This week our focus was on how to compare and order equivalent fractions. We continued working on how to use number lines and different models to compare both fractions greater than one and mixed fractions. For most of my students, this was the first time they had ever heard the word equivalent before. My CT and I kept interchanging equivalent and equal throughout the week so our kids would consistently hear that the words are synonymous. Before we began teaching, we became aware of a huge misconception that our kids believed. They thought two fractions could only be equal if they had the same denominator and the same numerator. So, 1/4 = 1/4, but 1/4 is not equal to 2/8 because they have different denominators and numerators. This informed me that they were only looking at the actual numbers and not thinking about what the value of the fraction is.
That being said, we spent many days with the fraction tiles, which allowed them to visually see that two 1/8 pieces fits perfectly and evenly in one 1/4 piece. We also did an activity (attached) that showed the different ways 1/2, 1/3 and 1/4 could be made. After looking over the completed activity, we asked them to look for any patterns that could help them find out if fractions are equivalent. It took a while, but two students finally noticed that if a fraction was equivalent to 1/4, the numerator would divide into the denominator evenly four times. The pattern is true for 1/2 and 1/3. While, I was glad they discovered this, we made it a point to continuously check in to make sure they understood the meaning behind it. It is an efficient strategy, but it's pointless it they don't have a true understanding of the meaning behind it. Today we took our unit test and I am anxious to find out how they did. I noticed that many kids used that strategy to check their work. Now, believe it or not, this week concluded our fraction unit and next week we will be starting a whole new unit on measurement!
That being said, we spent many days with the fraction tiles, which allowed them to visually see that two 1/8 pieces fits perfectly and evenly in one 1/4 piece. We also did an activity (attached) that showed the different ways 1/2, 1/3 and 1/4 could be made. After looking over the completed activity, we asked them to look for any patterns that could help them find out if fractions are equivalent. It took a while, but two students finally noticed that if a fraction was equivalent to 1/4, the numerator would divide into the denominator evenly four times. The pattern is true for 1/2 and 1/3. While, I was glad they discovered this, we made it a point to continuously check in to make sure they understood the meaning behind it. It is an efficient strategy, but it's pointless it they don't have a true understanding of the meaning behind it. Today we took our unit test and I am anxious to find out how they did. I noticed that many kids used that strategy to check their work. Now, believe it or not, this week concluded our fraction unit and next week we will be starting a whole new unit on measurement!