Dividing with mixed numbers and top-heavy fractions is one of those lessons where students have to combine a lot of topics they have learned in previous lessons. Equivalent fractions, mixed numbers, reciprocals and multiplying with fractions are all involved when dividing with mixed numbers.
The start of the lesson recaps division with fractions using the visual method which they learned the previously. More able students are normally comfortable using the written method and realise the 6/8 can be simplified to 3/4. The middle and lower ability students benefit from working on the diagram as this helps them visualise what is going on. This starter typically takes about 10 minutes once I have finished checking the student's mini-whiteboards and feeding back.
In the development phase we stick with the visual method for dividing with fractions but this time we use one whole circle and 3/4 of another. I find that once students are able to visualise dividing with normal fractions, dividing with mixed numbers and top-heavy fractions is much easier. To do this we work out how many eighths go into one and three quarters by counting the sectors then follow it up using the written method by converting the 1 3/4 to 7/4.
As we progress through the questions the majority of students move away from the visual method preferring instead
to use the written method. It really is fantastic watching the class put together so many aspects of their work on fractions to solve a single problem.
On the worksheet students are free to choose (within reason) their level of questions. Less able students use the diagrams to help them use the visual method. The core ability using the written method to attempt questions similar to those on the presentation. More able students apply their learning to the volume and lengths of cuboids. There's a challenge at the end where students combine multiplication and division of fractions and mixed numbers.
At the end of the lesson students match up a division with its solution. Questions range from dividing a mixed number or top-heavy fraction by an integer, ordinary fraction or another mixed number. The plenary takes around 8 to 12 minutes with students working on their mini-whiteboards so I can assess their progress and feedback.
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