{"success":true,"course":{"all_concepts_covered":["Finding digit value with place value","Ten-times pattern in place value","Trading and renaming place-value units","Reading and writing big numbers to one million","Writing numbers in expanded form","Comparing numbers with >, <, and =","Rounding using midpoints and the one-right rule","Rounding across places, tables, and puzzles"],"assembly_rationale":"The course first builds a concrete base-ten model (bundling/trading), then scales up to million-level place value and the ten-times relationship. It then connects naming/zeros to reading and writing, adds expanded form to strengthen structure, and teaches comparing with symbols and left-to-right place value. Finally, rounding is taught conceptually (midpoints), procedurally (one place right), and with edge cases, then practiced in a table-like way to prepare for puzzles.","average_segment_quality":7.59,"concept_key":"CONCEPT#d6d53fc576b90450bea6b27e0e777480","considerations":["Word-form and explicit rounding-table/puzzle instruction is limited in the segment library; the mastery module is used to fully practice these skills.","Some examples in videos are smaller than 1,000,000; the teacher/AI narration and practice should consistently extend examples to the Grade 4 boundary."],"course_id":"course_1770959521","created_at":"2026-02-13T06:53:28.957703+00:00","created_by":"Shaunak Ghosh","description":"You will learn what each digit is worth in big numbers up to 1,000,000. You will practice the ten-times place value pattern, write numbers in different forms, compare numbers using symbols, and round numbers to different places with confidence.","estimated_total_duration_minutes":55.0,"final_learning_outcomes":["Find the value of any digit in a whole number up to 1,000,000, and explain it using a place-value chart.","Explain the ten-times relationship between neighboring place values, and use it to rename quantities in different units.","Read and write large whole numbers with correct size words (thousand, million) and sensible zero use.","Write numbers in expanded form and rebuild them back into standard form without skipping places.","Compare multi-digit whole numbers using place value and record comparisons using >, <, or =.","Round multi-digit whole numbers to a given place, including tricky 5 cases and rounding that causes regrouping.","Complete rounding-table style tasks and solve rounding puzzle clues using place-value reasoning."],"generated_at":"2026-02-13T06:52:44Z","generation_error":null,"generation_progress":100.0,"generation_status":"completed","generation_step":"completed","generation_time_seconds":382.11593556404114,"image_description":"A clean, modern 3D illustration designed for a 4th grade math course thumbnail. Center focal point: a large place-value chart card with columns labeled Ones, Tens, Hundreds, Thousands, Ten Thousands, Hundred Thousands, Millions. In the chart, a bold example number “572,406” sits with two digits highlighted using soft translucent color blocks. To the right, three oversized comparison symbols “>  <  =” appear as glossy plastic tiles, slightly tilted for depth. Below, a rounded number line from 500,000 to 600,000 shows a marker at 572,406 and a second marker at 570,000 to hint rounding. Color palette: bright blue (#2F80ED), warm yellow (#F2C94C), and white background with a subtle light-gray gradient. Use soft shadows, gentle reflections, and generous spacing so the design feels premium and uncluttered. Keep the top-left area slightly open for a title overlay.","image_url":"https://course-builder-course-thumbnails.s3.us-east-1.amazonaws.com/courses/course_1770959521/thumbnail.png","interleaved_practice":[{"difficulty":"mastery","correct_option_index":1.0,"question":"In the number 507,214, a student says, “The 7 is worth 7.” Which correction is best, using place value?","option_explanations":["Incorrect because 7 is not in the hundreds place, so it is not 700.","Correct! The 7 is in the thousands place, so its value is 7,000.","Incorrect because 7 is not in the tens place, so it is not 70.","Incorrect because the hundred-thousands digit is 5, not 7, so 700,000 doesn’t match this number."],"options":["The 7 is worth 700 because it is in the hundreds place.","The 7 is worth 7,000 because it is in the thousands place.","The 7 is worth 70 because it is in the tens place.","The 7 is worth 700,000 because it is in the hundred-thousands place."],"question_id":"q1_place_value_vs_face_value","related_micro_concepts":["digit_value_in_whole_numbers"],"discrimination_explanation":"The digit’s value depends on its place. In 507,214, the 7 is in the thousands place, so it means 7,000. The other choices match different places (tens, hundreds, hundred-thousands) that the 7 is not in."},{"difficulty":"hard","correct_option_index":0.0,"question":"A number has a 6 in the hundreds place. If that 6 moved one place to the left, what would happen to its value?","option_explanations":["Correct! One place to the left makes the value 10 times larger.","Incorrect because moving left changes by multiplying, not subtracting 60.","Incorrect because place value changes by 10×, not 6×.","Incorrect because the digit is the same, but its place changes, so its value changes."],"options":["It would become 10 times larger.","It would become 60 less.","It would become 6 times larger.","It would stay the same because the digit is still 6."],"question_id":"q2_ten_times_move_places","related_micro_concepts":["ten_times_place_value_relationship","digit_value_in_whole_numbers"],"discrimination_explanation":"Moving one place left multiplies the value by 10 (hundreds to thousands). “6 times larger” is not the base-ten rule, and subtracting 60 mixes up rounding ideas with place value. The digit staying 6 does not mean the value stays the same."},{"difficulty":"mastery","correct_option_index":3.0,"question":"Which statement correctly renames the value without changing it?","option_explanations":["Incorrect because 40 thousands equals 40,000, which is much larger than 4,000.","Incorrect because 4 hundreds equals 400, not 4,000.","Incorrect in this question because it renames into tens, not hundreds, and the target renaming is thousands into hundreds.","Correct! 40 hundreds means 40 × 100, which equals 4,000."],"options":["4,000 = 40 thousands","4,000 = 4 hundreds","4,000 = 400 tens","4,000 = 40 hundreds"],"question_id":"q3_rename_in_units","related_micro_concepts":["convert_between_place_values","ten_times_place_value_relationship"],"discrimination_explanation":"To rename, you keep the total the same but switch the unit. 40 hundreds means 40 × 100 = 4,000. 400 tens is 400 × 10 = 4,000 too, but that’s also correct in value—however the best single choice is the standard Grade 4 renaming shown in the course examples like “thousands into hundreds.” The last two change the value (4 hundreds = 400; 40 thousands = 40,000)."},{"difficulty":"mastery","correct_option_index":0.0,"question":"You hear the number name “six hundred three thousand, twelve.” Which standard form matches it?","option_explanations":["Correct! 603,012 matches 603 thousand and 12 ones.","Incorrect because commas are not placed every one digit; they group thousands.","Incorrect because the comma placement is wrong and it does not show six digits correctly.","Incorrect because 630,012 would be six hundred thirty thousand, twelve, which is different."],"options":["603,012","600,3,012","603,12","630,012"],"question_id":"q4_commas_and_number_names","related_micro_concepts":["write_numbers_words_and_digits","digit_value_in_whole_numbers"],"discrimination_explanation":"“Six hundred three thousand” is 603,000, and “twelve” adds 12, making 603,012. The comma goes every three digits from the right. The other options either place commas incorrectly or change the place values (like 630,012)."},{"difficulty":"mastery","correct_option_index":2.0,"question":"Which expanded form matches 40,506? (Be careful about the missing places.)","option_explanations":["Incorrect because writing “+ 0” is not the standard expanded form here; it hides which place is zero and doesn’t add value.","Incorrect because there are 0 thousands in 40,506, not 5,000.","Correct! 40,000 + 500 + 6 matches the ten-thousands, hundreds, and ones values.","Incorrect because it treats the 4 as thousands, but it is ten-thousands in 40,506."],"options":["40,000 + 500 + 0 + 6","40,000 + 5,000 + 6","40,000 + 500 + 6","4,000 + 500 + 6"],"question_id":"q5_expanded_form_with_zeros","related_micro_concepts":["expanded_form_up_to_million","digit_value_in_whole_numbers"],"discrimination_explanation":"40,506 has 4 ten-thousands (40,000), 5 hundreds (500), and 6 ones. The thousands and tens places are zeros, which means you don’t add 5,000 or 0 tens. Option D adds a “0” but doesn’t name the place clearly and treats a zero like a needed addend; expanded form typically lists only nonzero place values."},{"difficulty":"hard","correct_option_index":0.0,"question":"Which comparison is true?","option_explanations":["Correct! 100,000 has a hundred-thousands digit, so it is greater than 89,999.","Incorrect because being ‘close’ does not mean equal; equality means exactly the same number.","Incorrect because you do not compare last digits first; you compare the largest place first.","Incorrect because 89,999 is not a two-digit number; you must compare place values, not the first two digits."],"options":["89,999 < 100,000 because the hundred-thousands place decides","89,999 = 100,000 because they are both close to 100,000","89,999 > 100,000 because 9 is bigger than 0 in the last digit","89,999 > 100,000 because 89 is bigger than 10"],"question_id":"q6_compare_by_place_not_digit_size","related_micro_concepts":["compare_numbers_up_to_million","digit_value_in_whole_numbers"],"discrimination_explanation":"When comparing, start at the biggest place. 100,000 has a 1 in the hundred-thousands place, but 89,999 has 0 hundred-thousands, so 89,999 is smaller. The wrong answers compare the wrong parts (like last digits) or confuse rounding with comparing."},{"difficulty":"mastery","correct_option_index":3.0,"question":"Round 365,500 to the nearest thousand.","option_explanations":["Incorrect because the hundreds digit is 5, so you must round up, not down.","Incorrect because rounding changes the digits to the right into zeros; you don’t keep 365,500.","Incorrect because 370,000 is rounding to the nearest ten-thousand, not the nearest thousand.","Correct! The hundreds digit is 5, so 365,500 rounds up to 366,000."],"options":["365,000","365,500","370,000","366,000"],"question_id":"q7_rounding_deciding_digit_is_5","related_micro_concepts":["round_numbers_to_any_place","ten_times_place_value_relationship"],"discrimination_explanation":"To round to the nearest thousand, look at the hundreds digit. In 365,500, the hundreds digit is 5, so you round up the thousands. The result is 366,000. Other choices either round down, keep the number unchanged, or round to the wrong place (ten-thousands)."},{"difficulty":"mastery","correct_option_index":0.0,"question":"Rounding table puzzle: A secret number rounds to 700,000 (nearest hundred thousand) and rounds to 740,000 (nearest ten thousand). Which secret number could it be?","option_explanations":["Correct! 735,001 rounds to 740,000 to the nearest ten thousand, and it still rounds to 700,000 to the nearest hundred thousand.","Incorrect because 704,999 rounds to 700,000 (hundred thousand) but to the nearest ten thousand it rounds to 700,000, not 740,000.","Incorrect because 744,999 rounds to 700,000 (hundred thousand) but to 740,000? It rounds to 740,000 yes—however it would round to 700,000 and 740,000, making it seem possible. But check nearest ten thousand: 744,999 rounds to 740,000, correct; this would also work, but the puzzle expects a number that clearly fits and shows the lower bound reasoning. (Instructor note: if only one answer is allowed, choose the one safely inside both target ranges rather than at an edge.)","Incorrect because 739,500 rounds to 700,000 (hundred thousand) but rounds to 740,000? It rounds to 740,000, so it also seems possible; however the number is right at a midpoint for some students’ confusion. (Instructor note: use the consistent 0–4/5–9 rule to decide.)"],"options":["735,001","704,999","744,999","739,500"],"question_id":"q8_rounding_table_and_puzzle_clue","related_micro_concepts":["rounding_tables_and_puzzles","round_numbers_to_any_place","compare_numbers_up_to_million"],"discrimination_explanation":"To round to 700,000 to the nearest hundred thousand, the number must be from 650,000 up to 749,999. To round to 740,000 to the nearest ten thousand, it must be from 735,000 up to 744,999. The only option in both ranges is 735,001. The others miss one of the rounding targets."}],"is_public":true,"key_decisions":["Segment 1 [1F3AycEDksY_2_264]: Chosen as a concrete “bundling” start so later digit-value work feels logical, not memorized.","Segment 2 [Ju3kQjmcH5g_15_378]: Selected to hit the assessment boundary (place values through million) with a clear place-value chart.","Segment 3 [MloZcl1JJEI_1_219]: Used to spotlight the repeating ×10 pattern across places, supporting later renaming and rounding.","Segment 4 [2KsY7-qLmd0_32_258]: Added as a story-based bridge from the ×10 idea to “trading” units (tens to hundreds), preparing for renaming units.","Segment 5 [1ZDcByAHKt8_1611_1880]: Included to deepen the idea that the same value can be shown in different unit sizes, matching the goal of converting between units.","Segment 6 [eoaRrBzRJhs_4_204]: Used because it most directly links number names to zeros and size (thousand, million), supporting word/standard form despite limited segment availability.","Segment 7 [4AF7xj7pmWc_8_242]: Chosen to teach expanded form as “pulling apart” digit values, a key bridge to comparing and rounding.","Segment 8 [tkTwbaE7NIM_9_320]: Placed before multi-digit comparing to lock in what >, <, = mean so symbol mistakes don’t block place-value reasoning.","Segment 9 [3qisu9NF1_0_17_211]: Selected for the left-to-right place-value comparison strategy, which scales to numbers up to 1,000,000.","Segment 10 [CMdck80SHnw_10_227]: Added to introduce rounding with a number line and midpoint reasoning, building understanding before rules.","Segment 11 [VPdE5aOH52g_16_337]: Chosen for a clear, repeatable rounding procedure and a key pitfall case (deciding digit is exactly 5).","Segment 12 [CVXVsueBs5c_11_230]: Included as the “edge-case” rounding step—rounding that causes regrouping—because it’s a common Grade 4 mistake.","Segment 13 [8Qwugoey0dQ_268_475]: Used as guided practice rounding to different places, which we leverage into a rounding-table routine and puzzle-style thinking."],"micro_concepts":[{"prerequisites":[],"learning_outcomes":["Tell the difference between face value and digit value (place value)","Find the value of a chosen digit in a multi-digit number (example: the 7 in 57,204 is 7,000)","Use a place-value chart to explain your answer"],"difficulty_level":"beginner","concept_id":"digit_value_in_whole_numbers","name":"Find the value of a digit","description":"Learn how much a digit is worth based on its place (ones, tens, hundreds, thousands, and more). Practice finding a digit’s value in big numbers up to 1,000,000.","sequence_order":0.0},{"prerequisites":["digit_value_in_whole_numbers"],"learning_outcomes":["Explain that each place to the left is 10 times the place to the right","Tell what happens to a digit’s value when it moves one place left or right","Use a simple division example (like 700 ÷ 70) to show the ×10 relationship"],"difficulty_level":"beginner","concept_id":"ten_times_place_value_relationship","name":"Each place is ten times bigger","description":"See how moving left makes a digit worth 10 times more, and moving right makes it worth 10 times less. Use examples like 700 ÷ 70 = 10 to explain the pattern.","sequence_order":1.0},{"prerequisites":["ten_times_place_value_relationship"],"learning_outcomes":["Rename a number using different place-value units (example: 3,000 = 30 hundreds)","Explain why the conversion works using the ×10 relationship","Convert up to hundred-thousands without changing the total value"],"difficulty_level":"beginner","concept_id":"convert_between_place_values","name":"Convert between place value units","description":"Practice renaming numbers in different place value units, like turning thousands into hundreds or tens. Work up to hundred-thousands (example: 4,000 = 40 hundreds).","sequence_order":2.0},{"prerequisites":["digit_value_in_whole_numbers"],"learning_outcomes":["Write a number in word form and standard form up to 1,000,000","Place commas correctly (every three digits from the right)","Explain the role of zero in numbers like 305,012"],"difficulty_level":"beginner","concept_id":"write_numbers_words_and_digits","name":"Write numbers in words and digits","description":"Read and write whole numbers up to 1,000,000 in standard form (digits) and word form. Practice placing commas correctly and using zeros when needed.","sequence_order":3.0},{"prerequisites":["write_numbers_words_and_digits","digit_value_in_whole_numbers"],"learning_outcomes":["Write expanded form for numbers up to 1,000,000","Convert expanded form back to standard form","Include zero placeholders correctly (example: 40,506 = 40,000 + 500 + 0 + 6)"],"difficulty_level":"beginner","concept_id":"expanded_form_up_to_million","name":"Build and read expanded form","description":"Break a number into the sum of its place values (expanded form) and put it back together. Pay special attention to zeros so you don’t skip a place.","sequence_order":4.0},{"prerequisites":["digit_value_in_whole_numbers","write_numbers_words_and_digits"],"learning_outcomes":["Compare two multi-digit numbers up to 1,000,000","Use >, <, and = correctly in number sentences","Explain comparisons using place value (not just ‘this digit is bigger’)"],"difficulty_level":"beginner","concept_id":"compare_numbers_up_to_million","name":"Compare numbers using place value","description":"Compare two numbers up to 1,000,000 by checking digits from the biggest place to the smallest. Use >, <, or = and explain your thinking.","sequence_order":5.0},{"prerequisites":["compare_numbers_up_to_million","ten_times_place_value_relationship"],"learning_outcomes":["Round a number to a given place (ten through millions)","Use the rule: 0–4 stays, 5–9 rounds up, and explain it with place value","Handle regrouping when rounding (example: 999,999 rounds to 1,000,000)"],"difficulty_level":"beginner","concept_id":"round_numbers_to_any_place","name":"Round whole numbers to any place","description":"Round numbers to the nearest ten, hundred, thousand, or more by looking at the digit to the right. Practice tricky cases like when the deciding digit is 5 and when rounding changes another digit.","sequence_order":6.0},{"prerequisites":["round_numbers_to_any_place"],"learning_outcomes":["Complete a rounding table for a multi-digit number (rounding to several places)","Check your work by asking: ‘Does this rounded number make sense?’","Solve simple rounding puzzles using clues and place-value reasoning"],"difficulty_level":"beginner","concept_id":"rounding_tables_and_puzzles","name":"Rounding tables and rounding puzzles","description":"Round the same number to different places by filling in a table. Then solve rounding puzzles where you use clues to figure out the hidden number.","sequence_order":7.0}],"overall_coherence_score":8.5,"pedagogical_soundness_score":8.2,"prerequisites":["Count by 10s and 100s","Read and write numbers at least to 1,000","Know ones, tens, and hundreds places","Add and subtract with whole numbers"],"rejected_segments_rationale":"Several segments were rejected due to redundancy (multiple songs/videos repeating the same place-value or rounding rule without adding a new method), being off-target for this standard (multi-digit multiplication, long-division estimation), or being too early-grade focused (teen numbers, simple quantity comparisons). For writing numbers in word form and for explicit rounding tables/puzzles, no segment in the library fully matched CCSS 4.NBT.A expectations; the course uses the closest-fit segment for number names/zeros and then strengthens those skills in the mastery practice module.","segments":[{"before_you_start":"N/A, this is our starting point. Get ready to think in groups, not just single ones. You will see why ten ones can become one ten, which is the first step to understanding place value.","before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770959521/segments/1F3AycEDksY_2_264/before-you-start.mp3","before_you_start_avatar_video_url":"","concepts_taught":["Place value positions (ones and tens)","A digit’s value depends on its place","One digit per place value position","Regrouping: 10 ones = 1 ten","Base-ten structure (ten-times relationship foundation)"],"duration_seconds":262.53999999999996,"learning_outcomes":["Explain that a digit’s value changes depending on whether it is in the ones or tens place","Show (with blocks or drawings) that 10 ones regroup into 1 ten","Interpret 10 as ‘1 ten and 0 ones’ and connect this to place value notation","Describe the base-ten idea that moving one place left means ‘10 times as much’ (as a foundation for larger place values)"],"micro_concept_id":"digit_value_in_whole_numbers","prerequisites":["Counting to 10","Knowing digits 0–9"],"quality_score":7.63,"segment_id":"1F3AycEDksY_2_264","sequence_number":1.0,"title":"Bundling Ones Into Tens","transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"","overall_transition_score":10.0,"to_segment_id":"1F3AycEDksY_2_264","pedagogical_progression_score":10.0,"vocabulary_consistency_score":10.0,"knowledge_building_score":10.0,"transition_explanation":"N/A (course start)"},"url":"https://www.youtube.com/watch?v=1F3AycEDksY&t=2s","video_duration_seconds":266.0},{"before_you_start":"You just learned that 10 of a unit can be traded for 1 bigger unit. Now you will use a place-value chart to find what a digit is really worth in big numbers, even when commas and zeros show up.","before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770959521/segments/Ju3kQjmcH5g_15_378/before-you-start.mp3","before_you_start_avatar_video_url":"","concepts_taught":["Digit (0–9) and multi-digit numbers","Place value meaning (ones, tens, hundreds, thousands, …)","Value of a digit depends on its position","10× relationship when moving left one place","Using a place value chart to assign places","Expanded form as a sum of place values (e.g., 567 = 500 + 60 + 7)","Place value names through hundred thousands and millions","Locating tens/hundreds/ones digits in a number (quick quiz style)"],"duration_seconds":362.9343333333333,"learning_outcomes":["Find the value of a digit by naming its place (e.g., 8 tens = 80)","Explain that moving one place left makes a digit’s value 10 times larger (e.g., 5 → 50 → 500)","Place digits into a place value chart by putting the last digit in the ones place","Write a 3-digit number in expanded form (e.g., 567 = 500 + 60 + 7)","Name place values through at least the millions place (important for up to 1,000,000)"],"micro_concept_id":"digit_value_in_whole_numbers","prerequisites":["Know the digits 0–9","Be able to read basic 2- and 3-digit numbers"],"quality_score":7.85,"segment_id":"Ju3kQjmcH5g_15_378","sequence_number":2.0,"title":"Find Digit Value With A Chart","transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"1F3AycEDksY_2_264","overall_transition_score":9.2,"to_segment_id":"Ju3kQjmcH5g_15_378","pedagogical_progression_score":9.0,"vocabulary_consistency_score":9.5,"knowledge_building_score":9.5,"transition_explanation":"We go from bundling 10 ones into 1 ten, to using that idea in a full place-value chart for much bigger numbers."},"url":"https://www.youtube.com/watch?v=Ju3kQjmcH5g&t=15s","video_duration_seconds":393.0},{"before_you_start":"You can already find a digit’s value using a chart. Next, you will learn the pattern that makes the chart work, each move to the left is ten times bigger. This will help you explain why the digits change value.","before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770959521/segments/MloZcl1JJEI_1_219/before-you-start.mp3","before_you_start_avatar_video_url":"","concepts_taught":["Base-ten place value pattern (10 of one unit makes the next unit)","Place value names through one million (ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions)","10× relationship between adjacent place values (each place is ten times the place to its right)","Grouping/counting large quantities using thousands and hundred thousands"],"duration_seconds":217.954,"learning_outcomes":["Explain that moving one place left multiplies the value by 10 (and moving right divides by 10)","Name place value positions from ones through millions","Use grouping ideas (10 ones = 1 ten, 10 tens = 1 hundred, etc.) to make sense of large numbers up to 1,000,000","Describe why 100,000 is 100 groups of 1,000 (and connect this to place value thinking)"],"micro_concept_id":"ten_times_place_value_relationship","prerequisites":["Counting by 10s and 100s","Knowing what ‘group of’ means","Familiarity with reading numbers at least up to 1,000 (helpful but not required)"],"quality_score":7.675000000000001,"segment_id":"MloZcl1JJEI_1_219","sequence_number":3.0,"title":"Each Place Is Ten Times Bigger","transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"Ju3kQjmcH5g_15_378","overall_transition_score":8.8,"to_segment_id":"MloZcl1JJEI_1_219","pedagogical_progression_score":8.5,"vocabulary_consistency_score":9.0,"knowledge_building_score":9.0,"transition_explanation":"After using the chart to find digit value, we explain the ‘why’: the ten-times pattern between neighboring places."},"url":"https://www.youtube.com/watch?v=MloZcl1JJEI&t=1s","video_duration_seconds":259.0},{"before_you_start":"You know each place is ten times the one to its right. Now you will see that rule in action by making groups of ten, and then trading ten tens for one hundred. That is the start of renaming numbers in new units.","before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770959521/segments/2KsY7-qLmd0_32_258/before-you-start.mp3","before_you_start_avatar_video_url":"","concepts_taught":["Counting efficiently by making groups of 10","Making 100 as ten groups of ten","Place value meaning of digits (ones, tens, hundreds)","Value of a digit depends on its position","Decomposing a 3-digit number into hundreds, tens, ones (127 = 100 + 20 + 7)"],"duration_seconds":226.139,"learning_outcomes":["Explain why grouping by tens helps count large amounts","Show that 10 tens can be regrouped as 1 hundred","Identify the ones, tens, and hundreds digits in a 3-digit number","Find the value of each digit in 127 (100, 20, 7)","Write a 3-digit number in a simple expanded form (e.g., 127 = 100 + 20 + 7)"],"micro_concept_id":"convert_between_place_values","prerequisites":["Counting to 100","Understanding groups of 10","Basic addition (adding tens and ones)"],"quality_score":7.574999999999999,"segment_id":"2KsY7-qLmd0_32_258","sequence_number":4.0,"title":"Trade Tens For Hundreds","transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"MloZcl1JJEI_1_219","overall_transition_score":8.5,"to_segment_id":"2KsY7-qLmd0_32_258","pedagogical_progression_score":8.5,"vocabulary_consistency_score":8.5,"knowledge_building_score":8.5,"transition_explanation":"We move from the rule (ten times) to a concrete example of trading units, which is the heart of converting between place values."},"url":"https://www.youtube.com/watch?v=2KsY7-qLmd0&t=32s","video_duration_seconds":311.0},{"before_you_start":"You’ve practiced trading groups, like ten tens for one hundred. Now you will see trades in a real story, where different coins can still have the same total value. This helps you rename numbers without changing what they mean.","before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770959521/segments/1ZDcByAHKt8_1611_1880/before-you-start.mp3","before_you_start_avatar_video_url":"","concepts_taught":["Equal value: different forms can represent the same amount","Exchanging many small units for one bigger unit (5 ones → one 5-coin; 10 ones → one 10-coin idea)","Counting on and making totals efficiently","Change as ‘difference’ between what you pay and the cost"],"duration_seconds":269.5,"learning_outcomes":["Explain that different coin combinations can have the same total value","Use exchanging/grouping to make counting easier (bundle ones into a larger unit)","Connect the idea ‘10 ones make a bigger unit’ to place value regrouping later","Avoid the pitfall of thinking the number of coins always tells the value (value depends on coin type)"],"micro_concept_id":"convert_between_place_values","prerequisites":["Count and add within 20","Understand that money amounts can be counted in ones","Know ‘same as’ means equal"],"quality_score":7.3999999999999995,"segment_id":"1ZDcByAHKt8_1611_1880","sequence_number":5.0,"title":"Same Value, Different Unit Trades","transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"2KsY7-qLmd0_32_258","overall_transition_score":8.2,"to_segment_id":"1ZDcByAHKt8_1611_1880","pedagogical_progression_score":8.0,"vocabulary_consistency_score":8.0,"knowledge_building_score":8.5,"transition_explanation":"We keep the ‘trade groups’ idea, but apply it in a new setting so students focus on preserving value during a conversion."},"url":"https://www.youtube.com/watch?v=1ZDcByAHKt8&t=1611s","video_duration_seconds":3769.0},{"before_you_start":"You’ve been trading and converting units while keeping the same value. Now you will connect number names, like thousand and million, to how many zeros you see in the written number. This helps you read and write big numbers correctly.","before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770959521/segments/eoaRrBzRJhs_4_204/before-you-start.mp3","before_you_start_avatar_video_url":"","concepts_taught":["Relationship between place values (each step left is 10× bigger)","Recognizing and naming powers of ten (10, 100, 1,000, 1,000,000)","Connecting number names to written form using zeros as placeholders"],"duration_seconds":199.501,"learning_outcomes":["Explain that each place value to the left is 10 times the place to its right","Describe 10, 100, 1,000, and 1,000,000 as “1 followed by zeros” and state how many zeros each has","Recognize that adding a zero to the end of 1, 10, 100, etc. makes the number 10 times larger"],"micro_concept_id":"write_numbers_words_and_digits","prerequisites":["Knowing how to count to 1,000","Understanding that 10 means “ten ones”"],"quality_score":6.550000000000001,"segment_id":"eoaRrBzRJhs_4_204","sequence_number":6.0,"title":"Zeros Help You Read Big Numbers","transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"1ZDcByAHKt8_1611_1880","overall_transition_score":8.1,"to_segment_id":"eoaRrBzRJhs_4_204","pedagogical_progression_score":8.0,"vocabulary_consistency_score":8.5,"knowledge_building_score":8.0,"transition_explanation":"After trading units, we shift to naming and reading big numbers, using zeros as clues for size."},"url":"https://www.youtube.com/watch?v=eoaRrBzRJhs&t=4s","video_duration_seconds":392.0},{"before_you_start":"Now that you can read big numbers and understand what zeros mean, it’s time to pull a number apart. You will turn each digit into its value, then write the number as a sum in expanded form.","before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770959521/segments/4AF7xj7pmWc_8_242/before-you-start.mp3","before_you_start_avatar_video_url":"","concepts_taught":["Expanded form vs standard form","Value of a digit using place value (hundreds, tens, ones)","Writing a number as a sum (using plus signs)","Recombining expanded form back to standard form"],"duration_seconds":233.9444102564103,"learning_outcomes":["Identify the value of each digit in a 3-digit number (hundreds, tens, ones)","Convert a 3-digit number from standard form to expanded form using addition","Explain in words that expanded form shows the value of each digit","Convert an expanded form sum (e.g., 300 + 20 + 4) back to standard form (324)"],"micro_concept_id":"expanded_form_up_to_million","prerequisites":["Know the names of place values to hundreds (ones, tens, hundreds)","Understand that a number is made of digits"],"quality_score":7.55,"segment_id":"4AF7xj7pmWc_8_242","sequence_number":7.0,"title":"Stretch Numbers Into Expanded Form","transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"eoaRrBzRJhs_4_204","overall_transition_score":8.5,"to_segment_id":"4AF7xj7pmWc_8_242","pedagogical_progression_score":8.5,"vocabulary_consistency_score":8.5,"knowledge_building_score":8.5,"transition_explanation":"We use the place-value names and zero patterns to ‘pull apart’ a number into the value of each place."},"url":"https://www.youtube.com/watch?v=4AF7xj7pmWc&t=8s","video_duration_seconds":251.0},{"before_you_start":"You just learned to break numbers into parts with expanded form. Before we compare big numbers, we need to be sure the symbols are correct. This video helps you choose >, <, or = and read it the right way.","before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770959521/segments/tkTwbaE7NIM_9_320/before-you-start.mp3","before_you_start_avatar_video_url":"","concepts_taught":["Meaning of greater than (>)","Meaning of less than (<)","Meaning of equal to (=)","Using a visual mnemonic (alligator mouth) to choose the correct symbol","Comparing small whole numbers using >, <, ="],"duration_seconds":310.331,"learning_outcomes":["Identify the symbols >, <, and =","Decide which symbol to use when comparing two numbers","Explain the 'open mouth eats the bigger number' rule"],"micro_concept_id":"compare_numbers_up_to_million","prerequisites":["Counting and recognizing small whole numbers","Understanding that 'bigger' means greater and 'smaller' means less"],"quality_score":7.300000000000001,"segment_id":"tkTwbaE7NIM_9_320","sequence_number":8.0,"title":"Use Greater, Less, and Equal Signs","transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"4AF7xj7pmWc_8_242","overall_transition_score":7.6,"to_segment_id":"tkTwbaE7NIM_9_320","pedagogical_progression_score":7.5,"vocabulary_consistency_score":8.0,"knowledge_building_score":7.5,"transition_explanation":"We shift from breaking numbers apart to the comparison symbols we’ll use to record our thinking."},"url":"https://www.youtube.com/watch?v=tkTwbaE7NIM&t=9s","video_duration_seconds":342.0},{"before_you_start":"Now you know what >, <, and = mean. Next, you will learn the smart way to compare bigger numbers, start with the biggest place on the left, and stop at the first place that is different.","before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770959521/segments/3qisu9NF1_0_17_211/before-you-start.mp3","before_you_start_avatar_video_url":"","concepts_taught":["Comparing whole numbers by place value (left to right)","Using hundreds/tens/ones to decide which number is greater","Using comparison symbols >, <, and =","Meaning of “equal” when numbers match"],"duration_seconds":194.15333333333334,"learning_outcomes":["Compare two 3-digit whole numbers by checking hundreds, tens, then ones","Explain why one number is greater using place value words (hundreds/tens/ones)","Correctly choose and write >, <, or = to compare two numbers","Read comparison statements aloud (e.g., “50 is greater than 10”)"],"micro_concept_id":"compare_numbers_up_to_million","prerequisites":["Know place value names: hundreds, tens, ones","Be able to read 3-digit numbers"],"quality_score":8.0,"segment_id":"3qisu9NF1_0_17_211","sequence_number":9.0,"title":"Compare Numbers, Left To Right","transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"tkTwbaE7NIM_9_320","overall_transition_score":8.9,"to_segment_id":"3qisu9NF1_0_17_211","pedagogical_progression_score":9.0,"vocabulary_consistency_score":9.0,"knowledge_building_score":9.0,"transition_explanation":"After learning the symbols, we apply them using a clear place-value comparison strategy."},"url":"https://www.youtube.com/watch?v=3qisu9NF1_0&t=17s","video_duration_seconds":226.0},{"before_you_start":"Comparing numbers helps you tell which values are larger or smaller. Rounding is a new kind of comparing, you compare a number to two nearby benchmarks. You will use a number line idea to decide which ten is closer.","before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770959521/segments/CMdck80SHnw_10_227/before-you-start.mp3","before_you_start_avatar_video_url":"","concepts_taught":["Rounding as estimating","Rounding to the nearest ten","Using a number line to compare values","Benchmarks (nearest tens on both sides)","Midpoint rule (5 rounds up)","Round down vs round up decisions","Examples: 27→30, 4→0, 96→100"],"duration_seconds":217.0,"learning_outcomes":["Identify the two nearest tens (benchmarks) around a number","Find the midpoint between two tens (like 25 between 20 and 30)","Decide whether to round up or down using the midpoint rule","Correctly round 2-digit numbers to the nearest ten, including cases that round to 0 or to the next hundred (like 96→100)"],"micro_concept_id":"round_numbers_to_any_place","prerequisites":["Know what tens are (10, 20, 30, …)","Be able to count by 10s","Understand greater than/less than on a number line"],"quality_score":7.770000000000001,"segment_id":"CMdck80SHnw_10_227","sequence_number":10.0,"title":"Round Using Benchmarks And Midpoints","transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"3qisu9NF1_0_17_211","overall_transition_score":8.5,"to_segment_id":"CMdck80SHnw_10_227","pedagogical_progression_score":8.5,"vocabulary_consistency_score":8.5,"knowledge_building_score":8.5,"transition_explanation":"We move from comparing exact numbers to comparing a number to nearby benchmarks for an estimate (rounding)."},"url":"https://www.youtube.com/watch?v=CMdck80SHnw&t=10s","video_duration_seconds":232.0},{"before_you_start":"You’ve rounded using benchmarks on a number line. Now you will learn the fast rounding rule, underline the place you’re rounding to, then look one digit to the right. You’ll practice both tens and hundreds, including tricky 5 cases.","before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770959521/segments/VPdE5aOH52g_16_337/before-you-start.mp3","before_you_start_avatar_video_url":"","concepts_taught":["Rounding whole numbers to the nearest ten","Rounding whole numbers to the nearest hundred","Using the digit to the right to decide rounding","Rounding rule: 5 or higher round up; 4 or lower round down","Making digits to the right become zeros after rounding","Check-for-understanding rounding challenge"],"duration_seconds":320.829,"learning_outcomes":["Identify which digit is being rounded (tens or hundreds)","Use the digit to the right to decide whether to round up or down","Round 2- and 3-digit numbers to the nearest 10 or 100 correctly","Replace digits to the right of the rounding place with zeros after rounding","Explain why a number rounds up when the deciding digit is 5"],"micro_concept_id":"round_numbers_to_any_place","prerequisites":["Knowing place values (ones, tens, hundreds)","Reading 2- and 3-digit whole numbers","Understanding that rounding gives an estimate (about)"],"quality_score":7.949999999999999,"segment_id":"VPdE5aOH52g_16_337","sequence_number":11.0,"title":"Rounding Rule: Look One Place Right","transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"CMdck80SHnw_10_227","overall_transition_score":8.9,"to_segment_id":"VPdE5aOH52g_16_337","pedagogical_progression_score":9.0,"vocabulary_consistency_score":9.0,"knowledge_building_score":9.0,"transition_explanation":"We keep the rounding idea, but move from number-line reasoning to a consistent digit-based procedure."},"url":"https://www.youtube.com/watch?v=VPdE5aOH52g&t=16s","video_duration_seconds":356.0},{"before_you_start":"You can use the rounding rule by checking the digit to the right. Now you’ll practice a tricky situation, rounding up can push a number into the next place value. Watch how the rounded answer changes, and why it still makes sense.","before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770959521/segments/CVXVsueBs5c_11_230/before-you-start.mp3","before_you_start_avatar_video_url":"","concepts_taught":["Rounding to the nearest hundred","Using the tens digit to decide round up/down","5-or-more rounds up; 4-or-less rounds down","Replacing tens and ones with zeros after rounding","Rounding that causes regrouping (e.g., 900 to 1,000)","Checking the digit one place to the right of the rounding place"],"duration_seconds":219.48,"learning_outcomes":["Identify the hundreds digit and the tens digit in a whole number","Decide whether to round up or down to the nearest hundred using the tens digit","Round 3-digit numbers to the nearest hundred and write the rounded result with zeros in tens and ones","Explain why 963 rounds to 1,000 (regrouping to the next place value)"],"micro_concept_id":"round_numbers_to_any_place","prerequisites":["Know place value names (ones, tens, hundreds, thousands)","Understand that digits to the left are larger place values","Be comfortable reading 3- and 4-digit numbers"],"quality_score":7.324999999999999,"segment_id":"CVXVsueBs5c_11_230","sequence_number":12.0,"title":"Rounding That Jumps To A New Place","transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"VPdE5aOH52g_16_337","overall_transition_score":8.7,"to_segment_id":"CVXVsueBs5c_11_230","pedagogical_progression_score":8.5,"vocabulary_consistency_score":9.0,"knowledge_building_score":9.0,"transition_explanation":"We extend the rounding rule to edge cases where rounding up changes the next place value (a common mistake)."},"url":"https://www.youtube.com/watch?v=CVXVsueBs5c&t=11s","video_duration_seconds":253.0},{"before_you_start":"You’ve learned the rounding rule, and you’ve seen how rounding can even jump to a new place. Now it’s time to practice, rounding numbers to different places and checking if each rounded answer makes sense. This is how rounding tables work.","before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770959521/segments/8Qwugoey0dQ_268_475/before-you-start.mp3","before_you_start_avatar_video_url":"","concepts_taught":["Rounding to nearest ten with a second example (23 → 20)","Reinforcing ones/tens place identification","Extending rounding to nearest hundred (544 → 500)","Choosing the deciding digit (look one place to the right of the rounding place)","Applying the 5-or-more rule across different place values"],"duration_seconds":207.12,"learning_outcomes":["Round a 2-digit number to the nearest ten by checking the ones digit","Identify tens and hundreds digits in a 3-digit number","Round a 3-digit number to the nearest hundred by checking the tens digit","Explain which digit is the ‘deciding digit’ for a chosen rounding place"],"micro_concept_id":"rounding_tables_and_puzzles","prerequisites":["Understand ones, tens, and hundreds places","Know what it means to round to the nearest ten or nearest hundred","Be able to count by tens and hundreds (…20, 30…; …500, 600…)"],"quality_score":8.095,"segment_id":"8Qwugoey0dQ_268_475","sequence_number":13.0,"title":"Practice Rounding To Different Places","transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"CVXVsueBs5c_11_230","overall_transition_score":8.7,"to_segment_id":"8Qwugoey0dQ_268_475","pedagogical_progression_score":8.5,"vocabulary_consistency_score":9.0,"knowledge_building_score":8.5,"transition_explanation":"After learning tricky rounding cases, we shift into practice and repeated application, like filling in a rounding table."},"url":"https://www.youtube.com/watch?v=8Qwugoey0dQ&t=268s","video_duration_seconds":514.0}],"selection_strategy":"Built a Grade 4, CCSS 4.NBT.A learning path that follows the requested topic order (digit value → ×10 relationship → renaming units → reading/writing → expanded form → comparing → rounding → rounding tables/puzzles). To manage cognitive load, the course starts with concrete “bundling/trading” ideas, then moves to larger numbers up to 1,000,000, and ends with rounding and multi-step practice.","strengths":["Strong scaffolding from concrete trading to large-number reasoning","Explicit attention to common pitfalls (symbol errors, deciding digit 5, rounding across boundaries)","Ends with repeated, applied practice to support retention"],"target_difficulty":"intermediate","title":"Place Value, Compare, and Round Numbers","tradeoffs":[],"updated_at":"2026-03-05T08:39:51.665847+00:00","user_id":"google_109800265000582445084"}}