Exploring the Role of Rounding and Estimating in Subtraction

All Things upper Elementary, a blog that I follow regularly recently had a post about teaching students to really develop problem-solving skills, rather than just learn rote algorithms.  See her fantastic post here.  This post really resonated with me as we are in the final days of our unit on subtraction.  Most of the kids can use the algorithm successfully to subtract multi-digit numbers.  Some cannot.  But even those that can use the algorithm don't really understand what they are doing.  To quote the ATUE:

"A written algorithm is meant to SHOW you have to think, NOT teach you how to think."

 

I realized that I needed to teach more thinking and less algorithm.  So today's freebie lesson plan is designed to focus students on using rounding and estimation to help them with subtraction.

 

Materials:  personal whiteboards, marker, and eraser for each child, the same for the teacher. 

Duration:  About 30 minutes (can be made longer or shorter)          Grade Level:     3-5

 

1.  Warm-Up:  Pose some subtraction problems using multiples of ten.  Start with problems like 90-70 = ? and end with problems like 8,000 - 5,000.

2.  Write your final problem in the warm up on the board (let's say it's 8,000 - 5,000).  Pose a related problem, leaving the first number the same, such as 8,000 - 4,875.  Have the students estimate a solution and show their answer.  If more than a few students get the answer wrong (it should still be 5,000), demonstrate how 4,875 rounds up to 5,000.  So the answer will be about the same as the original problem.  You can't just use the front of the number to estimate the answer.  You need to look at the whole number.

Do several more examples, coaching after each one as needed.  Once most of the class can successfully estimate the difference for each problem you pose, ask them to not end their estimates in zero. Pose problems in a sequence like this:

12,000 - 8,000 = (4,000)          12,000 - 7, 679 = (4,000)          12,000 - 7, 679 = (4,335)

Ask students to tell how they decided if the difference was more or less than their estimate.  If students do not come up with a method, show them how when the subtrahend is less than the estimate, the difference will be larger.  Pose several problems using this method. 

 

By using a lesson progression like this, you can help students think beyond the algorithm.  Enjoy!