A fifth grade teacher recently used the visible thinking routine Zoom In (from Making Thinking Visible by Ritchhart, Church, and Morrison) with her students to help them describe, infer and interpret multiplication arrays.
Read about the experience in the teacher's own words:
Beforehand, I created a simple picture array of identical plants, 3 rows by 6 columns, 18 total plants.
To start off, I told the students that we would start digging into our first math unit and we would be using the visible thinking routine Zoom In to help us do that. I explained that we’d start by looking at a small part of a picture and we’d reveal a little bit more each time. Their job was to observe and jot down what they noticed on their whiteboards.
First, I showed them just one plant.
The students focused on observations of what was in the picture - describing the plant.
Between each round, students shared out their observations and I recorded them on the SMART board. By having students share their thinking, it allowed their classmates to hear what others were thinking and noticing. This helped in making their own observations as they added on to what other students had shared. It also allowed me to ask students to tell more and explain what their thinking meant or how they came up with their predictions.
The next zoom moved across the row to show one more plant, doubling the plants but not yet revealing a full row or column. I asked them to again observe: "What did they see? What new things did they notice? How did their thinking change based on the new parts of the picture they were seeing?"
There were still many plant-based observations and a few mathematical words started to pop out (doubling, multiplying).
Again, I recorded their thinking on the board, as students shared their thinking.
Round 3 revealed two full columns. I reminded students at the beginning of this round that we were looking at the picture as mathematicians and asked them to think about their observations with a math mindset.
Again they wrote down observations, noting how their thinking had changed and how they might think about the picture mathematically. During this round, students independently began predicting what they thought might come next in the picture without any prompting from me.
A synthesis of the class's thinking:
Round 4 revealed a full row, in addition to the 2 full columns they had seen in the previous round.
During this round of observations, students had discovered the pattern of rows and columns, and most observations focused on predictions of how many plants were going to be in the full picture. Some students were observing using row-and-column strategies, while others were using multiples of 3 or 6.
Everyone's thinking together:
In the last round, the full array was displayed.
By this point, all students could name it as an array and write the corresponding number sentence.
Everyone's thinking after the last Zoom In round:
To wrap up, I asked students to draw another array for 18. All students were able to create another array, which showed me they all understood the concept of a rectangular array and equal rows and columns.
After reading about how this 5th grade teacher used the visible thinking routine Zoom In to help her students describe, infer, and interpret in math, how could you use a visible thinking routine to help your students think deeply about mathematical concepts?