Introduction to Fractions

in grade 9 we started working on some fraction fluency tasks. Today we got out the big bin of fraction strips and explored the connections we saw.

We noticed that the denominator showed how many equal sized parts that the 1 is split up into. We also noticed that when there are more parts each part is smaller.

Then we looked at how to make some equivalent fractions. We noticed for all of the things equal to 1/2 they had even number denominators. For all of the ways to make 1/3 the denominators were all multiples of 3 etc.

Then we started to get creative. We can see here that 1/2 can be written as 1/6+1/6+1/6 or 3/6. But it could also be written as 1/3 since 1/6+1/6=2/6 which is equivalent to 1/3. So we know 1/3+1/6 is another way to write 1/2.

Next we looked at this statement. 1/4=1/12+1/6. To make sense of this students saw that the 1/6 is also equal to 1/12+1/12 so we could write 1/4 as 1/12+1/12+1/12 which is 3/12. If we divide both the numerator and denominator by 3 we get 1/4. We know that if we split 1/4 up into 3 parts each one will be 1/12.

This could be written as 1/4=1/12+2/12. We saw that this could also be a subtraction. 1/4-1/6=1/12 as well.

We showed that we could start with the question written in fractions, model it, build it in the same sized pieces and then get the answer. 3/4+1/8 was the question. We built it as written. Students then saw that we needed to make each 1/4 into 2/8. Then we can count the number of 8ths.

next we tried adding 1/4+1/2+1/3+1/12. We decided that it made sense to write it as 12ths.

3/12+6/12+4/12+1/12=14/12 which is more than 1. We wrote it as 12/12+2/12 which is 1 and 2/12 which can be 1 and 1/6, which is exactly what we got with our blocks.

We are going to keep working on fractions for the next little while, building up skills and getting more confident with the concept and the different representations and manipulatives.