Just the other day, I taught a lesson about making a TEN to add sums greater than ten. For example, with 8 + 6, you could increase the 8 to a 10 and reduce the 6 accordingly by 2 to make a 4. Thus, 10 + 4 = 14. Adding with a zero easier to do mentally. But as I soon discovered, my second graders could NOT mentally make a ten in their heads. They did not have automaticity for the addends that made sums of 10. So I had to stop the lesson and go back and have them practice just making a ten with two addends.
Many, many years ago I taught first grade. Back then, I had been trained in Math Their Way. By the end of the year, my first graders could make ten mentally. They pretty much knew all the math facts to 20! Math Their Way is a developmentally appropriate curriculum to teach addition and subtraction. The ability to make ten or to mentally rearrange numbers and internalize the addition facts gave these first graders a tremendous conceptual understanding of addition. Why don’t we have that today?
WHAT’S THE PROBLEM?
Simple answer: time! We just do not give students enough time to internalize these strategies, so they use them effortlessly. The same thing happens in all the grades. In third grade, we just expect students to memorize the multiplication tables without internalizing strategies that help them learn those facts. My youngest son is in fourth grade, and the same thing is happening in which the school is using a math textbook and just going page by page. This results in literally overwhelming the student with strategies to multiply multi-digit numbers without giving the student time to internalize these strategies.
WORKING AT THE SYMBOLIC LEVEL FIRST IS A NO-NO!
I have been teaching third grade since the early 2000s. The last time I taught second grade was before the Common Core Standards were adopted. I’ve always wondered why my incoming third graders STILL struggled with basic addition and subtraction facts. I really didn’t have the luxury to slow down because I had to teach multiplication! So what ends up happening is we send third graders onto fourth grade still having NOT solidified addition and subtraction strategies.
If you look above at the textbook example problem, you will see that this is all done on an abstract level. Students in second grade still need to operate at the concrete level (manipulatives, realia) before moving to a connecting level (manipulatives and numbers/symbols) and finally working at the symbolic and abstract levels.
I had the great idea of using a laminated card with a math frame so we could do many of these problems as guided practice. What I quickly found out, was that my students could NOT mentally come up with an addend that would make a ten. I assumed that they had had enough practice with ten frames in first grade. Making a ten should have been second nature. But it was apparent that it was not! So I had to backtrack and begin by practicing making a ten. They just needed more practice in various ways, even if it meant using their fingers.
PRACTICE MAKING A TEN
Games are always a great way for kids to practice basic skills. We practiced making a ten using a die. I would roll one die, and the students had to hold up the number of fingers to complete the ten (what’s the missing addend? is the terminology I used).
Another way was to use the Chromebooks and find online games. I found 2 particular games that I found fun and accomplished the task of finding corresponding addends that add up to ten.
This online game can be found here: http://www.mathplayground.com/number_bonds_10.html.
This online game can be found here: http://gotkidsgames.com/tt/tt.html.
We also added all the combinations of 10 to our Math Journal for reference. There we noted that there were patterns to making a ten. Additionaly, we also found a double and demonstrated the Commutative Property of Addition.
I found this YouTube video particularly helpful to my students as well!
An anchor chart showing different addition strategies also hangs in our class. We have not added the Make a Ten strategy yet and won’t until the students are more proficient in just making a ten.
The empty space is for the Associative Property of Addition. We will use this property to make tens. I still to this day remember one of my math teachers showing us this simple trick. When adding numbers in a column find the combinations of ten first! So simple, but powerful.
USING THE CONNECTING LEVEL
If you’re familiar with Math Their Way, the connecting level is the level in which students connect conceptual understanding (using manipulatives) to symbols to represent the same. We used counters to represent each added in an addition sentence such as 7 + 5. We arranged each as a ten frame (5 across). Then we moved counters from one number to the other to make a ten. Then students could see that all we had left to do was add 10 + 2 = 12.
There is one more step I will use to teach this strategy before practicing in the book again. This video demonstrates it wonderfully. Instead of using numbers, the teacher draws circles for part of the making a ten strategy. This is perfect! The students can visually see what needs to be combined to make a ten and what is left to add. I’ve also added a link to this video for parents to watch as well!
Once your students can mentally make a ten, then it’s on to multi-digit addition. Check out this blog post on using the Compensation Strategy to add multi-digit numbers.