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CBSE Class 5 · Mathematics

We the Travellers — II

Official NCERT chapter from Math-Mela (book code eemm1). ExamMaster notes are original teaching at CBSE Class 5 depth.

This lesson follows the official chapter “We the Travellers — II” in Math-Mela. The words below are ExamMaster’s teaching, not a paste from the book. Use the NCERT chapter for the classroom sequence; use these notes to hold the idea without copying exercises or figures.

  • CBSE Class 5
  • Easy level
  • 8 concepts

1Making two group-sums equal by swapping

Two piles can be made equal by moving items from the heavier sum to the lighter. The total of both piles stays. Only the split changes.

Throwing items away is not a swap.

Figure. Two group-sums match after one swap. Start with 9+6=15 and 7+4=11. Exchange the 6 and the 4: 9+4=13 and 7+6=13. The tiles that moved are the whole method; nothing else is added.

How it works

  1. Add pile A and pile BTwo sums.
  2. See which is largerThe extra.
  3. Move half the difference if it is evenA swap that equalises.

2Fuel arithmetic is adding litres with place value

Litres add in ones, tens, hundreds — houses, not a mash. 28 L + 15 L is 43 L.

Adding 28 and 15 as 2815 is not litres.

Figure. Fuel is added in houses. 240 litres is 2 hundreds, 4 tens, and 0 ones — the 0 keeps the ones house open so the 4 stays a tens digit. Swapping ink to 204 litres would move 36 litres.

How it works

  1. Line up ones8 under 5.
  2. Add ones, then tensCarry if needed.
  3. Write L after the sum43 L.

Add two tank-fills

A tank holds 28 L. A can adds 15 L. How much fuel now?

  • Start28 L
  • Add15 L
  • Ones8+5=13 → 3 ones, 1 ten
  • Tens2+1+1=4
  • Now43 L

Pro tip. Litres add by houses. Check: 43 − 15 = 28.

3Regroup ones as tens when the tank fills

When ones of litres pass 9, trade 10 ones for 1 ten. The fuel amount stays; the houses change.

Writing 13 in the ones house is an unfinished trade.

Figure. When ones pass nine, bundle ten of them as one ten. 8 ones plus 5 ones is 13 ones, which is 1 ten and 3 ones left in the tank-counter. The tank did not gain a new kind of litre; the house changed.

How it works

  1. Add onesSee 10 or more.
  2. Trade 10 ones → 1 tenCarry.
  3. Leave leftover ones0 to 9.

4Different vehicles need different fuel amounts

A scooter and a bus are two stories. Do not add their litres unless you mean a total of both tanks.

“Fuel” without which vehicle is mute.

Figure. Different vehicles take different fuel amounts for the same trip idea. The bus bar is 40 L, the car 12 L, the scooter 3 L. Compare the litres, not the size of the drawing of the vehicle.

How it works

  1. Name the vehicleThis tank.
  2. Name its litresThat amount.
  3. Add across vehicles only if the question asks a combined totalTwo tanks.

5Subtract to find how much fuel was used

Start 43 L, now 17 L, used 26 L. Used is a take-away of litres.

Do not add when the story is a burn.

Figure. Used fuel is a take-away from a counted start. 40 L in the tank minus 15 L burned leaves 25 L. The 15 is a part of the 40, not a new tank.

How it works

  1. Write start litres43 L.
  2. Write now litres17 L.
  3. Subtract26 L used.

6Estimate first

28 + 15 is near 30 + 15 = 45. Estimate by nearby tens, then compute exactly.

The estimate is a neighbour.

Figure. Estimate on nearest tens before you add the exact litres. 38+41 is near 40+40=80; the exact sum is 79. The estimate is a neighbour, not a second answer you report as exact.

How it works

  1. Round each addend28 → 30.
  2. Add thoseA neighbour.
  3. Then compute exactlyCheck you are close.

7Check by the opposite action

After 43 − 15 = 28, check 28 + 15 = 43. Rebuild the start.

A new vehicle is not a check.

Figure. The opposite action puts the used 15 L back. If 40−15 made 25, then 25+15 must make 40. A check that fails means the take-away was miscounted, not that addition is a different story.

How it works

  1. Keep the result28.
  2. Do the opposite+ after −.
  3. Demand the start43, or redo.

8Save fuel is the story; the litres are the maths

Saving is the setting. Plus, minus, and houses are ordinary litre-arithmetic.

Do not invent a travel-only minus.

Figure. “Save fuel” is the story. The maths is a litre difference you can count — here 12 L less than the first tank. A story without a litre number is not yet a calculation.

How it works

  1. Keep the slogan as settingSave fuel.
  2. Compute on litresHouses.
  3. Use school + and −The trip is not a new rule.
Start 43 L, now 17 L. Fuel used is
  1. 26 L
  2. 60 L
  3. 17 L

Used is start minus now.

Notes

  • The official chapter title is “We the Travellers — II”. Teach the school test for that title, not a contest shortcut.
  • If a step needs a later class, stop. The next official chapter will pick it up.

Formulas

  • Now = start + filled (same unit).
  • Used = start - now.
  • If ones \ge 10, carry 1 ten.

Recap

Hold these pegs from the official chapter “We the Travellers — II”. The wording is ExamMaster’s teaching, not a textbook recap.

Making two group-sums equal by swapping
Two piles can be made equal by moving items from the heavier sum to the lighter.
Fuel arithmetic is adding litres with place value
Litres add in ones, tens, hundreds — houses, not a mash.
Regroup ones as tens when the tank fills
When ones of litres pass 9, trade 10 ones for 1 ten.
Different vehicles need different fuel amounts
A scooter and a bus are two stories. Do not add their litres unless you mean a total of both tanks.
Subtract to find how much fuel was used
Start 43 L, now 17 L, used 26 L. Used is a take-away of litres.
Estimate first
28 + 15 is near 30 + 15 = 45. Estimate by nearby tens, then compute exactly.

Practise We the Travellers — II

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