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Minds-On Activity: Dividing Fractions and Whole Numbers
Have the class stand up and coagulate in the centre of the classroom. Ask them to split themselves in half; direct where the split will be made if necessary. Pose the question "How many groups are there now in the room?" The students can see that there are two groups in the room. Let them know that they just witnessed a whole number being divided by a, and show it numerically on the board: 1 (class) / 1/2 = 2 (groups). Repeat the exercise by asking the class to split themselves in thirds, and quarters. Do they notice any patterns?

Challenge question. What if we started with two classes? How would this change the answers?

Minds-On Activity: Volume of a Cylinde**r (as taken from Nadine Long's Wiki)**


Take two different-sized* glasses (see below). You have to give one to yourself and one to your little brother or sister so you can both have a glass of chocolate milk. You want to get more chocolate milk than your brother or sister. Which glass has a larger volume?

 // "I want you to decide in your head if you think the short cup has a larger volume, or if you think the tall cup has a larger volume or if the two cups have the same volume. Please move to the sign in the classroom (posted on the wall) with the decision you came up with. The groups who had the same idea have five minutes to try and find out if your decision was correct. W hich cup has the larger volume?"//

Show the students using water that despite the height difference, they have the same volume.


 * note that this exercise is designed to be done with two glasses of similar volume, but different in dimension.

Linking Cubes - Solving Percentage Problems (partnered with Giti Gunarajah)

 * 1) Build the following object out of linking cubes. What is the percentage represented by the blue cubes? What is the percentage represented by the red?
 * 1) Build the following object out of linking cubes. What is the percentage represented by the blue cubes? What is the percentage represented by the red? Do you notice any patterns?




 * 1) Build a triangle with 1/36 green, 1/3 yellow, 2/9 blue, and 5/12 red.
 * 2) Build a parallelogram with an area that is 2/15 green, 2/5 yellow, 4/15 blue, and 1/5 red.
 * 3) What percentage of a yellow piece does a green piece represent?
 * 4) Build a hexagon with 2 red blocks, 2 blue blocks, and 6 green blocks.

A Lesson Script...
Based on the explanation video that I found, and my own thinking, the following is a partial script that I created for a Dividing Fractions lesson.

Explanation video: []

**Introduce topic:** //Dividing fractions and whole numbers looks intimidating. Thankfully there is a trick to solving these problems.//


 * Start with something they know:** //Remember how to multiply fractions? Multiply both the numerators and denominators to get your answer.//


 * Ask questions:** //How can we set up a fraction so that it is being divided, instead of multiplied? Can we use this technique in reverse? Is there an advantage to doing this?//


 * Reasonable explanations:** //By turning a division of fractions problem and into a multiplication of fractions problem, we have simplified the problem so that it can be easily solved.//

A Small Real-World Problem (partnered with Jess Stone)


The above Word document contains a fuel-consumption problem that Jess and I developed. It covers a number of concepts, including:


 * collecting data about cost of gas
 * collecting data about vehicle fuel consumption and capacity
 * collecting data about Trans-Canada Highway length
 * making assumptions about stop times
 * making assumptions about average speed
 * calculating rate of fuel consumption
 * ratios (fuel consumption to speed)
 * solving equations

http://awesome.good.is/transparency/web/1009/student-achievement/flat.html