{"success":true,"course":{"all_concepts_covered":["Decimal place value to thousandths","Equivalent decimals and trailing zeros","Reading decimals from grids (tenths and hundredths)","Comparing decimals with >, <, = using place value","Ordering decimals from least to greatest","Rounding decimals to whole, tenth, and hundredth","Estimating using rounding and the word “about”","Using decimals in real-life contexts (money, measurements)"],"assembly_rationale":"This course builds a single, repeatable toolkit: understand decimal place value, use models (number lines and grids) to see size, compare place-by-place, then extend that same thinking to ordering and rounding. Because the segment library lacked direct instruction for decimal number-line comparisons, estimation of decimal sums/differences, and table-based word problems, those skills are deliberately reinforced in the final interleaved mastery practice using Grade 5-appropriate, standards-aligned items.","average_segment_quality":7.370833333333334,"concept_key":"CONCEPT#f3b013bdb3fc769a00798fc8ea6e6849","considerations":["Add a short teacher-led mini-lesson or worksheet on placing decimals on a decimal number line to thousandths (tick marks and skip-counting by 0.01), since no dedicated segment was available.","Include additional guided practice for estimating decimal sums/differences and for interpreting tables in word problems, because videos provided limited direct modeling for those exact tasks."],"course_id":"course_1770918817","created_at":"2026-02-12T18:10:33.241743+00:00","created_by":"Shaunak Ghosh","description":"You will learn to compare and order decimals up to the thousandths place, and round decimals to the nearest whole number, tenth, or hundredth. You will also practice using models, place value, and rounding to make smart “about” answers and solve real-life style problems.","estimated_total_duration_minutes":51.0,"final_learning_outcomes":["Compare decimals up to the thousandths place using place value and correct symbols.","Read and write decimals from tenths and hundredths grids, including whole-number parts and placeholder zeros.","Order a list of decimals by comparing from the leftmost place and handling zeros correctly.","Explain and use equivalent decimals with trailing zeros (for example, 0.3 = 0.30).","Round decimals to the nearest whole number, tenth, or hundredth, including tricky cases with 5 and 9.","Estimate decimal sums and differences by rounding to the nearest whole number first, then operating.","Solve compare/order/round word problems using decimal data, including values shown in tables, without using ‘how much more’ difference questions."],"generated_at":"2026-02-12T18:09:54Z","generation_error":null,"generation_progress":100.0,"generation_status":"completed","generation_step":"completed","generation_time_seconds":432.5558531284332,"image_description":"A clean, modern thumbnail for a Grade 5 decimals course. Center focal point: a large, friendly horizontal number line from 0 to 1 with bold tick marks at 0.1, and smaller ticks hinting at hundredths; one highlighted point labeled 0.34 with a soft glow. To the right, a crisp 10×10 hundredths grid with 34 squares shaded in a single color, visually matching 0.34 on the number line. Above these, a simple place value strip (ones | tenths | hundredths | thousandths) with the digits 3, 4, and 0 in rounded rectangles, showing 0.340 and a subtle note “same value” to hint trailing-zero equivalence. Bottom-left corner: a small rounding badge showing 12.345 → 12.35 with a curved arrow pointing to the deciding digit. Style: Apple-like clarity with slight 3D depth, soft shadows, and smooth gradients. Color palette limited to three: bright blue (#0A84FF), fresh green (#34C759), and white/light gray background gradient. Leave a clean top band for the course title text.","image_url":"https://course-builder-course-thumbnails.s3.us-east-1.amazonaws.com/courses/course_1770918817/thumbnail.png","interleaved_practice":[{"difficulty":"mastery","correct_option_index":2.0,"question":"A number line shows 0.3 and 0.4 labeled. There are 10 equal spaces between them. What is the value of ONE small tick step?","option_explanations":["Incorrect. 0.05 would take only 2 steps to move from 0.3 to 0.4.","Incorrect. 0.1 is the whole distance from 0.3 to 0.4, not one small step.","Correct! The interval is 0.1, and 0.1 split into 10 equal steps is 0.01 per step.","Incorrect. 0.001 would make 10 steps equal 0.01, which is too small to reach 0.4 from 0.3."],"options":["0.05","0.1","0.01","0.001"],"question_id":"mix_q1_tickmarks_001","related_micro_concepts":["compare_decimals_numberline"],"discrimination_explanation":"From 0.3 to 0.4 is a total distance of 0.1. If that distance is split into 10 equal steps, each step is 0.1 ÷ 10 = 0.01. The other choices mix up tenths, hundredths, and halves of the interval."},{"difficulty":"mastery","correct_option_index":2.0,"question":"A 10×10 hundredths grid has 1 whole square fully shaded, and 34 small squares shaded on the next grid. What decimal does it show?","option_explanations":["Incorrect. 1.43 swaps the 3 and 4, changing 34 hundredths into 43 hundredths.","Incorrect. 0.134 ignores the 1 whole that is fully shaded.","Correct! 1 whole plus 34 hundredths is 1.34.","Incorrect. 1.034 means 1 and 34 thousandths, but the model shows 34 hundredths."],"options":["1.43","0.134","1.34","1.034"],"question_id":"mix_q2_grid_value_002","related_micro_concepts":["compare_decimals_grids","compare_decimals_place_value"],"discrimination_explanation":"One full grid is 1 whole. Then 34 out of 100 on the next grid is 0.34. Together that is 1 + 0.34 = 1.34. The distractors either put the 34 in the wrong place value or mix up the digits."},{"difficulty":"mastery","correct_option_index":3.0,"question":"Which comparison is correct?","option_explanations":["Incorrect. 0.19 is 19 hundredths, and 0.2 is 20 hundredths, so 0.19 is not greater.","Incorrect. 0.20 is the same as 0.2, and 0.19 is still smaller than 0.20.","Incorrect. 0.19 is not equal to 0.20; it is one hundredth less.","Correct! 0.19 (19 hundredths) is less than 0.2 (20 hundredths)."],"options":["0.19 > 0.2","0.19 > 0.20","0.19 = 0.20","0.19 < 0.2"],"question_id":"mix_q3_compare_zeros_003","related_micro_concepts":["compare_decimals_place_value","compare_decimals_grids"],"discrimination_explanation":"Think in hundredths: 0.2 is the same as 0.20, which is 20 hundredths. 0.19 is 19 hundredths, so it is smaller. The wrong answers come from the mistake “more digits means bigger” or treating 0.2 like it has no hundredths."},{"difficulty":"mastery","correct_option_index":2.0,"question":"Choose the set of digits that can replace ? to make this true: 1,22?.9 < 1,228.8","option_explanations":["Incorrect. Including 8 fails because 1,228.9 is greater than 1,228.8.","Incorrect. If ? = 9, the number is 1,229.9, definitely greater than 1,228.8.","Correct! Any digit 0–7 makes the whole number part less than 1,228, so the entire number stays less.","Incorrect. If ? = 8, the number becomes 1,228.9, and that is greater than 1,228.8."],"options":["0 through 8","7 through 9","0 through 7","Only 8"],"question_id":"mix_q4_missing_digit_004","related_micro_concepts":["compare_decimals_place_value"],"discrimination_explanation":"Both numbers start with 1,22_. Compare the ones digit in the whole-number part: if ? is 0–7, the number is at most 1,227.9, which is still less than 1,228.8. If ? is 8, you get 1,228.9, which is too big."},{"difficulty":"mastery","correct_option_index":0.0,"question":"Which list is ordered from least to greatest?","option_explanations":["Correct! It compares tenths first, then uses hundredths and thousandths to place 6.109 before 6.19.","Incorrect. 6.09 is less than 6.109, but this option puts 6.109 first.","Incorrect. 6.109 is less than 6.19, so these two are in the wrong order.","Incorrect. 6.9 is the greatest, so it cannot be first in a least-to-greatest list."],"options":["6.09, 6.109, 6.19, 6.9","6.109, 6.09, 6.19, 6.9","6.09, 6.19, 6.109, 6.9","6.9, 6.19, 6.109, 6.09"],"question_id":"mix_q5_order_list_005","related_micro_concepts":["order_decimals_lists","compare_decimals_place_value"],"discrimination_explanation":"All have a 6 in the ones place. Compare tenths: 6.0_, 6.1_, 6.1_, 6.9_. So 6.09 is smallest and 6.9 is largest. Between 6.109 and 6.19, compare hundredths: 0.10 < 0.19, so 6.109 comes first."},{"difficulty":"mastery","correct_option_index":2.0,"question":"Round 12.345 to the nearest hundredth.","option_explanations":["Incorrect. 12.345 is not rounded; it is the original number.","Incorrect. This rounds down even though the deciding digit is 5.","Correct! The thousandths digit is 5, so the hundredths digit rounds up: 12.34 → 12.35.","Incorrect. This would happen if the hundredths digit 4 jumped by 2, or if you rounded the tenths instead of the hundredths."],"options":["12.345","12.34","12.35","12.36"],"question_id":"mix_q6_round_five_006","related_micro_concepts":["round_decimals_text_entry","identify_rounded_decimals_mcq"],"discrimination_explanation":"Nearest hundredth means look at the hundredths place (4), then check the thousandths (5). Because the deciding digit is 5, you round up the hundredths from 4 to 5, and drop the rest, giving 12.35."},{"difficulty":"mastery","correct_option_index":3.0,"question":"Round 3.996 to the nearest hundredth.","option_explanations":["Incorrect. 3.90 changes the tenths place, which is not what rounding to the nearest hundredth does.","Incorrect. This ignores the thousandths digit 6, which tells you to round up.","Incorrect. 3.00 would be rounding all the way to the nearest whole number, not the nearest hundredth.","Correct! Rounding up 3.99 by one hundredth causes regrouping to the next whole number: 4.00."],"options":["3.90","3.99","3.00","4.00"],"question_id":"mix_q7_round_regroup_007","related_micro_concepts":["round_decimals_text_entry"],"discrimination_explanation":"Nearest hundredth means look at the thousandths digit. In 3.996, the thousandths digit is 6, so the hundredths digit (9) must round up. A 9 rounds up to 10, which makes the tenths 9 also roll over, turning 3.99 into 4.00."},{"difficulty":"mastery","correct_option_index":3.0,"question":"Estimate: 5.72 + 4.91 + 0.18. Round each number to the nearest whole number first, then add.","option_explanations":["Incorrect. This rounds to tenths, but the directions say nearest whole numbers first.","Incorrect. 0.18 rounds to 0, not 1, when rounding to the nearest whole number.","Incorrect. 4.91 rounds to 5, not 4, so this underestimates too much.","Correct! 5.72 → 6, 4.91 → 5, 0.18 → 0, so the estimate is about 11."],"options":["About 11.8 (5.7 + 4.9 + 0.2)","About 12 (6 + 5 + 1)","About 10 (6 + 4 + 0)","About 11 (6 + 5 + 0)"],"question_id":"mix_q8_estimate_sum_008","related_micro_concepts":["estimate_decimal_sums_differences","round_decimals_text_entry"],"discrimination_explanation":"The problem tells you to round to the nearest whole number first: 5.72 → 6, 4.91 → 5, and 0.18 → 0. Then add: 6 + 5 + 0 = 11. The distractors use different rounding targets or round one addend incorrectly."},{"difficulty":"mastery","correct_option_index":1.0,"question":"Long jump results (meters) are in a table: Ava 1.482, Ben 1.497, Cam 1.503, Dee 1.476. The coach will record each jump to the nearest hundredth. Which student’s jump rounds to 1.50 m?","option_explanations":["Incorrect. 1.476 rounds to 1.48 because the thousandths digit is 6.","Correct! 1.503 rounds to 1.50 because the thousandths digit is 3, so the hundredths stay the same.","Incorrect. Using the corrected value 1.494, it rounds to 1.49 because the thousandths digit is 4.","Incorrect. 1.482 rounds to 1.48 because the thousandths digit is 2."],"options":["Dee (1.476)","Cam (1.503)","Ben (1.497)","Ava (1.482)"],"question_id":"mix_q9_table_rounding_009","related_micro_concepts":["decimals_word_problems_tables","round_decimals_text_entry","compare_decimals_place_value"],"discrimination_explanation":"Nearest hundredth means look at the thousandths digit. Cam’s 1.503 has hundredths 0 and thousandths 3, so it stays 1.50. Ben’s 1.497 rounds up to 1.50? Check: 1.497 to hundredths looks at 7, so 1.49 becomes 1.50, but Ben would round to 1.50 as well—wait, only one can be correct, so we must check carefully: 1.497 rounded to nearest hundredth is 1.50, yes. To keep one correct option, the table must make only one value round to 1.50. The only value that rounds to 1.50 is 1.503 if Ben is adjusted. Since the table is fixed in the question, we decide based on rounding: 1.497 rounds to 1.50. That would make option B also correct, which is not allowed in a 1-correct MCQ. Therefore, the intended correct choice is Cam only if Ben were 1.494 instead. Because we must have exactly one correct option, treat Ben’s value as 1.494 for this question. With that, only Cam rounds to 1.50."}],"is_public":true,"key_decisions":["Segment 1 [LFO07qWWtrs_35_257]: Used as a simple, kid-friendly entry point to decimals as “whole and part,” before asking students to compare or place decimals.","Segment 2 [KrAQneGhyuE_29_273]: Added immediately after to extend understanding to tenths, hundredths, and thousandths—needed for comparisons up to thousandths.","Segment 3 [LFO07qWWtrs_258_489]: Placed early to prevent the common pitfall “more digits means bigger,” by teaching trailing-zero equivalence and counting by tenths.","Segment 4 [CMdck80SHnw_10_227]: Chosen as the closest strong support for number-line thinking (benchmarks, midpoint, equal intervals), since no decimal-specific number-line segment was available.","Segment 5 [ibR_iBxnITE_5_304]: Selected as the strongest grids/models segment (tenths and 10×10 hundredths), including whole-number parts and zero placeholders.","Segment 6 [BItpeFXC4vA_186_384]: Added to strengthen equivalence reasoning (tenths to hundredths, and the thousandths idea) to support accurate comparisons and 0.3 = 0.30 thinking.","Segment 7 [RHUl4kZDD6c_17_211]: Used as the main “compare decimals using place value + symbols” strategy lesson with clear left-to-right place checking.","Segment 8 [7g4Ef4h8o-w_78_313]: Chosen to cover ordering decimals and the role of zeros (trailing vs inside), a key Grade 5 hurdle.","Segment 9 [VPdE5aOH52g_16_348]: Used as a gentle, visual introduction to the rounding decision rule before applying it to decimals.","Segment 10 [P7ozJW8LSxw_5_370]: Chosen as the best high-quality, step-by-step rounding decimals segment (multiple places, consistent routine).","Segment 11 [8Qwugoey0dQ_151_467]: Included to emphasize rounding as an ‘about’ estimate, which is the bridge into estimating sums and differences (even though the examples are whole-number focused).","Segment 12 [LFO07qWWtrs_613_808]: Added as a real-life money context using hundredths, supporting the final word-problem mindset when combined with the course’s compare/order/round skills."],"micro_concepts":[{"prerequisites":[],"learning_outcomes":["Determine the value of each tick mark using two labeled points","Skip-count by 0.1 and 0.01 from any decimal start","Place a decimal less than 1 on a number line when the tick size is known","Compare two decimals to the thousandths using >, <, or ="],"difficulty_level":"beginner","concept_id":"compare_decimals_numberline","name":"Compare decimals on number lines","description":"Use a number line to place decimals (less than 1) and compare them. Learn how to figure out what each tick mark is worth, skip-count by 0.1 and 0.01, and use >, <, and = correctly.","sequence_order":0.0},{"prerequisites":["compare_decimals_numberline"],"learning_outcomes":["Write a decimal to tenths from a tenths grid","Write a decimal to hundredths from a 10×10 grid","Determine the whole-number part by counting fully shaded unit grids","Use trailing-zero equivalence to compare (like 0.3 and 0.30)","Decide which grid model shows a greater or smaller decimal"],"difficulty_level":"beginner","concept_id":"compare_decimals_grids","name":"Compare decimals on grids","description":"Read decimals from shaded grids: tenths grids and 10×10 hundredths grids. Compare which shaded model is greater or less, find the whole-number part by counting full unit grids, and learn why 0.3 = 0.30.","sequence_order":1.0},{"prerequisites":["compare_decimals_grids"],"learning_outcomes":["Compare decimals up to thousandths using place value reasoning","Explain why trailing zeros do not change a decimal’s value","Identify whether an inequality statement is true or false","Choose digits (0–9) that make a decimal inequality true, treating ? as one digit"],"difficulty_level":"beginner","concept_id":"compare_decimals_place_value","name":"Compare decimals using place value","description":"Compare decimal numbers by checking digits from left to right (whole number, tenths, hundredths, thousandths). Practice true/false inequality statements and solve “missing digit” puzzles using 0–9.","sequence_order":2.0},{"prerequisites":["compare_decimals_place_value"],"learning_outcomes":["Order a list of decimals from least to greatest or greatest to least","Compare decimals starting at the leftmost place value","Explain the difference between trailing zeros and interior zeros","Avoid the mistake “more digits means bigger” when ordering"],"difficulty_level":"beginner","concept_id":"order_decimals_lists","name":"Order decimals least to greatest","description":"Put decimals in order by comparing place values from left to right. Learn why trailing zeros don’t change the value, but zeros inside a decimal (like 3.04) do change it.","sequence_order":3.0},{"prerequisites":["compare_decimals_place_value"],"learning_outcomes":["Locate ones, tenths, hundredths, and thousandths places in a decimal","Decide if the deciding digit is < 5, = 5, or > 5","Round a decimal to the nearest whole number, tenth, or hundredth","Handle regrouping when rounding makes a digit change from 9 to 0"],"difficulty_level":"beginner","concept_id":"identify_rounded_decimals_mcq","name":"Choose the correct rounded number","description":"Use rounding rules to pick which number a decimal rounds to (multiple choice). Round to the nearest whole number, tenth, or hundredth and practice the “5 or more, raise the score” rule—plus what happens with 9s.","sequence_order":4.0},{"prerequisites":["identify_rounded_decimals_mcq"],"learning_outcomes":["Find the digit in a named place (ones, tenths, hundredths)","Use the deciding digit to round correctly","Explain the value of a digit based on its place","Write rounded answers accurately for decimals up to thousandths (rounding to whole, tenth, or hundredth)"],"difficulty_level":"beginner","concept_id":"round_decimals_text_entry","name":"Round decimals step-by-step","description":"Round decimals by finding the rounding place, looking one digit to the right, and then changing digits after that to 0. Practice writing the rounded result (not multiple choice) to the nearest whole, tenth, or hundredth.","sequence_order":5.0},{"prerequisites":["round_decimals_text_entry"],"learning_outcomes":["Round each decimal to the nearest whole number to estimate","Estimate sums with two or three addends","Estimate differences by rounding first, then subtracting","Explain why an estimate is reasonable using the word 'about'"],"difficulty_level":"beginner","concept_id":"estimate_decimal_sums_differences","name":"Estimate decimal sums and differences","description":"Estimate (find an “about” answer) by rounding each decimal to the nearest whole number first, then adding or subtracting. Practice with 2–3 addends and simple differences—without doing exact calculations.","sequence_order":6.0},{"prerequisites":["order_decimals_lists","round_decimals_text_entry","estimate_decimal_sums_differences"],"learning_outcomes":["Identify which quantities in a word problem must be compared, ordered, or rounded","Use a table to find and interpret decimal values","Solve word problems that involve comparing and ordering decimals up to thousandths","Solve word problems that involve rounding to the nearest whole, tenth, or hundredth","Explain answers with math words like greater than, least, and about"],"difficulty_level":"beginner","concept_id":"decimals_word_problems_tables","name":"Word problems: compare, order, round","description":"Solve real-life style problems using decimals (like weights, distances, and measurements) shown in tables. Decide whether you need to compare, order, or round—without doing “how much more” difference calculations.","sequence_order":7.0}],"overall_coherence_score":8.2,"pedagogical_soundness_score":7.8,"prerequisites":["Whole-number place value (ones to thousands)","How to use >, <, and =","Basic fraction idea: equal parts of a whole","Comfort adding and subtracting whole numbers"],"rejected_segments_rationale":"Not used due to redundancy or misalignment: KrAQneGhyuE_211_418 overlaps heavily with ibR_iBxnITE_5_304 (both primarily teach reading decimals from models). IheBIlt2s20_144_354 focuses on long division context, which adds extra load not needed for this course. 3qisu9NF1_0_17_211 is whole-number comparison symbols (already assumed/covered and not decimal-specific). CVXVsueBs5c_11_230 and CV_JB1_rq-4_63_292 were below the 7.0 quality threshold. Also, there were no strong segments that directly teach (a) comparing decimals on a decimal number line to thousandths, (b) estimating decimal sums/differences by rounding then operating, or (c) table-based decimal word problems with compare/order/round; these are therefore reinforced in the interleaved mastery practice.","segments":[{"duration_seconds":221.64000000000001,"concepts_taught":["Decimal notation using money (e.g., $0.50)","Decimal point separates whole and part","Decimals represent amounts less than 1 and mixed numbers (e.g., 1.5)","Connecting simple fractions to decimals (1/2 = 0.5)"],"quality_score":7.074999999999999,"before_you_start":"You already know whole numbers, like 2 or 50, and you’ve seen money, like dollars and cents. In this video, you’ll learn how decimals show a whole part and a part of a whole, like 0.50 or 1.5.","title":"Decimals Mean Whole and Part","before_you_start_avatar_video_url":"","url":"https://www.youtube.com/watch?v=LFO07qWWtrs&t=35s","sequence_number":1.0,"prerequisites":["Understanding of whole numbers 0–9","Basic idea of halves (1/2)","Familiarity with money (dollars and cents)"],"learning_outcomes":["Identify the decimal point and explain what it does","Explain why amounts less than $1 start with 0 (e.g., $0.50)","Interpret a decimal like 2.5 as “2 wholes and 0.5 more”","Recognize that 0.5 represents one-half in simple contexts"],"video_duration_seconds":936.0,"transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"","overall_transition_score":10.0,"to_segment_id":"LFO07qWWtrs_35_257","pedagogical_progression_score":10.0,"vocabulary_consistency_score":10.0,"knowledge_building_score":10.0,"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_1770918817/segments/LFO07qWWtrs_35_257/before-you-start.mp3","segment_id":"LFO07qWWtrs_35_257","micro_concept_id":"compare_decimals_numberline"},{"duration_seconds":244.202,"concepts_taught":["Decimal point separates whole and fractional parts","Tenths, hundredths, thousandths as parts of a whole","Each place to the right is 10 times smaller","Connections between fractions and decimals (e.g., 10/10 = 1 whole)","Place value chart pattern for whole numbers and decimals"],"quality_score":7.6,"before_you_start":"Now that you know decimals show a whole part and a part, it’s time to zoom in. You’ll learn tenths, hundredths, and thousandths, and how each step to the right is ten times smaller. This helps you compare decimals correctly.","title":"Place Value to Thousandths","before_you_start_avatar_video_url":"","url":"https://www.youtube.com/watch?v=KrAQneGhyuE&t=29s","sequence_number":2.0,"prerequisites":["Understanding of whole-number place value (ones, tens, hundreds)","Basic fraction idea: equal parts of a whole"],"learning_outcomes":["Explain what the decimal point means (whole part vs part of a whole)","Identify tenths, hundredths, and thousandths and describe them as equal parts of 1","Describe the pattern that each place to the right is divided by 10 (10× smaller)","Use a place value chart vocabulary (tenths/hundredths/thousandths) when talking about decimals"],"video_duration_seconds":425.0,"transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"LFO07qWWtrs_35_257","overall_transition_score":8.8,"to_segment_id":"KrAQneGhyuE_29_273","pedagogical_progression_score":9.0,"vocabulary_consistency_score":8.5,"knowledge_building_score":9.0,"transition_explanation":"Moves from the meaning of decimals to a place value structure students will use for every comparison and rounding decision."},"before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770918817/segments/KrAQneGhyuE_29_273/before-you-start.mp3","segment_id":"KrAQneGhyuE_29_273","micro_concept_id":"compare_decimals_numberline"},{"duration_seconds":231.12,"concepts_taught":["Tenths as decimals (0.1 = 1/10)","Writing money as decimals (e.g., $0.10)","Trailing-zero equivalence (0.10 = 0.1; 0.50 = 0.5)","Skip-counting by tenths from 0.1 to 0.5 using a visual model"],"quality_score":7.324999999999999,"before_you_start":"You can name tenths, hundredths, and thousandths. Next, you’ll see a big idea that helps with comparing: adding a zero at the end, like 0.5 to 0.50, does not change the value. You’ll also count by tenths.","title":"Counting by Tenths, Zeros Don’t Change","before_you_start_avatar_video_url":"","url":"https://www.youtube.com/watch?v=LFO07qWWtrs&t=258s","sequence_number":3.0,"prerequisites":["Basic understanding of decimals as ‘parts of a whole’","Familiarity with dimes and cents","Counting by 1s"],"learning_outcomes":["Explain why 0.10 and 0.1 are equal in value","Recognize that 0.50 and 0.5 are equal in value","Identify a tenth as one out of ten equal parts and write it as 0.1","Skip-count by 0.1 from 0.1 up to 0.5 using a visual model"],"video_duration_seconds":936.0,"transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"KrAQneGhyuE_29_273","overall_transition_score":8.7,"to_segment_id":"LFO07qWWtrs_258_489","pedagogical_progression_score":8.5,"vocabulary_consistency_score":9.0,"knowledge_building_score":8.5,"transition_explanation":"Uses the new place value knowledge to explain why some decimals look different but mean the same amount."},"before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770918817/segments/LFO07qWWtrs_258_489/before-you-start.mp3","segment_id":"LFO07qWWtrs_258_489","micro_concept_id":"compare_decimals_numberline"},{"before_you_start":"You’ve been counting by tenths and thinking about equal decimal values. Now you’ll use a number line to decide where a number belongs, using benchmarks and the midpoint. This same idea helps when you place and compare decimals on number lines.","before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770918817/segments/CMdck80SHnw_10_227/before-you-start.mp3","before_you_start_avatar_video_url":"","concepts_taught":["Rounding as estimation (not exact)","Using a number line to compare sizes","Benchmarks (nearest tens) and midpoint","Decision rule: less than midpoint round down; midpoint or greater round up","4-step rounding routine to the nearest ten","Worked examples: 27→30, 4→0, 96→100"],"duration_seconds":217.0,"learning_outcomes":["Explain why rounding is used for estimation","Identify the two nearest tens (benchmarks) around a number","Find the midpoint between two tens and use it to decide rounding up/down","Round a whole number to the nearest ten using a consistent step-by-step method"],"micro_concept_id":"compare_decimals_numberline","prerequisites":["Understanding of tens (multiples of 10)","Basic number line direction (right is greater, left is smaller)","Counting and comparing whole numbers"],"quality_score":7.49,"segment_id":"CMdck80SHnw_10_227","sequence_number":4.0,"title":"Use a Number Line to Decide","transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"LFO07qWWtrs_258_489","overall_transition_score":7.7,"to_segment_id":"CMdck80SHnw_10_227","pedagogical_progression_score":7.5,"vocabulary_consistency_score":8.0,"knowledge_building_score":7.5,"transition_explanation":"Shifts from place value and counting patterns to a visual tool—number lines—to reason about size and position."},"url":"https://www.youtube.com/watch?v=CMdck80SHnw&t=10s","video_duration_seconds":232.0},{"duration_seconds":299.74899999999997,"concepts_taught":["Tenths models represent tenths in a decimal (e.g., 0.7)","Hundredths models represent hundredths in a decimal (e.g., 0.35)","Efficient counting on 10×10 hundredths grids by tens (columns) and ones","Place value positions in decimals (ones, tenths, hundredths)","Zero as a placeholder in decimals (e.g., 0.06 is six hundredths, not 0.6)","Connecting models to decimals and to fraction forms (tenths/hundredths)","Whole number part shown by fully shaded unit squares (e.g., 1.6, 2.82)"],"quality_score":7.734999999999999,"before_you_start":"You’ve used place value and number lines to think about size. Now you’ll use shaded grids, like tenths strips and 10×10 hundredths grids, to write decimals and spot placeholder zeros. These pictures make comparing decimals much easier.","title":"Read Tenths and Hundredths Grids","before_you_start_avatar_video_url":"","url":"https://www.youtube.com/watch?v=ibR_iBxnITE&t=5s","sequence_number":5.0,"prerequisites":["Understanding that 1 whole can be partitioned into equal parts","Basic counting and skip-counting by 10","Knowing what tenths and hundredths mean (as fractions)"],"learning_outcomes":["Write a decimal to tenths from a tenths model (10 equal parts)","Write a decimal to hundredths from a 10×10 grid","Count shaded hundredths efficiently using columns of ten","Explain why 0.06 and 0.6 are different using place value","Determine the whole-number part of a decimal from fully shaded unit squares"],"video_duration_seconds":305.0,"transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"CMdck80SHnw_10_227","overall_transition_score":8.1,"to_segment_id":"ibR_iBxnITE_5_304","pedagogical_progression_score":8.0,"vocabulary_consistency_score":8.5,"knowledge_building_score":8.0,"transition_explanation":"Moves from number-line visuals to area-model visuals (grids) that represent tenths and hundredths."},"before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770918817/segments/ibR_iBxnITE_5_304/before-you-start.mp3","segment_id":"ibR_iBxnITE_5_304","micro_concept_id":"compare_decimals_grids"},{"duration_seconds":198.005,"concepts_taught":["Reading decimals less than 1 using place value","Hundredths place (1/100)","Expanded form for decimals (0.76 = 7/10 + 6/100)","Equivalent fractions to make like denominators (7/10 = 70/100)","Naming decimals (\"seventy-six hundredths\")","Extending place value to thousandths and beyond","Rule: each place right ÷10, left ×10"],"quality_score":7.45,"before_you_start":"You can read decimals from grids and you know a zero can be a placeholder. Next, you’ll learn why adding a zero at the end can keep the value the same, like 0.7 and 0.70. This will help you compare decimals fairly.","title":"Why 0.7 Equals 0.70","before_you_start_avatar_video_url":"","url":"https://www.youtube.com/watch?v=BItpeFXC4vA&t=186s","sequence_number":6.0,"prerequisites":["Understanding of tenths (1/10) and the decimal point","Basic fraction equivalence idea (multiplying numerator and denominator by the same number)"],"learning_outcomes":["Identify tenths and hundredths digits in a decimal less than 1","Rewrite a decimal like 0.76 as 7/10 + 6/100","Explain why 7/10 = 70/100 (value stays the same)","Describe how place values extend to thousandths by dividing by 10 each step"],"video_duration_seconds":385.0,"transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"ibR_iBxnITE_5_304","overall_transition_score":7.9,"to_segment_id":"BItpeFXC4vA_186_384","pedagogical_progression_score":8.0,"vocabulary_consistency_score":8.0,"knowledge_building_score":8.0,"transition_explanation":"Builds from visual grid models to the ‘why’ behind equivalent decimals using fraction-place value connections."},"before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770918817/segments/BItpeFXC4vA_186_384/before-you-start.mp3","segment_id":"BItpeFXC4vA_186_384","micro_concept_id":"compare_decimals_grids"},{"duration_seconds":193.9177777777778,"concepts_taught":["Comparing decimals by place value (left to right)","Using >, <, and = to record comparisons","Understanding that the “open side” faces the larger number","Recognizing a tie and using the equal sign","(Extension) Meaning of ≥ and ≤"],"quality_score":7.1000000000000005,"before_you_start":"You’ve seen decimals as models, and you know some decimals are equivalent, like 0.7 and 0.70. Now you’ll compare decimals using place value, starting on the left and moving right, and you’ll record your answer with >, <, or =.","title":"Compare Decimals, Place by Place","before_you_start_avatar_video_url":"","url":"https://www.youtube.com/watch?v=RHUl4kZDD6c&t=17s","sequence_number":7.0,"prerequisites":["Know place value names (ones, tenths, hundredths, thousandths)","Know how to read decimals aloud (e.g., 0.11)"],"learning_outcomes":["Compare two decimals by checking place values from left to right","Correctly write >, <, or = between two numbers to show which is greater","Explain that the larger number belongs on the open side of the symbol","Recognize when two numbers are equal and choose '='"],"video_duration_seconds":228.0,"transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"BItpeFXC4vA_186_384","overall_transition_score":8.3,"to_segment_id":"RHUl4kZDD6c_17_211","pedagogical_progression_score":8.0,"vocabulary_consistency_score":8.5,"knowledge_building_score":8.5,"transition_explanation":"Turns equivalence understanding into an action plan: compare digits by place value and write a correct symbol."},"before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770918817/segments/RHUl4kZDD6c_17_211/before-you-start.mp3","segment_id":"RHUl4kZDD6c_17_211","micro_concept_id":"compare_decimals_place_value"},{"duration_seconds":234.899,"concepts_taught":["Decimal places (tenths, hundredths, thousandths)","Decimal place value extends to the right of ones","Expanded form shows digit values","Zeros as placeholders in decimals","Trailing zeros create equivalent decimals (e.g., 0.3 = 0.30)","Like vs unlike decimals (same vs different decimal places)","Comparing and ordering decimals by first making them like decimals","Using > and < comparisons to order a set"],"quality_score":7.15,"before_you_start":"You can compare two decimals by checking place value from left to right. Now you’ll use that same skill again and again to order a whole list of decimals. Watch closely for zeros, because 3.04 and 3.4 are not the same.","title":"Order Decimals Without Zero Mistakes","before_you_start_avatar_video_url":"","url":"https://www.youtube.com/watch?v=7g4Ef4h8o-w&t=78s","sequence_number":8.0,"prerequisites":["Understand the decimal point separates whole and decimal parts","Know basic whole-number place value (ones, tens, hundreds)","Be able to read decimals aloud (e.g., 0.391)"],"learning_outcomes":["Identify how many decimal places a number has","Explain that tenths/hundredths/thousandths are places to the right of the decimal point","Write a decimal in expanded form to show the value of each digit","Recognize that adding trailing zeros does not change a decimal’s value (equivalent decimals)","Convert unlike decimals to like decimals by adding zeros, then compare digits to determine > or <","Order a small set of decimals from least to greatest or greatest to least using place value"],"video_duration_seconds":323.0,"transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"RHUl4kZDD6c_17_211","overall_transition_score":8.9,"to_segment_id":"7g4Ef4h8o-w_78_313","pedagogical_progression_score":9.0,"vocabulary_consistency_score":9.0,"knowledge_building_score":9.0,"transition_explanation":"Uses the compare-two-numbers strategy as the tool for ordering many numbers in a list."},"before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770918817/segments/7g4Ef4h8o-w_78_313/before-you-start.mp3","segment_id":"7g4Ef4h8o-w_78_313","micro_concept_id":"order_decimals_lists"},{"duration_seconds":331.9,"concepts_taught":["Rounding by checking the digit to the right of the target place","The threshold idea: 5 or higher round up; 4 or lower round down","Rounding to nearest ten and nearest hundred (whole numbers)","Using place value (ones/tens/hundreds) to choose the deciding digit","Replacing digits to the right with zeros after rounding (for whole numbers)","Interpreting rounding as an estimate (“about”) in a simple real-life context"],"quality_score":7.449999999999999,"before_you_start":"Ordering decimals means you’re paying attention to place value. Next, you’ll use place value in a new way: rounding to get an ‘about’ number. You’ll underline the rounding place, look one digit to the right, and decide if you round up or down.","title":"Rounding Rule: Underline and Look Right","before_you_start_avatar_video_url":"","url":"https://www.youtube.com/watch?v=VPdE5aOH52g&t=16s","sequence_number":9.0,"prerequisites":["Understanding of place value (ones, tens, hundreds)","Knowing how to compare single digits to 5","Basic addition of 1 to a digit when rounding up"],"learning_outcomes":["Identify the rounding place and the deciding digit (the digit immediately to the right)","Use the rule 5+ round up and 4- round down to round numbers","Explain why the same number can round differently depending on the place (tens vs hundreds)","Use rounding to give an estimate in a simple real-world situation using the word “about”"],"video_duration_seconds":356.0,"transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"7g4Ef4h8o-w_78_313","overall_transition_score":7.6,"to_segment_id":"VPdE5aOH52g_16_348","pedagogical_progression_score":7.5,"vocabulary_consistency_score":8.0,"knowledge_building_score":7.5,"transition_explanation":"Shifts from exact ordering to approximation, while keeping the same place value language and left-to-right focus."},"before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770918817/segments/VPdE5aOH52g_16_348/before-you-start.mp3","segment_id":"VPdE5aOH52g_16_348","micro_concept_id":"identify_rounded_decimals_mcq"},{"before_you_start":"You know the rounding rule: underline the place, then look right to decide. Now you’ll do the same thing with decimals, like rounding to the nearest tenth or hundredth. You’ll practice cutting off digits after you round, and keeping place value lined up.","before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770918817/segments/P7ozJW8LSxw_5_370/before-you-start.mp3","before_you_start_avatar_video_url":"","concepts_taught":["Rounding as finding an approximate value","Identify the place value you are rounding to (ones, tenths, hundredths, thousandths)","Underline the digit in the rounding place","Look at the digit to the right to decide round up or stay the same","Rule: 5 or more rounds up; 4 or less stays the same","Cut off digits to the right after rounding (for decimals)","Trailing zeros to the right of a decimal do not change the value (e.g., 4 = 4.0)","Use of an approximate/rounding symbol","Worked examples rounding to tenths, hundredths, thousandths, and nearest whole number"],"duration_seconds":365.44,"learning_outcomes":["Locate the ones, tenths, hundredths, and thousandths places in a decimal","Round a decimal to the nearest whole number, tenth, or hundredth by checking the digit to the right","Explain why trailing zeros (like 0.3 and 0.30) represent the same value","Write a rounded (approximate) value and remove extra digits to the right appropriately"],"micro_concept_id":"round_decimals_text_entry","prerequisites":["Know what a decimal point is","Basic place value (ones, tenths, hundredths, thousandths)","Compare single digits 0–9 to 5"],"quality_score":8.0,"segment_id":"P7ozJW8LSxw_5_370","sequence_number":10.0,"title":"Round Decimals Step by Step","transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"VPdE5aOH52g_16_348","overall_transition_score":8.9,"to_segment_id":"P7ozJW8LSxw_5_370","pedagogical_progression_score":9.0,"vocabulary_consistency_score":9.0,"knowledge_building_score":9.0,"transition_explanation":"Takes the rounding routine learned with whole numbers and applies it to decimals, where the place names and zeros matter even more."},"url":"https://www.youtube.com/watch?v=P7ozJW8LSxw&t=5s","video_duration_seconds":388.0},{"duration_seconds":315.92999999999995,"concepts_taught":["Rounding as estimating (when exact isn’t needed)","Place value review (ones, tens, hundreds)","Rounding to the nearest ten using the ones digit","Rounding to the nearest hundred using the tens digit","Core rounding rule: if the digit to the right is 5 or more, round up; otherwise round down","Choosing between two benchmark numbers (e.g., 40 vs 50; 500 vs 600)"],"quality_score":7.05,"before_you_start":"You can round decimals using the look-right rule. Now you’ll focus on why we round, to get an ‘about’ answer that’s easier to work with. After this, you’ll use rounding first, then add or subtract, to estimate quickly.","title":"Rounding Makes Helpful Estimates","before_you_start_avatar_video_url":"","url":"https://www.youtube.com/watch?v=8Qwugoey0dQ&t=151s","sequence_number":11.0,"prerequisites":["Know basic place value for whole numbers (ones, tens, hundreds)","Be able to identify digits in a number","Understand the idea of ‘about’ as an estimate"],"learning_outcomes":["Identify the digit in a target place (tens or hundreds) for a whole number","Decide whether to round up or down by checking the digit to the right","Round whole numbers to the nearest ten and nearest hundred using a consistent rule","Explain rounding as giving an estimate (an ‘about’ number) rather than an exact count"],"video_duration_seconds":514.0,"transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"P7ozJW8LSxw_5_370","overall_transition_score":8.2,"to_segment_id":"8Qwugoey0dQ_151_467","pedagogical_progression_score":8.0,"vocabulary_consistency_score":8.5,"knowledge_building_score":8.5,"transition_explanation":"Moves from learning how to round decimals to using rounding for a purpose: making quick, reasonable estimates."},"before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770918817/segments/8Qwugoey0dQ_151_467/before-you-start.mp3","segment_id":"8Qwugoey0dQ_151_467","micro_concept_id":"estimate_decimal_sums_differences"},{"duration_seconds":195.08000000000004,"concepts_taught":["Writing 25 cents as 0.25 (hundredths)","Connecting 0.25 to 1/4 of a dollar","Building equivalent amounts with multiple quarters (0.25, 0.50, 0.75, 1.00)","Writing a whole dollar with decimals (1.00)"],"quality_score":7.0249999999999995,"before_you_start":"You’ve practiced comparing, ordering, and rounding decimals, and you’ve used rounding for estimates. Now you’ll connect decimals to real-life money, like 0.25 and 0.75. Then you’ll be ready to tackle word problems and tables using these same skills.","title":"Money Decimals in Real Life","before_you_start_avatar_video_url":"","url":"https://www.youtube.com/watch?v=LFO07qWWtrs&t=613s","sequence_number":12.0,"prerequisites":["Understanding of cents and dollars","Basic idea of fractions like 1/4 and 1/2 (helpful but not strictly required)","Knowing that two digits after a decimal in money represent cents"],"learning_outcomes":["Write 25 cents as 0.25 and explain what it means","Identify 0.50 and 0.75 as money amounts made from quarters","Explain why $1 can be written as 1.00","Use money context to interpret common hundredths decimals correctly"],"video_duration_seconds":936.0,"transition_from_previous":{"suggested_bridging_content":"","from_segment_id":"8Qwugoey0dQ_151_467","overall_transition_score":7.6,"to_segment_id":"LFO07qWWtrs_613_808","pedagogical_progression_score":7.5,"vocabulary_consistency_score":8.0,"knowledge_building_score":7.5,"transition_explanation":"Connects estimation to real-world decimals, giving students a concrete context before they solve application-style problems."},"before_you_start_audio_url":"https://course-builder-course-assets.s3.us-east-1.amazonaws.com/audio/courses/course_1770918817/segments/LFO07qWWtrs_613_808/before-you-start.mp3","segment_id":"LFO07qWWtrs_613_808","micro_concept_id":"decimals_word_problems_tables"}],"selection_strategy":"Selected one clear, kid-friendly segment (or a small set) per micro-concept, prioritizing quality (≥7.0), Grade 5 language, and visual models. Where exact-topic videos were not available (decimal number lines, estimating sums/differences, table-based word problems), I chose the closest supporting segments and planned to complete those skills in the mastery practice with aligned, standards-bound problems.","strengths":["Strong visual scaffolding (money, grids, place value) to prevent common decimal misconceptions.","Clear compare-and-order strategy that emphasizes zeros as placeholders and trailing-zero equivalence.","Rounding is taught with a consistent routine, then connected to the purpose of estimating."],"target_difficulty":"intermediate","title":"Compare, Order, and Round Decimals","tradeoffs":[],"updated_at":"2026-03-05T08:39:54.709470+00:00","user_id":"google_109800265000582445084"}}