Justifying and Conjectures

The students are continuing to justify their mathematical thinking. They are encouraged to show their mathematical understanding in more than one way as a way to back up and prove their work and understanding. The above picture illustrates some of the work we have done on odd and even numbers. The students have explored what happens to numbers as odd and even numbers are added together in a very systematic way. Each time 2 numbers were added together, the students showed their thinking using tiles and a traditional number sentence and sketch. The students started by adding 2 odd numbers together. As they added more number sentences using only 2 odd numbers, they were challenged to see if any patterns or similarities occured. Then, the students added 2 even numbers together, following the same systematic sequence as described above. Lastly, the students added an odd and an even number together (once again, following the same overall structure mentioned above). As the students explored the numbers and shared their findings, we were able to come up with a classroom conjecture: If you add 2 odd numbers together, you always get an even number. The students also discovered that if you add 2 even numbers together, you get an even number.
Ask your child to prove to you that this holds true for us now. For example, ask your child to show you how 3+5, or 5+7 can show this, or how 2+4 or 6+6 proves this. Challenge your child to show you with many more number sentences. Have fun and Happy Math!