This is the final installment of my posts about a unit I planned on area for my first graders.

Day 6
As we were nearing the end of our unit, I wanted to do a full-class activity to explore the concept of iteration and give students a chance to collaborate and get in more "accountable talk" about their learning. It was a chance for them to work together, learn from each other, and provide meaningful feedback to one another. Iteration is the ability to use a limited number of units to measure a large space by repeatedly moving and using the same unit. So, I posed the problem of needing to measure the area of our carpet. As a class, we first had to decide on our unit. There were many suggestions and we weighed the pros and cons of each. In the end, we went with the large, flat blocks because the only con was that we only had seven. We anticipated that it would pose a problem for us, but it was the only unit that was large enough and portable enough to be suitable. We estimated how many blocks it would take and recorded our unit and estimate on chart paper. Then we began the challenge of actually measuing the carpet.

The students started by measuring the short side of the carpet, which was easy because we had more than enough to cover the width. But then we hit a road block because we didn't have enough to cover the whole carpet. A few students were able to see that it would take 10 to make two rows of blocks across the carpet, but when it came to figuring out additional rows, we couldn't figure out how to space the blocks to measure accurately. It was then that I reminded them about we had counted the tiles when we measured the big, flat block (see activity from Day 2). This got them thinking about measuring the length. However, this posed another problem because we didn't have enough blocks to cover the entire length. The students tried several ideas; I had each student share and we discussed the pros and cons of each idea. Eventually, one student came up with the idea of using 3 blocks to measure out spaces that would be the same size as a block. She put three blocks together, then took out the middle block, leaving a block-sized shape. She then continued until she had a pattern of blocks and spaces along the entire length of the carpet. We had just enough blocks to measure the length this way.

Once we knew the length and width, we were able to count our rows to determine the area. Since it took five blocks to measure the width, it was easy to count by fives for each block and space along the length of the carpet. The only difficulty we had was that sometimes they forgot to count a space as a block/row, so we had several students count until we came up with a consistent answer.

To wrap up the activity, I recorded all of the steps we took to find the area on our chart. This meant that they had to communicate what they did, with some prompting, to clearly explain their thinking to others. I then hung up our procedure on the wall to use as an anchor chart for my final activity the next day.

Day 7
For my final activity, I wanted the students to work with the concept of iteration once more, but independently this time. I asked each student to select an object to measure and a unit with which to measure its area. The catch was that they could only use two units for measuring (i.e. two blocks, or two cards, or two tiles, etc). I had them record their work in their math journals using pictures, numbers, and words to explain their thinking. I reminded students to look at the chart we made when measuring the carpet to help them explain what they did in words. This is still difficult for most of my students; they can explain what they did orally, but have much more difficulty writing their thinking down. This will improve as their writing skills develop. I didn't spend a lot of time assessing this activity; I glanced over them as the students finished and prompted students if they needed additional details. Since this unit was finishing the same week my report cards were due, I decided not to rush through it to get a mark for their reports. Since I didn't need to get a mark, I didn't do a formal summative assessment. However, through the formative assessments I completed, I am confident that my students all have a strong understanding of finding area using non-standard units.

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