Predict, test, check

This game shows a random number between 100 and 99,999 on a number line, along with the two nearest multiples of 100 (or of 1,000) on either side. You choose which one it is closer to. There are 10 rounds, untimed, with points for each correct choice and a streak counter.

The rule you practise: look at the digit just to the right of the place you are rounding to. If it is 5 or more, round up; if it is 4 or less, round down.

Examples you might meet:

• 4,872 to the nearest hundred: the tens digit is 7, so round up to 4,900. To the nearest thousand: the hundreds digit is 8, so 5,000.
• 63,149 to the nearest thousand: the hundreds digit is 1, so round down to 63,000.
• 850 to the nearest hundred: the tens digit is 5, so round up to 900 (halfway rounds up by the usual school rule).
• 99,960 to the nearest hundred: round up to 1,00,000, one lakh.

Try saying each rounded number aloud in the Indian system before you pick.

This sprint gives 10 additions and subtractions of a four-digit number and a three-digit number, untimed. Before you type the exact answer, it asks you for an estimate. Then it shows how close your estimate was.

A good way to estimate here is to round both numbers to the nearest hundred. For example, 6,428 + 781: 6,400 + 800 = 7,200; the exact answer is 7,209. For 5,013 − 468: 5,000 − 500 = 4,500; exact 4,545.

Notice two things as you play. Your estimate is usually within about 100 of the exact answer, because each rounding moves a number by at most 50. And if your exact answer is far from your estimate, recheck the columns: a missed carry or borrow usually changes the answer by 10, 100 or 1,000.

This sorting game shows 12 word-problem cards. Each one is a division that does not come out exactly. Drag or tap each card into one of four bins: Round up, Round down, The remainder is the answer, or Split the remainder.

• Round up: 250 students with 45 seats per bus (5 r 25 → 6 buses); 100 mangoes, 12 per box (8 r 4 → 9 boxes); 27 people, lift for 6 (4 r 3 → 5 trips); 130 books, 25 per shelf (5 r 5 → 6 shelves).
• Round down: ₹500 for ₹45 notebooks (11 r 5 → 11); 100 cm ribbon into 15 cm pieces (6 r 10 → 6); 40 players into teams of 11 (3 r 7 → 3).
• Remainder is the answer: 50 laddoos among 8, how many left (2); change from ₹200 buying ₹30 pens (₹20); 45 days, how many days beyond full weeks (3).
• Split the remainder: 7 rotis between 2 (3½ each); ₹25 between 2 (₹12.50 each).

The lesson: always reread the question after dividing. Ask, "What exactly are they asking for?"

This game gives 12 story cards to sort into Add, Subtract, Multiply or Divide. Many cards contain a misleading clue word on purpose.

• Subtract: "Ravi has 12, 5 more than Sita" (Sita has 7); "245 km vs 180 km, how much farther" (65 km); "target 287, scored 198, how many more" (89).
• Add: "gave away 8, has 15 left, how many at start" (23); "38 students, 6 fewer than Class B" (B has 44); "spent ₹245, ₹55 left, how much at first" (₹300).
• Multiply: "₹12 pen, bag 25 times as much" (₹300); "18 rows of 24 chairs" (432); "12 buses of 45 pilgrims altogether" (540).
• Divide: "6 pens per packet, how many packets for 48" (8); "1,260 mangoes in 7 equal days" (180 a day); "₹360 shared equally by 4" (₹90).

For each card, picture the situation: joining, separating, comparing, equal groups or scaling. Then decide what is unknown.

This untimed sprint has 20 rounds. Up to half of them are word problems, picked at random from the ten below; the rest are generated sums with all four operations, where you estimate first. For each word problem, make your own quick estimate on paper, then give the exact answer.

1. Chennai–Delhi round trip, 2,182 km each way: 2,182 × 2 = 4,364 km.
2. Kirana sales ₹18,450 + ₹22,785 = ₹41,235.
3. Wheat 3,250 kg − 1,875 kg sold = 1,375 kg left.
4. 36 chairs at ₹845: 36 × 845 = ₹30,420.
5. ₹7,560 shared by 12 families: ₹630 each.
6. Runs needed: 287 − 198 = 89.
7. A 5,000 L tank at 250 L a day lasts 20 days.
8. Mumbai–Pune 148 km × 25 trips = 3,700 km.
9. Village of 4,68,352 plus 97,648 more = 5,66,000 people.
10. 1,440 laddoos in boxes of 24 = 60 boxes.

Each time, decide the structure first (join, separate, compare, equal groups, scale), then check by undoing.

This lab shows six expressions that come from word problems. You choose which operation to do next; the expression shrinks one step at a time. A rule card reminds you: brackets first, then × and ÷, then + and −.

• 4500 + 45 × 60 (school trip): 45 × 60 = 2,700 first, then 4,500 + 2,700 = 7,200.
• 500 - 11 × 45 (₹500, eleven ₹45 notebooks): 11 × 45 = 495, then 500 − 495 = 5 rupees change.
• (250 + 175) ÷ 5 (two classes sharing 5 buses equally): 425 ÷ 5 = 85 per bus.
• 287 - (98 + 100) (runs still needed after two partnerships): 198, then 287 − 198 = 89.
• 7560 ÷ 12 - 30 (each family's share minus a ₹30 fee): 630 − 30 = 600.
• (48 - 6) × 2300 (quintals of paddy sold at ₹2,300 each): 42 × 2,300 = 96,600 rupees.

Try doing the wrong step first in your head and see how far off the answer goes.