defining criteria (MS-ETS1-1), evaluating designs (MS-ETS1-2) and combining their best features (MS-ETS1-3).
What kinds of models count for MS-ETS1-4?
Physical models (scale models and prototypes), mathematical models (rules, tables and graphs), computer models (simulations and spreadsheets) and process models (step-by-step maps or role-plays). What matters is that the model generates data the team can use to improve the design.
What does iterative testing mean?
It means testing a design, studying the results, changing it and testing again, in repeated rounds. Each round should change one variable so the team can tell what that change did.
How do students know when a design is optimal?
When it meets the criteria within the constraints and further changes no longer improve the results by more than the normal spread between trials. Optimal means the best the team can find, not perfect.
Does MS-ETS1-4 include processes as well as objects?
Yes. The standard names an object, a tool or a process. A process model, such as the order of stations in a car wash or a checkout line, can be tested and improved the same way as an object.
Why change only one variable at a time?
If several things change in one round, the team cannot tell which change caused the result. Changing one variable at a time keeps the test fair and makes the data useful for choosing the next change.
What are the limits of a model?
Every model leaves things out. A scale model may not show real wind or real loads, and a math model only knows the rules written into it. Teams should name what their model leaves out and test the final design under real conditions.
How is MS-ETS1-4 assessed?
Students may be asked to build or describe a model, plan rounds of testing, use data to choose the next change, and justify when a design is optimal. Strong answers name the variable changed, the data collected and the stopping rule.
How does MS-ETS1-4 connect to high school?
In high school, HS-ETS1-4 asks students to use computer simulations to model the effects of proposed solutions to complex real-world problems, and HS-ETS1-2 asks them to break a complex problem into smaller problems that engineering can solve.
07
Related Standards
5 standards
These standards connect to MS-ETS1-4: prerequisites to review first, parallel standards at the same level, and next steps that build on it.
Before this lesson
3-5-ETS1-3Prerequisite
Plan and carry out fair tests to find parts of a model or prototype to improve
Lesson coming soon
MS-ETS1-3Prerequisite
Analyze test data from several designs to combine their best characteristics
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