{"success":true,"course":{"all_concepts_covered":["Reading decimals using models and a place value chart","Saying and writing decimals with place value names","Finding a digit’s place and value","Writing numbers in expanded form","Connecting decimal places to fractional parts (tenths, hundredths, thousandths)","Equivalent decimals and trailing zeros","Regrouping and decomposing using the ×10 pattern"],"assembly_rationale":"The course begins with concrete base-ten models so students have a reliable counting-and-grouping strategy, then transfers that strategy to decimal models and placeholder zeros. Next, it builds accurate place-value language and digit-place identification, which are prerequisites for expanded form. Finally, it connects decimals to fractional parts and equivalence (trailing zeros), then closes with the ×10 structure used to regroup and decompose decimals in multiple ways. Total runtime is limited by the provided segment library, but the sequence is designed to maximize coverage and minimize confusion.","average_segment_quality":7.303125,"concept_key":"CONCEPT#6ba8653032588e6f8ba9fa77fb50f382","considerations":["The available library has limited direct instruction on writing expanded form specifically with decimal values (0.1, 0.01, 0.001) and with unit-fraction expressions (n × 1/10, etc.); students may need extra teacher-led examples or practice worksheets for those exact formats.","Total video time is ~35 minutes because only 8 self-contained segments are available; add practice time (10–20 minutes) after the videos to reach a full lesson block."],"course_id":"course_1770911828","created_at":"2026-02-12T16:16:02.630520+00:00","created_by":"Shaunak Ghosh","description":"You will learn to read and write decimals up to thousandths using models, place value words, and charts. You will also practice writing decimals in expanded form, connecting decimals to fractions, spotting equivalent decimals with trailing zeros, and decomposing decimals in more than one way.","estimated_total_duration_minutes":35.0,"final_learning_outcomes":["Read and write decimals up to thousandths using place value meaning, not digit-by-digit reading.","Use models and a place value chart to write decimals correctly, including zeros as placeholders (like 3.04).","Identify the place and value of digits in whole numbers (to thousands) and decimals (to thousandths).","Write and recognize expanded form representations and connect decimal places to tenths, hundredths, and thousandths.","Explain and use equivalence rules, including trailing zeros and regrouping across places by factors of 10."],"generated_at":"2026-02-12T16:15:15Z","generation_error":null,"generation_progress":100.0,"generation_status":"completed","generation_step":"completed","generation_time_seconds":339.5471360683441,"image_description":"Create a clean, modern thumbnail for a Grade 5 decimals course. Center focal point: a large, friendly place value chart that clearly shows Ones | . | Tenths | Hundredths | Thousandths, with the number 3.04 placed in the chart (highlight the 0 in the tenths place to emphasize the placeholder). To the left, show simple base-ten blocks in an isometric style: one “flat” square, one “rod,” and a few small “unit cubes,” arranged neatly with soft shadows to create depth. To the right, show a small set of equivalent decimals stacked vertically, like 0.7, 0.70, 0.700, with a subtle equals sign to suggest “same value.” Use a two-color palette: bright blue (#2D7FF9) and fresh green (#34C759) on a light background gradient (white to very pale blue). Keep shapes crisp with rounded corners and minimal text. Add gentle highlights and a slight vignette for premium depth. Leave clear space at the top for the course title.","image_url":"https://course-builder-course-thumbnails.s3.us-east-1.amazonaws.com/courses/course_1770911828/thumbnail.png","interleaved_practice":[{"difficulty":"mastery","correct_option_index":1.0,"question":"A student says, “0.700 is bigger than 0.70 because it has more digits.” Which explanation best fixes the mistake using place value?","option_explanations":["Incorrect because the size of thousandths vs hundredths doesn’t make 0.700 larger; it’s still 7 tenths.","Correct! Adding a zero in the thousandths place means “0 more thousandths,” so 0.70 and 0.700 name the same value.","Incorrect because the number of decimal places doesn’t multiply the value; place value names the unit size.","Incorrect because a zero digit doesn’t automatically make a number smaller; it depends on its place and what it replaces."],"options":["0.700 is bigger because thousandths are smaller than hundredths, so you need more of them.","0.700 and 0.70 are equal because adding zeros to the right of a decimal doesn’t change the value.","0.700 is bigger because three decimal places means three times as much.","0.700 is smaller because the last digit is 0, and zeros always make a number smaller."],"question_id":"q1_equiv_trailing_zeros","related_micro_concepts":["equivalent_decimals","decimal_digit_values"],"discrimination_explanation":"Option B is correct because trailing zeros to the right of the decimal are just extra place-value spots with zero of that unit, so the amount stays the same. The other choices misuse the idea of place size or treat “more digits” as “more value,” which is the exact misconception."},{"difficulty":"mastery","correct_option_index":2.0,"question":"You measure a ribbon as 3 ones and 4 hundredths. There are 0 tenths. What is the correct decimal?","option_explanations":["Incorrect because 3.004 would mean 4 thousandths, not 4 hundredths.","Incorrect because 3.4 means 3 ones and 4 tenths, not 4 hundredths.","Correct! The 0 tenths must be shown as a placeholder, so the 4 can sit in the hundredths place: 3.04.","Incorrect because 3.40 means 3 ones and 4 tenths (or 40 hundredths), not 4 hundredths."],"options":["3.004","3.4","3.04","3.40"],"question_id":"q2_missing_zero_placeholder","related_micro_concepts":["decimal_place_value_models","decimal_digit_values"],"discrimination_explanation":"3 ones and 4 hundredths means the tenths place must be 0, so the number is 3.04. The other answers either skip the placeholder zero (changing the value), put the 4 in the thousandths place, or change the meaning to 40 hundredths."},{"difficulty":"mastery","correct_option_index":0.0,"question":"In the decimal 0.154, which digit is in the ones place?","option_explanations":["Correct! The ones digit is the digit immediately left of the decimal point, which is 0.","Incorrect because 1 is in the tenths place.","Incorrect because 5 is in the hundredths place.","Incorrect because 4 is in the thousandths place."],"options":["0","1","5","4"],"question_id":"q3_digit_in_named_place","related_micro_concepts":["decimal_digit_values"],"discrimination_explanation":"The ones place is just left of the decimal point. In 0.154, the digit left of the decimal is 0, even though there are digits to the right. The other digits are tenths, hundredths, and thousandths digits."},{"difficulty":"mastery","correct_option_index":3.0,"question":"A base-ten model uses this rule: 1 small cube = 0.01. The model shows 3 rods (each rod is 10 cubes) and 4 small cubes. What decimal does the model represent?","option_explanations":["Incorrect because 3.4 treats the rods as whole ones and the cubes as tenths, which doesn’t match the given unit.","Incorrect because 0.304 would mean 3 tenths and 4 thousandths, but the cubes are hundredths here.","Incorrect because 0.034 would mean 3 hundredths and 4 thousandths, but rods are tenths in this model.","Correct! 3 rods = 0.30 and 4 cubes = 0.04, so the total is 0.34."],"options":["3.4","0.304","0.034","0.34"],"question_id":"q4_base_ten_unit_switch","related_micro_concepts":["decimal_place_value_models","decimal_digit_values"],"discrimination_explanation":"If one cube is 0.01, then one rod (10 cubes) is 0.10. Three rods make 0.30, and four cubes make 0.04, totaling 0.34. The distractors come from misplacing the digits or treating rods as whole ones."},{"difficulty":"mastery","correct_option_index":3.0,"question":"Which expanded form with decimals matches 4.506?","option_explanations":["Incorrect because it leaves out the 0 hundredths term, which changes how you track the places.","Incorrect because 5 is not in the hundredths place; in 4.506, the hundredths digit is 0.","Incorrect because expanded form uses single digits for each place; 50 × 0.01 is not matching the digit 5 in the tenths place.","Correct! It matches 5 tenths (0.1), keeps 0 hundredths (0.01), and shows 6 thousandths (0.001)."],"options":["4 × 1 + 5 × 0.1 + 6 × 0.01","4 × 1 + 5 × 0.01 + 6 × 0.001","4 × 1 + 50 × 0.01 + 6 × 0.001","4 × 1 + 5 × 0.1 + 0 × 0.01 + 6 × 0.001"],"question_id":"q5_expanded_form_decimals_synthesis","related_micro_concepts":["expanded_form_decimals","decimal_digit_values"],"discrimination_explanation":"4.506 has 5 tenths, 0 hundredths, and 6 thousandths. Option B matches each digit to its place value and keeps the needed zero placeholder. The others misplace the 5, drop the zero hundredths, or use a two-digit factor (50), which breaks place-value meaning."},{"difficulty":"mastery","correct_option_index":2.0,"question":"Which fraction-expanded form matches 3.47?","option_explanations":["Incorrect because 3.47 has hundredths, not thousandths; 7 belongs with 1/100, not 1/1000.","Incorrect because it swaps tenths and hundredths (4 is tenths, 7 is hundredths in 3.47).","Correct! 4 tenths is 4 × 1/10 and 7 hundredths is 7 × 1/100.","Incorrect because 0.47 is not the same as 47 hundredths added to 3 in this place-value matching format; it doesn’t show tenths and hundredths separately."],"options":["3 × 1 + 4 × 1/10 + 7 × 1/1000","3 × 1 + 4 × 1/100 + 7 × 1/10","3 × 1 + 4 × 1/10 + 7 × 1/100","3 × 1 + 47 × 1/100"],"question_id":"q6_unit_fraction_match","related_micro_concepts":["expanded_form_fractions","decimal_digit_values"],"discrimination_explanation":"3.47 means 3 ones, 4 tenths, and 7 hundredths. Option C matches tenths to 1/10 and hundredths to 1/100. The distractors swap place values, combine digits into 47 hundredths, or put 7 in the thousandths place."},{"difficulty":"mastery","correct_option_index":1.0,"question":"Which is the best correct word name for 12.305?","option_explanations":["Incorrect because it changes 0.305 into 0.035 (thirty-five thousandths).","Correct! 12.305 is twelve and three hundred five thousandths, because the last digit is in the thousandths place.","Incorrect because “point three zero five” is a common way to say it, but it’s not the place-value word name expected for this standard.","Incorrect because 0.305 is not “three thousand five hundredths”; that would be 3.05."],"options":["Twelve and thirty-five thousandths","Twelve and three hundred five thousandths","Twelve point three zero five","Twelve and three thousand five hundredths"],"question_id":"q7_word_name_to_standard","related_micro_concepts":["decimal_number_names","decimal_digit_values"],"discrimination_explanation":"12.305 has three decimal places, so the last place is thousandths. The digits 305 mean “three hundred five thousandths.” Other options either use the wrong ending place, read digit-by-digit, or change 305 to 35."},{"difficulty":"mastery","correct_option_index":0.0,"question":"A teacher writes: 8 ones + 17 hundredths + 6 thousandths. What is the decimal in standard form?","option_explanations":["Correct! 17 hundredths = 0.17 and 6 thousandths = 0.006, so the decimal part is 0.176, giving 8.176.","Incorrect because 8.1706 has four decimal places and places the 6 in the ten-thousandths place.","Incorrect because it swaps the tenths/hundredths/thousandths order and doesn’t match 0.176.","Incorrect because 8.167 treats 17 hundredths as if it were 16 hundredths and 7 thousandths; it doesn’t match the given decomposition."],"options":["8.176","8.1706","8.716","8.167"],"question_id":"q8_decompose_and_regroup","related_micro_concepts":["decomposing_decimals_multiple_ways","decimal_digit_values"],"discrimination_explanation":"17 hundredths is 0.17 and 6 thousandths is 0.006, so together they make 0.176. Add 8 ones to get 8.176. The distractors come from swapping digits, putting digits in the wrong places, or ignoring that 6 thousandths needs three decimal places."}],"is_public":true,"key_decisions":["Segment eC1dPiC9PyM_240_608: Chosen first to ground everything in reading base-ten models (tens/ones) before moving to decimal models, matching the ‘blocks and counting’ part of the standard.","Segment KrAQneGhyuE_185_423: Chosen next because it directly teaches reading decimals from models and using zeros as placeholders, a key Grade 5 pitfall.","Segment LFO07qWWtrs_31_257: Placed here to shift from pictures to spoken/real-life reading of decimals, preparing students for correct number names.","Segment Ju3kQjmcH5g_15_378: Used to sharpen the skill ‘Which digit is in which place?’ using a chart idea students can extend to decimal places.","Segment 4AF7xj7pmWc_8_250: Included as the only expanded-form-focused segment available; placed after digit-place work so students can “stretch” a number using place values.","Segment KrAQneGhyuE_0_185: Placed after expanded form to connect decimal places to fractional parts of a whole (tenths/hundredths/thousandths) and the ×10 relationship needed for later regrouping.","Segment LFO07qWWtrs_258_462: Selected because it explicitly targets the major misconception that trailing zeros change a decimal’s value.","Segment MloZcl1JJEI_1_255: Final segment to reinforce the ‘ten times’ pattern so students can regroup and decompose decimals in multiple equivalent ways."],"micro_concepts":[{"prerequisites":[],"learning_outcomes":["Identify ones, tenths, and hundredths places in a decimal model","Count cubes, rods, and flats to find a decimal value","Use a stated unit (e.g., cube = 0.01) to find rod and flat values","Write a decimal to hundredths from ones/tenths/hundredths counts, using 0 as a placeholder"],"difficulty_level":"beginner","concept_id":"decimal_place_value_models","name":"Decimal place value with base-ten blocks","description":"Use base-ten models (flats, rods, cubes) to represent decimals. Practice counting blocks, using the given unit (like 1 cube = 0.01), and writing a decimal to hundredths using zeros for missing places.","sequence_order":0.0},{"prerequisites":["decimal_place_value_models"],"learning_outcomes":["Read decimals to thousandths using place value words (example: 12.305)","Write a decimal from a correct word name","Write a correct word name from a decimal","Avoid common word-form mistakes (like saying 'ten tenths' or skipping place value names)"],"difficulty_level":"beginner","concept_id":"decimal_number_names","name":"Decimal number names to thousandths","description":"Learn to read and write decimals to thousandths in word form and standard form. Use correct place value names (tenths, hundredths, thousandths) instead of incorrect phrases like “twenty-one tenths.”","sequence_order":1.0},{"prerequisites":["decimal_number_names"],"learning_outcomes":["Name the place of a digit in a decimal (example: the 7 is in the thousandths place)","Identify the digit in a named place (example: ones digit in 0.154 is 0)","Explain the difference between a digit’s face value and its place value","Use zeros correctly when a place is missing (like 3.04)"],"difficulty_level":"beginner","concept_id":"decimal_digit_values","name":"Find digit values in decimals","description":"Practice two skills: (1) name the place of a digit in a decimal, and (2) tell which digit is in a given place. Work with whole numbers up to thousands and decimals to thousandths.","sequence_order":2.0},{"prerequisites":["decimal_digit_values"],"learning_outcomes":["Write a decimal to thousandths in expanded form with decimals","Match each digit to its decimal value (tenths = 0.1, hundredths = 0.01, thousandths = 0.001)","Convert expanded form back to standard form correctly","Keep zeros when needed in the middle (example: 4.506)"],"difficulty_level":"beginner","concept_id":"expanded_form_decimals","name":"Expanded form using decimal values","description":"Write decimals to thousandths in expanded form using decimal values (0.1, 0.01, 0.001). Use single-digit factors for each place and avoid endings like 5.230 (write 5.23).","sequence_order":3.0},{"prerequisites":["expanded_form_decimals"],"learning_outcomes":["Match decimal places to unit fractions (0.1 = 1/10, etc.)","Write a decimal to thousandths in expanded form using fractions","Interpret n × 1/10, n × 1/100, and n × 1/1000 correctly","Convert fraction expanded form back to standard decimal form"],"difficulty_level":"beginner","concept_id":"expanded_form_fractions","name":"Expanded form using unit fractions","description":"Write decimals to thousandths in expanded form using unit fractions (1/10, 1/100, 1/1000). Read and understand expressions like 7 × 1/100 as “seven hundredths.”","sequence_order":4.0},{"prerequisites":["expanded_form_fractions"],"learning_outcomes":["Explain why trailing zeros to the right of the decimal do not change value","Identify pairs/groups of equivalent decimals (example: 3.4 = 3.40)","Use place value reasoning to justify equivalence (not guessing)","Compare decimals more accurately by aligning place values"],"difficulty_level":"beginner","concept_id":"equivalent_decimals","name":"Equivalent decimals and trailing zeros","description":"Learn why decimals like 0.70, 0.700, and 0.7000 are equal. Practice identifying equivalent decimals (up to thousandths) and avoid the mistake of thinking extra zeros change the value.","sequence_order":5.0},{"prerequisites":["equivalent_decimals"],"learning_outcomes":["Decide which expanded forms are equal to a given decimal","Use the idea 10 thousandths = 1 hundredth (and similar) to regroup","Convert word-based decompositions into standard decimal form","Write at least two different decompositions for the same decimal"],"difficulty_level":"beginner","concept_id":"decomposing_decimals_multiple_ways","name":"Decompose decimals in more than one way","description":"Break a decimal into different equal expanded forms and place-value word decompositions (like 8 ones + 17 hundredths + 6 thousandths). Use the idea that 10 of one place equals 1 of the place to the left.","sequence_order":6.0}],"overall_coherence_score":8.3,"pedagogical_soundness_score":7.8,"prerequisites":["Whole-number place value (ones, tens, hundreds, thousands)","Comfort counting by tens and ones","Understanding that a whole can be split into equal parts","Basic money sense (dollars and cents)"],"rejected_segments_rationale":"No segments were rejected because the library is small and we needed maximum coverage. However, some micro-concepts (especially writing decimals in expanded form with decimal values and expanded form with unit fractions) are only partially supported by the available videos; the course relies on combining ideas across segments to meet those targets.","segments":[{"duration_seconds":367.35333333333324,"concepts_taught":["Place value determines a digit’s value","Ones place vs tens place","Tens are 10 times ones","Using base-ten-like models to represent numbers","Organizing counting with a tens/ones T-chart"],"quality_score":6.875,"before_you_start":"You already know how to count and group objects. In this video, you’ll use models with tens and ones to build numbers. This will help you later when the model pieces stand for tenths and hundredths in decimals.","title":"Read Base-Ten Models: Tens and Ones","before_you_start_avatar_video_url":"","url":"https://www.youtube.com/watch?v=eC1dPiC9PyM&t=240s","sequence_number":1.0,"prerequisites":["Counting to 100","Understanding that 10 ones make 1 ten","Basic addition/counting on"],"learning_outcomes":["Explain why a digit’s value changes based on its place","Find the value of a digit in the tens and ones places","Read a simple base-ten-style model and write the correct whole number","Use a tens/ones T-chart to organize place value information"],"video_duration_seconds":793.0,"transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"","overall_transition_score":0.0,"to_segment_id":"eC1dPiC9PyM_240_608","pedagogical_progression_score":0.0,"vocabulary_consistency_score":0.0,"knowledge_building_score":0.0,"transition_explanation":"N/A (first segment)"},"before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770911828/segments/eC1dPiC9PyM_240_608/before-you-start.mp3","segment_id":"eC1dPiC9PyM_240_608","micro_concept_id":"decimal_place_value_models"},{"duration_seconds":237.60259016393445,"concepts_taught":["Real-world contexts where decimals appear (money, time, measurements)","Using a place value chart to organize decimal places","Identifying tenths/hundredths/thousandths positions (names end in -ths)","Reading a shaded model as a decimal (e.g., 2/10 → 0.2)","Writing a zero as a placeholder (e.g., 6 hundredths → 0.06)","Representing a decimal by drawing/shading tenths or hundredths models","Quick independent practice identifying decimals from models"],"quality_score":8.4,"before_you_start":"Now that you can read a model by counting groups, you’re ready to change what “one piece” means. In this video, you’ll use a place value chart and shaded models to write decimals, including using 0 when a place is missing.","title":"Read Decimals from Shaded Models","before_you_start_avatar_video_url":"","url":"https://www.youtube.com/watch?v=KrAQneGhyuE&t=185s","sequence_number":2.0,"prerequisites":["Understanding that tenths/hundredths/thousandths are equal parts of 1 whole","Comfort counting shaded parts in a simple model"],"learning_outcomes":["Use a place value chart to decide whether a model represents tenths, hundredths, or thousandths","Write a decimal that matches a model, including using 0 as a placeholder (e.g., 0.06)","Explain why 0.06 is different from 0.6 based on place value","Draw/shade a tenths or hundredths model to represent a given decimal like 0.7 or 0.21"],"video_duration_seconds":425.0,"transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"eC1dPiC9PyM_240_608","overall_transition_score":8.7,"to_segment_id":"KrAQneGhyuE_185_423","pedagogical_progression_score":8.5,"vocabulary_consistency_score":8.5,"knowledge_building_score":9.0,"transition_explanation":"Builds on reading tens/ones models, then transfers the same counting-and-grouping idea to tenths and hundredths in decimal models."},"before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770911828/segments/KrAQneGhyuE_185_423/before-you-start.mp3","segment_id":"KrAQneGhyuE_185_423","micro_concept_id":"decimal_place_value_models"},{"duration_seconds":225.20000000000002,"concepts_taught":["Decimal point separates whole and part","Writing money amounts as decimals (0.50)","Decimals represent amounts less than 1 or between whole numbers","Connecting 0.5 to one-half (informal equivalence)","Reading simple decimals (tenths) in context"],"quality_score":7.625,"before_you_start":"You’ve seen decimals in pictures and charts. Next, you’ll connect decimals to real life, like money and amounts between whole numbers. Listen for how the decimal point separates the whole number part from the part of a whole.","title":"What Decimals Mean in Real Life","before_you_start_avatar_video_url":"","url":"https://www.youtube.com/watch?v=LFO07qWWtrs&t=31s","sequence_number":3.0,"prerequisites":["Understanding of whole numbers","Basic money knowledge (dollars and cents)","Basic fraction idea of one-half (helpful but not required)"],"learning_outcomes":["Identify the decimal point and explain its job in a number","Write 50 cents as 0.50 and explain why there is a 0 in the ones place","Interpret simple decimals like 1.5 or 2.5 as “and a half” in real-world examples"],"video_duration_seconds":936.0,"transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"KrAQneGhyuE_185_423","overall_transition_score":8.1,"to_segment_id":"LFO07qWWtrs_31_257","pedagogical_progression_score":8.0,"vocabulary_consistency_score":8.5,"knowledge_building_score":8.0,"transition_explanation":"Moves from visual models to real-world meaning and reading decimals, helping students attach number names to what they just wrote from models."},"before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770911828/segments/LFO07qWWtrs_31_257/before-you-start.mp3","segment_id":"LFO07qWWtrs_31_257","micro_concept_id":"decimal_number_names"},{"duration_seconds":362.9343333333333,"concepts_taught":["Digit (0–9) definition","Place value idea: a digit’s value depends on its position","Ones, tens, hundreds places and their values","Reading numbers using place value (e.g., 567 as 500 + 60 + 7)","Locating digits in a place value chart","Extending place value beyond hundreds (thousands to billions)","Quick checks/quiz to identify digits in places"],"quality_score":6.824999999999999,"before_you_start":"Now that decimals make sense as parts of a whole, it’s time to zoom in on each digit. In this video, you’ll use a place value chart to name a digit’s place and explain what that digit is really worth.","title":"Find a Digit’s Place and Value","before_you_start_avatar_video_url":"","url":"https://www.youtube.com/watch?v=Ju3kQjmcH5g&t=15s","sequence_number":4.0,"prerequisites":["Understanding of counting and basic whole numbers","Knowing that 10 ones make 1 ten and 10 tens make 1 hundred (basic base-ten idea)"],"learning_outcomes":["Define what a digit is","Explain what place value means (a digit’s value depends on its position)","Identify the ones, tens, and hundreds digits in a whole number","State the value of a digit in a whole number (e.g., 8 tens = 80)","Rewrite a 3-digit number in expanded form as a sum (e.g., 567 = 500 + 60 + 7)","Recognize the repeating place-value naming pattern into larger whole numbers (thousands, millions, billions)"],"video_duration_seconds":393.0,"transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"LFO07qWWtrs_31_257","overall_transition_score":8.2,"to_segment_id":"Ju3kQjmcH5g_15_378","pedagogical_progression_score":8.0,"vocabulary_consistency_score":8.0,"knowledge_building_score":8.5,"transition_explanation":"Builds from reading decimals in context to analyzing exactly where each digit lives on a place value chart."},"before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770911828/segments/Ju3kQjmcH5g_15_378/before-you-start.mp3","segment_id":"Ju3kQjmcH5g_15_378","micro_concept_id":"decimal_digit_values"},{"before_you_start":"You can find a digit’s place and value, so you’re ready to “stretch” a number apart. This video shows how to write expanded form using place values. After this, you can use the same idea with tenths and hundredths, too.","before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770911828/segments/4AF7xj7pmWc_8_250/before-you-start.mp3","before_you_start_avatar_video_url":"","concepts_taught":["Standard form vs expanded form (whole numbers)","Place value determines digit value (hundreds, tens, ones)","Writing numbers as sums of place values (e.g., 300 + 50 + 8)","Recombining expanded form back to standard form","Using plus signs correctly in expanded form"],"duration_seconds":241.99,"learning_outcomes":["Identify the hundreds, tens, and ones digits in a whole number","State the value of a digit based on its place (e.g., 5 tens = 50)","Write a 3-digit whole number in expanded form as a sum","Convert from expanded form back to standard form by adding"],"micro_concept_id":"expanded_form_decimals","prerequisites":["Understanding of ones, tens, and hundreds place value","Comfort with addition of whole numbers"],"quality_score":6.925000000000001,"segment_id":"4AF7xj7pmWc_8_250","sequence_number":5.0,"title":"Stretch Numbers into Expanded Form","transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"Ju3kQjmcH5g_15_378","overall_transition_score":8.5,"to_segment_id":"4AF7xj7pmWc_8_250","pedagogical_progression_score":8.5,"vocabulary_consistency_score":8.5,"knowledge_building_score":8.5,"transition_explanation":"Uses the place-value idea from the last segment, then turns it into a new way to write numbers: expanded form."},"url":"https://www.youtube.com/watch?v=4AF7xj7pmWc&t=8s","video_duration_seconds":251.0},{"duration_seconds":185.393,"concepts_taught":["Definition of decimals and decimal point","Whole-number side vs decimal side of a number","Tenths, hundredths, thousandths as partitions of 1 whole","Counting tenths/hundredths/thousandths in a model","Base-10 relationship across places (10 tenths = 1 whole; 10 hundredths = 1 tenth; 10 thousandths = 1 hundredth)","Connecting decimals to fractions (as “decimal fractions”)"],"quality_score":7.625,"before_you_start":"Expanded form is about matching each digit to its place value. Now you’ll learn the names of the decimal places, tenths, hundredths, and thousandths, and how each place is 10 times smaller. This helps you connect decimals to fractions like 1/10.","title":"Tenths, Hundredths, and Thousandths Places","before_you_start_avatar_video_url":"","url":"https://www.youtube.com/watch?v=KrAQneGhyuE&t=0s","sequence_number":6.0,"prerequisites":["Basic whole-number place value (ones, tens, hundreds)","Understanding that a whole can be split into equal parts"],"learning_outcomes":["Explain what the decimal point tells you about a number","Describe what tenths, hundredths, and thousandths mean using a partitioned whole","Use the idea ‘each place to the right is 10× smaller’ to relate tenths, hundredths, and thousandths","Recognize equivalences like 10/10 = 1 whole and 10 thousandths = 1 hundredth"],"video_duration_seconds":425.0,"transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"4AF7xj7pmWc_8_250","overall_transition_score":8.1,"to_segment_id":"KrAQneGhyuE_0_185","pedagogical_progression_score":8.0,"vocabulary_consistency_score":8.5,"knowledge_building_score":8.0,"transition_explanation":"Builds on expanded form by clarifying what the decimal place-value units mean, which is needed to write expanded form with tenths, hundredths, and thousandths."},"before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770911828/segments/KrAQneGhyuE_0_185/before-you-start.mp3","segment_id":"KrAQneGhyuE_0_185","micro_concept_id":"expanded_form_fractions"},{"duration_seconds":204.07999999999998,"concepts_taught":["Writing 10 cents as 0.10","Tenths as one-tenth (0.1 = 1/10) in context","Equivalent decimals with trailing zeros (0.10 = 0.1; 0.50 = 0.5)","Visual tenths model: 10 equal parts in a circle","Counting tenths in decimal form (0.1, 0.2, 0.3, 0.4)"],"quality_score":7.575,"before_you_start":"You know decimal places and how they change by tens. Now you’ll tackle a super common mistake, thinking extra zeros change a decimal. This video shows why 0.1, 0.10, and 0.100 are the same value.","title":"Trailing Zeros Make Equal Decimals","before_you_start_avatar_video_url":"","url":"https://www.youtube.com/watch?v=LFO07qWWtrs&t=258s","sequence_number":7.0,"prerequisites":["Basic money knowledge (dime = 10 cents)","Understanding that a whole can be split into equal parts"],"learning_outcomes":["Explain why 0.10 and 0.1 represent the same amount","Recognize that trailing zeros to the right of a decimal do not change value","Use a tenths model to name shaded parts as decimals (0.1 to 0.4)"],"video_duration_seconds":936.0,"transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"KrAQneGhyuE_0_185","overall_transition_score":8.3,"to_segment_id":"LFO07qWWtrs_258_462","pedagogical_progression_score":8.0,"vocabulary_consistency_score":8.5,"knowledge_building_score":8.5,"transition_explanation":"Uses the tenths idea from the previous segment, then applies it to prove when decimals are equivalent."},"before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770911828/segments/LFO07qWWtrs_258_462/before-you-start.mp3","segment_id":"LFO07qWWtrs_258_462","micro_concept_id":"equivalent_decimals"},{"duration_seconds":253.301,"concepts_taught":["Base-ten place value structure (ones, tens, hundreds, thousands...)","Each place value is 10 times the place to its right","Counting and grouping in powers of 10","Reading and naming large whole numbers up to millions (and beyond)"],"quality_score":6.574999999999999,"before_you_start":"You’ve learned that zeros can be added without changing a decimal’s value. Next, you’ll use the rule that each place is 10 times the next one. This lets you trade, regroup, and write the same decimal in different ways.","title":"Regroup by Tens to Decompose Decimals","before_you_start_avatar_video_url":"","url":"https://www.youtube.com/watch?v=MloZcl1JJEI&t=1s","sequence_number":8.0,"prerequisites":["Counting to 1,000","Understanding that 10 of something can be regrouped into 1 larger unit (e.g., 10 ones = 1 ten)"],"learning_outcomes":["Explain why regrouping happens at 10 (10 ones = 1 ten, 10 tens = 1 hundred, etc.)","Identify that each place to the left is 10× larger than the place to the right (for whole numbers)","Use a place value chart idea to organize large whole numbers (ones, thousands, millions)"],"video_duration_seconds":259.0,"transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"LFO07qWWtrs_258_462","overall_transition_score":8.0,"to_segment_id":"MloZcl1JJEI_1_255","pedagogical_progression_score":8.0,"vocabulary_consistency_score":8.0,"knowledge_building_score":8.0,"transition_explanation":"Extends equivalence from ‘adding zeros’ to ‘regrouping across places,’ using the same base-ten, ×10 structure."},"before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770911828/segments/MloZcl1JJEI_1_255/before-you-start.mp3","segment_id":"MloZcl1JJEI_1_255","micro_concept_id":"decomposing_decimals_multiple_ways"}],"selection_strategy":"Use the highest-quality, kid-friendly decimal segments as the spine (Doodles and Digits + Homeschool Pop), then fill unavoidable content gaps (expanded form, regrouping) with short, Grade-appropriate whole-number place-value segments that transfer directly to decimals. Keep one clear purpose per segment to avoid redundancy, and sequence from concrete models → place-value language → digit/place identification → expanded form → fraction connections → equivalence → regrouping/decomposing.","strengths":["Strong misconception support for placeholder zeros and trailing zeros","Clear scaffolding from models → chart → representations (expanded form)","Kid-friendly pacing with short segments and frequent concrete examples"],"target_difficulty":"intermediate","title":"Read, Write, and Expand Decimals","tradeoffs":[],"updated_at":"2026-03-05T08:39:50.298755+00:00","user_id":"google_109800265000582445084"}}