All questions
Question 1
A toy car rolls down longer tracks: 1 m track takes 4 s, 2 m takes 8 s, and 3 m takes 12 s. Use the pattern to predict time for 4 m.
- 6 s because it should get faster on longer tracks
- 8 s because 2 m took 8 s
- 12 s because that was the last time
- 16 s because it increases by 4 s for each 1 m (correct answer)
Explanation: This question tests 3-PS2-2: using motion patterns to predict future motion. Understanding proportional relationships between distance and time helps predict motion for longer distances. The pattern shows time increases by 4 seconds for each additional meter: 1m→4s, 2m→8s, 3m→12s, maintaining a constant rate of 4 seconds per meter. For a 4-meter track, the time would be 16 seconds (4m × 4s/m = 16s). Option B just repeats the last time, option C incorrectly assumes faster motion on longer tracks, and option D uses data from only one trial. When dealing with proportional patterns, calculate the rate (time per distance), verify it remains constant across all data points, then multiply by the new distance.
Question 2
A ball is dropped: 100 cm drop bounces 50 cm, 150 cm drop bounces 75 cm, 200 cm drop bounces 100 cm. If the pattern continues, how high from 250 cm?
- 75 cm because 150 cm dropped bounced 75 cm
- 125 cm because the bounce is half the drop height (correct answer)
- 100 cm because that was the last bounce height
- 150 cm because it adds 50 cm each time
Explanation: This question tests 3-PS2-2: using motion patterns to predict future motion. Identifying consistent relationships between variables helps us predict motion under new conditions. The data reveals bounce height is always half the drop height: 100cm drop→50cm bounce, 150cm→75cm, 200cm→100cm (each bounce is 0.5 times drop height). Following this pattern, a 250 cm drop would produce a 125 cm bounce (250×0.5=125). Option B just uses the last bounce height, option C incorrectly adds 50 cm each time, and option D uses data from a different trial. To identify proportional patterns, calculate the ratio between related measurements (50÷100=0.5, 75÷150=0.5), verify consistency, then apply the same ratio to new situations.
Question 3
A block slides on a table: Monday 45 cm, Tuesday 47 cm, Wednesday 46 cm, Thursday 45 cm. If the pattern stays about the same, what will it slide on Friday?
- 47 cm because Tuesday was 47 cm
- 30 cm because it should keep getting smaller
- 46 cm because it stays around 45–47 cm (correct answer)
- 60 cm because it should keep getting bigger
Explanation: This question tests 3-PS2-2: using motion patterns to predict future motion. Some motion patterns show consistency rather than systematic change, which is also valuable for prediction. The sliding distances vary slightly but stay within a narrow range: 45cm, 47cm, 46cm, 45cm, all clustering around 45-47 cm with no clear increasing or decreasing trend. Based on this stable pattern, Friday's slide would likely be about 46 cm, staying within the established range. Option B incorrectly predicts continuous increase, option C predicts decrease without evidence, and option D just copies one day's result. When data shows small variations around a central value rather than a clear trend, predict the next value will fall within the same range.
Question 4
A ball was dropped and bounced: 100 cm→50 cm, 150→75 cm, 200→100 cm. If the pattern continues, how high will it bounce from 250 cm?
- 125 cm because the bounce is half the drop height (correct answer)
- 150 cm because it bounces 50 cm higher each time
- 100 cm because it will stay the same as the last bounce
- 75 cm because 150 cm dropped bounced 75 cm
Explanation: This question tests the skill of using motion patterns to predict future motion (3-PS2-2). Observing consistent patterns in repeated trials helps us predict future motion under similar conditions. The data shows the ball bounces to exactly half the drop height: 100 cm drop→50 cm bounce (50%), 150 cm→75 cm (50%), 200 cm→100 cm (50%). Answer A correctly applies this pattern, predicting a 125 cm bounce from a 250 cm drop (250÷2=125). The distractors fail because B incorrectly sees an addition pattern, C assumes no change from the last bounce, and D only considers one data point instead of the overall pattern. To identify patterns, calculate the relationship between each pair of values - here, bounce height divided by drop height always equals 0.5, confirming the half-height pattern.
Question 5
A ball was dropped: 100 cm→bounce 50 cm, 150 cm→75 cm, 200 cm→100 cm. If the pattern continues, how high will it bounce from 250 cm?
- 100 cm because it will match the last bounce
- 50 cm because that was the first bounce height
- 150 cm because it should bounce higher than the drop
- 125 cm because it bounces half the drop height (correct answer)
Explanation: The skill being assessed is 3-PS2-2: Use motion patterns to predict future motion. Patterns facilitate prediction as observations show consistent relationships, like proportions, extendable to new cases with similar setups. The ball bounces 50 cm from 100 cm drop, 75 cm from 150 cm, and 100 cm from 200 cm, following a pattern of bouncing half the drop height. Choice A properly applies this ratio, predicting 125 cm from 250 cm, which matches the proportional trend. Distractors incorrectly assume bounces exceed drops, repeat previous heights, or use isolated data points without the half-rule. Teach by calculating ratios of bounce to drop for each trial to confirm the pattern. Then, apply the ratio to the new drop height and assess if the prediction is logical for energy loss in bounces.
Question 6
A toy car stops after 3 m on smooth, 2 m on slightly rough, and 1 m on rough. If the pattern continues, where will it stop on very rough?
- 1 m because that was the last distance
- 2.5 m because that seems about in the middle
- 0 m because it keeps stopping 1 m less each time (correct answer)
- 3 m because it stopped 3 m on smooth
Explanation: This question tests 3-PS2-2: using motion patterns to predict future motion. When we observe repeated motion under changing conditions, we can identify patterns and extend them to make predictions about what will happen next. The pattern shows the toy car stopping distance decreases by 1 meter each time as the surface gets rougher: smooth (3m) → slightly rough (2m) → rough (1m), decreasing by 1m at each step. Following this pattern, on very rough surface the car would stop at 0m (1m - 1m = 0m), meaning it wouldn't move at all. Option B incorrectly uses only the smooth surface data, option C uses only the last measurement without considering the pattern, and option D makes an arbitrary guess. To solve pattern problems, first identify what changes between observations (surface roughness), then calculate the consistent change in the outcome (stopping distance decreases by 1m), and apply this rule to predict the next value.
Question 7
A toy car stops after 3 m on smooth, 2 m on slightly rough, and 1 m on rough. If the pattern continues, where will it stop on very rough?
- 0 m because it keeps stopping 1 m less each time (correct answer)
- 3 m because it stopped 3 m on smooth
- 1 m because that was the last distance
- 2.5 m because that seems about in the middle
Explanation: This question tests 3-PS2-2: using motion patterns to predict future motion. When we observe repeated motion under changing conditions, we can identify patterns and extend them to make predictions about what will happen next. The pattern shows the toy car stopping distance decreases by 1 meter each time as the surface gets rougher: smooth (3m) → slightly rough (2m) → rough (1m), decreasing by 1m at each step. Following this pattern, on very rough surface the car would stop at 0m (1m - 1m = 0m), meaning it wouldn't move at all. Option B incorrectly uses only the smooth surface data, option C uses only the last measurement without considering the pattern, and option D makes an arbitrary guess. To solve pattern problems, first identify what changes between observations (surface roughness), then calculate the consistent change in the outcome (stopping distance decreases by 1m), and apply this rule to predict the next value.
Question 8
A ball rolls off ramps: 20 cm high rolls 80 cm, 40 cm rolls 160 cm, 60 cm rolls 240 cm. If the pattern continues, how far from 80 cm?
- 80 cm because it rolled 80 cm the first time
- 240 cm because that was the last distance
- 400 cm because it adds 160 cm each time
- 320 cm because it increases by 80 cm each time (correct answer)
Explanation: This question tests 3-PS2-2: using motion patterns to predict future motion. By observing how motion changes with different starting conditions, we can identify mathematical relationships and extend them to new situations. The pattern shows rolling distance increases by 80 cm for each 20 cm increase in ramp height: 20cm→80cm, 40cm→160cm, 60cm→240cm. Following this pattern, an 80 cm high ramp (60+20) would result in 320 cm rolling distance (240+80). Option B just repeats the last measurement, option C uses only the first data point, and option D miscalculates the pattern as adding 160 cm. To solve these problems, first identify the relationship between input (height) and output (distance), calculate the consistent change (80 cm per 20 cm height), then apply this ratio to make predictions.
Question 9
A ball rolled down ramps: low angle 2 m/s, medium 4 m/s, high 6 m/s. Based on the pattern, what speed on a very high angle ramp?
- 8 m/s because the speed increases by 2 m/s each time (correct answer)
- 2 m/s because that was the low ramp speed
- 5 m/s because it should be between 4 m/s and 6 m/s
- 4 m/s because it will stay the same as the medium ramp
Explanation: The skill being assessed is 3-PS2-2: Use motion patterns to predict future motion. Patterns allow prediction because they reveal trends from observations, like steady increases, which can be projected forward if conditions are comparable. The ball speeds are 2 m/s on low angle, 4 m/s on medium, and 6 m/s on high, indicating a pattern of increasing by 2 m/s per angle step. Choice B correctly extends this by adding another 2 m/s for very high, predicting 8 m/s, aligning with the arithmetic progression. Distractors fail by averaging without basis, repeating a prior speed, or ignoring the incremental pattern. A strategy is to identify the pattern by subtracting consecutive speeds to find the difference. Apply the same difference to predict the next and evaluate if it makes sense with increasing steepness.
Question 10
A swing stops after gentle 10 s, medium 20 s, strong 30 s pushes. If the pattern continues, how long for a very strong push?
- 5 s because stronger pushes stop faster
- 15 s because it should be about halfway
- 30 s because it will match the last time
- 40 s because the time increases by 10 s each push (correct answer)
Explanation: This question aligns with the skill 3-PS2-2: Use motion patterns to predict future motion. Patterns in motion allow us to predict future outcomes because repeated observations reveal consistent trends, and under similar conditions, we can expect similar results that can be extended forward. In this case, the stopping time increases by 10 s with each stronger push: gentle at 10 s, medium at 20 s, strong at 30 s. The correct answer, 40 s, works because it extends the pattern by adding another 10 s for the very strong push, aligning with the trend. Distractors fail by averaging times, assuming constancy, or incorrectly suggesting shorter times without following the increase. To teach this, first identify the pattern type by finding differences between stopping times. Then, apply the same addition rule to predict the next time, and check if the prediction is reasonable given the push strength.
Question 11
A ball rolled off ramps: 20 cm high→80 cm, 40→160 cm, 60→240 cm. Based on the pattern, how far from an 80 cm ramp?
- 260 cm because it increases by 20 cm each time
- 320 cm because it rolls 4 times the ramp height (correct answer)
- 240 cm because it will match the last distance
- 200 cm because it adds 40 cm each time
Explanation: This question tests the skill of using motion patterns to predict future motion (3-PS2-2). Patterns in motion data allow us to predict future outcomes when similar conditions are repeated. The data shows a proportional relationship where the ball rolls 4 times the ramp height: 20 cm ramp→80 cm (4×20), 40 cm→160 cm (4×40), 60 cm→240 cm (4×60). Answer B correctly identifies this pattern and predicts 320 cm for an 80 cm ramp (4×80=320). The distractors fail because A assumes a constant increase of 20 cm which doesn't match the data, C incorrectly assumes no change from the last measurement, and D misidentifies the pattern as adding 40 cm each time. When analyzing patterns, calculate the relationship between input and output values - here dividing distance by height consistently gives 4, revealing the proportional pattern.
Question 12
A swing was pushed: gentle 10 s, medium 20 s, strong 30 s until it stopped; based on the pattern, how long for a very strong push?
- 25 s
- 40 s because the time increases by 10 s each time (correct answer)
- 10 s
- 30 s
Explanation: This question tests the ability to use motion patterns to predict future motion (3-PS2-2). When we observe how motion changes under different conditions, we can identify patterns that help predict future behavior. The data shows that as push strength increases (gentle→medium→strong), the swing time increases in a linear pattern: 10 s, 20 s, 30 s, with each step adding 10 seconds. Answer B correctly extends this pattern by adding another 10 seconds to reach 40 s for a very strong push. The incorrect answers don't follow the established pattern - A (25 s) uses an incorrect increment, C (10 s) goes back to the beginning value, and D (30 s) just repeats the last measurement. When analyzing motion patterns, first identify the type of change (here, constant addition), calculate the exact amount of change between steps, then apply this same rule consistently to predict the next value.
Question 13
A ball rolls down ramps: low angle 2 m/s, medium 4 m/s, high 6 m/s. Based on the pattern, what speed for a very high ramp?
- 6 m/s because it will stay the same as high
- 8 m/s because the speed increases by 2 m/s each time (correct answer)
- 4 m/s because medium was 4 m/s
- 12 m/s because it should double from 6 m/s
Explanation: This question tests 3-PS2-2: using motion patterns to predict future motion. Observing how motion changes under different conditions helps us identify patterns that can be extended to make predictions. The data shows ball speed increases consistently as ramp angle increases: low (2 m/s) → medium (4 m/s) → high (6 m/s), with speed increasing by 2 m/s each time. Applying this pattern, a very high ramp would produce 8 m/s (6 + 2 = 8). Option A incorrectly assumes speed stays constant, option C ignores the pattern by using an intermediate value, and option D wrongly assumes doubling rather than adding. When analyzing motion patterns, calculate the difference between consecutive measurements (4-2=2, 6-4=2), verify the pattern is consistent, then apply the same change to predict the next value.
Question 14
A marble rolls farther each try: Trial 1 is 10 cm, Trial 2 is 20 cm, Trial 3 is 30 cm, Trial 4 is 40 cm. If the pattern continues, how far in Trial 5?
- 80 cm because it doubles each time
- 40 cm because that was the last distance
- 50 cm because it increases by 10 cm each time (correct answer)
- 10 cm because Trial 1 was 10 cm
Explanation: This question tests 3-PS2-2: using motion patterns to predict future motion. Identifying arithmetic sequences in motion data allows us to extend patterns and make accurate predictions. The marble rolls 10 cm farther each trial: Trial 1 (10cm) → Trial 2 (20cm) → Trial 3 (30cm) → Trial 4 (40cm), showing a consistent +10cm pattern. Following this sequence, Trial 5 would be 50 cm (40+10=50). Option A incorrectly identifies doubling when the pattern is actually adding 10, option B just repeats the last value, and option D uses only the first measurement. To solve arithmetic sequences, calculate the difference between consecutive terms (20-10=10, 30-20=10), verify consistency, then add the same amount to predict the next term.
Question 15
A wind-up car goes 30 cm with 2 turns, 60 cm with 4, and 90 cm with 6. Use the pattern to predict the distance with 8 turns.
- 90 cm because it will stay the same as the last try
- 60 cm because it will match the 4-turn distance
- 120 cm because it increases 30 cm for every 2 turns (correct answer)
- 100 cm because it should be a little more than 90 cm
Explanation: This question aligns with the skill 3-PS2-2: Use motion patterns to predict future motion. Patterns in motion allow us to predict future outcomes because repeated observations reveal consistent trends, and under similar conditions, we can expect similar results that can be extended forward. In this case, the distance increases by 30 cm for every additional 2 turns: 2 turns at 30 cm, 4 at 60 cm, 6 at 90 cm. The correct answer, 120 cm, works because it adds another 30 cm for 8 turns, correctly extending the incremental pattern. Distractors fail by assuming slight increases, constancy, or repeats of earlier distances without following the consistent addition. To teach this, first identify the pattern type by calculating differences between distances per turn increment. Then, apply the same increment rule to predict the next distance, and verify it aligns with the proportional trend.
Question 16
A wind-up car went 30 cm with 2 turns, 60 cm with 4 turns, and 90 cm with 6 turns. Based on the pattern, what distance with 8 turns?
- 105 cm because it should go up a little from 90 cm
- 60 cm because that was the 4-turn distance
- 120 cm because it adds 30 cm for each 2 turns (correct answer)
- 180 cm because it should double every time
Explanation: The skill being assessed is 3-PS2-2: Use motion patterns to predict future motion. Patterns in motion enable prediction because repeated observations show trends like proportional increases, and these can be extended assuming similar conditions persist. Here, the wind-up car travels 30 cm with 2 turns, 60 cm with 4 turns, and 90 cm with 6 turns, demonstrating a pattern of adding 30 cm for every additional 2 turns or proportionally 15 cm per turn. Choice B correctly extends this by adding another 30 cm for 8 turns, resulting in 120 cm, matching the additive and proportional trend. Distractors fail by guessing slight increases, repeating prior distances, or assuming doubling without evidence. A teaching strategy is to calculate differences or ratios, like added distance per turns, to identify the pattern. Then, apply the rule to the new input and verify if the prediction aligns with the observed progression.
Question 17
A ball rolled down ramps: low 2 m/s, medium 4 m/s, high 6 m/s. If the pattern continues, what speed on a very high ramp?
- 6 m/s because it will stay the same as the last speed
- 5 m/s because it should be somewhere in the middle
- 2 m/s because it will match the first ramp speed
- 8 m/s because the speed increases by 2 m/s each time (correct answer)
Explanation: This question aligns with the skill 3-PS2-2: Use motion patterns to predict future motion. Patterns in motion allow us to predict future outcomes because repeated observations reveal consistent trends, and under similar conditions, we can expect similar results that can be extended forward. In this case, the ball's speed increases by 2 m/s with each increase in ramp height: from low at 2 m/s, to medium at 4 m/s, to high at 6 m/s. The correct answer, 8 m/s, works because it logically extends the pattern by adding another 2 m/s for the very high ramp, matching the established trend. Distractors fail by either assuming the speed stays constant, repeats the first value, or averages without following the incremental pattern. To teach this, first identify the pattern type by looking at differences between speeds. Then, calculate the consistent increase and apply the same rule to predict the next speed, finally checking if the prediction aligns with the observed trend.
Question 18
A toy car stopped after 3 m on smooth, 2 m on slightly rough, and 1 m on rough. If the pattern continues, how far will it go on very rough?
- 4 m because it should go farther on rougher ground
- 1 m because it will stay the same as rough
- 2 m because that was the slightly rough distance
- 0 m because it decreases by 1 m each time (correct answer)
Explanation: The skill being assessed is 3-PS2-2: Use motion patterns to predict future motion. Patterns in motion enable prediction because repeated observations reveal consistent trends, and under similar conditions, these trends can be extended to forecast future outcomes. In this case, the toy car goes 3 m on smooth, 2 m on slightly rough, and 1 m on rough surfaces, showing a pattern of decreasing by 1 m as roughness increases. Choice C correctly applies this pattern by subtracting another 1 m for very rough, predicting 0 m, which logically extends the established trend. The distractors fail because they repeat a previous distance, assume an illogical increase on rougher surfaces, or incorrectly think the pattern halts. To teach this, first identify the pattern type by looking at differences between observations, such as consistent subtraction. Then, apply the same rule to predict the next outcome and check if the prediction makes physical sense in the context of increasing friction.
Question 19
A swing is pushed harder and swings longer: gentle 10 s, medium 20 s, strong 30 s. Use the pattern to predict how long it swings with a very strong push.
- 25 s because it is between 20 s and 30 s
- 40 s because it increases by 10 s each time (correct answer)
- 30 s because it will match the strong push
- 5 s because it should stop faster when pushed harder
Explanation: This question assesses using motion patterns to predict future motion (3-PS2-2). Patterns in motion allow us to predict outcomes because consistent relationships exist between input forces and resulting motion. The swing data shows a clear linear pattern: gentle push gives 10 seconds of swinging, medium push gives 20 seconds, and strong push gives 30 seconds - each increase in push strength adds 10 seconds of swing time. Answer B correctly extends this pattern: a very strong push (the next level up) would result in 40 seconds of swinging (30 + 10). Answer A makes an arbitrary guess between values, Answer C incorrectly assumes no further increase, and Answer D contradicts physics by suggesting harder pushes lead to shorter swing times. To identify linear patterns, calculate differences between consecutive measurements (20-10=10, 30-20=10). When differences are constant, add this same amount to predict the next value.
Question 20
A wind-up toy car goes 30 cm with 2 turns, 60 cm with 4 turns, and 90 cm with 6 turns. Use the pattern to predict distance with 8 turns.
- 150 cm because it adds 60 cm each time
- 30 cm because 2 turns went 30 cm
- 120 cm because it increases by 30 cm every 2 turns (correct answer)
- 90 cm because that was the last distance
Explanation: This question tests 3-PS2-2: using motion patterns to predict future motion. Recognizing proportional relationships in motion data allows us to predict future outcomes under similar conditions. The pattern shows distance is proportional to wind-up turns: 2 turns→30cm, 4 turns→60cm, 6 turns→90cm, which means 15 cm per turn (30÷2=15, 60÷4=15, 90÷6=15). With 8 turns, the car would travel 120 cm (8×15=120). Option A incorrectly calculates by adding 60 cm, option B uses only the first data point, and option D ignores the pattern entirely. When working with proportional patterns, calculate the rate (distance per turn), verify it's consistent across all data points, then multiply by the new input value.