All Possible Combinations

When introducing how to determine all possible combinations of a given set of data or objects, we start slowly. We start listing out different combinations when looking at two spinners - one with the numbers 0-9 on it, and one with the colors red, green, blue, and yellow on it. The kids usually start volunteering different combinations, like 1 and green, 2 and blue, 5 and red, etc.

Where the thinking comes in is when I ask them if we've found all possible combinations. It doesn't take long for them to figure out they need some organization for their combination. Enter the tree diagram! We begin listing out our combinations using a tree diagram, then check to make sure we get all possible combinations. We usually only have to do this process two or three times before the kids see the relationship between the tree diagrams and multiplication. When you give kids tedious work, they naturally find the shortcuts on their own! :) 

I do point out it's important they understand the process of the tree diagram to see why the multiplication strategy works! It's SO important they understand the "why" of math!!!

Probability

Today we worked on probability. Probability is the measure of how likely it is something is going to happen. Up till now, most the kids have used words such as these for probability: certain, impossible, more likely, less likely, etc.We take it a step farther so that we may be more precise, and find the probability in fraction form.

Temperature

Temperature is nothing new for 4th graders, but some of the vocabulary can be unfamiliar. We worked with various thermometers (traditional, round, etc.) to determine the temperature. We also found the differences between two temperatures. Finally, we discussed words that could be used to describe what is happening to the temperature - rising, falling, increasing, decreasing, etc.

Relating Congruence to Transformations

4th graders should already have a good grasp on the definition of congruence - same size, same shape. After a brief review of what congruence it, we take it a step farther and decide what transformation has taken place between two shapes that are congruent.