{"success":true,"course":{"all_concepts_covered":["Lining up multi-digit numbers by place value","Standard algorithm for addition","Carrying (regrouping) in addition","Solving addition word problems by finding totals","Standard algorithm for subtraction with regrouping","Borrowing across zeros in subtraction","Solving subtraction word problems by finding what’s left or the difference"],"assembly_rationale":"This course follows a deliberate scaffold: correct setup (place value alignment) → procedural fluency (standard algorithm) → handling regrouping decisions (carry/borrow) → applying skills in word problems. Subtraction is intentionally supported with a quick structure refresher before regrouping and multi-digit work, then ends with the highest-error edge case (zeros) right before subtraction word problems.","average_segment_quality":7.680000000000001,"concept_key":"CONCEPT#217b09844e13bf65045e973caf71919b","considerations":["There is no available segment that demonstrates full six-digit addition explicitly; the course relies on place-value extension plus repeating the same standard-algorithm steps across more columns.","Students may benefit from pausing to complete 1–2 extra teacher-provided practice problems after the addition and subtraction algorithm segments to build fluency."],"course_id":"course_1770964113","created_at":"2026-02-13T06:41:50.282890+00:00","created_by":"Shaunak Ghosh","description":"You will learn to neatly line up big numbers, then fluently add and subtract multi-digit whole numbers using the standard algorithm. You will also solve word problems by choosing the correct operation, setting up the problem, and checking that your answer makes sense.","estimated_total_duration_minutes":44.0,"final_learning_outcomes":["I can line up whole numbers correctly through the hundred-thousands place.","I can add whole numbers using the standard algorithm, including carrying when a column sum is 10 or more.","I can solve addition word problems by choosing addition, writing an equation, and using the standard algorithm.","I can subtract whole numbers using the standard algorithm with regrouping, including borrowing across zeros.","I can solve subtraction word problems by choosing subtraction, setting up the work neatly, and checking that my answer makes sense."],"generated_at":"2026-02-13T06:41:05Z","generation_error":null,"generation_progress":100.0,"generation_status":"completed","generation_step":"completed","generation_time_seconds":218.34919786453247,"image_description":"A modern, kid-friendly math thumbnail with a clean Apple-style layout. Center focal point: a large, crisp white sheet of paper at a slight angle with two vertical problems shown in bold, rounded type—one addition and one subtraction—using six-digit numbers, perfectly aligned in place-value columns. Above the ones column, small labeled headers read “Hundred-Thousands, Ten-Thousands, Thousands, Hundreds, Tens, Ones” in tiny, neat text to hint at alignment. Use a limited, high-contrast palette: deep blue (#1E3A8A) for numbers and lines, bright green (#22C55E) for carry/borrow marks, and a soft off-white to light-gray gradient background (#F8FAFC to #E5E7EB). Add subtle drop shadows under the paper and a faint grid pattern in the background to suggest place-value columns without clutter. Include a small, friendly pencil icon near the bottom right, and a simple arrow showing “start here” at the ones place. Leave a clear top band of space for a title overlay.","image_url":"https://course-builder-course-thumbnails.s3.us-east-1.amazonaws.com/courses/course_1770964113/thumbnail.png","interleaved_practice":[{"difficulty":"mastery","correct_option_index":1.0,"question":"You want to add 47,305 + 6,982 using the standard algorithm. Which setup lines up the place values correctly?","option_explanations":["Incorrect because adding a zero on the right makes 6,9820, which is a different number (it changes the value).","Correct! Writing 06,982 keeps the ones digit (2) under the ones digit (5), and all other digits line up by place value.","Incorrect because 6,982 is not lined up under 47,305 by ones place; the columns won’t match.","Incorrect because 47,305 was rewritten with digits in the wrong places, so the place values no longer match."],"options":["  47,305\n+ 6,9820\n------","  47,305\n+ 06,982\n------","  47,305\n+ 6,982\n------","  473,05\n+ 6,982\n------"],"question_id":"mq_01_align_add","related_micro_concepts":["place_value_line_up_digits","add_standard_algorithm_6digit"],"discrimination_explanation":"Option B is correct because adding a leading zero keeps the digits in the correct place-value columns: ones under ones, tens under tens, and so on. Option A shifts the 6,982 too far left (making the ones not match). Option C adds an extra zero at the end, changing the number’s value. Option D rewrites 47,305 incorrectly and breaks place value."},{"difficulty":"mastery","correct_option_index":3.0,"question":"While adding 68,759 + 24,586, you start in the ones place. Since 9 + 6 = 15, what should you write and carry?","option_explanations":["Incorrect because you don’t carry the whole 15; you carry only the tens part, which is 1.","Incorrect because it flips the digits; 5 stays in the ones place and 1 is the carry.","Incorrect because you can’t write two digits (15) in the ones column in the standard algorithm.","Correct! You write 5 in the ones place, and carry 1 ten to the tens column."],"options":["Write 0 in the ones place, carry 15 to the tens.","Write 1 in the ones place, carry 5 to the tens.","Write 15 in the ones place, carry nothing.","Write 5 in the ones place, carry 1 to the tens."],"question_id":"mq_02_carry_step","related_micro_concepts":["add_regrouping_carry","add_standard_algorithm_6digit"],"discrimination_explanation":"Option C matches the standard algorithm: keep the ones digit (5) in the ones place, and carry the tens digit (1) to the next column. Option A breaks the one-digit-per-column rule. Option B swaps the carry and the written digit. Option D carries too much; you never carry “15,” you carry only the tens part."},{"difficulty":"mastery","correct_option_index":0.0,"question":"A museum sold 248,910 tickets last year and 12,405 tickets this year. The question asks, “How many tickets were sold in all?” Which equation matches the story?","option_explanations":["Correct! The story combines two amounts, so addition matches the situation.","Incorrect because subtraction would find a difference, not the total sold in all.","Incorrect because it subtracts in the wrong direction and still doesn’t match “in all.”","Incorrect because the “− 1” is not in the story and changes what you’re solving."],"options":["248,910 + 12,405 = ____","248,910 − 12,405 = ____","12,405 − 248,910 = ____","248,910 + 12,405 − 1 = ____"],"question_id":"mq_03_add_word_problem","related_micro_concepts":["addition_word_problems_6digit","add_standard_algorithm_6digit"],"discrimination_explanation":"Option C is correct because “in all” means combine to find a total, so you add the two amounts. Options A and B subtract, which would mean taking away, not totaling. Option D changes the story by subtracting 1 for no reason, which is a common mistake when guessing operations."},{"difficulty":"mastery","correct_option_index":2.0,"question":"You are solving 50,002 − 1,876. Before subtracting, you regroup across zeros. What should the top number look like after regrouping so you can subtract in the ones and tens places?","option_explanations":["Incorrect because the borrowing steps don’t match the correct place-value trades for 50,002.","Incorrect because the regrouping described doesn’t correctly change the tens and ones needed for subtracting 6 tens and 6 ones.","Correct! Regrouping across the zeros turns 50,002 into 49,912 so the ones column becomes 12 and the tens column becomes 9.","Incorrect because you still can’t borrow from a 0 in the tens place; the regrouping chain isn’t finished."],"options":["49,992 (because you borrow 1 ten-thousand, then 1 hundred, then 1 ten)","49,102 (because you borrow 1 thousand and make the hundreds 10)","49,912 (because you turn both zeros into 9s and add 10 to the ones place)","50,012 (because you only add 10 to the ones place)"],"question_id":"mq_04_borrow_across_zeros","related_micro_concepts":["subtract_across_zeros","subtract_regrouping_standard"],"discrimination_explanation":"Option A is correct because 50,002 becomes 49,912 after borrowing across the zeros: the thousands place drops by 1 (50,002 → 49,002), then the hundreds become 9, tens become 9, and ones become 12. Option B doesn’t fix the zero in the tens place. Option C borrows from the wrong place and leaves the tens issue. Option D describes an incorrect borrowing chain that doesn’t match the place values in 50,002."},{"difficulty":"mastery","correct_option_index":2.0,"question":"A student tries to solve 72,400 − 5,786 but writes it like this:\n  72,400\n− 5,786\nThey start subtracting right away and get a strange answer. What is the most important mistake to fix first?","option_explanations":["Incorrect because the standard algorithm subtracts right to left, starting with ones.","Incorrect because you borrow from the next column to the left (like tens), not from the ones place.","Correct! Misaligned place values will ruin every step, so lining up ones under ones is the first fix.","Incorrect because subtraction is absolutely used with multi-digit numbers; the issue is setup, not the operation."],"options":["They should subtract left to right, starting with the ten-thousands.","They should borrow from the ones place before subtracting the ones.","They did not line up the digits by place value; the ones digits must be in the same column.","They should change it to addition because subtraction is not allowed with big numbers."],"question_id":"mq_05_misalignment_subtract","related_micro_concepts":["place_value_line_up_digits","subtract_regrouping_standard"],"discrimination_explanation":"Option C is correct because the standard algorithm only works when place values line up (ones under ones). Option A is wrong because we subtract right to left. Option B is false—subtraction is fine for big numbers. Option D is not a real step; you borrow from the next place to the left, not from the ones place."},{"difficulty":"mastery","correct_option_index":1.0,"question":"A stadium has 125,000 seats. 97,586 seats are filled. The question asks, “How many seats are empty?” Which equation best matches the story?","option_explanations":["Incorrect because adding would make a bigger number and doesn’t represent empty seats.","Correct! Empty seats are the total seats minus the filled seats.","Incorrect because it subtracts in the wrong direction and doesn’t represent “how many are left.”","Incorrect because addition does not represent finding what is empty."],"options":["97,586 + 125,000 = ____","125,000 − 97,586 = ____","97,586 − 125,000 = ____","125,000 + 97,586 = ____"],"question_id":"mq_06_sub_word_problem_equation","related_micro_concepts":["subtraction_word_problems_6digit","subtract_regrouping_standard"],"discrimination_explanation":"Option B is correct because empty seats means the total minus the filled seats. Options A and D add, which would be like combining seats, not finding what’s left. Option C subtracts in the wrong order and would not match the story situation."},{"difficulty":"mastery","correct_option_index":0.0,"question":"You solved 403,210 − 189,765 = 213,445. Which check best matches the standard way to see if your subtraction is reasonable?","option_explanations":["Correct! If your subtraction is correct, the subtrahend plus the difference equals the minuend.","Incorrect because adding the minuend and subtrahend doesn’t connect to the subtraction result.","Incorrect because subtracting again in that way doesn’t directly confirm the original subtraction.","Incorrect because changing digits is guessing, not checking."],"options":["Add 189,765 + 213,445 and see if you get 403,210.","Add 403,210 + 189,765 and see if you get 213,445.","Subtract 403,210 − 213,445 and hope the answer is 0.","Move the digits around until the last digit matches."],"question_id":"mq_07_check_subtraction","related_micro_concepts":["subtract_regrouping_standard","subtraction_word_problems_6digit"],"discrimination_explanation":"Option A is correct because subtraction and addition are inverse operations: if the difference is right, then difference + subtrahend equals the original number. Option B doesn’t test the relationship correctly. Option C adds the wrong quantities. Option D is not a math check."},{"difficulty":"mastery","correct_option_index":3.0,"question":"When you add 398,742 + 257,589 using the standard algorithm, which place value will need the first carry?","option_explanations":["Incorrect because the tens digits are 4 and 8, but you don’t get there first, and the first carry happens earlier.","Incorrect because the hundreds digits are 7 and 5, but the first carry happens in the ones place.","Incorrect because the thousands digits are 8 and 7, but the first carry happens earlier in the ones place.","Correct! You start in the ones place, and 2 + 9 = 11, so you write 1 and carry 1 to the tens."],"options":["Tens place (because 4 + 8 is more than 10)","Hundreds place (because 7 + 5 is more than 10)","Thousands place (because 8 + 7 is more than 10)","Ones place (because 2 + 9 is more than 9)"],"question_id":"mq_08_where_carry_first","related_micro_concepts":["add_regrouping_carry","add_standard_algorithm_6digit"],"discrimination_explanation":"Option D is correct because you always start in the ones place, and 2 + 9 = 11, so the first carry happens immediately there. The other options look at later columns or add the wrong digits from the problem."}],"is_public":true,"key_decisions":["Segment Ju3kQjmcH5g_15_378: Chosen first to lock in place-value alignment up to hundred-thousands, directly preventing the common pitfall of misaligned columns before any standard algorithm work.","Segment Q9sLfMrH8_w_116_297: Selected to introduce the standard vertical addition routine (ones then tens) in a low-stress way, so students can later repeat the same pattern across more place values.","Segment Q9sLfMrH8_w_406_699: Added next to target the biggest addition pitfall, forgetting to carry when a column sum exceeds 9, with a clear decision rule.","Segment tuVI8Uv0SAI_0_288: Used as the addition word-problem bridge, emphasizing choosing addition from the situation, not just grabbing a keyword.","Segment qKxQ33KcRWQ_101_327: Included as a short subtraction structure refresher (ones then tens), making the later multi-digit subtraction feel like the same steps repeated.","Segment qKxQ33KcRWQ_314_585: Placed right after subtraction structure to introduce regrouping (borrowing) as the new move when the top digit is smaller, preparing for multi-digit regrouping.","Segment cLHu-zuTPk8_19_419: Selected as the main multi-digit subtraction standard-algorithm lesson, showing stacking, right-to-left subtraction, and regrouping across multiple columns.","Segment 7rLFrT2BQ00_9_312: Added as an essential edge-case lesson because borrowing across zeros is a high-error area in Grade 4 and a stated common pitfall.","Segment tuVI8Uv0SAI_291_581: Finished with subtraction word-problem clues to help students correctly choose subtraction and then apply the standard algorithm."],"micro_concepts":[{"prerequisites":[],"learning_outcomes":["I can line up multi-digit numbers by place value.","I can spot and fix a misaligned problem (like a tens digit under hundreds).","I can rewrite a word problem’s numbers in a vertical format correctly."],"difficulty_level":"beginner","concept_id":"place_value_line_up_digits","name":"Line up place values correctly","description":"Before you add or subtract, you must stack numbers so ones are under ones, tens under tens, and so on. This keeps every digit in the correct place so your answer makes sense.","sequence_order":0.0},{"prerequisites":["place_value_line_up_digits"],"learning_outcomes":["I can add two multi-digit numbers using the standard algorithm.","I can add from ones to hundred-thousands without skipping columns.","I can write a neat, readable vertical addition problem."],"difficulty_level":"beginner","concept_id":"add_standard_algorithm_6digit","name":"Add up to six digits standard","description":"Use the standard algorithm to add whole numbers up to 999,999. Add from right to left (ones to highest place), writing each digit in the correct column.","sequence_order":1.0},{"prerequisites":["add_standard_algorithm_6digit"],"learning_outcomes":["I can tell when to carry (when a column sum is 10 or more).","I can carry to the next column and keep adding correctly.","I can check my work to make sure I didn’t forget a carry."],"difficulty_level":"beginner","concept_id":"add_regrouping_carry","name":"Add with regrouping (carrying)","description":"Sometimes a column adds to 10 or more. You write the ones digit and “carry” the tens to the next column to the left.","sequence_order":2.0},{"prerequisites":["add_regrouping_carry"],"learning_outcomes":["I can decide when a word problem uses addition (not just by keywords).","I can write an equation and solve it with the standard algorithm.","I can label my answer and check if it makes sense."],"difficulty_level":"beginner","concept_id":"addition_word_problems_6digit","name":"Addition word-problems up to six digits","description":"Solve story problems that mean “put together” or “total.” First decide what the problem is asking, then add using the standard algorithm.","sequence_order":3.0},{"prerequisites":["addition_word_problems_6digit"],"learning_outcomes":["I can subtract multi-digit numbers using the standard algorithm.","I can regroup from the next column when needed.","I can keep digits lined up and subtract right to left."],"difficulty_level":"beginner","concept_id":"subtract_regrouping_standard","name":"Subtract with regrouping standard algorithm","description":"Use the standard algorithm to subtract multi-digit numbers up to 999,999. When the top digit is smaller, regroup (borrow) from the next place to the left.","sequence_order":4.0},{"prerequisites":["subtract_regrouping_standard"],"learning_outcomes":["I can regroup across zeros correctly in subtraction.","I can explain what happens to zeros when I borrow from the left.","I can avoid common mistakes (like borrowing but not changing the digits)."],"difficulty_level":"intermediate","concept_id":"subtract_across_zeros","name":"Subtract across zeros (borrow chain)","description":"Sometimes you need to regroup across one or more zeros (like 50,002 − 1,876). You may need to “borrow” from farther left and turn zeros into 9s.","sequence_order":5.0},{"prerequisites":["subtract_across_zeros"],"learning_outcomes":["I can decide when a word problem uses subtraction (not just keywords).","I can solve multi-digit subtraction story problems with regrouping.","I can check my answer by estimating or using addition to verify."],"difficulty_level":"beginner","concept_id":"subtraction_word_problems_6digit","name":"Subtraction word-problems up to six digits","description":"Solve story problems that mean “take away,” “how many left,” or “find the difference.” Decide if subtraction is needed, then subtract using the standard algorithm and check your answer.","sequence_order":6.0}],"overall_coherence_score":8.8,"pedagogical_soundness_score":8.7,"prerequisites":["Basic place value (ones, tens, hundreds)","Addition and subtraction facts within 20","Reading multi-step sentences in word problems","Writing numbers neatly in columns"],"rejected_segments_rationale":"MloZcl1JJEI_1_219 was not included because place-value-to-a-million patterns overlap heavily with the first place-value alignment lesson, and time was better used on algorithm and regrouping. ayFAh4VNMFA_5_304 was rejected to avoid duplicating addition regrouping already taught (carry rule) and to honor the anti-redundancy rule. rPVdItitgIU_11_241 and JC0ASSHfzWY_133_349 were too basic for Grade 4 goals (they focus on very small numbers/operation meaning). oHAH377vLO8_123_323 scored below the ≥7.0 “good enough” bar and includes a noted misleading regrouping moment, which is risky for fluency with the standard algorithm.","segments":[{"before_you_start":"Before we add or subtract big numbers, we need to know where each digit belongs. In this video, you’ll use place-value columns, so ones stay under ones, tens under tens, and so on, all the way to hundred-thousands.","before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770964113/segments/Ju3kQjmcH5g_15_378/before-you-start.mp3","before_you_start_avatar_video_url":"","concepts_taught":["Digit (0–9) vs. multi-digit numbers","Place value meaning (ones, tens, hundreds)","How a digit’s value changes by its position","Reading numbers as expanded form (e.g., 500 + 60 + 7)","Placing digits into a place value chart","Key alignment rule: last digit goes in ones column","Extending place values beyond hundreds (thousands, ten-thousands, hundred-thousands; pattern repeats)","Using place value to correctly set up arithmetic problems (connection stated at end)"],"duration_seconds":362.9343333333333,"learning_outcomes":["Identify the value of each digit in a multi-digit whole number","Write a multi-digit number in expanded form (sum of place values)","Correctly line up numbers by place value (ones under ones, tens under tens, etc.) when setting up vertical addition or subtraction","Name place values through at least hundred-thousands (helpful for working up to 6-digit numbers)"],"micro_concept_id":"place_value_line_up_digits","prerequisites":["Counting and reading whole numbers","Knowing the digits 0–9","Basic understanding of ones, tens, and hundreds (helpful but introduced)"],"quality_score":7.35,"segment_id":"Ju3kQjmcH5g_15_378","sequence_number":1.0,"title":"Line Up Digits in Place Columns","transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"","overall_transition_score":10.0,"to_segment_id":"Ju3kQjmcH5g_15_378","pedagogical_progression_score":10.0,"vocabulary_consistency_score":10.0,"knowledge_building_score":10.0,"transition_explanation":"N/A (first segment)"},"url":"https://www.youtube.com/watch?v=Ju3kQjmcH5g&t=15s","video_duration_seconds":393.0},{"before_you_start":"Now that you can line up digits by place value, you’re ready to add using columns. Watch how we start in the ones place, write each answer digit in the correct column, and move left one place at a time.","before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770964113/segments/Q9sLfMrH8_w_116_297/before-you-start.mp3","before_you_start_avatar_video_url":"","concepts_taught":["Setting up addition by place value (ones/tens)","Adding ones first, then tens (standard algorithm structure)","Keeping digits aligned in columns","Using a story/word problem to represent addition","Vocabulary: sum"],"duration_seconds":181.26,"learning_outcomes":["Set up a 2-digit addition problem with correct place-value alignment","Add ones first and tens second to find the sum","Explain why we keep ones under ones and tens under tens","Use the term “sum” correctly"],"micro_concept_id":"add_standard_algorithm_6digit","prerequisites":["Understanding tens and ones place value","Single-digit addition facts (0–9)"],"quality_score":7.55,"segment_id":"Q9sLfMrH8_w_116_297","sequence_number":2.0,"title":"Add in Columns, Right to Left","transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"Ju3kQjmcH5g_15_378","overall_transition_score":9.3,"to_segment_id":"Q9sLfMrH8_w_116_297","pedagogical_progression_score":9.0,"vocabulary_consistency_score":9.5,"knowledge_building_score":9.5,"transition_explanation":"Uses the place-value columns from the first lesson to set up vertical addition correctly."},"url":"https://www.youtube.com/watch?v=Q9sLfMrH8_w&t=116s","video_duration_seconds":936.0},{"before_you_start":"You already know how to add in columns from right to left. Now you’ll learn what to do when a column sum is 10 or more, so your answer still fits one digit per column, and the extra gets carried to the next place.","before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770964113/segments/Q9sLfMrH8_w_406_699/before-you-start.mp3","before_you_start_avatar_video_url":"","concepts_taught":["Regrouping/carrying in addition when a column sum is 10 or more","Writing the ones digit and carrying the tens digit","Decision rule: regroup if ones-column sum is double-digit","Practice deciding whether regrouping is needed","Completing a regrouping example (32 + 19)"],"duration_seconds":293.2653846153845,"learning_outcomes":["Decide whether regrouping is needed by checking the ones-column sum","Regroup correctly by writing the ones digit and carrying the tens digit","Complete a 2-digit addition problem with regrouping using the standard algorithm","Explain what the carried ‘1’ means (one ten)"],"micro_concept_id":"add_regrouping_carry","prerequisites":["Adding ones and tens in vertical (column) form","Understanding that 10 ones = 1 ten (place value)","Single-digit addition facts"],"quality_score":7.4,"segment_id":"Q9sLfMrH8_w_406_699","sequence_number":3.0,"title":"Carry When a Column Makes Ten","transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"Q9sLfMrH8_w_116_297","overall_transition_score":8.8,"to_segment_id":"Q9sLfMrH8_w_406_699","pedagogical_progression_score":8.5,"vocabulary_consistency_score":9.0,"knowledge_building_score":9.0,"transition_explanation":"Builds on the same column-by-column addition routine, adding the new skill of carrying when a column total is too large."},"url":"https://www.youtube.com/watch?v=Q9sLfMrH8_w&t=406s","video_duration_seconds":936.0},{"before_you_start":"You can add in columns, and you know how to carry when you need to. Now you’ll practice reading a story problem, deciding it’s asking for a total, and writing an addition equation you can solve with the standard algorithm.","before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770964113/segments/tuVI8Uv0SAI_0_288/before-you-start.mp3","before_you_start_avatar_video_url":"","concepts_taught":["What a word problem is (story format)","Using key words to choose addition (altogether, in all, now, in total)","Interpreting situations as ‘combine to find the total’","Checking that the question asks for a total/sum"],"duration_seconds":288.0,"learning_outcomes":["Identify clue words that usually signal addition in a word problem","Explain in simple words why the problem is asking for a total (sum)","Set up the situation as an addition equation (e.g., 56 + 13) and solve"],"micro_concept_id":"addition_word_problems_6digit","prerequisites":["Understanding that addition means putting amounts together","Ability to add 2- and 3-digit numbers (basic fluency)"],"quality_score":7.8100000000000005,"segment_id":"tuVI8Uv0SAI_0_288","sequence_number":4.0,"title":"Choose Addition in Word Problems","transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"Q9sLfMrH8_w_406_699","overall_transition_score":8.7,"to_segment_id":"tuVI8Uv0SAI_0_288","pedagogical_progression_score":8.5,"vocabulary_consistency_score":9.0,"knowledge_building_score":9.0,"transition_explanation":"Moves from doing the algorithm to deciding when to use it in a story situation and setting it up correctly."},"url":"https://www.youtube.com/watch?v=tuVI8Uv0SAI&t=0s","video_duration_seconds":582.0},{"before_you_start":"In word problems, sometimes you’re not finding a total, you’re finding what’s left or the difference. This video starts subtraction in columns, beginning with the ones place, so you keep your digits in the right spots as you move left.","before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770964113/segments/qKxQ33KcRWQ_101_327/before-you-start.mp3","before_you_start_avatar_video_url":"","concepts_taught":["Subtraction as taking away","Difference (subtraction answer) vocabulary","Standard algorithm idea for 2-digit subtraction (subtract ones, then tens)","Place value columns: ones and tens","Checking subtraction step-by-step with examples"],"duration_seconds":226.3618947368421,"learning_outcomes":["Set up and solve 2-digit subtraction problems using columns (ones and tens)","Subtract the ones column first and record the digit in the ones place","Subtract the tens column next and record the digit in the tens place","Use and understand the term difference for the answer"],"micro_concept_id":"subtract_regrouping_standard","prerequisites":["Know what subtraction means (take away)","Recognize ones and tens place value","Single-digit subtraction facts within 10"],"quality_score":7.6,"segment_id":"qKxQ33KcRWQ_101_327","sequence_number":5.0,"title":"Subtract in Columns, Ones Then Tens","transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"tuVI8Uv0SAI_0_288","overall_transition_score":8.6,"to_segment_id":"qKxQ33KcRWQ_101_327","pedagogical_progression_score":8.5,"vocabulary_consistency_score":8.5,"knowledge_building_score":8.5,"transition_explanation":"Shifts from addition stories to the subtraction algorithm, while keeping the same place-value column idea."},"url":"https://www.youtube.com/watch?v=qKxQ33KcRWQ&t=101s","video_duration_seconds":679.0},{"before_you_start":"You can subtract in columns when the top digit is big enough. Now you’ll learn what to do when it isn’t, by borrowing from the next place value. This helps you avoid getting stuck in the ones place.","before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770964113/segments/qKxQ33KcRWQ_314_585/before-you-start.mp3","before_you_start_avatar_video_url":"","concepts_taught":["When regrouping is needed in subtraction (bottom digit larger than top)","Regrouping/borrowing from the tens to the ones","Turning 1 ten into 10 ones (e.g., 2 tens 2 ones becomes 1 ten 12 ones)","Applying the standard algorithm after regrouping","Worked examples with regrouping (22 − 17, 43 − 25)"],"duration_seconds":270.79999999999995,"learning_outcomes":["Identify when regrouping is needed in a subtraction problem (bottom digit > top digit in a column)","Regroup by borrowing 1 ten from the tens column and adding 10 to the ones column","Solve 2-digit subtraction problems that require regrouping using the standard algorithm","Explain in simple words what happened during regrouping (a ten became ten ones)"],"micro_concept_id":"subtract_regrouping_standard","prerequisites":["Understand ones and tens place value","Be able to subtract within 20 (including 12 − 7, 13 − 5)","Know the basic column subtraction steps (ones then tens)"],"quality_score":7.7749999999999995,"segment_id":"qKxQ33KcRWQ_314_585","sequence_number":6.0,"title":"Borrow to Subtract When Needed","transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"qKxQ33KcRWQ_101_327","overall_transition_score":8.8,"to_segment_id":"qKxQ33KcRWQ_314_585","pedagogical_progression_score":8.5,"vocabulary_consistency_score":9.0,"knowledge_building_score":9.0,"transition_explanation":"Keeps the same subtraction steps but adds the new skill of regrouping when the top digit is smaller."},"url":"https://www.youtube.com/watch?v=qKxQ33KcRWQ&t=314s","video_duration_seconds":679.0},{"before_you_start":"Borrowing works the same way even when numbers have many digits. In this video, you’ll practice stacking multi-digit numbers carefully, subtracting from right to left, and regrouping when a top digit is smaller than the one below it.","before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770964113/segments/cLHu-zuTPk8_19_419/before-you-start.mp3","before_you_start_avatar_video_url":"","concepts_taught":["Subtraction order matters (not commutative)","Place value alignment when stacking numbers","Standard algorithm for multi-digit subtraction","Regrouping/borrowing from tens and hundreds","Writing the difference in the correct place-value columns","Checking work by moving right-to-left through columns (ones to higher places)"],"duration_seconds":399.68,"learning_outcomes":["Stack two whole numbers so each place value lines up correctly","Start subtraction in the ones column and move left","Regroup (borrow) from the next place-value column when needed","Solve multi-digit subtraction problems (3–4 digits here) using the standard algorithm","Explain what borrowing means using place-value language (e.g., 1 ten = 10 ones)"],"micro_concept_id":"subtract_regrouping_standard","prerequisites":["Know place value (ones, tens, hundreds, thousands)","Know basic subtraction facts within 20","Understand how to write numbers in columns (vertical format)"],"quality_score":7.825,"segment_id":"cLHu-zuTPk8_19_419","sequence_number":7.0,"title":"Subtract Multi-Digit Numbers with Regrouping","transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"qKxQ33KcRWQ_314_585","overall_transition_score":8.9,"to_segment_id":"cLHu-zuTPk8_19_419","pedagogical_progression_score":8.5,"vocabulary_consistency_score":9.0,"knowledge_building_score":9.5,"transition_explanation":"Takes the regrouping idea from two digits and applies it to larger numbers with more place-value columns."},"url":"https://www.youtube.com/watch?v=cLHu-zuTPk8&t=19s","video_duration_seconds":457.0},{"before_you_start":"You can regroup when you need more in a column. Now you’ll handle the tricky case with zeros, where you can’t borrow from a zero right away. You’ll learn how the zeros change as you borrow from farther left.","before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770964113/segments/7rLFrT2BQ00_9_312/before-you-start.mp3","before_you_start_avatar_video_url":"","concepts_taught":["Standard algorithm for multi-digit subtraction","Regrouping (borrowing) across zeros","Place value reasoning (hundreds → tens → ones)","Checking each place from right to left (ones, tens, hundreds)","Avoiding regrouping mistakes when a digit is 0"],"duration_seconds":303.15000000000003,"learning_outcomes":["Set up a subtraction problem vertically with correct place-value alignment","Explain why you cannot subtract when the top digit is smaller than the bottom digit in a place","Regroup across a zero by borrowing from the next place to the left first (hundreds → tens), then borrowing again (tens → ones)","Correctly complete 3-digit subtraction problems like 700 − 258 using the standard algorithm"],"micro_concept_id":"subtract_across_zeros","prerequisites":["Understanding place value (ones, tens, hundreds)","Basic subtraction facts within 20","Knowing that regrouping means trading 1 ten for 10 ones (and 1 hundred for 10 tens)","How to line up numbers by place value in vertical subtraction"],"quality_score":7.87,"segment_id":"7rLFrT2BQ00_9_312","sequence_number":8.0,"title":"Subtract Across Zeros Step by Step","transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"cLHu-zuTPk8_19_419","overall_transition_score":8.8,"to_segment_id":"7rLFrT2BQ00_9_312","pedagogical_progression_score":8.5,"vocabulary_consistency_score":9.0,"knowledge_building_score":9.0,"transition_explanation":"Builds on multi-digit regrouping and zooms in on the toughest version: borrowing when there are zeros in the middle."},"url":"https://www.youtube.com/watch?v=7rLFrT2BQ00&t=9s","video_duration_seconds":325.0},{"before_you_start":"You can subtract big numbers, even across zeros, using the standard algorithm. Now you’ll read story problems and decide when subtraction fits the situation. Then you’ll write the equation and solve it, checking that the answer makes sense.","before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770964113/segments/tuVI8Uv0SAI_291_581/before-you-start.mp3","before_you_start_avatar_video_url":"","concepts_taught":["Using key words to choose subtraction (left, remaining, taken out)","Interpreting situations as ‘take away to find what’s left’","Understanding ‘now’ can mean subtraction when something was given away","Writing subtraction equations from story contexts"],"duration_seconds":290.75,"learning_outcomes":["Identify clue words that usually signal subtraction in a word problem","Explain why the problem should be modeled with subtraction (start amount minus removed amount)","Write and solve a subtraction equation from a simple story situation"],"micro_concept_id":"subtraction_word_problems_6digit","prerequisites":["Understanding subtraction as take away / find what’s left","Ability to subtract 2- and 3-digit numbers (basic fluency)"],"quality_score":7.9399999999999995,"segment_id":"tuVI8Uv0SAI_291_581","sequence_number":9.0,"title":"Choose Subtraction in Word Problems","transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"7rLFrT2BQ00_9_312","overall_transition_score":8.6,"to_segment_id":"tuVI8Uv0SAI_291_581","pedagogical_progression_score":8.5,"vocabulary_consistency_score":9.0,"knowledge_building_score":8.5,"transition_explanation":"Moves from the hardest subtraction procedure (across zeros) to applying subtraction in real stories, where the main challenge is choosing the correct operation."},"url":"https://www.youtube.com/watch?v=tuVI8Uv0SAI&t=291s","video_duration_seconds":582.0}],"selection_strategy":"Built a single, step-by-step path that follows the micro-concepts and the learner’s requested order (addition skills, addition word problems, subtraction skills, subtraction word problems). To reduce cognitive load, the course starts with lining up place values, then teaches the standard algorithm in small numbers and scales the same steps to larger numbers (up to six digits). Subtraction is scaffolded from simple two-digit structure to regrouping and then to the hard edge case of subtracting across zeros.","strengths":["Directly targets the most common Grade 4 mistakes: misalignment, missed carries, and borrowing across zeros","Strong progression from simple structure to complex edge cases","Word-problem lessons emphasize understanding the situation, not only keywords"],"target_difficulty":"intermediate","title":"Add and Subtract Up to 999,999","tradeoffs":[],"updated_at":"2026-03-05T08:39:57.344060+00:00","user_id":"google_109800265000582445084"}}