{"success":true,"course":{"all_concepts_covered":["Place value names and periods (ones, thousands, millions)","Zeros as placeholders in whole numbers","Finding what a digit is worth using place value","Exponents as repeated multiplication (powers of 10 idea)","Division strategies, rules, and long division steps","Multiplying by 10 using place value patterns","Rounding to estimate and check reasonableness"],"assembly_rationale":"This course starts with the simplest idea—digits and their positions—then builds to larger place values and period grouping up to hundred-millions. Next, it introduces exponents as repeated multiplication, which supports understanding powers of 10. It then scaffolds division from meaning to rules to a full algorithm, and finishes with multiplication-by-10 patterns and rounding as a tool for checking mixed work. Where the video library lacked direct coverage (expanded/word form to hundred-millions, zero-cancel division, and ×100/×1,000/… patterns), the final interleaved practice explicitly targets those required skills and the listed common pitfalls.","average_segment_quality":7.209166666666667,"concept_key":"CONCEPT#228963e50785e96d393969c08445400a","considerations":["The available videos do not directly teach writing word form and full expanded form up to 999,999,999; the quiz and teacher guidance should reinforce this.","Zero-cancel division (e.g., 2,100 ÷ 70) and multiplying by 100/1,000/… to 1,000,000 are not directly demonstrated in the selected videos; these are taught and corrected in the mastery practice feedback."],"course_id":"course_1770910674","created_at":"2026-02-12T15:59:30.256844+00:00","created_by":"Shaunak Ghosh","description":"You will learn to read, build, and break apart whole numbers up to the hundred-millions place. You will also learn what exponents mean, and use place value patterns to make division and multiplication with tens and zeros easier.","estimated_total_duration_minutes":59.0,"final_learning_outcomes":["Read and write whole numbers using correct place value language through hundred-millions","Explain how zeros act as placeholders so digits keep their correct places","Find the value of a digit by combining the digit with its place value","Explain 10^n as repeated multiplication and avoid the mistake 10^n = 10 × n","Use division facts and long division steps to compute quotients and interpret remainders","Use place value patterns to multiply by powers of 10 and solve missing-factor problems","Use rounding and estimation to check whether answers are reasonable"],"generated_at":"2026-02-12T15:58:48Z","generation_error":null,"generation_progress":100.0,"generation_status":"completed","generation_step":"completed","generation_time_seconds":394.74959087371826,"image_description":"Modern, kid-friendly math thumbnail in a clean Apple-style layout. Center focal point: a bright, slightly 3D place value chart card floating at a slight angle, labeled ONES, THOUSANDS, MILLIONS with neat columns and commas, showing a sample number like 305,020,004 in bold dark text. Next to it, a big “10^n” tile with a small superscript and a short chain of 10×10×10 icons to hint at repeated multiplication. Add a simple division example badge like “2,100 ÷ 70” and a multiplication badge like “6 × 40,000” as smaller supporting elements, not cluttered. Background: smooth gradient from soft sky blue to white, with very subtle geometric dot patterns suggesting base-ten blocks. Use only 2–3 main colors: blue (#2F80ED), warm yellow (#F2C94C), and dark navy for text. Include soft drop shadows under the cards for depth, crisp edges, and plenty of breathing room. Reserve clear space at the top for the course title, with strong contrast and a friendly, classroom feel.","image_url":"https://course-builder-course-thumbnails.s3.us-east-1.amazonaws.com/courses/course_1770910674/thumbnail.png","interleaved_practice":[{"difficulty":"mastery","correct_option_index":3.0,"question":"A teacher writes the number 305,020,004 on the board. Which choice shows the correct expanded form using place value (millions, thousands, ones), without changing any digit’s place?","option_explanations":["Incorrect because 5,000 and 20 are far too small; this choice drops the thousands and millions places completely.","Incorrect because 50,000,000 would mean the digit 5 is in the ten-millions place, but in 305,020,004 the 5 is in the millions place.","Incorrect because 2,000 uses the thousands place, but the number has 20,000 in the ten-thousands place.","Correct! 305,020,004 = 300,000,000 + 5,000,000 + 20,000 + 4, and the zeros are placeholders for the other places."],"options":["300,000,000 + 5,000 + 20 + 4","300,000,000 + 50,000,000 + 20,000 + 4","300,000,000 + 5,000,000 + 2,000 + 4","300,000,000 + 5,000,000 + 20,000 + 4"],"question_id":"mq_01_expanded_form_commas","related_micro_concepts":["standard_word_expanded_forms","place_value_words_hundred_millions","value_of_a_digit_face_vs_place"],"discrimination_explanation":"Option B keeps every digit in its correct place: 3 hundred-millions, 0 ten-millions, 5 millions, 0 hundred-thousands, 2 ten-thousands, 0 thousands, and 4 ones. The other options move digits into the wrong period (thousands vs ten-thousands) or change 5 millions into 50 millions, which is a place value mistake."},{"difficulty":"mastery","correct_option_index":1.0,"question":"You hear someone say, “8 millions.” How many hundred-thousands is that? (Use the idea that each place is 10 times the one to the right.)","option_explanations":["Incorrect because decimals are not being used here, and 0.8 hundred-thousands would be only 80,000.","Correct! 1 million = 10 hundred-thousands, so 8 millions = 8 × 10 = 80 hundred-thousands.","Incorrect because it treats 1 million as 1 hundred-thousand, but 1 million is much larger.","Incorrect because 800 hundred-thousands would equal 80,000,000, which is 80 million, not 8 million."],"options":["0.8 hundred-thousands","80 hundred-thousands","8 hundred-thousands","800 hundred-thousands"],"question_id":"mq_02_place_value_unit_trade","related_micro_concepts":["place_value_words_hundred_millions","powers_of_10_exponents"],"discrimination_explanation":"One million equals 10 hundred-thousands. So 8 millions equals 8 × 10 = 80 hundred-thousands. The other choices either forget the ×10 relationship, multiply by 100 instead of 10, or incorrectly use decimals (not part of this unit)."},{"difficulty":"mastery","correct_option_index":3.0,"question":"In the number 572,000, what is the value of the digit 7? (Be careful: value is not the same as the face value.)","option_explanations":["Incorrect because 7,000 would mean the 7 is in the thousands place.","Incorrect because 7 is only the face value (the digit), not what it is worth in this number.","Incorrect because 700 would mean the 7 is in the hundreds place.","Correct! The 7 is in the ten-thousands place, so it is worth 70,000."],"options":["7,000","7","700","70,000"],"question_id":"mq_03_digit_value_not_face_value","related_micro_concepts":["value_of_a_digit_face_vs_place","place_value_words_hundred_millions"],"discrimination_explanation":"The 7 is in the ten-thousands place, so its value is 7 × 10,000 = 70,000. The distractors are the same digit in smaller places (ones, hundreds, or thousands), which would be true only if the 7 were in a different position."},{"difficulty":"mastery","correct_option_index":0.0,"question":"Which expression matches 10^4 exactly, and also shows why 10^4 is NOT the same as 10 × 4?","option_explanations":["Correct! 10^4 means 10 × 10 × 10 × 10, and the 4 tells how many 10s you multiply.","Incorrect because the base is 10, not 4, so this does not match 10^4.","Incorrect because exponents are repeated multiplication, not repeated addition.","Incorrect because 10 × 4 equals 40, but 10^4 equals 10,000."],"options":["10 × 10 × 10 × 10, because the exponent counts how many 10s are multiplied","4 × 4 × 4 × 4, because the exponent means multiply the small number","10 + 10 + 10 + 10, because you use the exponent as how many tens to add","10 × 4, because the exponent tells you what to multiply by"],"question_id":"mq_04_power_of_10_meaning","related_micro_concepts":["powers_of_10_exponents","multiply_powers_of_10_patterns"],"discrimination_explanation":"An exponent means repeated multiplication of the base. So 10^4 is four factors of 10 multiplied together. The other options confuse exponents with repeated addition, confuse exponent with “times,” or switch the base to 4."},{"difficulty":"mastery","correct_option_index":1.0,"question":"Solve 2,100 ÷ 70 using the idea of canceling common zeros (common factors of 10), then use an easier fact to finish.","option_explanations":["Incorrect because decimals are not part of this unit, and 0.3 would mean the quotient is less than 1, which cannot be true here.","Correct! Cancel one zero to get 210 ÷ 7, then 210 ÷ 7 = 30.","Incorrect because 300 would be too large; you would be acting like you multiplied instead of divided after canceling.","Incorrect because 210 ÷ 7 is 30, not 3; dropping a zero from the quotient is a place value mistake."],"options":["0.3","30","300","3"],"question_id":"mq_05_cancel_zeros_division","related_micro_concepts":["divide_numbers_ending_zeros","place_value_words_hundred_millions"],"discrimination_explanation":"Both numbers have a factor of 10. Cancel one zero: 2,100 ÷ 70 becomes 210 ÷ 7. Then use the easier fact 21 ÷ 7 = 3, so 210 ÷ 7 = 30. The other answers come from canceling the wrong amount or misplacing zeros."},{"difficulty":"mastery","correct_option_index":2.0,"question":"A student tries to do 4,500 ÷ 30 and says, “I’ll cancel two zeros to make it 45 ÷ 3.” What is the correct quotient, and what is the correct cancellation?","option_explanations":["Incorrect because canceling two zeros is not allowed when the divisor has only one zero; that changes the value of the division.","Incorrect because 45 ÷ 0.3 is not an equivalent simplification here and uses decimals, which are outside this unit.","Correct! Cancel one zero: 4,500 ÷ 30 = 450 ÷ 3 = 150.","Incorrect because it incorrectly introduces decimals (0.3) and also changes the problem."],"options":["15, because 4,500 ÷ 30 = 45 ÷ 3","150, because 4,500 ÷ 30 = 45 ÷ 0.3","150, because 4,500 ÷ 30 = 450 ÷ 3","1,500, because 4,500 ÷ 30 = 450 ÷ 0.3"],"question_id":"mq_06_cancel_only_common_zeros","related_micro_concepts":["divide_numbers_ending_zeros","value_of_a_digit_face_vs_place"],"discrimination_explanation":"You can only cancel the same number of zeros that both numbers share. 30 has one zero, so cancel one zero: 4,500 ÷ 30 becomes 450 ÷ 3. Then 450 ÷ 3 = 150. Canceling two zeros changes the size of the problem and gives the wrong answer."},{"difficulty":"mastery","correct_option_index":0.0,"question":"Find 6 × 40,000. Use a place value pattern, not repeated addition.","option_explanations":["Correct! 6 × 40,000 = 6 × (4 × 10,000) = 24 × 10,000 = 240,000.","Incorrect because it uses one extra zero, making the product 10 times too large.","Incorrect because it uses one fewer zero, as if multiplying by 4,000 instead of 40,000.","Incorrect because 240,00 is not a correctly written whole number with commas."],"options":["240,000","2,400,000","24,000","240,00"],"question_id":"mq_07_multiply_single_digit_power10","related_micro_concepts":["multiply_powers_of_10_patterns","place_value_words_hundred_millions"],"discrimination_explanation":"40,000 is 4 × 10,000. First do 6 × 4 = 24, then keep the 10,000 (four zeros): 24 × 10,000 = 240,000. The distractors come from using the wrong number of zeros or writing the number incorrectly."},{"difficulty":"mastery","correct_option_index":0.0,"question":"Solve the missing-factor puzzle: ? × 8 = 400,000. Which number makes the equation true?","option_explanations":["Correct! 400,000 ÷ 8 = 50,000, and 50,000 × 8 = 400,000.","Incorrect because 5,000 × 8 = 40,000, which is 10 times too small.","Incorrect because 40,000 × 8 = 320,000, not 400,000.","Incorrect because 500,000 × 8 would be 4,000,000, which is too large."],"options":["50,000","5,000","40,000","500,000"],"question_id":"mq_08_missing_factor_large_number","related_micro_concepts":["multiply_powers_of_10_patterns","divide_numbers_ending_zeros","value_of_a_digit_face_vs_place"],"discrimination_explanation":"If ? × 8 = 400,000, then ? = 400,000 ÷ 8. Since 8 × 50,000 = 400,000, the missing factor is 50,000. The distractors are off by a factor of 10 or 100, which is a place value scaling error."},{"difficulty":"mastery","correct_option_index":3.0,"question":"You multiply and get an answer of 3,720 for 372 × 10. To quickly check if that makes sense, what is the best rounding-based estimate, and what does it tell you?","option_explanations":["Incorrect because 372 × 10 is 3,720, not 372; it forgets the ×10 scaling.","Incorrect because 370 × 10 is 3,700, not 370; it forgets the ×10 scaling.","Incorrect because 300 × 10 is 3,000, not 300; it forgets the ×10 scaling.","Correct! 372 is close to 400, and 400 × 10 = 4,000, so 3,720 is a reasonable exact answer."],"options":["About 372 × 10 = 372, so 3,720 is reasonable","About 370 × 10 = 370, so 3,720 is too big","About 300 × 10 = 300, so 3,720 is too big","About 400 × 10 = 4,000, so 3,720 is reasonable"],"question_id":"mq_09_rounding_reasonableness_check","related_micro_concepts":["mixed_practice_fix_common_pitfalls","multiply_powers_of_10_patterns","place_value_words_hundred_millions"],"discrimination_explanation":"Rounding 372 to about 400 makes the mental check easy: 400 × 10 = 4,000. Since 3,720 is close to 4,000, the answer is in the right size range. The other options forget that multiplying by 10 should make the number 10 times larger, not smaller."}],"is_public":true,"key_decisions":["Segment 6t3DMk4-9KU_1372_1566: Placed first to define “digits” and “place value” in Grade 5 language, reducing cognitive load before working with larger numbers.","Segment 6t3DMk4-9KU_1566_1942: Selected next to practice finding digits in places and highlight zero as a placeholder, which supports later expanded-form thinking and prevents misreading numbers.","Segment MloZcl1JJEI_1_255: Used as the main bridge to large-number place value, because it clearly introduces ONES/THOUSANDS/MILLIONS periods and names up to hundred-millions in a kid-friendly way.","Segment xA1XEVWzAYg_2916_3460: Chosen to reinforce digit value using a chart-based strategy, which directly targets the common pitfall of miscounting digit positions.","Segment -zUmvpkhvW8_46_303: Picked for exponents because it clearly explains “repeated multiplication” and addresses the misconception that an exponent is “times.”","Segment -zUmvpkhvW8_303_586: Added as a higher-complexity exponent follow-up to solidify reading/evaluating powers and avoiding mix-ups with base/exponent order.","Segment qZ2R1tbUZaw_1638_1872: Placed as the first division piece to re-ground division in fair sharing with strong visuals before moving to more symbolic methods.","Segment rGMecZ_aERo_211_474: Added to teach key ‘division facts’ and formats (÷, slash, fraction bar), which supports later simplification and error-checking in division problems.","Segment wAxEdmutf98_13_248: Included after concept-building to show a complete step-by-step division method (long division), useful when numbers get larger after simplifying.","Segment FG18571ruVQ_2468_2727: Used to introduce ×10 as ‘tens’ (meaning first), which supports place-value reasoning instead of only memorizing a rule.","Segment dPksJHBZs4Q_400_580: Followed with a procedural ×10 pattern on bigger numbers to connect the concept of tens to writing correct multi-digit products.","Segment 8Qwugoey0dQ_20_467: Used last as a mixed, place-value-based checking strategy (rounding) to help students catch unreasonable answers and place-value slips during mixed practice."],"micro_concepts":[{"prerequisites":[],"learning_outcomes":["Convert between standard form and expanded form for numbers less than 1,000,000,000","Write a number in word form using correct period names (thousands, millions)","Explain how zero can hold a place (placeholder) in a number","Use commas to group digits into periods (ones, thousands, millions)"],"difficulty_level":"beginner","concept_id":"standard_word_expanded_forms","name":"Standard, word, and expanded forms","description":"Learn to write the same number in standard form, word form, and expanded form. Use period grouping (ones, thousands, millions) and remember zero can be a placeholder.","sequence_order":0.0},{"prerequisites":["standard_word_expanded_forms"],"learning_outcomes":["Name the value of each place from ones to hundred millions","Compose a number when given place value parts (example: 3 millions + 5 thousands + 2)","Decompose a number into place value units using words (example: 48 million = 4 ten-millions + 8 millions)","Convert between place value units (example: 8 millions = 80 hundred thousands)","Write numbers correctly from spoken form without shifting digits into the wrong period"],"difficulty_level":"beginner","concept_id":"place_value_words_hundred_millions","name":"Place value words to hundred millions","description":"Use place value names (ones through hundred millions) to build (compose) and break apart (decompose) numbers. Practice writing numbers from spoken form and trading units (like millions to hundred thousands).","sequence_order":1.0},{"prerequisites":["place_value_words_hundred_millions"],"learning_outcomes":["Tell the difference between face value and place value","Find the value of a digit in numbers up to 999,999,999 (example: the 7 in 572,000 is 70,000)","Use a place value chart idea to avoid counting errors","Explain digit value as (digit) × (place value)"],"difficulty_level":"beginner","concept_id":"value_of_a_digit_face_vs_place","name":"Find the value of a digit","description":"Learn the difference between face value (the digit) and place value (what it’s worth). Find the value of any digit by multiplying the digit by its place value.","sequence_order":2.0},{"prerequisites":["value_of_a_digit_face_vs_place"],"learning_outcomes":["Explain an exponent as “how many times you multiply by 10”","Rewrite 10^n as repeated multiplication for n from 1 to 10","Rewrite repeated multiplication as exponential form (example: 10×10×10 = 10^3)","State clearly why 10^n is not the same as 10 × n"],"difficulty_level":"beginner","concept_id":"powers_of_10_exponents","name":"Powers of 10 and exponents","description":"Learn what an exponent means using only base 10. Connect 10^n to repeated multiplication (10 × 10 × 10…) and avoid the mistake of thinking it means 10 × n.","sequence_order":3.0},{"prerequisites":["powers_of_10_exponents"],"learning_outcomes":["Identify when zeros can be canceled (both dividend and divisor have factors of 10)","Cancel the same number of zeros from both numbers correctly","Use easier facts to compute the quotient after canceling (example: 210 ÷ 7 = 30)","Explain why you cannot cancel zeros if they are not common to both numbers"],"difficulty_level":"beginner","concept_id":"divide_numbers_ending_zeros","name":"Divide numbers ending with zeros","description":"Learn to divide when both numbers end in zeros by canceling common zeros (common factors of 10). Use fact families to finish the division, like 2,100 ÷ 70 and 8,000 ÷ 400.","sequence_order":4.0},{"prerequisites":["divide_numbers_ending_zeros"],"learning_outcomes":["Multiply whole numbers by 10, 100, 1,000, 10,000, 100,000, and 1,000,000","Multiply a single digit by a multiple of 10 (example: 6 × 40,000)","Explain the pattern as “each ×10 moves digits one place left” (no decimals in this unit)","Find missing factors (example: ? × 8 = 400,000) using place value and multiplication facts","Avoid the mistake of just appending zeros without checking the size of the factor"],"difficulty_level":"beginner","concept_id":"multiply_powers_of_10_patterns","name":"Multiply using powers of 10 patterns","description":"Multiply whole numbers by 10, 100, 1,000 up to 1,000,000 and notice the pattern of shifting digits and adding zeros. Multiply a single digit by a power of 10 (like 6 × 40,000) and solve missing factor puzzles.","sequence_order":5.0},{"prerequisites":["standard_word_expanded_forms","place_value_words_hundred_millions","value_of_a_digit_face_vs_place","powers_of_10_exponents","divide_numbers_ending_zeros","multiply_powers_of_10_patterns"],"learning_outcomes":["Solve mixed problems with whole numbers less than 1,000,000,000 (no decimals/fractions)","Catch and correct these errors: wrong digit place, face value confusion, 10^n misunderstanding, incorrect zero canceling","Explain your thinking using place value words (not just an answer)","Use quick checks (like estimation) to see if an answer is reasonable"],"difficulty_level":"intermediate","concept_id":"mixed_practice_fix_common_pitfalls","name":"Mixed practice and common mistakes","description":"Do a short mixed set of problems using all skills: forms, place value words, digit value, exponents, dividing with zeros, and multiplying by powers of 10. Check for the most common Grade 5 mistakes and fix them.","sequence_order":6.0}],"overall_coherence_score":8.06,"pedagogical_soundness_score":7.7,"prerequisites":["Read and write whole numbers to at least 10,000","Basic multiplication facts (0–9) and understanding of “groups of”","Basic division as sharing into equal groups","Comfort using commas in large numbers"],"rejected_segments_rationale":"Several segments were not included due to redundancy with already-selected primary outcomes: multiple Numberblocks ‘×10 add a zero’ videos (pEbjmAsrOic_1363_1597, FG18571ruVQ_1396_1671) overlapped with the chosen ×10 concept+procedure pair. Additional division-introduction videos (rGMecZ_aERo_0_215, qZ2R1tbUZaw_2145_2406, qZ2R1tbUZaw_1876_2119, qZ2R1tbUZaw_2145_2406) repeated the core “division means sharing/opposite of multiplication” already covered. Multiplication-introduction videos (eW2dRLyoyds_45_375, pEbjmAsrOic_29_264) were either lower quality or would repeat meaning-of-multiplication instruction beyond what this course needs. Note: the available library does not contain direct, high-quality segments specifically teaching (a) standard/word/expanded form through hundred-millions, (b) converting between place-value units like ‘8 millions = 80 hundred-thousands,’ (c) canceling common zeros in division, or (d) multiplying by 100/1,000/... up to 1,000,000. These are therefore emphasized and corrected in the final interleaved practice explanations.","segments":[{"duration_seconds":194.07899999999995,"concepts_taught":["Digits as parts of a number","Place value as a digit’s worth based on position","Place value names: ones, tens, hundreds, thousands"],"quality_score":7.574999999999999,"before_you_start":"Before we work with really big numbers, you need a clear idea of what a digit is, and why its spot matters. In this video, you will learn how a digit’s position changes its value, like ones, tens, and hundreds.","title":"Digits and Place Value Basics","before_you_start_avatar_video_url":"","url":"https://www.youtube.com/watch?v=6t3DMk4-9KU&t=1372s","sequence_number":1.0,"prerequisites":["Recognize the digits 0–9","Read and write two- and three-digit numbers"],"learning_outcomes":["Explain what a digit is","Explain what place value means in simple words","Name the ones, tens, hundreds, and thousands places"],"video_duration_seconds":4747.0,"transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"","overall_transition_score":0.0,"to_segment_id":"6t3DMk4-9KU_1372_1566","pedagogical_progression_score":0.0,"vocabulary_consistency_score":0.0,"knowledge_building_score":0.0,"transition_explanation":"N/A for first segment"},"before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770910674/segments/6t3DMk4-9KU_1372_1566/before-you-start.mp3","segment_id":"6t3DMk4-9KU_1372_1566","micro_concept_id":"standard_word_expanded_forms"},{"before_you_start":"You already know digits have different values based on their place. Now you will practice finding the digit in each place, and see how zeros can hold a spot when there is “nothing” in that place.","before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770910674/segments/6t3DMk4-9KU_1566_1942/before-you-start.mp3","before_you_start_avatar_video_url":"","concepts_taught":["Identify which digit is in a given place","Zero as a placeholder in numbers like 4,000","Reading a 4-digit number by decomposing places (8,763 = 8 thousands + 7 hundreds + 6 tens + 3 ones)"],"duration_seconds":375.2625384615385,"learning_outcomes":["Identify the digit in the ones, tens, hundreds, or thousands place","Explain why zeros are written in 4,000 (placeholders)","Decompose a 4-digit number into thousands, hundreds, tens, and ones"],"micro_concept_id":"standard_word_expanded_forms","prerequisites":["Understand the names ones, tens, hundreds, thousands","Recognize commas in 4-digit numbers (e.g., 8,763)"],"quality_score":7.5249999999999995,"segment_id":"6t3DMk4-9KU_1566_1942","sequence_number":2.0,"title":"Finding Digits, Including Placeholder Zeros","transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"6t3DMk4-9KU_1372_1566","overall_transition_score":8.925,"to_segment_id":"6t3DMk4-9KU_1566_1942","pedagogical_progression_score":9.0,"vocabulary_consistency_score":9.0,"knowledge_building_score":9.0,"transition_explanation":"Moves from defining place value to using it to locate digits and explain what zeros are doing in a number."},"url":"https://www.youtube.com/watch?v=6t3DMk4-9KU&t=1566s","video_duration_seconds":4747.0},{"duration_seconds":253.301,"concepts_taught":["Base-ten grouping (ten of a unit makes the next unit)","Counting by place value units (ones, tens, hundreds, thousands, ten-thousands, hundred-thousands, millions)","Period grouping vocabulary (ONES, THOUSANDS, MILLIONS)","Understanding that each place value is 10 times the place to its right","Composing large quantities by grouping (e.g., 100 groups of 1,000 = 100,000)","Extending place value beyond millions (mentions billion and trillion)"],"quality_score":7.590000000000001,"before_you_start":"You can find ones, tens, hundreds, and thousands, and you know zeros can hold places. Now you will zoom out to bigger place values, and learn how commas group digits into ONES, THOUSANDS, and MILLIONS.","title":"Place Value Periods to Hundred Millions","before_you_start_avatar_video_url":"","url":"https://www.youtube.com/watch?v=MloZcl1JJEI&t=1s","sequence_number":3.0,"prerequisites":["Counting to at least 1,000","Understanding what ‘groups of’ means","Familiarity with tens and hundreds"],"learning_outcomes":["Explain the base-ten pattern that each place is 10× the place to its right","Name place value positions from ones through hundred millions (and recognize the next names: billion, trillion)","Group numbers into periods (ones period, thousands period, millions period) when reading or organizing large whole numbers","Interpret grouping statements like “100 groups of 1,000 equals 100,000”"],"video_duration_seconds":259.0,"transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"6t3DMk4-9KU_1566_1942","overall_transition_score":8.575,"to_segment_id":"MloZcl1JJEI_1_255","pedagogical_progression_score":8.5,"vocabulary_consistency_score":9.0,"knowledge_building_score":8.5,"transition_explanation":"Extends the same place-value idea from thousands into period grouping and place names up to hundred-millions."},"before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770910674/segments/MloZcl1JJEI_1_255/before-you-start.mp3","segment_id":"MloZcl1JJEI_1_255","micro_concept_id":"place_value_words_hundred_millions"},{"before_you_start":"You can name big places like millions, and you know commas separate periods. Next, you will practice using place value to tell what a digit is really worth, so you do not mix up the digit with its value.","before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770910674/segments/xA1XEVWzAYg_2916_3460/before-you-start.mp3","before_you_start_avatar_video_url":"","concepts_taught":["Digits are the parts of a number","Place value: a digit’s worth depends on its position","Place value names: ones, tens, hundreds, thousands","Zero as a placeholder in whole numbers (e.g., 4,000)","Reading a number using place values (e.g., 8,763)"],"duration_seconds":543.2689999999998,"learning_outcomes":["Identify the ones, tens, hundreds, and thousands digits in a whole number","Explain that the same digit can represent different amounts depending on its place","Explain how zeros can act as placeholders in numbers like 4,000","Read a 4-digit number by composing it from thousands, hundreds, tens, and ones"],"micro_concept_id":"value_of_a_digit_face_vs_place","prerequisites":["Understanding of whole numbers","Knowing how to read and write digits 0–9","Basic counting and the idea of grouping by tens"],"quality_score":6.95,"segment_id":"xA1XEVWzAYg_2916_3460","sequence_number":4.0,"title":"Using a Place Value Chart for Value","transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"MloZcl1JJEI_1_255","overall_transition_score":7.675,"to_segment_id":"xA1XEVWzAYg_2916_3460","pedagogical_progression_score":7.5,"vocabulary_consistency_score":8.5,"knowledge_building_score":7.5,"transition_explanation":"Shifts from naming large places to using those places to decide a digit’s value and avoid place-counting mistakes."},"url":"https://www.youtube.com/watch?v=xA1XEVWzAYg&t=2916s","video_duration_seconds":4904.0},{"before_you_start":"You now know place value grows by tens, and a digit’s position changes its worth. In this video, you will learn what an exponent means, and why it stands for multiplying the same base again and again, not just “times.”","before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770910674/segments/-zUmvpkhvW8_46_303/before-you-start.mp3","before_you_start_avatar_video_url":"","concepts_taught":["Exponents as repeated multiplication","Multiplication as repeated addition (comparison)","Base and exponent roles","How to read exponent expressions (“to the nth power”)","Recognizing exponent notation vs. normal digits","Caret (^) notation for typing exponents"],"duration_seconds":256.86,"learning_outcomes":["Explain that an exponent tells how many times to multiply the base by itself","Identify the base and exponent in an expression like 10^6","Rewrite an exponent expression as repeated multiplication (e.g., 10^4 = 10×10×10×10)","Avoid the common mistake of thinking 10^n means 10×n","Recognize the caret notation (^) as another way to write exponents"],"micro_concept_id":"powers_of_10_exponents","prerequisites":["Understanding of multiplication facts","Idea that multiplication can be written as repeated addition","Comfort reading whole numbers"],"quality_score":7.950000000000001,"segment_id":"-zUmvpkhvW8_46_303","sequence_number":5.0,"title":"Exponents Mean Repeated Multiplication","transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"xA1XEVWzAYg_2916_3460","overall_transition_score":7.575,"to_segment_id":"-zUmvpkhvW8_46_303","pedagogical_progression_score":7.5,"vocabulary_consistency_score":7.5,"knowledge_building_score":7.5,"transition_explanation":"Builds on the idea of “powers of ten” by introducing exponents as a shortcut for repeated multiplying."},"url":"https://www.youtube.com/watch?v=-zUmvpkhvW8&t=46s","video_duration_seconds":604.0},{"before_you_start":"You know an exponent means repeated multiplication, and the base is the big number. Now you will practice reading and evaluating powers more carefully, including why switching the numbers changes the meaning and the answer.","before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770910674/segments/-zUmvpkhvW8_303_586/before-you-start.mp3","before_you_start_avatar_video_url":"","concepts_taught":["Exponents are not commutative (base and exponent can’t be swapped)","Evaluating exponents as repeated multiplication","Exponent patterns (same base, increasing exponent)","Using a calculator to evaluate powers","Common exponents: squared (power of 2) and cubed (power of 3)"],"duration_seconds":282.98,"learning_outcomes":["Explain why 10^n is different from n^10 (order matters)","Expand an exponent like 3^5 into a multiplication sentence","Recognize and use the words squared (power of 2) and cubed (power of 3) correctly","Use a calculator’s exponent function to evaluate a power (when allowed)"],"micro_concept_id":"powers_of_10_exponents","prerequisites":["Understanding of multiplication","Knowing what exponents mean from Segment 1 (base and exponent)"],"quality_score":7.365000000000001,"segment_id":"-zUmvpkhvW8_303_586","sequence_number":6.0,"title":"Exponents: Order Matters, Squared, Cubed","transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"-zUmvpkhvW8_46_303","overall_transition_score":8.85,"to_segment_id":"-zUmvpkhvW8_303_586","pedagogical_progression_score":8.5,"vocabulary_consistency_score":9.0,"knowledge_building_score":9.0,"transition_explanation":"Continues the exponent topic by adding common errors and higher-level patterns, without changing the core definition."},"url":"https://www.youtube.com/watch?v=-zUmvpkhvW8&t=303s","video_duration_seconds":604.0},{"before_you_start":"You just learned a new symbol idea with exponents, which can feel different from place value. Now we switch back to operations, starting with a clear picture of division, sharing fairly so every group gets the same amount.","before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770910674/segments/qZ2R1tbUZaw_1638_1872/before-you-start.mp3","before_you_start_avatar_video_url":"","concepts_taught":["Division as equal sharing (fair shares)","Keeping two groups equal by alternating items (one-for-you, one-for-me)","Division with different numbers of groups (2, 3, 4 groups)","Using rows/arrays to organize equal groups","Checking totals to avoid missing items"],"duration_seconds":234.75,"learning_outcomes":["Explain division as sharing a set into equal groups","Use a fair-sharing method to split objects into 2, 3, or 4 equal groups","Organize counting with rows to check that all items were shared"],"micro_concept_id":"divide_numbers_ending_zeros","prerequisites":["Counting to 20","Understanding ‘equal’ means the same amount"],"quality_score":6.6,"segment_id":"qZ2R1tbUZaw_1638_1872","sequence_number":7.0,"title":"Division Means Sharing Equally","transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"-zUmvpkhvW8_303_586","overall_transition_score":6.85,"to_segment_id":"qZ2R1tbUZaw_1638_1872","pedagogical_progression_score":7.0,"vocabulary_consistency_score":7.0,"knowledge_building_score":6.5,"transition_explanation":"Switches from exponent notation to division meaning; it resets with concrete visuals so the next procedures make sense."},"url":"https://www.youtube.com/watch?v=qZ2R1tbUZaw&t=1638s","video_duration_seconds":2417.0},{"duration_seconds":263.15999999999997,"concepts_taught":["Division by zero is undefined","Different ways to write division (÷, slash, fraction bar)","Fact-family idea: swapping divisor and quotient for the same dividend (e.g., 10÷2=5 and 10÷5=2)"],"quality_score":6.275,"before_you_start":"You can picture division as equal sharing. Now you will learn a few key division facts and different ways division can be written, so you can rewrite problems in a simpler form and avoid common mistakes like dividing by zero.","title":"Division Facts and Helpful Notations","before_you_start_avatar_video_url":"","url":"https://www.youtube.com/watch?v=rGMecZ_aERo&t=211s","sequence_number":8.0,"prerequisites":["Basic understanding of division as equal groups","Some familiarity with multiplication facts (helpful for the ‘flipping’ examples)"],"learning_outcomes":["State why division by zero is not allowed and label it ‘undefined’","Recognize division written as ÷, /, or a fraction bar","Use simple fact-family relationships to generate a related division fact"],"video_duration_seconds":504.0,"transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"qZ2R1tbUZaw_1638_1872","overall_transition_score":8.0,"to_segment_id":"rGMecZ_aERo_211_474","pedagogical_progression_score":8.0,"vocabulary_consistency_score":8.0,"knowledge_building_score":8.0,"transition_explanation":"Builds from the meaning of division to rules and notations that help you handle more complicated division problems."},"before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770910674/segments/rGMecZ_aERo_211_474/before-you-start.mp3","segment_id":"rGMecZ_aERo_211_474","micro_concept_id":"divide_numbers_ending_zeros"},{"duration_seconds":235.069,"concepts_taught":["Meaning of division as equal groups","Division vocabulary: dividend, divisor, quotient, remainder","Long division algorithm (choose digits, estimate using multiplication facts, subtract, bring down)","Exact vs inexact division (remainder 0 vs not 0)"],"quality_score":7.005,"before_you_start":"You have division facts and you have seen different ways to write a division problem. Now you will learn a step-by-step long division routine, so you can finish harder quotients carefully and keep track of remainders.","title":"Long Division Steps, One Clear Example","before_you_start_avatar_video_url":"","url":"https://www.youtube.com/watch?v=wAxEdmutf98&t=13s","sequence_number":9.0,"prerequisites":["Understanding basic division as sharing/equal groups","Basic subtraction within 100","Multiplication facts (especially 5s)"],"learning_outcomes":["Identify the dividend and divisor in a division problem","Use long division steps to compute a 3-digit ÷ 1-digit problem like 125 ÷ 5","Explain what the quotient and remainder represent in a word problem","Tell whether a division is exact or inexact based on the remainder"],"video_duration_seconds":284.0,"transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"rGMecZ_aERo_211_474","overall_transition_score":8.5,"to_segment_id":"wAxEdmutf98_13_248","pedagogical_progression_score":8.5,"vocabulary_consistency_score":8.5,"knowledge_building_score":8.5,"transition_explanation":"Moves from rules and notations to a full algorithm that can be used when mental division facts are not enough."},"before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770910674/segments/wAxEdmutf98_13_248/before-you-start.mp3","segment_id":"wAxEdmutf98_13_248","micro_concept_id":"divide_numbers_ending_zeros"},{"duration_seconds":258.41899999999987,"concepts_taught":["Interpreting n × 10 as n tens","Multiplication by 10 pattern (60, 70, 80, 90)","Skip counting by tens","Relating groups of ten to base-ten structure (tens unit)"],"quality_score":7.25,"before_you_start":"Division and multiplication are connected, and place value helps in both. Next, you will look at multiplying by 10 in a simple way, by thinking in tens. This prepares you to scale numbers up quickly and correctly.","title":"Multiplying by 10 Means Tens","before_you_start_avatar_video_url":"","url":"https://www.youtube.com/watch?v=FG18571ruVQ&t=2468s","sequence_number":10.0,"prerequisites":["Know what ‘ten’ means and be able to count by tens","Basic multiplication idea: ‘times’ means equal groups"],"learning_outcomes":["Solve problems of the form n × 10 using the idea of ‘n tens’","Skip count by tens to generate multiples of 10","Explain why numbers like 70 and 80 represent 7 tens and 8 tens"],"video_duration_seconds":2739.0,"transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"wAxEdmutf98_13_248","overall_transition_score":7.25,"to_segment_id":"FG18571ruVQ_2468_2727","pedagogical_progression_score":7.5,"vocabulary_consistency_score":7.5,"knowledge_building_score":7.0,"transition_explanation":"Shifts from dividing to multiplying by 10, but stays connected through place value and using patterns to compute efficiently."},"before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770910674/segments/FG18571ruVQ_2468_2727/before-you-start.mp3","segment_id":"FG18571ruVQ_2468_2727","micro_concept_id":"multiply_powers_of_10_patterns"},{"duration_seconds":180.18,"concepts_taught":["Practicing multiplication facts (skip counting, memorizing)","9s finger trick (pattern-based strategy)","Multiplying by 10 by appending a zero","Seeing multiplication results as tens-and-ones (place value connection)"],"quality_score":7.3,"before_you_start":"You know that multiplying by 10 makes tens, and the answer has zero ones. Now you will practice the pattern on bigger numbers, so you can write the new digits in the correct places without shifting the number the wrong way.","title":"The ×10 Pattern With Bigger Numbers","before_you_start_avatar_video_url":"","url":"https://www.youtube.com/watch?v=dPksJHBZs4Q&t=400s","sequence_number":11.0,"prerequisites":["Understanding multiplication as equal groups","Knowing ones and tens place (basic place value)","Counting and basic multiplication facts up to 9×9"],"learning_outcomes":["Explain why practice (facts/skip counting) improves multiplication fluency","Use the finger method to solve single-digit × 9 problems","Multiply a whole number by 10 using the ‘append a zero’ pattern","Check that the product makes sense by noticing the number becomes 10 times larger"],"video_duration_seconds":653.0,"transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"FG18571ruVQ_2468_2727","overall_transition_score":8.45,"to_segment_id":"dPksJHBZs4Q_400_580","pedagogical_progression_score":8.5,"vocabulary_consistency_score":8.5,"knowledge_building_score":8.5,"transition_explanation":"Moves from the meaning of ×10 to writing correct multi-digit products using the same place-value idea."},"before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770910674/segments/dPksJHBZs4Q_400_580/before-you-start.mp3","segment_id":"dPksJHBZs4Q_400_580","micro_concept_id":"multiply_powers_of_10_patterns"},{"duration_seconds":446.42999999999995,"concepts_taught":["Rounding as estimating (“about/roughly”)","Using place value to decide how to round","Identifying ones and tens places (2-digit numbers)","Identifying tens and hundreds places (3-digit numbers)","Rounding to the nearest ten","Rounding to the nearest hundred","Rule: look at the digit to the right; 5 or more rounds up"],"quality_score":7.125,"before_you_start":"You have worked with place value, exponents, division, and the ×10 pattern. Now you will practice using place value to make a quick estimate by rounding. This helps you check if your answers make sense, and catch mistakes early.","title":"Rounding to Check Place Value Sense","before_you_start_avatar_video_url":"","url":"https://www.youtube.com/watch?v=8Qwugoey0dQ&t=20s","sequence_number":12.0,"prerequisites":["Understanding that numbers are made of digits","Basic place value for ones, tens, hundreds","Counting by tens and hundreds"],"learning_outcomes":["Explain what rounding means and when it’s used (estimating)","Identify the ones, tens, and hundreds digits in a number","Round a 2-digit number to the nearest ten using the ones digit","Round a 3-digit number to the nearest hundred using the tens digit","Justify rounding decisions using the “5 or more, round up” rule"],"video_duration_seconds":514.0,"transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"dPksJHBZs4Q_400_580","overall_transition_score":7.75,"to_segment_id":"8Qwugoey0dQ_20_467","pedagogical_progression_score":8.0,"vocabulary_consistency_score":8.0,"knowledge_building_score":7.5,"transition_explanation":"Uses the same place-value thinking from ×10, but now for estimation and error-checking, which supports mixed practice and avoiding common mistakes."},"before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770910674/segments/8Qwugoey0dQ_20_467/before-you-start.mp3","segment_id":"8Qwugoey0dQ_20_467","micro_concept_id":"mixed_practice_fix_common_pitfalls"}],"selection_strategy":"Prioritized kid-friendly, self-contained segments that could cover the requested Grade 5 NBT progression with minimal redundancy. Because the library has limited direct coverage of (1) word/expanded forms to hundred-millions, (5) zero-cancel division, and (6) ×10/×100/×1,000 patterns, I used the closest instructional videos for the core ideas (place value periods, digit value, exponent meaning, division strategies, ×10 pattern), then designed the final interleaved practice to explicitly test and correct the missing-but-required skills and pitfalls.","strengths":["Kid-friendly explanations and visuals (Homeschool Pop, Numberblocks, NUMBEROCK)","Clear scaffolding from vocabulary to procedures","Strong focus on avoiding common misunderstandings (exponents, place value slips)","Ends with an estimation habit (rounding) for self-checking"],"target_difficulty":"intermediate","title":"Big Numbers and Powers of Ten","tradeoffs":[],"updated_at":"2026-03-05T08:39:48.607808+00:00","user_id":"google_109800265000582445084"}}