Reasoning · Grade 2-2 Making Four-Digit Numbers
Problem
Only 1, 3, 7 can lead, so there are 3 × 6 = 18 numbers.
Each leading digit (1, 3, or 7) starts its own group of 6 numbers, so a tidy count of 18 tells me how big the staircase is.
4.NBT.A.2Make A Systematic ListEach of the three possible leading digits opens a group of 6 numbers, so 18 numbers can be built in all.
After the leading card is chosen, the three cards left can be ordered in the remaining places without the first choice restricting them.
A number has exactly one leading digit, so the three groups never overlap and their sizes can simply be added.
Grouped by leading digit, the whole list comes out ordered.
Sorting first by the thousands digit, then the hundreds, then the tens, then the ones gives the exact order, just like alphabetical order for numbers.
4.NBT.A.2Make A Systematic ListThe two ends of the list are 1037 and 7310.
To make the biggest number put the biggest cards in the highest places; to make the smallest, the smallest allowed cards go up front.
4.NBT.A.2Look For A PatternCounting six in from each end gives 7013 and 1730.
The six biggest numbers are exactly the ones starting with 7, and the six smallest are the ones starting with 1, so the 6th from each end is the smallest 7-number and the largest 1-number.
4.NBT.A.2Make A Systematic ListList the numbers neatly by their first digit and the order falls right out - then just count six in from each end!