Numbers, properties; expressions involve numbers and variables.
Smart estimates on the calculation results. If calculation result is an integer, them the simplest guessing technique is using divisors and check the last digit (that is the units-place digit).
There are more involved estimate techniques of expressions. Specifically, radicals can be approximated by fractions, so expressions involved radicals can be approximated.
A discussion on how to add two fractions with different denominators; with both a clear presentation of concepts and use visualize help.
For educators, when a student has made a mistake in calculation, sometimes we have to understand first why student thinks and does in that way, and then persuade them with clear concepts and strong reasoning.
The problem is about filling numbers 1 – 11 into all vertices and edges of a tetrahedron, and the numbers assigned to edges equals the numbers assigned to its two endpoints.
(It’s not really scrambling BUT looks like scrambling until you know or find the equalities on edge-endpoint numbers). The problem is interesting — but you got to know where to look, and how to search for a solution!
We reformulated the problem in previous post as numbers pair, both perfect squares.
Several approaches to the problem! Each has its own flavor and deserved mentioning.
Given an expression of n, like n square plus 6n plus 24, and declare it’s a perfect number. Can you find the integer n?
Seems clueless, eh?
And what’s the pair of numbers: both perfect squares, as mentioned in the title? Not in the original problem, but it’s one clue calling for you to construct; and to solve!
The answer to the Hunchbacked shopkeeper’s story: Simple! Both sheets are indeed balanced.
Read this post for more explanations!
— It’s a mystery!
Once there was a hunch-backed shopkeeper.
And he told the following story:
(For readers at grade 6/7 level and up)
“Once I lent 100 dinars, 50 to a sheik from Medina and another 50 to a merchant from Cairo. ..
Continue to read: you are invited to solve one math mystery!