I recently prepared a series of number explorations for a 2nd grade classroom. The students in this classroom have been working with base ten concepts and place value and are now beginning to compare numbers. In this post I'll share a menu of activities that can be used to support deeper understanding of these concepts. The goal here was to help students reason about the relative size of numbers and quantities without relying on an algorithm to compare numbers. I've also tried to help students build some bridges between various representations of numbers.
1. We started with Andrew Stadel's Estimation 180. While many of his explorations might be targeted at an older audience, I found the following extremely well-received in this 2nd grade classroom.
First huge moment: seeing licorice on the big screen at 12:45 in the afternoon.
Second huge moment: getting to guess and seeing those guesses on the board.
Two equally huge final comments: "I was sooo close!" vs "Wow, I was not even close!" These are both satisfying to me.
Students had opportunities to consider the relative size of numbers as each classmate shared a guess. We discussed our smallest and largest guesses and any that appeared more than once. It was quite evident that students were wondering whether they should guess a really big number, and if so, what that number would be in this scenario.
2. We followed this up with some number line estimation. I used the cards below with the students seated on the carpet for a brief number talk. Along with estimating the location of the red dot, students answered the question, "How did you decide?" This line of questioning encouraged students to use the numbers given as landmarks and do some broad thinking about tens and hundreds.
3. Next we pulled from the deep constructivist work of John Van de Walle. I was first introduced to John Van de Walle's work in my teacher credential program back in 1996. These activities are great work for both teacher and student and make mathematical reasoning about number the focus.
4. I pulled this next task from Illustrative Mathematics as a progressive step toward more challenging estimation with number lines. I drew a long number line across the board at the front of the room and labeled every hundred up to one thousand. Students teamed up and together discussed and decided where to place their number.
5. The final selection in this menu of activities is from the National Library of Virtual Manipulatives. I used the Practice mode with one dot in which you are asked to drag the dot onto the number line to match the value shown. If the location you choose is not close enough to the actual value, you are asked to zoom in and be more precise.