These last few months we have been focusing on place value. Place value is such an important beginning for any primary student in mathematics. We have started the unit with basic counting. Now this may seem too basic and you may think, “what kid doesn’t know how to count by grade two?” This may seem an obvious skill to many but it is something that many (not some) still struggle with.
Counting goes beyond being ale to tag each object and say its corresponding number. By grade two students should be seeing groups of objects, especially twos, fives and tens, and be able to count by them efficiently and effectively. Students are still grasping with recognizing fives and tens as they count often still counting by ones till they get to five and then putting that aside. Students should start to see 5′s as 2+3 or 4+1 or even better 10′s as 9+1. 5+5, 2+8, 4+6, 7+3, without having to count.
To help with this we have been collecting and organizing objects in our classroom. Students have been counting bins, pencils, books, etc. in order to tell me how many is in each basic. We then moved to figure out how many bundles of tens there was in each basket and if there was any patterns we noticed in the numbers. Students soon realized that the number (or numbers) to the left became the amount of groups of tens. I told them that this was because that is called the tens column in the place value system and really it is saying 1 group of 10 or 1 x 10.
We are now trying to see how many groups of fives and tens there are in the bins. Now again, I thought to myself this should be an easier concept. Obviously if they see the fives then they will see how many tens. I also thought that since we worked on doubling so much in patterning that they would see that there was two fives in one ten. However, I was wrong again. Like many students, we are struggling to see how one group of objects can be called a 1 group but still be 5 or 10 things. Another mistake that my students are making is assuming that the ones place value tells us how many tens we have. They assume that if the left column told us the tens then the right must tell us the ones. We are currently working on this concept by looking at numbers and asking how many tens and how many fives? The follow up questions are simple: What patterns do you notice? Why does this occur? My hope is that students will see that there are two fives for every ten and if the leftovers (after making a group of ten) is greater then five it is just one more group. Example: 76: The number 76 has 7 groups of tens because there is 7 tens in 70 (10+10+10+10+10+10+10=70). We also have 15 fives because there are two fives in one ten and we have 7 tens so you double it; however, we also have 6 leftover which can make another group of five; making the total 15 fives, with one leftover.