There are 100 multiplication facts students are expected to know, from 0X0 to 9X9. These are developed over grades 3 and 4, so full automaticity isn’t expected yet for all the facts. To this we typically add the 10X facts, which are technically double digit multiplication.
Research suggests that sheer memorization is less useful than using an understanding of numbers to help learn the facts. A variety of strategies are used to support memorization. These strategies also help with various number relationships in later years. Most of the strategies rely on derived fact strategies, which have students use a fact or skills they already know to help find the unknown fact.
The buttons on the right lead to a variety of strategies. While the Ontario curriculum states that students multiply to 7X7 in grade 3, many researchers suggest this split is not as effective as doing the facts in a different order. A solution is to discuss facts beyond 7X7 when looking at a strategy, but then only assess students on the lower facts.