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Predicting Future Motion - 3rd Grade Science

  1. 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?
    Answer: 125 cm because it bounces half the drop height 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.
  2. 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?​
    Answer: 320 cm because it increases by 80 cm each time 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.
  3. A toy car rolls farther with more wind-up turns: 2 turns=30 cm, 4=60 cm, 6=90 cm. Based on the pattern, how far will it go with 10 turns?​​
    Answer: 150 cm because it adds 30 cm every 2 turns This question assesses using motion patterns to predict future motion (3-PS2-2). Patterns in motion data allow us to make predictions by extending observed trends to new conditions. The toy car data shows that distance increases consistently with wind-up turns: 2 turns gives 30 cm, 4 turns gives 60 cm, 6 turns gives 90 cm - an increase of 30 cm for every 2 additional turns. Answer A correctly extends this pattern: from 6 turns (90 cm) to 10 turns requires adding 4 more turns, which means adding 60 cm (2 sets of 30 cm), resulting in 150 cm total. Answer B incorrectly assumes distance plateaus, Answer C misidentifies the pattern as 15 cm per turn, and Answer D ignores the pattern entirely. To solve linear patterns with steps, first identify the change per step (30 cm per 2 turns), then calculate how many steps are needed (10-6=4 turns = 2 steps), and multiply to find the total change.
  4. A swing stops after 10 s with a gentle push, 20 s with a medium push, and 30 s with a strong push. Based on the pattern, how long for a very strong push?
    Answer: 40 s because it increases by 10 s each time This question tests 3-PS2-2: using motion patterns to predict future motion. Observing how motion duration changes with different initial forces helps us identify patterns for prediction. The swing time increases by 10 seconds with each stronger push: gentle (10s) → medium (20s) → strong (30s), showing a consistent +10s pattern. A very strong push would result in 40 seconds of swinging (30+10=40). Option A incorrectly averages the values, option C repeats a previous measurement, and option D unrealistically suggests immediate stopping. When analyzing time-based patterns, calculate differences between consecutive measurements, verify the pattern is consistent, then extend it logically to the next condition.
  5. A wind-up car goes 3030 cm with 22 turns, 6060 cm with 44, and 9090 cm with 66. Use the pattern to predict the distance with 88 turns.
    Answer: 120 cm because it increases 3030 cm for every 22 turns 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.
  6. 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.​​
    Answer: 40 s because it increases by 10 s each time 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.
  7. A ball rolls down ramps and speeds up: low angle 2 m/s, medium 4 m/s, high 6 m/s. If the pattern continues, what will its speed be on a very high ramp?​​
    Answer: 8 m/s because it increases by 2 m/s each step This question evaluates using motion patterns to predict future motion (3-PS2-2). Identifying patterns in motion data allows us to extend trends and predict outcomes for untested conditions. The data shows that as the ramp angle increases from low to medium to high, the ball's speed increases in a regular pattern: 2 m/s, 4 m/s, 6 m/s - an increase of 2 m/s for each step up in angle. Answer B correctly extends this pattern: a very high ramp (the next step) would produce a speed of 8 m/s (6 + 2). Answer A incorrectly assumes speed plateaus, Answer C ignores the increasing trend, and Answer D suggests doubling which doesn't match the actual pattern of adding 2 m/s. When analyzing patterns, calculate the difference between consecutive values (4-2=2, 6-4=2) to identify constant addition patterns. Then add this same amount to predict the next value in the sequence.
  8. A wind-up car went 30 cm with 2 turns, 60 cm with 4 turns, and 90 cm with 6 turns. If the pattern continues, how far with 8 turns?
    Answer: 120 cm because it increases by 30 cm every 2 turns 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 increasing by 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 proportional trend. Distractors fail by repeating a single data point, ignoring the consistent increase, or assuming an unrealistic jump without pattern support. A teaching strategy is to calculate ratios, like distance per turn, to identify the pattern. Then, apply the rule to the new input and verify if the prediction aligns with the observed progression.
  9. 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?​
    Answer: 46 cm because it stays around 45–47 cm 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.
  10. 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?
    Answer: 125 cm because the bounce is half the drop height This question evaluates the skill of using motion patterns to predict future motion (3-PS2-2). Observing repeated trials under different conditions reveals patterns that can be mathematically extended to make predictions. The data shows a proportional relationship: when dropped from 100 cm the ball bounces to 50 cm, from 150 cm it bounces to 75 cm, and from 200 cm it bounces to 100 cm - in each case, the bounce height is exactly half the drop height. Answer A correctly applies this pattern by calculating half of 250 cm to get 125 cm. The other options fail to recognize this proportional relationship - B (100 cm) just repeats a previous measurement, C (250 cm) incorrectly suggests the ball bounces to the same height, and D (110 cm) uses an arbitrary value. To identify proportional patterns, calculate the ratio between paired values, verify it's consistent across all data points, then apply the same ratio to make predictions.
  11. A toy car stops after smooth 33 m, slightly rough 22 m, rough 11 m. Use the pattern to predict the stop distance on extra rough.
    Answer: 0 m because it decreases by 11 m each time 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 distance decreases by 1 m with each increase in roughness: smooth at 3 m, slightly rough at 2 m, rough at 1 m. The correct answer, 0 m, works because it subtracts another 1 m for extra rough, providing a logical extension of the decreasing pattern. Distractors fail by repeating values, matching the first, or assuming increases without following the trend. To teach this, first identify the pattern type by calculating differences in distances. Then, apply the subtraction rule for the prediction, and ensure it fits the context of heightened friction.
  12. A scooter rolled down longer ramps: 1 m ramp→2 m roll, 2 m ramp→4 m roll, 3 m ramp→6 m roll; if the pattern continues, how far will it roll from 4 m ramp?
    Answer: 8 m because the roll distance is double the ramp length This question tests the ability to use motion patterns to predict future motion (3-PS2-2). Proportional relationships in motion data show that one quantity changes in direct proportion to another, allowing for reliable predictions. The data reveals a clear pattern: the scooter rolls exactly twice as far as the ramp length (1 m ramp→2 m roll, 2 m ramp→4 m roll, 3 m ramp→6 m roll), establishing a 2:1 ratio. Answer A correctly applies this proportional relationship by calculating that a 4 m ramp would result in an 8 m roll (4 × 2 = 8). The other options fail to recognize this doubling pattern - B (6 m) uses an incorrect ratio, C (7 m) adds an arbitrary amount, and D (4 m) incorrectly suggests the roll equals the ramp length. To identify proportional patterns, calculate the ratio between paired values, confirm it's constant across all examples, then apply the same ratio to new situations.
  13. A ball rolled off ramps: 20 cm high→80 cm, 40 cm→160 cm, 60 cm→240 cm. Use the pattern to predict the roll distance from an 80 cm ramp.
    Answer: 320 cm because it keeps adding 80 cm each time The skill being assessed is 3-PS2-2: Use motion patterns to predict future motion. Patterns enable prediction as repeated observations establish trends, such as consistent additions, allowing extension to new scenarios under similar conditions. The ball rolls 80 cm from 20 cm height, 160 cm from 40 cm, and 240 cm from 60 cm, showing a pattern of adding 80 cm for each 20 cm height increase or multiplying height by 4. Choice A accurately applies this by adding another 80 cm for the 80 cm ramp, predicting 320 cm, which fits the multiplicative and additive trend. Distractors err by repeating the last distance, guessing without pattern, or using only the initial data point. Teach by first calculating differences between roll distances to spot the addition rule. Then, extend it to the new height and check if the prediction is reasonable based on the pattern's consistency.
  14. 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?
    Answer: 320 cm because it increases by 80 cm each time 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.
  15. A wind-up toy car went: 2 turns 30 cm, 4 turns 60 cm, 6 turns 90 cm; based on the pattern, how far with 8 turns?
    Answer: 120 cm because every 2 turns adds 30 cm This question evaluates the skill of using motion patterns to predict future motion (3-PS2-2). Identifying patterns in motion data allows us to make accurate predictions by recognizing the mathematical relationship between variables. The data shows a proportional relationship between wind-up turns and distance: 2 turns→30 cm, 4 turns→60 cm, 6 turns→90 cm, where every 2 turns adds 30 cm of distance. Answer A correctly applies this pattern by recognizing that 8 turns (2 more than 6) would add another 30 cm to reach 120 cm total. The incorrect options fail to identify the proportional relationship - B (90 cm) just repeats the last value, C (100 cm) uses an incorrect increment, and D (60 cm) goes backward in the sequence. When solving proportional patterns, look for consistent ratios or differences, express the relationship mathematically (here, distance = 15 × turns), then use this formula to make predictions.
  16. A block slides: Monday 4545 cm, Tuesday 4747 cm, Wednesday 4646 cm, Thursday 4545 cm. If the pattern stays about the same, what on Friday?
    Answer: 46 cm because it stays around 4545–4747 cm 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 slide distances fluctuate slightly but stay around 45–47 cm each day: 45 cm, 47 cm, 46 cm, 45 cm. The correct answer, 46 cm, works because it logically extends the pattern of staying within that narrow range, matching the trend of consistency. Distractors fail by assuming dramatic increases or decreases, or requiring exact matches to specific days without recognizing the stable pattern. To teach this, first identify the pattern type as stable with minor variations by observing the range. Then, predict within the same range and check if it makes sense given the lack of significant changes over time.
  17. 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?
    Answer: 8 m/s because the speed increases by 2 m/s each time 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.
  18. A ball rolls off ramps: 20 cm high→80 cm, 40 cm→160 cm, 60 cm→240 cm. Based on the pattern, how far will it roll from an 80 cm ramp?​​
    Answer: 320 cm because it rolls 4 times the ramp height This question assesses using motion patterns to predict future motion (3-PS2-2). Patterns in motion data allow us to make reliable predictions because similar conditions typically produce similar results. The data shows a clear proportional pattern: when the ramp is 20 cm high, the ball rolls 80 cm (4 times the height); at 40 cm high, it rolls 160 cm (4 times); at 60 cm high, it rolls 240 cm (4 times). Answer B correctly identifies and applies this pattern - an 80 cm ramp would result in the ball rolling 320 cm (80 × 4). Answer A incorrectly assumes a constant addition pattern, Answer C fails to extend the pattern, and Answer D incorrectly predicts the distance would decrease. To identify proportional patterns, divide the output by the input for each data point (80÷20=4, 160÷40=4, 240÷60=4). When the ratio is constant, multiply the new input by this ratio to predict the output.
  19. A swing stops after 10 s with a gentle push, 20 s with a medium push, and 30 s with a strong push. Based on the pattern, how long for a very strong push?​
    Answer: 40 s because it increases by 10 s each time This question tests 3-PS2-2: using motion patterns to predict future motion. Observing how motion duration changes with different initial forces helps us identify patterns for prediction. The swing time increases by 10 seconds with each stronger push: gentle (10s) → medium (20s) → strong (30s), showing a consistent +10s pattern. A very strong push would result in 40 seconds of swinging (30+10=40). Option A incorrectly averages the values, option C repeats a previous measurement, and option D unrealistically suggests immediate stopping. When analyzing time-based patterns, calculate differences between consecutive measurements, verify the pattern is consistent, then extend it logically to the next condition.
  20. A ball dropped 100100 cm bounces 5050 cm, 150150 cm bounces 7575 cm, 200200 cm bounces 100100 cm. If the pattern continues, what bounce from 300300 cm?
    Answer: 150 cm because the bounce is half the drop height 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 bounce height is half the drop height: 100 cm to 50 cm, 150 cm to 75 cm, 200 cm to 100 cm. The correct answer, 150 cm, works because it halves the 300 cm drop, accurately applying the proportional pattern. Distractors fail by assuming constancy, incorrect increments, or full rebound without matching the halving ratio. To teach this, first identify the pattern type by finding ratios of bounce to drop. Then, apply the ratio to the new height for prediction, and confirm it extends the observed trend consistently.

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