1.
Three students charted stars one night: Musa, Idris, and Bilal. Together they charted 14 stars. Idris charted 6 and Bilal charted 3. How many did Musa chart? Whose number was in the middle?
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Answer:
Did you know? Al-Sufi drew a star atlas in the year 964 that described the Andromeda Galaxy — over 900 years before telescopes could show what it was.
2.
An astrolabe is engraved with a ring of numbers: 5, 10, 15, 20, ___, ___ . What are the next two, and what is the rule?
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Answer:
Did you know? An astrolabe was a handheld computer made of brass. It could tell you the time, find your direction, and locate a star.
3.
Aisha counted 11 stars through a sighting tube. She saw 3 more bright ones than dim ones. How many bright and how many dim? (Hint: try pairs that add to 11.)
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Answer:
Did you know? Many star names we still use are Arabic — Betelgeuse, Rigel, Aldebaran, Vega.
4.
Four scholars finished copying a manuscript: Hamza, Layla, Omar, and Zayd. Hamza finished 1st. Zayd finished last. Layla finished ahead of Omar. List all four in order.
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Answer:
Did you know? Paper reached Baghdad in the 700s, and books became cheap enough that the city had over 100 bookshops.
5.
Musa is making an observation kit with one tool — astrolabe, quadrant, or sundial — and one notebook, leather or cloth. How many different kits can he make? List them.
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Answer:
Did you know? A quadrant measures the angle between the horizon and a star, which tells you how far north or south you are.
1.
In a stargazing game, spotting a planet earns 5 points, a bright star earns 2, and a cloudy night costs 3. Yusuf spots 3 planets and 4 bright stars but loses 2 nights to clouds. Zaid spots 2 planets, 6 bright stars, and loses 1 night. Who has more, and by how much?
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Answer:
Did you know? Only five planets can be seen without a telescope: Mercury, Venus, Mars, Jupiter, and Saturn.
2.
Three astronomers — Yusuf, Idris, and Hamza — each have one job: measuring, recording, and drawing. Clue 1: Yusuf is not the recorder. Clue 2: Hamza is the artist who draws. Who does what?
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Answer:
Did you know? Al-Battani measured the length of a year as 365 days, 5 hours, 46 minutes, 24 seconds — off by only about 2 minutes.
3.
An observatory starts with 96 star charts. Each year, half of them are recopied onto fresh paper and the old ones retired. After 4 years, how many of the original charts are left? How many were retired in all?
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Answer:
Did you know? The Maragheh observatory in Persia had a library of 40,000 books and a staff of astronomers from as far away as China.
4.
Two brothers recorded moon sightings all month. Together they recorded 28. Yusuf recorded 8 more than Musa. How many did each record?
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Answer:
Did you know? The Islamic calendar follows the moon, so its months shift about 11 days earlier each solar year.
5.
A school of 18 students is split into equal groups of 6 to share telescopes. How many groups? Within one group, each student compares notes with every other student exactly once. How many comparisons happen in that group?
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Answer:
Did you know? The word 'algebra' comes from al-jabr, the title of a book written in Baghdad around 820.
3rd Grade
1. Musa charted 5; Musa is the middle.
14 − 6 − 3 = 5. In order: Bilal 3, Musa 5, Idris 6 → Musa is in the middle.
2. 25 and 30. Rule: add 5.
Each number goes up by 5. 20 + 5 = 25, 25 + 5 = 30.
3. 7 bright, 4 dim.
Adds to 11, differs by 3. 7 + 4 = 11 and 7 − 4 = 3. So 7 bright, 4 dim.
4. Hamza, Layla, Omar, Zayd.
Hamza 1st, Zayd 4th. Layla ahead of Omar → Layla 2nd, Omar 3rd.
5. 6 kits.
3 tools × 2 notebooks = 6. (astrolabe-leather, astrolabe-cloth, quadrant-leather, quadrant-cloth, sundial-leather, sundial-cloth.)
4th Grade
1. Yusuf 17, Zaid 19. Zaid leads by 2.
Yusuf: (3×5) + (4×2) − (2×3) = 15 + 8 − 6 = 17. Zaid: (2×5) + (6×2) − (1×3) = 10 + 12 − 3 = 19. 19 − 17 = 2.
2. Hamza draws, Yusuf measures, Idris records.
Hamza draws (Clue 2). Yusuf isn't the recorder (Clue 1) and drawing is taken → Yusuf measures. Idris records.
3. 6 charts left; 90 retired.
96 → 48 → 24 → 12 → 6 after 4 years. Retired: 96 − 6 = 90.
4. Musa 10, Yusuf 18.
Take the 8 off first: 28 − 8 = 20, then 20 ÷ 2 = 10 for Musa. Yusuf = 10 + 8 = 18. Check: 10 + 18 = 28. ✓
5. 3 groups; 15 comparisons per group.
18 ÷ 6 = 3 groups. In a group of 6 (A–F): 5+4+3+2+1 = 15 pairs.