{"success":true,"course":{"all_concepts_covered":["Place values from hundreds to thousandths","The 10× and 1/10 relationship between adjacent places","One tenth as 1/10 and 0.1, and placeholder zeros","Powers of 10 written with exponents (10^n)","Multiplying by powers of 10 by shifting place value left","Dividing by powers of 10 by shifting place value right","Implied decimal point in whole numbers and writing leading zeros correctly"],"assembly_rationale":"The course starts with a strong place-value foundation, then extends the same base-ten pattern into decimals through thousandths. Next it introduces exponents to name powers of 10, then applies the ideas to multiplication and division while repeatedly highlighting the most common errors: wrong direction, misreading 10^n, and missing placeholder zeros.","average_segment_quality":7.3125,"concept_key":"CONCEPT#c65c3cb6a904d19922ed8f9a9e164805","considerations":["There is no dedicated video segment showing many examples of multiplying/dividing decimals by 10^n by ‘shifting the digits,’ so the final interleaved practice is essential for applying the rule repeatedly.","The last two division segments use long-division context; students should still use the simpler place-value shift method for dividing by 10, 100, 1,000, and 10^n."],"course_id":"course_1770911878","created_at":"2026-02-12T16:15:08.154082+00:00","created_by":"Shaunak Ghosh","description":"You will learn how decimal place values are connected, and how each step left means 10 times as much and each step right means one tenth as much. Then you will use exponents to understand powers of 10, and practice multiplying and dividing by 10, 100, 1,000, and more without mixing up the direction or the zeros.","estimated_total_duration_minutes":30.0,"final_learning_outcomes":["Name each place from hundreds through thousandths, and state the value of a digit based on its place.","Explain and use the rule: one place left is 10 times as much, and one place right is one tenth as much.","Write and interpret one tenth as 1/10 and as 0.1, and recognize that trailing zeros don’t change a decimal’s value.","Interpret powers of 10 using exponents from 10^1 to 10^5, without confusing 10^n with 10×n.","Multiply and divide whole numbers and decimals (to thousandths) by 10^n by shifting digits the correct direction and using zeros as placeholders."],"generated_at":"2026-02-12T16:14:27Z","generation_error":null,"generation_progress":100.0,"generation_status":"completed","generation_step":"completed","generation_time_seconds":288.8574197292328,"image_description":"A clean, modern thumbnail designed for 5th graders. Center focal point: a large, friendly place-value chart that stretches from “Hundreds” down to “Thousandths,” with one example number placed in it: 7.905 (digits sitting in labeled columns). A bright arrow pointing left is labeled “×10 each move,” and a matching arrow pointing right is labeled “÷10 each move,” both in simple, bold text. Above the chart, show a crisp notation bubble reading “10³ = 1,000” in a kid-friendly font, connecting exponents to powers of ten. Use a limited palette: deep blue (#1D4ED8), bright teal (#14B8A6), and white background with a very light gradient. Add subtle shadows and layered cards for depth, like an Apple-style educational UI. Keep the composition uncluttered: one chart, two arrows, one exponent bubble. Leave clean space at the top for the course title. Style should feel playful but polished, with smooth rounded corners and clear, high-contrast labels.","image_url":"https://course-builder-course-thumbnails.s3.us-east-1.amazonaws.com/courses/course_1770911878/thumbnail.png","interleaved_practice":[{"difficulty":"mastery","correct_option_index":0.0,"question":"Fill in the blank: ___ is 10 times as much as 0.005.","option_explanations":["Correct! 0.005 × 10 shifts the digits one place left, so the 5 thousandths becomes 5 hundredths: 0.05.","0.0050 is the same value as 0.005, because a trailing zero doesn’t change the number.","0.0005 is 1/10 of 0.005, not 10 times as much.","0.5 would be 0.005 × 100, because it moves two places left, not one."],"options":["0.05","0.0050","0.0005","0.5"],"question_id":"q1_times10_thousandths","related_micro_concepts":["ten_times_one_tenth","place_value_map"],"discrimination_explanation":"When you multiply by 10, every digit moves one place left on the place-value chart, so 0.005 becomes 0.05. The other choices match common mistakes: not changing the value, moving the wrong direction (÷10), or moving too far."},{"difficulty":"mastery","correct_option_index":1.0,"question":"Which value is equal to 10^4?","option_explanations":["4,000 mixes up the exponent with the digit 4, but 10^4 is not ‘four thousand.’","Correct! 10^4 has four zeros, so it equals 10,000.","1,000 is 10^3, which has three zeros, not four.","40 matches the mistake of thinking 10^4 means 10×4."],"options":["4,000","10,000","1,000","40"],"question_id":"q2_power10_value","related_micro_concepts":["multiply_powers10"],"discrimination_explanation":"10^4 means four factors of 10 multiplied: 10×10×10×10, which equals 10,000. The distractors come from confusing the exponent with multiplication (10×4) or choosing the wrong number of zeros."},{"difficulty":"mastery","correct_option_index":1.0,"question":"Compute: 30.4 × 10^3 = ?","option_explanations":["30.04 is smaller than 30.4, so it comes from shifting right (division idea), not multiplying.","Correct! 30.4 × 1,000 shifts digits three places left, giving 30,400.","3.04 is even smaller and comes from shifting right twice (dividing), not multiplying by 1,000.","304.0 is 30.4 × 10, which is only one place left (10^1), not three."],"options":["30.04","30,400","3.04","304.0"],"question_id":"q3_multiply_decimal_10pow3","related_micro_concepts":["multiply_powers10","place_value_map"],"discrimination_explanation":"10^3 = 1,000, so multiplying by 10^3 shifts digits three places left (or multiplies by 10 three times). 30.4 becomes 30,400. The wrong answers reflect shifting the wrong direction or the wrong number of places."},{"difficulty":"mastery","correct_option_index":0.0,"question":"Compute: 5 ÷ 10^3 = ?","option_explanations":["Correct! 5 ÷ 1,000 shifts three places right: 5.000 → 0.005.","0.5 is 5 ÷ 10, only one place right.","5,000 would happen if you multiplied by 1,000 instead of dividing.","0.0005 is 5 ÷ 10^4, which would be four places right, not three."],"options":["0.005","0.5","5,000","0.0005"],"question_id":"q4_divide_whole_10pow3","related_micro_concepts":["divide_powers10","place_value_map","multiply_powers10"],"discrimination_explanation":"10^3 = 1,000, so dividing by 10^3 shifts digits three places right. Think of 5 as 5.000, then move three places to get 0.005. The distractors show wrong direction or wrong number of shifts."},{"difficulty":"mastery","correct_option_index":3.0,"question":"Fill in the blank: ___ is 1/10 of 7.9.","option_explanations":["79 is 7.9 × 10, which is the opposite direction.","7.09 is close-looking, but it does not represent dividing 7.9 by 10.","0.079 would be 1/100 of 7.9, because it shifts two places right.","Correct! 7.9 ÷ 10 shifts one place right, giving 0.79."],"options":["79","7.09","0.079","0.79"],"question_id":"q5_one_tenth_of_decimal","related_micro_concepts":["ten_times_one_tenth","place_value_map"],"discrimination_explanation":"Taking 1/10 means divide by 10, so digits move one place right: 7.9 becomes 0.79. The distractors match common place-value slips, like moving the decimal two places or mixing decimals with whole numbers."},{"difficulty":"mastery","correct_option_index":2.0,"question":"In the number 8.203, what is the value of the digit 2?","option_explanations":["2 would be correct only if the 2 were in the ones place.","0.02 would be 2 hundredths, but the 2 is not in the hundredths place here.","Correct! The 2 is in the tenths place, so it equals 2 tenths = 0.2.","0.002 would be 2 thousandths, but the 2 is not in the thousandths place here."],"options":["2","0.02","0.2","0.002"],"question_id":"q6_digit_value_in_decimal","related_micro_concepts":["place_value_map"],"discrimination_explanation":"The 2 is in the tenths place, so its value is two tenths, which is 0.2. The other choices treat the 2 as ones, hundredths, or thousandths, which are different places."},{"difficulty":"mastery","correct_option_index":2.0,"question":"Which expression shows what 10^3 means?","option_explanations":["10 × 10 + 10 is not three factors of 10; it mixes operations.","10 + 10 + 10 is repeated addition, not repeated multiplication of 10 by itself.","Correct! 10^3 means 10 × 10 × 10.","10 × 3 is the exact misconception: the exponent is not ‘times 3.’"],"options":["10 × 10 + 10","10 + 10 + 10","10 × 10 × 10","10 × 3"],"question_id":"q7_meaning_of_10cubed","related_micro_concepts":["multiply_powers10"],"discrimination_explanation":"An exponent tells repeated multiplication of the base. So 10^3 is 10 multiplied by itself three times. The other options are common mix-ups: repeated addition, ‘10 times 3,’ or mixing multiplication and addition."},{"difficulty":"mastery","correct_option_index":0.0,"question":"Compute: 0.06 × 10^2 = ?","option_explanations":["Correct! 0.06 × 100 shifts two places left: 0.06 → 6.","60 would be 0.06 × 1,000, which is three places left (10^3).","0.006 is 0.06 ÷ 10, which shifts right, not left.","0.6 is 0.06 × 10, which is only one place left (10^1)."],"options":["6","60","0.006","0.6"],"question_id":"q8_multiply_with_placeholders","related_micro_concepts":["multiply_powers10","place_value_map"],"discrimination_explanation":"10^2 = 100, so multiplying by 100 shifts digits two places left: 0.06 becomes 6. The distractors reflect shifting only one place, shifting the wrong direction, or shifting too far."}],"is_public":true,"key_decisions":["Segment 1 Ju3kQjmcH5g_49_378: Used as the anchor for whole-number place value (to 999) so later power-of-10 moves have a clear “places” meaning.","Segment 2 KrAQneGhyuE_29_210: Chosen to introduce tenths/hundredths/thousandths with the repeated ÷10 relationship, which is the backbone of shifting place values.","Segment 3 KrAQneGhyuE_211_418: Added next to convert the idea into a usable tool (place-value chart) and to explicitly address placeholder zeros like 0.06 and 0.015.","Segment 4 LFO07qWWtrs_258_489: Selected to lock in 1/10 as both a unit fraction and a decimal (0.1) and to reinforce that zeros can be placeholders (0.10 = 0.1).","Segment 5 NS4vHqJIPiE_0_180: Included to directly target the big misconception (10^n is not 10×n) and to give clear base/exponent language.","Segment 6 pEbjmAsrOic_1363_1597: Placed after exponents to connect 10^1 = 10 to the multiply-by-10 pattern and the role of zeros as placeholders.","Segment 7 IheBIlt2s20_4_189: Used to highlight decimal-point placement and placeholder zeros during division, supporting the “implied decimal point” pitfall when starting from whole numbers.","Segment 8 IheBIlt2s20_144_343: Added last to strengthen correct zero use (adding zeros without changing value), which helps students write results like 0.005 cleanly and confidently."],"micro_concepts":[{"prerequisites":[],"learning_outcomes":["Name each place from hundreds through thousandths","Tell the value of a digit in a number (example: the 7 in 7.9 is 7 ones; the 9 is 9 tenths)","Explain why moving one place left means ×10 and one place right means ÷10 (or ×1/10)"],"difficulty_level":"beginner","concept_id":"place_value_map","name":"Place values to thousandths place","description":"Learn how each digit’s value depends on its position (hundreds, tens, ones, tenths, hundredths, thousandths). Use the rule: one place left is 10 times bigger; one place right is 1/10 as big.","sequence_order":0.0},{"prerequisites":["place_value_map"],"learning_outcomes":["Explain that 1/10 means one tenth and equals 0.1","Fill in equation-style sentences like “___ is 10 times as much as 0.005” (answer: 0.05)","Fill in equation-style sentences like “___ is 1/10 of 7.9” (answer: 0.79)","Use the idea ‘×10 makes it bigger’ and ‘×1/10 makes it smaller’ for decimals up to thousandths"],"difficulty_level":"beginner","concept_id":"ten_times_one_tenth","name":"Ten times and one tenth","description":"Practice the place-value relationship using decimals: each place left is 10 times as much, and each place right is 1/10 as much. Connect 1/10 (one tenth) to the decimal 0.1, and read “times as much” as multiplication.","sequence_order":1.0},{"prerequisites":["ten_times_one_tenth"],"learning_outcomes":["Evaluate powers of 10 with exponents 1–5 (10^1=10, 10^2=100, …, 10^5=100,000)","Explain why multiplying by 10^n shifts digits left n places (making the number bigger)","Multiply numbers (whole numbers up to 999 and decimals to thousandths) by 10^n using correct place-value shifts and zeros","Avoid the mistake of thinking 10^n means 10 × n"],"difficulty_level":"beginner","concept_id":"multiply_powers10","name":"Multiply by powers of 10","description":"Learn what powers of 10 mean using exponents (like 10^3 = 1,000). Multiply whole numbers and decimals by 10^1 to 10^5 by shifting digits left the correct number of places and using zeros as placeholders when needed.","sequence_order":2.0},{"prerequisites":["multiply_powers10"],"learning_outcomes":["Explain why dividing by 10^n shifts digits right n places (making the number smaller)","Use an implied decimal point for whole numbers when dividing (e.g., 5 = 5.)","Correctly write answers with placeholder zeros and leading zeros (e.g., 5 ÷ 10^3 = 0.005)","Divide decimals to thousandths by 10^n with exponents 1–5 without shifting the wrong direction"],"difficulty_level":"beginner","concept_id":"divide_powers10","name":"Divide by powers of 10","description":"Divide whole numbers and decimals by 10^1 to 10^5 by shifting digits right the correct number of places. Use the implied decimal point in whole numbers (like 5 = 5.) and add zeros as placeholders to show the answer correctly (like 0.005).","sequence_order":3.0}],"overall_coherence_score":8.0,"pedagogical_soundness_score":8.1,"prerequisites":["Read whole numbers to 999","Know what a decimal point is","Basic multiplication and division facts","Understand “one tenth” as a fraction idea"],"rejected_segments_rationale":"Several segments were excluded due to redundancy with earlier, higher-quality picks (e.g., multiple ‘multiply by 10’ or ‘each place left is 10×’ songs), or because they primarily taught off-target skills for this standard (comparing decimals, rounding decimals). Money/quarter-focused decimal segments were skipped because they don’t directly advance powers of 10 or place-value shifting to thousandths within the assessment boundary.","segments":[{"duration_seconds":329.0933333333333,"concepts_taught":["Whole-number place value (ones, tens, hundreds, thousands...)","Using a place-value chart to read numbers","Expanded form (e.g., 567 = 500 + 60 + 7)","Recognizing repeating place-value patterns beyond hundreds"],"quality_score":7.1,"before_you_start":"You already know numbers have digits, like hundreds, tens, and ones. In this video, you will use a place-value chart to see how the same digit can mean different amounts, depending on where it sits.","title":"Digits Change Value by Place","before_you_start_avatar_video_url":"","url":"https://www.youtube.com/watch?v=Ju3kQjmcH5g&t=49s","sequence_number":1.0,"prerequisites":["Knowing digits 0–9","Basic understanding of counting and whole numbers"],"learning_outcomes":["Identify the ones, tens, and hundreds digits in a 3-digit number","Explain how moving the same digit to a different place changes its value (e.g., 5 vs 50 vs 500)","Write a 3-digit number in expanded form (e.g., 786 = 700 + 80 + 6)","Recognize that place-value names continue in a pattern beyond hundreds (thousands, ten thousands, etc.)"],"video_duration_seconds":393.0,"transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"","overall_transition_score":0.0,"to_segment_id":"Ju3kQjmcH5g_49_378","pedagogical_progression_score":0.0,"vocabulary_consistency_score":0.0,"knowledge_building_score":0.0,"transition_explanation":"N/A for first"},"before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770911878/segments/Ju3kQjmcH5g_49_378/before-you-start.mp3","segment_id":"Ju3kQjmcH5g_49_378","micro_concept_id":"place_value_map"},{"duration_seconds":181.306,"concepts_taught":["Decimal point separates whole and part","Tenths, hundredths, thousandths as fractional parts of 1","Adjacent place-value relationship (divide by 10 each step right)","Equivalences across places (10/10=1, 10 hundredths=1 tenth, 10 thousandths=1 hundredth)","Connecting fractions to decimal place names"],"quality_score":7.725,"before_you_start":"Now that you can name places in whole numbers, it’s time to cross the decimal point. You’ll learn tenths, hundredths, and thousandths, and you’ll notice a pattern, each step right means divide by 10.","title":"Tenths to Thousandths, Step by Ten","before_you_start_avatar_video_url":"","url":"https://www.youtube.com/watch?v=KrAQneGhyuE&t=29s","sequence_number":2.0,"prerequisites":["Understanding of whole numbers (ones, tens, hundreds)","Basic fraction idea: a whole split into equal parts"],"learning_outcomes":["Explain what the decimal point tells you about a number","Describe tenths, hundredths, and thousandths as 1 whole divided into 10, 100, or 1,000 equal parts","State and use the relationship that each place to the right is 1/10 of the place to its left (and each place to the left is 10× as much)"],"video_duration_seconds":425.0,"transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"Ju3kQjmcH5g_49_378","overall_transition_score":8.3,"to_segment_id":"KrAQneGhyuE_29_210","pedagogical_progression_score":8.0,"vocabulary_consistency_score":8.5,"knowledge_building_score":8.5,"transition_explanation":"This builds on whole-number place value by extending the same base-ten pattern to decimal places."},"before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770911878/segments/KrAQneGhyuE_29_210/before-you-start.mp3","segment_id":"KrAQneGhyuE_29_210","micro_concept_id":"place_value_map"},{"duration_seconds":207.916,"concepts_taught":["Place value chart for whole numbers and decimals","Pattern across the decimal point (ones ↔ tenths, tens ↔ hundredths, etc.)","Naming decimals from models (tenths/hundredths)","Using 0 as a placeholder in decimals (e.g., 0.06)","Reading/writing decimals including thousandths (e.g., 0.015)"],"quality_score":7.275,"before_you_start":"You’ve learned the tenths, hundredths, and thousandths pattern. Next, you’ll use a place-value chart to read and write decimals, and you’ll see why zeros matter when a place has nothing in it.","title":"Use a Place-Value Chart for Decimals","before_you_start_avatar_video_url":"","url":"https://www.youtube.com/watch?v=KrAQneGhyuE&t=211s","sequence_number":3.0,"prerequisites":["Understanding that tenths/hundredths/thousandths are decimal places","Basic ability to read a place value chart"],"learning_outcomes":["Use a place value chart to name the value of digits in decimals through thousandths","Write decimals correctly using zeros as placeholders (e.g., 0.06, 0.05, 0.015)","Match visual models of tenths/hundredths/thousandths to their decimal forms"],"video_duration_seconds":425.0,"transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"KrAQneGhyuE_29_210","overall_transition_score":8.8,"to_segment_id":"KrAQneGhyuE_211_418","pedagogical_progression_score":8.5,"vocabulary_consistency_score":9.0,"knowledge_building_score":9.0,"transition_explanation":"After defining decimal places, this shows how to organize them in a chart and write numbers accurately with placeholders."},"before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770911878/segments/KrAQneGhyuE_211_418/before-you-start.mp3","segment_id":"KrAQneGhyuE_211_418","micro_concept_id":"place_value_map"},{"duration_seconds":231.12,"concepts_taught":["A dime as one tenth of a dollar","Unit fraction 1/10 written as decimal 0.1","Trailing zeros don’t change value (0.10 = 0.1; 0.50 = 0.5)","Tenths on a model: 0.1, 0.2, 0.3, 0.4, 0.5"],"quality_score":7.7749999999999995,"before_you_start":"You can now read decimals using a place-value chart. In this video, you’ll zoom in on one special unit, one tenth, and connect 1/10 to 0.1, including why 0.10 means the same thing.","title":"One Tenth Is 0.1","before_you_start_avatar_video_url":"","url":"https://www.youtube.com/watch?v=LFO07qWWtrs&t=258s","sequence_number":4.0,"prerequisites":["Basic coin values (dime = 10 cents)","Understand ‘one out of ten equal parts’"],"learning_outcomes":["Explain why 1/10 of a dollar is written as 0.1","Interpret 0.1 as ‘one tenth’","Recognize that 0.10 and 0.1 are equal in value","Read tenths on a model and name them as decimals from 0.1 to 0.5"],"video_duration_seconds":936.0,"transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"KrAQneGhyuE_211_418","overall_transition_score":8.2,"to_segment_id":"LFO07qWWtrs_258_489","pedagogical_progression_score":8.0,"vocabulary_consistency_score":8.5,"knowledge_building_score":8.5,"transition_explanation":"This narrows from the full chart to the key unit (one tenth) that powers the ×10 and ÷10 relationships."},"before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770911878/segments/LFO07qWWtrs_258_489/before-you-start.mp3","segment_id":"LFO07qWWtrs_258_489","micro_concept_id":"ten_times_one_tenth"},{"duration_seconds":179.881,"concepts_taught":["Base and exponent vocabulary","Exponent as repeated multiplication","Expanded form of an exponent","Evaluating simple exponents (squared, cubed)","Common misconception: exponent is not multiplication by the exponent"],"quality_score":7.675000000000001,"before_you_start":"You’ve been using the idea of ten times and one tenth in place value. Now you’ll learn exponent notation, like a small number that tells how many times to multiply, and you’ll avoid the mistake of thinking it means ‘times the exponent.’","title":"Exponents Show Repeated Multiplying","before_you_start_avatar_video_url":"","url":"https://www.youtube.com/watch?v=NS4vHqJIPiE&t=0s","sequence_number":5.0,"prerequisites":["Understanding multiplication facts (up to at least 9×9)","Knowing what “multiply” means"],"learning_outcomes":["Identify the base and the exponent in an expression like 5^3","Rewrite an exponent expression as repeated multiplication (expanded form)","Evaluate simple exponents like 5^2 and 5^3","Explain why 10^n does NOT mean 10×n (it means 10 multiplied by itself n times)"],"video_duration_seconds":441.0,"transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"LFO07qWWtrs_258_489","overall_transition_score":7.4,"to_segment_id":"NS4vHqJIPiE_0_180","pedagogical_progression_score":7.5,"vocabulary_consistency_score":7.5,"knowledge_building_score":7.5,"transition_explanation":"This connects the repeated ×10 idea to a compact way of writing repeated multiplication: exponents."},"before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770911878/segments/NS4vHqJIPiE_0_180/before-you-start.mp3","segment_id":"NS4vHqJIPiE_0_180","micro_concept_id":"multiply_powers10"},{"duration_seconds":233.66000000000008,"concepts_taught":["Multiplying by 10 as counting tens","Using zero as a placeholder when multiplying by 10","Recognizing patterns in multiples of 10 (10, 20, 30, …)"],"quality_score":6.675000000000001,"before_you_start":"Now that you know what exponents mean, you’re ready to connect that idea to powers of 10. In this video, you’ll see the multiply-by-10 pattern, and why zeros can be placeholders when the digits shift left.","title":"Multiply by 10, Use Placeholder Zeros","before_you_start_avatar_video_url":"","url":"https://www.youtube.com/watch?v=pEbjmAsrOic&t=1363s","sequence_number":6.0,"prerequisites":["Counting by 10s","Understanding that multiplication means ‘groups of’"],"learning_outcomes":["Generate multiples of 10 (up to at least 100)","Explain that multiplying a whole number by 10 makes it 10 times as large and often results in an added zero at the end","Describe zero as a placeholder in place value when making tens"],"video_duration_seconds":1625.0,"transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"NS4vHqJIPiE_0_180","overall_transition_score":7.9,"to_segment_id":"pEbjmAsrOic_1363_1597","pedagogical_progression_score":8.0,"vocabulary_consistency_score":7.5,"knowledge_building_score":8.0,"transition_explanation":"After learning what exponents mean, this shows the concrete effect of multiplying by 10, the first power of ten (10^1)."},"before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770911878/segments/pEbjmAsrOic_1363_1597/before-you-start.mp3","segment_id":"pEbjmAsrOic_1363_1597","micro_concept_id":"multiply_powers10"},{"before_you_start":"You’ve practiced making numbers bigger by multiplying by powers of 10. Now you’ll switch to division, and focus on keeping the decimal point in the right place, plus writing zeros when a place needs a placeholder.","before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770911878/segments/IheBIlt2s20_4_189/before-you-start.mp3","before_you_start_avatar_video_url":"","concepts_taught":["Dividend vs. divisor in long division","Placing the decimal point in the quotient when the divisor is a whole number","Long division steps with decimals (divide, multiply, subtract, bring down)","Using a 0 as a placeholder in the quotient when needed"],"duration_seconds":184.79999999999998,"learning_outcomes":["Identify the dividend and divisor in a decimal-division problem","Correctly place the decimal point in the quotient when dividing by a whole number","Use long-division steps to compute a decimal ÷ whole number problem","Explain why a 0 can be written as a placeholder in the quotient"],"micro_concept_id":"divide_powers10","prerequisites":["Know what division means (sharing/splitting)","Basic multiplication facts (up to 10×10)","Understand what a decimal point is"],"quality_score":6.95,"segment_id":"IheBIlt2s20_4_189","sequence_number":7.0,"title":"Dividing Decimals, Keep the Decimal Lined Up","transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"pEbjmAsrOic_1363_1597","overall_transition_score":7.7,"to_segment_id":"IheBIlt2s20_4_189","pedagogical_progression_score":7.5,"vocabulary_consistency_score":7.5,"knowledge_building_score":8.0,"transition_explanation":"This flips the operation from multiplying to dividing, while keeping the focus on place value and correct use of zeros."},"url":"https://www.youtube.com/watch?v=IheBIlt2s20&t=4s","video_duration_seconds":362.0},{"before_you_start":"You know how to place the decimal point and use zeros as placeholders. Next, you’ll learn why you can add zeros to the end of a decimal, like 95.1 becoming 95.10, so you can keep dividing without changing the value.","before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770911878/segments/IheBIlt2s20_144_343/before-you-start.mp3","before_you_start_avatar_video_url":"","concepts_taught":["Dividing a decimal by a whole number (long division)","When division doesn’t end: extending the dividend with zeros","Equivalent decimals (adding zeros to the end doesn’t change value)","Remainders in decimal division become digits after the decimal"],"duration_seconds":198.479,"learning_outcomes":["Explain why adding a zero to the end of a decimal creates an equivalent decimal (same value)","Continue a decimal division problem by adding zeros when needed","Avoid writing a remainder as a whole-number remainder at the end of a decimal answer","Complete a long-division calculation for a decimal ÷ whole number"],"micro_concept_id":"divide_powers10","prerequisites":["Understand decimal place value to tenths/hundredths","Basic long-division steps","Multiplication facts (especially 6s in the example)"],"quality_score":7.325,"segment_id":"IheBIlt2s20_144_343","sequence_number":8.0,"title":"Add Zeros to Keep Dividing","transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"IheBIlt2s20_4_189","overall_transition_score":8.7,"to_segment_id":"IheBIlt2s20_144_343","pedagogical_progression_score":8.5,"vocabulary_consistency_score":9.0,"knowledge_building_score":9.0,"transition_explanation":"This builds on decimal placement by adding the next skill: extending decimals with zeros to show the division result clearly."},"url":"https://www.youtube.com/watch?v=IheBIlt2s20&t=144s","video_duration_seconds":362.0}],"selection_strategy":"Built a tight 30-minute path that follows the required topic order: (1) place value relationships through thousandths, (2) multiplying by powers of 10 using exponents, then (3) dividing by powers of 10 with careful attention to zeros and decimal placement. Chose the fewest high-quality, grade-appropriate segments that each add a new learning outcome (no same-goal repeats), then used the final interleaved practice to force “which rule do I use?” decisions.","strengths":["Clear scaffolding from whole-number place value to decimal place value to exponent notation","Multiple, non-redundant reminders that zeros can be placeholders and do not always change value","Targets the biggest misconceptions directly (direction of shifts, 10^n vs 10×n)"],"target_difficulty":"intermediate","title":"Decimal Places and Powers of Ten","tradeoffs":[],"updated_at":"2026-03-05T08:39:51.997980+00:00","user_id":"google_109800265000582445084"}}