When it comes to teaching the multiplication facts, students will often find multiplying by 6, 7, 8 and 9 the trickiest to master.
There are two main reasons why.
- Students don't understand the Commutative Property of Multiplication. They don't see 6 x 4 and 4 x 6 as being equivalent. While they can answer 4 x 6, the answer to 6 x 4 eludes them. This means that when they learn the 6x facts rather than understanding they only need to learn 6 x 6, 6 x 7, 6 x 8 (and 6 x 9 if you haven't taught it earlier), they think they need to learn 11 new multiplication facts (0 – 10x) or 13 if you're teaching to the 12s multiplication facts. That can be overwhelming.
- Students don't know any multiplication strategies to help them.
Sadly it's thought that as many as
40% of students have not developed a confident knowledge of these facts by the time they leave primary school.(Siemon et all cited in McIntyre 2014)
Using Multiplication Strategies
In a previous blog post, I've talked about the need to introduce the facts in an order other than numerical. That is, we don't introduce the facts starting at 0 and going through to 12x. If we change the order so we are beginning with the foundation facts 2, 5 and 10s multiplication facts, students can build upon the facts they know to help them with unknown facts.
The 6, 7 and 8s multiplication facts rely on skip counting from a known fact to find the answer to an unknown fact. For example, if a child knows the answer to 5 x 8, to find the answer to 6 x 8 they would count on (or add) one more group of 8. They should not be counting through all the multiples of 6 to find the answer.
The 9s multiplication facts can also use this strategy but students need to subtract a group of nine. If you've taught the facts in the recommended order, students will already know their 10s facts. 10 x 6 is 60 therefore 9 x 6 is one less group of 6 so the answer is 54 (60 – 6 = 54). There is another thinking strategy for the 9s facts but I won't talk about it here.
We can encourage skip counting for multiplication by using a hundreds chart, skip counting cards, and by playing the class game Buzz which has students practicing counting in multiples.
Provide Meaningful Practice
When it comes to practicing difficult concepts, worksheets that focus on answering rows and rows of multiplication facts are not the answer. Children are more likely to switch off or give up when presented with difficult concepts (or concepts thought to be difficult). It's not uncommon to hear a student say they're bad at multiplying or worse, bad at math. Of course, that's not the case, but once the belief is in a child's head, it's hard to shake.
Games are the best way to provide meaningful practice with these ‘harder facts'. Actually with all the multiplication facts!
Games are perfect to use not only in math centers but at your guided math table. When given the opportunity to play with you, students can explain their thinking. You get to see who is using effective strategies, who understands the commutative property of multiplication and who needs more time to master these facts.
Peer tutoring can also be an effective way of reinforcing the strategies. Pairing students with a good recall of the facts with students who need more support can work well. It's important that your more competent student understands their role in tutoring and is not just supplying the answers.
If you're looking for games with a strong focus on the ‘harder facts', these games will be perfect for you. You can grab them from my teachers pay teachers store by clicking the image below.
McIntyre, A. 201. Teaching the Basic Facts of Multiplication. Prime Number 29 (1): 14-15.