Problem
Build the largest three-digit number
Order the digits from greatest to least: 9, 8, 5, 1, 0. The largest three-digit number puts the three biggest in the hundreds, tens, ones places: 9, then 8, then 5.
Bigger digits in higher place values make a bigger number - basic place-value sense.
4.NBT.B.4Make A Systematic ListTurn each digit 180 degrees
Turning the digits of 985 each 180 degrees: 9 becomes 6, 8 becomes 8, 5 becomes 2.
A half-turn changes each digit into the shape it looks like when read upside down.
4.G.A.3Draw A DiagramReverse the order to read the rotated number
Because the whole number is turned at once, the order reverses too. The original ones digit ends up on the left. So 985 (turned) reads as the reverse of 6, 8, 2, which is 2, 8, 6 = 286.
Spinning a strip of digits halfway around flips left-right as well as turning each symbol.
4.G.A.3Draw A DiagramTurning the whole three-digit block 985 a half turn makes its digits come out in reversed left-to-right order, so the turned digits 6, 8, 2 are read as 286.
Why?
The three digits are spun together as one rigid block, so afterward they are still three same-size digits standing in a straight row, only turned to face the other way.
Why?
A turn lays the figure exactly onto its turned copy, point for point, so every length and angle stays equal and no digit is stretched or bent.
Why?
Turning that row a half turn carries the far-left digit over to the far right and the far-right digit over to the far left, so the digits end up read in the opposite order.
Why?
A half turn is a turn through 180 degrees, which is a straight angle, and a straight angle faces the exact opposite direction, so leftward is carried to rightward.
Subtract to find the difference
Find the difference between the original number and the rotated number.
Straightforward multi-digit subtraction once both numbers are known.
4.NBT.B.4Make A Systematic ListPut the biggest digits first to make 985, then turn it upside-down (digits change AND flip order) to get 286 - easy Grade 4 place-value and subtraction!
- Build the largest three-digit number
- Turn each digit 180 degrees
- Reverse the order to read the rotated number
- Subtract to find the difference