Recently, while tutoring a group of grade 2 students, I realized that some of them were having a hard time understanding the value of each digit when representing 2-digit numbers. For example, when asked to represent the number 23, they would draw 2 hearts and 3 squares. When I asked them to use Base-Ten blocks, they knew to use 2 rods and 3 units, however, when I inquired to why they chose the rods, their only explanation was that they needed to choose two different things, one for each digit. Although used to work with Base-ten blocks at school, they clearly didn’t associate the value of each rod as being the same as ten units. After thinking about this for a while, I decided to try a new strategy. I wanted them to be able to visualize the value of each digit, so I enlisted the help of my children’s building blocks. So how exactly did I go about it? I provided the students with a pile of blocks, all the same size. We have square ones, so I used those because they closely resemble the units of the Base-Ten manipulatives. I asked each student to retrieve 16 blocks from the pile and place them on the table, in front of them. They counted the blocks once again and we verified that each child had 16 blocks. Then, I asked them to group the blocks in groups of 10. I explained that our numeration system is based in the number 10 because it is easier for us t remember how to count by 10’s (we proceeded to count by 10’s to exemplify just how easy it is 🙂 ). After they were done grouping the blocks, we discussed how we could only make one pile of ten units and one of six. I then asked them to stack the blocks from the pile of ten, and set this stack next to the loose blocks. At this point, I asked them to pretend the blocks were Base-Ten manipulatives. What did they see? Immediately they recognized the stacked blocks as being a rod, and the loose blocks as being units. I then asked them if they could tell me how many units a rod is worth. And the answer? An immediate 10! 🙂 Finally, I made a connection to how they use Base-Ten manipulatives to represent the number 16, and asked them how many units the digit 1 was worth in this case. They immediately answered 10! It was fun to see their facial expressions as the light bulbs finally went on, lol. We proceeded to represent other numbers, and when asked about the value of the ten’s digit, they were able to reply accurately every single time. To further explore this concept, I made the connection to expanded form. We started by analyzing the number 23 in order to figure out what 23 was equal to. We worked with the building blocks in the same way as we did for the number 16 and the children came to the conclusion that 23 is the same as having 20+3. 🙂 Finally, we consolidated this new knowledge by completing a place value booklet I had designed for this lesson. You can get a free sample by clicking here or by clicking on the image below. The children absolutely loved completing this booklet. It has numbers represented in Base-Ten blocks, ten-frames and tallies, but this did not pose any problem :). At last they understood the concepts behind place value, and I felt accomplished for being able to help them with it 🙂

What strategies do you use to teach your students about the value of each digit in numbers higher than 10? Please share your ideas in the comments’ area below.

Take care, Catia