Eureka Math Module 1: Sums and Differences to 100
Our year begins with students beginning to master sums and differences to 20, and later applying these skills to one- and two-digit numbers up to 100. The children will call upon their budding knowledge of place value, and their understandings of the relationship between addition and subtraction to help them.
They will build upon skills they learned in first grade to do addition, such as counting on, in addition to learning skills which will help them make problems easier, by making ten and taking from ten.
Conversely, students can “count back” to subtract.
Making ten (or a multiple of ten) to add: You see that 79 is very near 80. Adding a number to a multiple of 10 is a lot easier! So you can break up the 6, adding 79 + 1 to make 80, then adding 5 to make 85.
We encourage children to be flexible with numbers, which includes “breaking them up” or decomposing numbers into smaller parts, as represented in number bonds.
With subtraction, a strategy that at first requires quite a bit of flexibility on the part of the students, but which will come in incredibly handy always, is the “take out ten” strategy when subtracting a single digit number:
In both cases children see that they cannot just simply subtract like units (take ones from ones, and tens from tens). We show them how to decompose the first number by taking out ten from the first number, and then subtracting the second number from the ten. In future lessons, the children will subtract two-digit numbers, which we will explain soon.
If children can mentally decompose numbers, and then use basic addition and subtraction facts to solve the problem, they will have acquired an incredibly useful mental strategy which will save them lots of time and which, in the long run, will not require pencil and paper. How cool is that?
Something we DON’T teach the second graders is the traditional algorithm.
The traditional algorithm always requires the use of pencil and paper! And it requires an excellent understanding of place value for it to make any sense.
We use manipulatives every day in our classes, such as base ten blocks, unifix cubes and ten frames.
base ten blocks unifix cubes ten frame cards
We have children draw numbers in base ten notation (example follows) and encourage them to organize their numbers neatly to facilitate counting.
For example, when making a representation of the number 17, we have them draw the number in base ten notation as follows, drawing a line to represent a ten, and then 7 black circles which represent ones as they are shown in a ten frame configuration:
base ten notation
They needn’t draw in the actual lines of the ten frame, only the black circles. These ten frame configurations are very easy for the children to identify without counting, and using them to organize their drawings helps children become more efficient.
In Eureka Math, the numbers are represented in a slightly different way:
Here is a way of representing 17, yet we find that as the children draw the circles in a line, they tend to smash them all together into a continuous line which they then need to count over again. The ten frame configurations place the circles into more easily identified groups.
You may find Eureka Math’s Parent Tip Sheet helpful:
The Second Grade Team