Comparing and ordering numbers is an important skill for students at any grade level. But there is more to comparing and ordering numbers than comparing the individual digits in each of the placeholders. When we teach children to look a the first number, furthest to the left, and then if they are the same, look at the second number, we are teaching children a rote procedure to compare and order numbers. Are students really grasping the size of the numbers, the difference in the numbers, the real-world reason to compare numbers? We wonder why students don't have number sense. I believe it's because we teach routines and procedures that does not require them to have number sense. We are a huge part of the problem. The way we teach and our beliefs about mathematics. If you have read any of my blogs or have worked with me, you know I am big advocate and believe math is about understanding, not just memorizing rules and procedures.

I have been working on a series of math lessons to teach students conceptually the size of four digit numbers. This concept and lessons can obviously be scaffold down to smaller numbers and scaffold up to include numbers with decimals.

#1 __Roll and Build__ is designed to help students learn the representational value of numbers. Students chose to either use concrete materials (base ten blocks) or pictorial representations to build numbers.

#2 __Base Ten Match__, or base ten war is a game that uses pictorial representations and expanded form to conceptually understand number size.

#3 __Reach The Top__ is a game when students have the conceptual understanding and no longer require concrete or pictorial representation to compare and order numbers.

#4 Story problems, comparison problems specifically, give students the real-world application problems. For example: Sarah has 4,0981stamps in her collection and Joe has 4,100 stamps in his collection. Who has more? How do you know? How many more? For more information on comparison problems, check out my blog on Cognitively Guided Instruction.

If you have other ideas, please don't hesitate to email me at michellef@essdack.org. I am always looking for better lessons to use with students at all grade levels.