Equivalent fraction mosaics
The lesson began with this mosaic on the board. I asked children how they knew what fraction of it was blue. They said count the blue squares. They knew the denominator would be 36 because they used their knowledge of arrays to explain that 6 rows across and 6 rows down meant there were 36 rows inside.
I set the children off in partners to work on this first activity and observed and intervened where necessary. They were all able to write the fraction in its simplest form because of all our prior work on equivalent fractions.
I then was very interested to see how children rearranged the squares on the black 6x6 grids. They chose to colour the squares instead of cutting out. Lots of discussion and reasoning was generated through this. Examples are below this PDF.
12 of your mosaic must be green.pdfN.B - my children noticed the relationship between the numerator and denominator of unit fractions so were using that to know what it was equivalent to - e.g. 3/9 is 1/3 because 3 goes into 9 three times - this was helpful when we were using the context of a picnic. The next step is to show the division of numerator and denominator. I'm going to do this using bar models. So 3 divided by 3 = 1
and 9 divided by 3 = 3
I got the children who finished first to share how they had 'proven' their answers and to compare with each other to come up with which way was the clearest.
The children came to the board to model how they had coloured it in and explained why. We discussed the bottom image being better for proving the answers because you could fold the paper into 3 to clearly see the third, and also fold it into sixths.
