Foundational maths facts

Principle: With spoken languages, native speakers don't construct complicated sentences using grammar rules on the fly. Instead, they have heard many examples of different forms. For example, the 'there is' forms can get really complicated, even in English:

There is a dog... Is there a cat? There used to be a house there. Shouldn't there be another option? Wouldn't there be a problem? Could there not have been another solution? And so on.

However, the experienced native speaker will just say them automatically without thinking. When learning a foreign language however, these are a nightmare. Most educational settings would have students learn the grammar rules in order to construct these phrases on the fly:

Il y a un chien. y a-t-il un chat? Il y avait une maison la-bas. Ne devrait-t-il pas une autre option? N'y aurait-t-il pas un probleme? Ne pourrait-t-il pas une autre solution?

These are just some of the possible French translations of the previous list. One of the main reasons then why we fail to learn foreign languages is that we are taught to construct with grammar - instead of learning the tricky scenarios by heart.


It's the same thing with basic maths.

We are typically only taught times tables by heart, and maybe some basic number bonds. Maybe a few prime and square numbers, but that's it. The reality however is that people who get on and do well with maths will have a much greater repertoire of learned maths facts. The point of this flashcard set is thus to provide learn-by-heart practice with the essentials (with a few bells and whistles.)

For example, school students in 'top set' will typically 'just know' that multiplying by 0.75 means 75%, which means halving something and adding on half as much again, whereas the lower set student, not having that learned knowledge, typically struggles and tries to work things out from first principles, which is again is even more harder if their times tables and basic halving knowledge is poor.


As such, this flashcard set is a 200-odd set of great essential arithmetic facts / knowledge that if practised and learned by heart, will both speed up mental arithmetic and more importantly, reduce the fear and improve the confidence of the learner in general.

As such, the set includes the following types of facts:

1. The trickier times tables pruned from the normal ones
2. low-end 13,14,15,16,17,18,19 and 20 times tables, up to about 5 e.g. 5 × 13
3. Basic primes, squares, cubes, and triangle numbers
4. Powers of 2
5. Some approximate constants like pi and √2
6. Doubling and halving up to 50
7. Divisibility rules
8. Basic algebra
9. Basic number bonds
10. Decimal - fraction - percentage equivalents for the most common fractions
11. Basic multiplication and division reasoning
12. Basic fraction knowledge
13. Basic modulo / remainder
14. Basic Formulas

There are currently two versions of these foundational maths facts - small ( about 200 ) and large ( about 400. )

Note: This is the same set no matter what the difficulty level has been set to, as it is supposed to be foundational.