We are almost done with our first module in math, sums and differences to 100. This is actually a concept we will be visiting and revisiting all throughout the year! Mastery in this topic is not expected till the end of the year. In this first module the children have been working hard learning some new strategies for addition and subtraction that are a natural continuation to those they learned in first grade.
Many addition or subtraction problems require no new strategies on the part of the children; they can clearly use their knowledge of basic facts to know, for instance, that 25 – 3 = 2, taking ones away from the ones. They can see that 30 + 30 = 60, adding tens to tens. No sweat!
Other types of problems require more work, and to do so we have been teaching the students different strategies. A goal for us in second grade, as indeed it is in all grades, is for our students to be flexible thinkers in math. In order to do so, they need knowledge of more than one approach or strategy for problem solving. If children have that flexibility in math, they will be able to easily choose the most appropriate strategy for any problem they encounter, and they will also be able to double check their work.
With this flexibility in mind, the children have worked on the following strategies in this module, which involve making the problems easier, by using our knowledge of basic facts:
Addition: Make a 10 with quick tens, and Make a ten with number bonds
Subtraction: Take out 10 with quick tens, and Take out 10 with number bonds.
Make a 10 with quick tens
39 + 4 = _____
a. Make 39 with quick tens:
b. Now, add 4 X’s. (We use a different shape, here X’s, to make a visual difference between the addends.) Make a ten with the first X you put down, by putting that X above the 9 ones (the circles). The rest of the X’s will go to the right:
c. We add up 1, 2, 3, 4 tens, plus 3 ones. The answer is 43.
40 + 3 = 43
39 + 4 = 43
Make a ten with number bonds
39 + 4 = _____
a. We look at the addend 4, and think how we can split it up and add part to 39 to make the next (multiple of) 10, which is 40. 40 is an easy number to add.
b. If I add 39 + 1, I have 40. So I break up 4 in a number bond of 1 + 3.
c. I add 39 + 1, which equals 40. Now I just have to add the last part of the equation, which is 3. 40 + 3 = 43.
In the above example of 39 + 4 using quick tens, we can see that the 4 X’s have also been split apart in the same manner as they have here in the number bond (1 + 3).
Take out 10 with quick tens
a. Make 35 with quick tens:
b. Often, we can take ones from ones, and tens from tens. Here we can’t, as the 9 is bigger than the 5 ones in 35.
I need to change one of my tens to ten ones, so that I can subtract 9 from it.
c. Now I can take away 9 easily, all at once with a line.
d. When I count what’s left, I have 26. 35 – 9 = 26
Take out 10 with number bonds.
a. The 9 in the ones is bigger than the 5 in 35. I take out a 10 from 35, so that I am able to subtract 9. I make a number bond. I know that 10 + 25 = 35, so I know what numbers to put in the number bond. (We have the children write this 10 in RED, and place it to the right, for closer proximity to the 9 which we’ll soon subtract from it.)
b. Now I can subtract. 10 – 9 = 1. (In the above example of subtraction with quick tens, we also took away nine ones from the group of 10, all together with a single line.)
10 – 9 = 1
c. Now I need to add up the 1 and the 25.
25 + 1 = 26
As noted before, we don’t expect mastery of addition and subtraction within 100 until the end of the year! There is lots of time for exploration and practice. Soon we hope the children will add these and other strategies to their “math tool box” which will help them become more flexible thinkers and problem solvers.
The Second Grade Team