Place Value

Developing Whole- Number Place-Value Concepts

This chapter really challenged me to reflect on my teaching practices when it comes to teaching place value. This is a big part of first grade and like the chapter stated it is a concept that students are going to continue to build on in their future math classes. It was good to see the alignment of this topic throughout grade levels.

“In first grade, students count and are exposed to patterns in numbers up to 120 and they learn to think about groups of ten objects as a unit. By second grade, there initial ideas of patterns and groups of ten are formally connected to three-digit numbers, and in grade 4 students extend their understanding to numbers up to 1,000,000 in a variety of contexts. In four and fifth grades, the ideas of whole numbers are extended to decimals (CCSSO, 2010) (Van de Wall and Karp and Bay-Williams, p 222).” 

The three ways of counting that are referred to in this text are unitary, base ten, and equivalent counting. Unitary counting is when students are counting each single unit by ones. They can count all of the objects in a set and tell you what number is represented in the set. However, they do not have a understanding of the value that each digit holds in the number.The base ten counting is when students organize a set of objects in a set into the maximum amount of tens and then provide the other counters as left overs. They understand what the digits in a two digit number represent and can connect that to their counters. They can count by tens and ones and know that 5 tens and 3 is the same as 53. Equivalent counting is when students are shown a set with some groupings already made, but there are more than 9 single units left over. Students would know to continue grouping sets until there are nine or less single units left before counting. They understand that just because they change the grouping does not mean that they are changing the number. For example, 3 tens and 23 ones is the same as 5 tens and 3 ones.  

The three different models used to help students grasp place value are groupable models, pregrouped models, and nonproportional grouped models. Groupable models allow students to put the groups together themselves. This model allows students with limited exposure to place value to have the opportunity to manipulate and create groups to develop an understanding that you are placing single units together to make a group and then you can take them back apart. Items that could be groupable are beans, straws, and digiblocks. Pregrouped models are items that are already put together and cannot be physically taken apart they must be traded for single units. I think that this is a common manipulative used in many elementary classrooms, including my own. I know that when teaching place value in my classroom we spend many weeks using and manipulating our place value blocks. I know understand that to help children understand why there are ten little blocks glued together we must first allow them to use the groupable manipulatives. Nonproportional models should not be used in an elementary classroom as this model can be very confusing for students. They need to be able to see the visual difference between a group of ten and a single unit. A group of ten should be ten times bigger than a single unit.

Students can use place value pictures, manipulatives, cards, and mats to help them write two and three digit numbers. I have used many of these methods in my classroom, such as having students draw pictures and then write the number or use mats to lay out their number and then record the written numeral in their journal. However, I have never used the place value cards before and think that they would be helpful to have in your classroom. They would look something like this.

Hundreds Cards would look like this.

 

            9               0                        0

Tens Cards would look like this.

 

                               7              0

Ones Cards would look like this.

                          

                                                                        7

(I am going to ask you to imagine that they numbers are in the box like that are for the first one I am having formatting trouble and I am not sure why it is not working correctly, but I think you can understand what I am trying to demonstrate.)                                                                                 

                        

Students could then stack them on top of each other to see the written numeral they are trying to make.

Hundreds charts can be used to help students become fluent at skip counting, identifying two digit numbers, recognizing patterns when counting by 10’s, filling in missing numbers, and identifying relationships among numbers. They are great visual to help students understand numbers and where they are located. There are many different ways to engage students in learning with hundreds boards.

Benchmark numbers are numbers that students learn to use as they learn informal methods of computation. Common benchmark numbers are multiples of 10 and 100 and occasionally 25. When students are learning to do computation you want them to easily be able to create a benchmark number. For example, when adding 74+126 you would want them to add 6 to 74 to make 80 and then add 80+120= 200. This is why it is important for younger students to become fluent in making 10. If students can make ten then when they being adding and subtracting bigger numbers they will be able to do it more fluently.

One of the activities that was describe to help children with using benchmark numbers was to give them a set of three numbers and then ask questions to guide discussion about the given numbers. See page 241 for more in depth instructions.