Scaffolding division!
In schools, there is huge variation in how much emphasis teachers put on looking at division and multiplication facts together.
Division is often treated as the poor relation of multiplication and neglected!
Generally it is taught after multiplication and not alongside it, as though somehow it is a separate thing to multiplication rather than an integral part of it. The neglect of division leads to fear of division and this can become a vicious cycle, for students and teachers!
In England the introduction of a statutory multiplication check for our 9 year olds has exacerbated the problem. The test comprises 25 multiplication questions. Not a division in sight!
Making the link between multiplication and division facts is integral to the FunKey Five Steps program. In Step Five children are asked a division question in the form: How many x in y? They answer with a known multiplication fact.
Stem division question: How many x in y?
The child in the video below is 8 years old (Year 3 in England) and has English as a second language. Before we worked with the stem division question, I got the counters out. I asked her: How many 2s in 10? I modelled how to work it out. We counted out 10 counters and then made 2s until we’d used up all 10 counters. We had made 5 twos. We did it again with all the other multiples of 2. By then I was confident she understood the meaning of the stem question.
I was also confident she knew her 2x table multiplication facts. (She’d cracked Steps 1 - 4 of the Five Steps program!) We were ready to have a go at Step 5!
The FunKey Times Table cards provided a wonderful scaffold for her. I was holding the multiples of 2 in random order. She could see the numbers on the card so she didn’t need to hold them in her head, which allowed her to focus on language and meaning. Her fluency and confidence in interpreting the question and providing the reply improved quickly.
The visual support provided by the FunKey Times Table cards was an essential part of how the child in the video managed to bring together her understanding of mathematical structure and the language needed to talk about the mathematical structure. The cards provided an easy vehicle for repetition of the stem question and strong visual support to bridge from the known multiplication fact to the related division fact.
The next step would be to remove the cards from sight and ask the same stem question. This is what you can see the children doing in the video for Step 5 (go to Five Steps). One child asks the stem question, and the other child answers it.
There is a growing understanding that good maths teaching includes helping children to express themselves mathematically. Ideally we want children to learn the maths and the language of maths simultaneously. That places significant cognitive demand on a child, particularly one operating in a second language.
To ensure success, we need to carefully scaffold the learning. In the video you see the combined power of a stem question and the visual support of the FunKey Times Table cards producing fun and effective learning.