Problem
The star means greatest common factor, and 48 = 16 x 3 with 64 = 16 x 4 gives 16.
Finding the largest number that divides two numbers is just factor-pair thinking, which fourth graders practice when they hunt for common factors.
4.OA.B.4Make A Systematic ListThe bracket counts factors, and 16 has 1, 2, 4, 8 and 16, so it comes to 5.
Listing all the divisors of a small number in order is the same factor-finding skill, just counting how many there are instead of which is biggest.
4.OA.B.4Make A Systematic ListThe diamond means least common multiple, and 5 and 12 share no factor, so it is 60.
Replacing each defined symbol from the inside out and respecting the brackets is exactly how we read nested expressions with parentheses.
5.OA.A.1Identify Subproblems5 ◆ 12 comes to 60.
The ◆ was defined as the least common multiple, so the task is to find the smallest number that both 5 and 12 divide exactly.
A rule that defines a symbol says the symbol and its recipe always name the same number, so one may be written in place of the other.
5 and 12 share no factor except 1, so the smallest number reachable by whole 5s and also by whole 12s is 5 times 12 itself.
Counting up in whole groups of 5 lands on a whole number of 12s only after twelve of those groups, because no group of 5 can be split to help fill a 12.
When new symbols are defined, just swap each one for its rule and work from the inside out, like peeling an onion.