My fourth graders are really struggling. How do I get them to see what and why? Then how we change to decimals and how they are connected. I think once they "get it", they'll progress in the concepts. Any tips on how your students began to see the light?
I use Skittles in grade 2. Each gets 10 such as 1/10 are red 4/10 are green 3/10 are yellow 2/10 are orange red + orange = 1/10 + 2/10 = 3/10 green's 4/10 > red's 1/10 Convert that to decimals... .10 are red etc. Easy to go to 100 too. Not sure if this is what you are looking for grade 4. But maybe you can tweak it for what you need.?
Well, these are bigger numbers; equivalent fractions, mixed and improper. We have worked with number lines. I want to give them some real world uses so that they understand the purpose of why they need to know these things. I keep getting this blank look from them. Like "why are you making us do this?" kind of look. I was thinking of getting about 35 dimes and doing some activities with them. Many of them understand money.
Recipes and food talk are helpful. Example- if Jamie ate half a pizza and Sam ate one-fourth, how much pizza is left for dad?
We've done this. I am talking bigger fractions now, like why do we need to know all of the equivalent fractions? Why are they changing them. When will they use it? How will they apply it? Right now it's just a bunch of numbers to them.
We used fraction bars to introduce the concepts. We've used worksheets with the bars, circles and other shapes that they color in to represent the fractions. They aren't getting why they need equivelant fractions. The uses for it. And then mixed numbers, and then improper. They get confused with the three different ways to say the same numbers, at this point in the learning.
Equivalent, simplified fractions are easier to visualize in our head. Would you give your friend 317/951 of a pie or 1/3 of the pie? An extreme example, but kids should see the value in making things simpler for themselves. Have your kids define the words fraction, proper and improper. A fraction is just a part of a whole. As long as you have a part of a whole, it is proper. It is improper when you have a fake or impostor fraction, like 5/4. There is no way you can teach simplified fractions, improper fractions, and mixed numbers in a few weeks with fourth graders. It is going to take a lot of repetition and practice. Except at least a month for your kids to gain real competency of these skills, so don't worry if you're kids aren't readily grasping the concepts.
I always joke that I won't teach over 3rd because the math makes my brain hurt. I love teaching fractions because I can add in lots of crafty projects to help them understand. The most effective for me is having them cut different strips of colored paper to make fractions and then piecing them together to show equivalents. You could adapt some of the "primary" style activities to apply to the higher level math.
Money would probably be a good bet--we do some with that when introducting decimals, and it seems to give them a good reference. Then, you can look at some of the different coins--a quarter is 1/4 of a dollar, or $0.25.
I've found that having the students draw their own models is more effective than using fraction bars. To start off with, we talk about the figures best used for various fractions (i.e. a circle works well for halves, fourths, and eighths; a square/rectangle works well for any fraction). I also show them how you can easily turn a rectangle of halves into fourths, fourths into eighths, etc. by drawing a line that the divides the parts in half. This is very helpful for later when we start equivalent fractions! Also, for mixed numbers/improper fractions, I will present a problem such as "Jim ate one whole pizza pie and 2/8 of the second pie. Draw a picture to show how much he ate. How many eighths did he eat altogether?" and then "Joe ate 10 eighths of pizza. Draw pictures to represent. How many whole pies/parts of a pie did he eat?" and since the kids are so familiar with drawing models it clicks very easily for them and it's easy for them to grasp how mixed numbers can equal an improper fraction.
Have them do a survey. Have them ask 20-30 people 3 or 4 multiple choice questions. Then have them analyze the results. So, for example: What is your favorite ice cream flavor? A) Vanilla B) Chocolate C) Strawberry They survey 20 people and 10 choose chocolate, 8 choose vanilla and two people choose strawberry. Then they put their results in the form of a fraction. Ask them if it's easy to visualize exactly what portion of the people liked chocolate if it's in the form of 10/20. Show them the fraction in reduced form, then ask if it's easier to visualize 10/20 or 1/2. Repeat with the rest of the results.
One thing that has been important for our struggling fourth graders is to link different fraction representations: visual area (circular, rectangular, etc.), linear (fraction bars) and/or locations on a number line, and as parts of a set (we like arranging items into arrays to make partitions easy). (Fractions as division or proportions gets worked into higher grades.) We played games linking four models: area/visual models, parts of a set, on a number line, and in standard form. We talk a lot about comparing part to whole (e.g. it's 3 jumps on the number line out of 8 equal jumps from 0 to 1. Each jump is 1/8, and it's 3 out of 8 or 3/8 of the way from 0 to 1.) Then move onto lots of work with equivalent fractions!
