## Monday, November 3, 2014

### Subtraction

Subtraction!  Why don't they get it?  I have been teaching mathematics for over 22 years.  I have taught elementary school and middle school math and it's the same story each and every year.  There are just some children who can't subtract.   Why?  I have yet to figure that out.  After many hands-on activities, plenty of practice of the skill, individual small groups, one-on-one conferences, not to mention computer and iPad games, there will still be a few students who "don't get it."

I worry about these kids.  Subtraction isn't a fluff n' stuff math algorithm.  Subtraction is a life skill that individuals need in the real world.

I can tell you everything that a 4th grader will do incorrectly when I first begin teaching subtraction. You know...things such as subtracting from the bottom up, if it is convenient, borrowing from the next place even if it isn't needed, beginning at the highest place value and, (Oh my goodness!), making a complete mess when borrowing across zeros. You would think that once these items are cleared up, every student could subtract by the age of 9 and 10 years old.

If I had to pick a standard that gives many students difficulty, it is the good old-fashioned subtraction algorithm.  This week-end, while working on my lesson plans, (I'm sure no other teacher has to spend parts of their weekend on school work), I came across a new idea for a hands-on activity for subtracting numbers.  I had already included the basic blah, blue base-ten blocks in my lesson plans for introducing subtraction with borrowing/regrouping.  Once I read the blog post about this new idea, I immediately edited my lesson plan.

The idea is to use unifix cubes for introducing subtraction with borrowing.  Instead of the students using the base-ten rod to represent the tens place, 10 unifix cubes are connected together.  When a child needs to borrow and regroup, the unifix cubes can be pulled apart and placed in the ones column.

This activity came from this link:  Break Those Numbers Apart , Beyond Traditional Math
There is an excellent explanation along with pictures to go with it.

I made the activity a whole class activity.  I participated with the students by modeling the problems along with them.  We took our time and went over each step in detail.  I loved the fact that my students could actually grab a ten and put it in the ones place by breaking it up.  Many of my students did not understand until today that the "1" they borrow actually is 1 ten.

We began by setting up our unifix cubes to represent only one number, 34.
(I finally got a chance to use my large jumbo magnetic unifix cubes! YaY!)

My students had containers of unifix cubes at their desks.  My desks are arranged in groups, so I placed a container in the center of the desks.  (If you teach an upper grade and you do not have enough unifix cubes for everyone, ask a Kindergarten teacher!)  I have as many as 30 students in a couple of my classes, and I am very thankful for Kindergarten teachers today.

Once they decided that color coordination was not necessary and took too much time, my students modeled the number 34.

Next, we wrote down 15 as the number to be subtracted.  As a whole class, we decided that 5 could not be subtracted from 4.  My students talked about how this issue could be solved.  The conclusion was that 1 ten could be moved to the ones place.  This would give the ones place 14 units.

Next, we broke the ten into pieces.  It was an eye-opening experience for some of my kids.  We made sure to use the unifix cube model with the algorithm as we continued the subtraction process.

Next, we subtracted 5 from the 14 unifix cubes in the ones place.  We made the connection to the algorithm.  The last step was to subtract the 1 in the tens place from the 2.  We discussed once again how the 1 in the tens place is actually a ten and the 2 is really 20.  This activity emphasizes that borrowing a 1 is really borrowing a ten.
For some reason, I did not get a photo of the subtraction in the tens place but, once we subtracted 1 ten from 2 tens we all had 1 ten left and 9 ones.

All in all, it was an excellent activity to introduce subtraction with borrowing/regrouping!  I will include it with my lesson plans each year. :)

If you are interested in trying this activity, please make sure and check out the Beyond Traditional Math link above.

If you think the magnetic unifix cubes are as cool as I do, here is some information about where to order them: