What should be written in the blanks circles rectangle so that the sum of fraction on each side of the triangle is the same
Answers
Answer:
Step-by-step explanation:
This problem solving unit is suitable for Level 5 (or Level 6) students.
In this problem solving unit, we look at numbers that fit into a triangular arrangement of circles. The point of this unit is to give students a chance to
see how mathematicians operate
display ingenuity and creativity
practice arithmetic in context
learn what generalisations, extensions, conjectures, theorems, and proofs are
work through a completely novel situation and try to develop a mathematical theory around it
Specific Learning Outcomes
Solve a mathematical problem.
See how to generalise and extend a problem.
Understand why and how mathematical statements may be justified.
Work with others to solve a problem and generate ideas.
Description of Mathematics
Like all of the Problem Solving units, this one aims to introduce students to the underlying ideas of mathematics through a problem. The problem here requires only a simple knowledge of arithmetic but the process we go through demands a considerable use of ingenuity and creativity. In this unit we see how a mathematical theory might develop through experimentation, conjecturing, proving, generalising and extending. We also see that some proofs are ‘nicer’ than others.
As with all of these units it is difficult to break the development here up into lessons as we can never be quite sure how any particular class will progress. This will depend both on their ability and on your scaffolding. The right question asked at the right time will enable more rapid progress. However, you don’t want to make it too rapid!
Again like many of the units this one can be used at a variety of Levels. We have used it with students from 8 years old upwards. (It also makes a useful workshop for teachers.) Naturally you will expect older students to get further. With younger students it is probably enough to get all four answers and to make conjectures about the sorts of sets that will work and the number of answers that might be possible. But most classes we have worked with can be scaffolded into noticing Method 4 of the proof that there are only four answers for 1, 2, 3, 4, 5, 6. They can also start on the Eighth Circle Problem and the Homelink.
If your class hasn’t attempted the V-sets Problem Solving unit, we suggest you do that before this unit as it will give your students a good lead into some of the ideas that we used here.
As we have listed this unit for Levels 5 and 6, we have included some algebra. This may be omitted if you feel that it is too hard for your class. However, it might be a good extension aspect of the main problem and be valuable for your brighter students
Answer:
You can refer to KHANACADEMY for your doubt.