1. Mathematical Reasoning

2. “People who reason and think analytically tend to note patterns, structure, or regularities in both real-world situations and symbolic objects; they ask if those patterns are accidental or if the occur for a reason; and they conjecture and prove.” National Council of Teachers of Mathematics (NCTM) (2000).Principles and Standards for School Mathematics. Reston, VA: NCTM.

3. Mathematical Reasoning “From children’s earliest experiences with mathematics, it is important to help them understand that assertions should always have reasons.” d “Why do you think that?” “Does anyone have a different answer?” “Oh, really?” National Council of Teachers of Mathematics (NCTM) (2000).Principles and Standards for School Mathematics. Reston, VA: NCTM.

4. Mathematical Reasoning “Classrooms in which students are encouraged to present their thinking and in which everyone contributes by evaluating one another’s thinking provide rich environments for learning mathematical reasoning.” y x ½ x y y x National Council of Teachers of Mathematics (NCTM) (2000).Principles and Standards for School Mathematics. Reston, VA: NCTM. What can we say about the second rectangle and the triangle? A = ½ x * y A = ½ base x height

5. What do you get when you add two odd numbers? An even…. …. an odd The sum of two odd numbers: Really? Really?

6. What do you get when you add two odd numbers? An even…. …. an odd The sum of two odd numbers: Really? Really?

7. Sidewalk Square Problem lines # of fields 0 1 2 3 4 5 6 7 8 9 10