Following the established quick flash routine (http://www.cc.betterlesson.com/lesson/501226/quick-flash). Show set one of cards (see resource section). Then repeat with set two (see resource section). When you are done compare the arrangements. The students are being proficient with making sense of quantities and their relationships in the problem situations (CCSS.Math.Practice.MP2).
Advanced Preparation: You will need a die and 60 connecting cubes (2 different colors).
Start by asking a student to model the game with you. Explain to the class that they will be playing a new game today called 3 Columns. Tell them that they will play with a partner and work together to build three columns. Each column must be the same number of cubes high. Today we will build towers that are 10 cubes high.
There is a video of my introduction of this activity to the class. This is a rather tricky task (especially the recording) and I wanted the reader to be able to see the introduction. The video is about 10 minutes but you could watch part of it and get the gist. However, I wanted to leave the whole video for those who were needing to see and hear the discussion.
Students will use the recording sheet to play the game with their partner. Each teammate can fill out their own sheet (see resource entitled Three Towers) but should work on the same towers.
The students will now play three columns with their partner. As they play, circulate and ask students how many cubes are in their tower so far (an example video clip is in the resource section)? How many more do you need. This will get students to start thinking about the compliments of 10(CCSS.Math.Content.1.OA.C.6). The students are adding within 20, demonstrating fluency for addition within 10 and using strategies such as counting on and making ten. Some will need to use the visual model to figure out how many more, some will count on, and some will just know the fact (CCSS.Math.Practice.MP2). The students are again making sense of quantities of 10 and the relationships of sums of 10.
The focus for this discussion will be on how to use standard notation to represent their columns.
Start by showing the students a set of three columns. Tell them that this was a set of towers that you saw today (just make up a set of towers). For this case I have blue and yellow cubes. The first column has 2 blue, then 3 yellow, and then 5 blue cubes. The second is 1 blue, 6 yellow, and 3 blue and the third has 5 yellow and 5 blue. I then ask the students how many blue cubes were used for the first column? Once the total of blue and yellow cubes are determined (for the 1st column) ask how we could represent this on paper. Students will suggest drawing the column on paper. After it is drawn and labeled, repeat that we agree that there were 7 blue and 3 yellow. I will then review the addition notation by writing 10=7+3 on the chart paper (CCSS.Math.Practice.MP2) The students are making sense of the quantity of cubes in each column.
Then review the symbols used in the equation and ask how does this equation connect with the column we built. Continue doing this process with the other two columns.
I have included an example (see Jack's Work in resources) of the finished student sheet. This would be a great example for leading the discussion of the use of equations.