Carnival Bears The bears could only do two different kinds of moves. They could slide onto the next mat if it were empty. If the next mat was not empty, they could jump over one other bear to an empty mat. The black bears only moved from left to right and the brown bears only moved from right to left.

Carnival Bears When the trick was over, the bears had switched places. All the black bears were on the right side, and all the brown bears were on the left. The bears needed 15 moves to switch places. Explain how they did it.

Mathematical Thinking Reflection Which domain of the standards do you find it difficult to make a connection to Algebraic Thinking? Describe an activity that you use that helps make the connection.

Marcy’s Dots A pattern of dots is shown below. At each step, more dots are added to the pattern. The number of dots added at each step is more than the number added in the previous step. The pattern continues infinitely. Marcy has to determine the number of dots in the 20th step, but she does not want to draw all 20 pictures and then count the dots. Explain or show how she could do this and give the answer that Marcy should get for the number of dots. 1st step 2nd step 3rd step

Wrap Up & Homework Homework Complete Marcy’s Dots problem Analyze at least two students’ work on Marcy’s Dots using NEHI Read Never Say Anything a Kid Can Say Respond in your journal to the prompt: “How can I apply . . . ”