Improper Fractions and Mixed Numbers
At some point at the end of last year, I decided that I was going to teach multiplication and division concepts each Monday and fractions and decimals each Friday. My goal was for my students to find this concepts and skills tied into all of the other math we do during the year, as these are some of the critical learning targets for fourth grade math.
But I have also taught comprehensive of these topics as they came up in our math curriculum. So now we are working on our fractions and decimals units. We took time yesterday to review adding and subtracting fractions with like denominators. Today was a review of mixed numbers and improper fractions.
In the process of teaching how to convert improper fractions into mixed numbers, someone in the class suddenly realised that what they were doing was just division with remainders! They also realised why I had been suggesting that they list the remainder as a fraction. Once they made this connection, they were able to easily determine that 100/8 is equal to 12 4/8, since 8 x 12 = 96 and 96 + 4 = 100.
So we ended the math lesson with a challenge: 1000/21 is equal to what mixed number? I gave them
20 x 50 = 1000 and 21 x 100 = 21000 as helper facts. Working in groups, the students were tasked with solving the problem. They worked on it for almost 15 minutes before some of them figured out the answer. It was really cool seeing them tackle a math problem that they came up with on their own!