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Improper Fractions and Mixed Numbers



This is my first year teaching 4th grade and my students are struggling with the concept of changing between mixed numbers and improper fractions. Any ideas to reinforce and review this concept??


I teach 5th but this is what I show them. Let's say the mixed number is 3 1/4. I tell them that changing it into an improper fraction is really putting the whole thing into fraction form. I remind them that the denominator tells me how big the pieces are and the numerator tells me how many of those pieces I have. Then I draw four circles on the board. (We also use individual white boards a lot, so sometimes I have them draw the circles and do this process.) Then I tell them to think of these as pizzas (or pies - whatever). I tell them I have 3 whole pizzas, so I shade in three of the circles - and I also have 1/4th of a pizza, so I divide the 4th circle into 4ths and color in one of the pieces. I show them how this represents 3 1/4. Then I ask, how many pieces would we have altogether if I "cut" the other pizzas up into the same size pieces? (I remind them that I'm not taking any of the pizza away or adding any more to it.) So then I draw lines on the other (whole) circles showing them divided into 4ths and mention that "all of these pieces are 4ths, right?" (even though they are are still together as a "whole" pizza). So then I ask "now how many pieces (4ths) do we have all together?" and we count up all the pieces. We see that we have 13 pieces and those pieces are 4ths, which makes 13/4. Then I do a quick "review" of how multiplication is like counting sets of things - and don't we have 3 sets of 4 pieces here? So 3 times 4 is twelve, but we also have to count the one other piece, so that makes 13 pieces altogether. I then use another mixed number and show them that now I can multiply the whole number by the denominator and then add the numerator to find out how many pieces there would be if I were to cut up the wholes into the same size pieces as the fractional part and that gives me the equivalent improper fraction. (I'm assuming they already know what "improper fraction" means.) Then to change from improper fraction to mixed numbers, just do the whole process backwards (explaining how division is putting things into groups).

I suppose if you wanted to, you could even use paper circles (or paper bars - call them candy bars) and have them actually cut them into pieces. You may need to have them do this a few times to see the connection between "cutting up the pieces" and just multiplying the whole number by the denominator and adding the numerator. Hope it helps. Have fun!