Determining the number of items in a disorganized group can be very difficult, especially if it must be an accurate count. I illustrate this idea by relating it to counting the stars in the sky.
Since our school is in an urban area with many bright lights, it is sometimes difficult for the students to fully appreciate how many stars actually could be seen in the sky. I present the students with a picture of a starry night sky and ask them to try to figure out how many stars might be in the picture.
I ask, "How can we even begin figure out how many stars might be visible in the sky? What strategies could be used to keep it organized?"
I have the students discuss some ideas with their shoulder partners where they are seated on the carpet in the classroom. Some of the ideas overheard including marking colors in patterns, numbering, and circling groups. As the students share out their ideas, I ask them to think about which one would be the easiest and most accurate.
I demonstrate different strategies for the students using an example of several dots on a piece of white copy paper to simulate stars in the sky. I choose to use a different copy for each of the strategies and I ask the students to try each of the strategies on their individual whiteboards at the same time.
The first strategy is color coding. This proves difficult for the students on their whiteboards because they don't have many different colors of markers to use. The second strategy demonstrated is counting/labeling. This is also difficult because the stars are so close together and writing in numerals in a limited space is not clear. Trying to count the stars becomes confusing and I purposely recount stars to show students where potential errors can occur. Because the Common Core Math Practices include constructing arguments and critiquing the work of others (MP3), I have the students discuss with their shoulder partner how easy each strategy is after the first few demonstrations are completed.
The last strategy demonstrated is creating equal groups. I ask the students to determine how many stars should be in each group. There answers vary from two, three, and even five. It is important to me to determine their preference for skip counting based on this information. Some students remain focused on the ease of counting by two and five, but other students say it is easier to see the stars in groups of three (subitize) without having to count to five. I demonstrate some of their ideas and plans, and then I ask the students to once again discuss a plan that will be the easiest for them to use.
The students are focusing on using color and equal groups for the plan, and they have quickly eliminated counting the stars in the picture. Using equal groups in this lesson is the focus as they begin working on their own.
During the independent practice, I have a separate page of stars for the students to use to create equal groups. This page intentionally includes a more manageable quantity of stars, but still a challenging number. This is an easy way to differentiate.
Students have the option of circling groups with color, or even cutting out the stars to create their own manipulative and use a hands on learning format. Their goal is to create equal groups and write the multiplication sentence to match their model.
I encourage students to use the hands on model so that they don't spend the entire time circling and erasing. During this part of the lesson, the students are working individually so that they can develop their own understanding of equal groups. Many of the students cut out the stars and a few of the students decide to cut out stars in groups of two.