# Adding and Subtracting Using Place Values

Learning how to add and subtract by using place values is a first grade, Common Core math skill: 1.NBT.4. Below we show two videos that demonstrate this standard. Then, we provide a breakdown of the specific steps in the videos to help you teach your class.

Prior Learnings

Your students should be familiar with counting from 1 to 100 using 1’s and 10’s, starting from any number. They should also be able to read, write, and represent objects using numbers between 0 and 20 (K.CC.1-3).

Future Learnings

Later on, understanding place values will enable your students to skip-count within 1000 (counting by 5’s, 10’s, and 100’s). They will also be able to read and write numbers by using “base ten numerals, number names, and expanded form” (2.NBT.1-3).

Common Core Standard: 1.NBT.4 - Add within 100, both one and two-digit numbers and multiples of 10; use concrete models, drawings, and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction

Students who understand this principle can:

1. Use physical models, drawings, etc. to explain addition within 100 by adding a one and a two-digit number.
2. Use physical models, drawings, etc. to explain addition within 100 by adding a two-digit number and a multiple of ten.
3. Use physical models, drawings, etc. to explain addition within 100 by adding 2 two-digit numbers.
4. Break down both addends, using partial sums, to add within 100.
5. Break down one addend, using partial sums, to add within 100.
6. Explain why, when adding numbers, a “new ten” is sometimes made.

Video 1: Different Methods to Add Large Numbers

This video demonstrates three different ways to solve adding two large numbers together. The girl in the video is confused because she at first does not know how to solve 43 + 21. Then, she remembers 3 different methods she learned in school for how to solve these types of problems.

The first method uses blocks to solve the equation.

1. First, break the numbers into 10s and 1s.
a. The video shows 43 and 21 as blocks, broken down  into groups of 10s and 1s.
2. Add the two 10s together.
a. 40 + 20.
3. Add the two 1s together.
a. 3 + 1.
4. Then combine them to find the total: 64.

The next example follows the same pattern, except without blocks for aid.

1. 40 + 20 = 60.
2. 3 + 1 = 4.
3. 60 + 4 = 64.

The last example uses a number line to solve the equation.

1. Start at 43 (the bigger number) on the number line.
2. Then add 20 by 10s.
a. One 10 to get 53 and another 10 to get 63.
3. Then, only one more number is left: 1.
a. 63 + 1 = 64.

The video ends by reminding students that they can add large numbers by breaking them into 10s and 1s and using a number line.

Video 2: Adding Large Numbers in Columns

The video begins by doing a brief review on place values and what they are: “A place value shows the position of a digit in a number.” For example, if a number has 6 tens and 2 ones, then the number is 62.

Boddle then explains that place values can be used to make addition and subtraction easier. The video then provides a few examples for students to see how the concept works.

1. In the equation 23 + 5, students can line them up in a column.
a. Make sure the place values are aligned.
b. 1s over 1s and 10s over 10s.
2. Start by adding the numbers in the 1s place.
a. 3 + 5 = 8.
3. Then add the numbers in the 10s place.
a. Since, 2 is alone in the 10s place, bring it down to the total.
b. Or think of it as 2 + 0 = 2.
4. 23 + 5 = 28.

The video then gives another example: 35 + 7. It demonstrates how students can handle an addition equation that carries a new number over into the 10s place.

1. Write the equation in a column.
2. Add the values in the 1s place.
a. 5 + 7 = 12.
3. The video then reminds students that only 1 number can be written per place value.
4. Only the 2 from the 12 is written, and it is in 1s place.
5. The 1 goes on top of the 3 as they are both in the 10s place.
6. The 1 and the 3 are added together.
7. The answer is 42, so 35 + 7 = 42.

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