The Pythagoras table and how results depend on the numbers
Explore the multiplication table, multiply and divide in sequence, see how a product and a quotient depend on their components.
- Ukraine: grade 2
- Russia: grade 3
Guide
A studio for Ukrainian grade 3 (НУШ textbooks, parts 1 and 2). The multiplication table is called «Pythagoras table» in Ukrainian books. It is good to explore: numbers repeat in mirror positions because 4 · 7 = 7 · 4.
Sequential multiplication and division: 3 · 2 · 5 is done from left to right, and so is 24 : 2 : 3. This gives handy calculation tricks.
Dependence of results: if one factor grows several times, the product grows as many times. If the dividend grows several times, the quotient grows as many times; if the divisor grows, the quotient shrinks.
Note: the full 10 × 10 grid is not drawn here, only columns of it in a table, but they show the same symmetry. The «why?» question links the result to the rule.