Dufferin-Peel Catholic DSB Lesson Study #3

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Dufferin-Peel Catholic DSB Lesson Study #3

Debrief: What Is Capacity?

by Nina Bekanovic, OCT, Tony Cabral, OCT, Shannon Jordan, Natasha Moore, OCT, Athena Prosdocimo, OCT

Introduction (Athena Prosdocimo, Natasha Moore)

The observational focus for this lesson was to analyse the gender differences between students who produce Level 3 to Level 4 work ability. These students were encouraged to participate, and observational notes were taken on each of them throughout the lesson.

Observational Notes

Next Steps

We need to review the definition of capacity to ensure that the students understand the concept and can apply their knowledge to items in the classroom. We have decided that, for the next lesson, we will begin with a concept-attainment activity. Here, students will look at pictures that are containers and pictures that are not containers. This will, we hope, develop their understanding that a container is a three-dimensional shape that can hold units.

Next, as a class, students will review their estimations based on the question: What is the capacity of the bag if we filled it with textbooks? After reviewing their estimations, students will work in groups of three or four to test the capacity of the bag by filling it with textbooks. We hope that in this experiment some of the bags will break and students will start to question if the number of units is the only factor they have to worry about when finding capacity. We anticipate that some students will discover that mass is also a factor.

Student RY and Student JY Observations (Nina Bekanovic)

Level 3/4 learners, Grade 4 males

Both students displayed a high level of engagement throughout the entire lesson. Both boys put their hands up to participate in class discussion very often. Student RY often raised his hand as soon as he heard the question, without knowing what the entire question was. He would lower his hand and raise it again soon after, when he figured out the answer.

When asked to estimate how many notebooks would fit into the given bag, Student RY estimated 35, while student JY estimated 15. When Student RY compared his estimation to those of Student JY and his other group member, who estimated five, he changed his estimation to 20.

As the group experimented with putting the notebooks into the bag, Student RY held the bag while Student JY filled it. When 10 notebooks were in the bag, Student RY stopped his group members and held the bag up to see if the books were too heavy for the bag. Student RY was confusing capacity with mass. Student JY agreed with him, which means that he was also confusing capacity with mass.

When the teacher asked if anyone had filled the bag to maximum capacity, both RY and JY put up their hands, even though only the bottom portion of the bag was filled. They had put 16 notebooks into the bag. When another student said that she had fit in 18 notebooks, Students RY and JY both appeared surprised and looked around the classroom at the other groups’ results.

Student RY explained to the teacher that the bag was filled to its maximum capacity and that he knew this because when they had tried to add one more book to the bag, the sides of the bag began to rip. Both students appeared confused when the teacher asked why the top of the bag was not filled. The looks on their faces were questioning as they pondered the teacher’s inquiry. The teacher then asked, “What is capacity?” Both students put their hands up immediately and seemed confident about their answers. The teacher then asked, “How do you know when the bag has been filled to capacity?” Student JY answered, “When it begins to overflow.” (Is he beginning to understand the concept of capacity?)

Student RY appeared confused. When the teacher posed a question, he put his hand up immediately and then lowered it after taking a few seconds to think about his answer. (Is he starting to question whether his bag is filled to capacity?)

The teacher discussed what would happen if textbooks were sticking out the top of the bag. Student JY seemed to have lost interest and was staring at the ceiling. The teacher asked the class if the Cheerios bag was filled to capacity. Student RY answered, “No, because there is still room at the top of the bag, and Cheerios are small and they don’t weigh that much.” It appeared that he had still not completely distinguished between capacity and mass. Student JY had disengaged from the lesson but began to participate again when the group began work on the T-chart (Slide #5). He explained that a backpack was not filled to capacity. He explained that a pencil case was not filled to capacity. He explained that a cereal box was not filled to capacity. He re-read the question out loud three times during this process to make sure he understood. Student RY added that their plastic bag was filled to capacity with notebooks. Study JY agreed and wrote this down in the appropriate column. It seemed that Student RY still did not have a concrete understanding at this point and may have been influencing Student JY, who was on the right track.

When the homework question was given, both students wrote it down, and Student RY asked student JY, “How are we supposed to know how many textbooks will fit?” Student JY answered, “You have to estimate.”

Student N and Student P Observations (Shannon Jordan)

Level 3/4 learners, Grade 5 females

The lesson began with a slide on the Smart Board that engaged students’ thoughts about the term capacity. The question posed to the class was, “What is the capacity of the bag if we filled it with notebooks?” (The teacher held up clear plastic bags for the class to observe.)

Students had a moment to think and to brainstorm with a partner to come up with their estimates. When the teacher asked students to share their estimates, Student N and Student P both raised their hands. Student N estimated that 12 to 15 notebooks would fill the plastic bag to capacity, and Student P estimated 12 notebooks. The teacher let the students know that their estimates would be applied as they engaged in a guess-and-check activity. The class was instructed to work in groups of three to experiment with classroom notebooks to fill the plastic bags to capacity. (Students N and P were grouped with a Grade 4 male student.)

When asked to open their notebooks and record their estimates and the instructions for the activity, both Student N and Student P focused on what needed to be done and then sat quietly, listening for further instructions.

During the activity, Student N and Student P both participated well. They seemed to have a clear understanding that, if handled roughly, the plastic bag would tear. Student N held the bag open while Student P and the Grade 4 male student carefully filled it with notebooks. Student P seemed to take on a leadership role. A few times, when the group slowed down their actions to take a look at the space remaining in the bag, Student P strongly suggested adding more notebooks. When the group had used up its allotment of notebooks, Student P travelled away from the group to acquire more.

When the teacher signalled that time had expired for the activity, Students N and P sat quietly listening. The teacher then asked the class, “Which groups filled their bags to maximum capacity?” Students  N and P did not raise their hands, noticing that their bag was not filled all the way to the top. (Approximately one-third of the bag remained empty at the top.) The teacher then inquired, “How many books did your group fill the plastic bag with before stopping?” After listening to a few other answers, Students N and P both raised their hands. The teacher called on Student N, who said that her group’s bag contained “24 40-page notebooks.”

The teacher addressed the issue of bags having a large amount of empty space (one-third of the bag) at the top when groups had stopped filling them with notebooks. She then asked, “If this bag were this tall, would it be filled to capacity?” (She folded down a bag so it was flush with the height of the notebooks inside.) A student responded that “yes” the bag would be filled to capacity if that were the case. Students N and P both raised their hands in agreement with this statement.

Both girls remained attentive through this part of the discussion. The teacher asked, “How did you know when to stop filling the bag?” Student P raised her hand and was called on to answer. She said, “If it gets smaller, then it cannot hold anymore.” The teacher clarified the “it” part of Student P’s answer, saying, “If the extra space in the bag gets smaller.”

The teacher then asked, “How do you know it has exceeded capacity?” Students N and P both listened to explanations given by other classmates.

(Slide #4) The next slide on the Smart Board showed the question: What is capacity? Students N and P both raised their hands to answer. The teacher called on Student N, who responded, “It’s the total amount an item can hold.” The teacher revealed the definition of capacity, which had been covered, at the bottom of the Smart Board. It read: Capacity – The amount of units a container can hold (millimetres, litres). Student N’s definition was very close to the one the teacher had revealed.

Both girls continued to remain attentive during this part of the discussion and raised their hands to answer throughout. The teacher posed the question, “What could I have done to keep making the notebooks fit?” Student N raised her hand and answered, “Fold it” (meaning notebooks). “Keep folding books to make them fit and keep folding.”

The next slide showed a T-chart with the headings, Items Filled to Capacity and Items Not Filled to Capacity. The teacher gave out a worksheet, provided examples of items that could potentially be listed on either side of the T-chart, and asked the students to look around the classroom and come up with additional items. Students N and P quickly looked around the class and suggested appropriate items. Student N took the initiative to be the recorder. Under the heading Items Filled to Capacity, she wrote “N_____’s TNA bag” and “N_____’s pencil sharpener.” (She stated, “I just checked this one and filled it to capacity,” meaning she had checked her sharpener and did indeed use it until it was filled to capacity with pencil shavings.) Under the heading, Items Not Filled to Capacity, she wrote “bottles of glue,” “the cabinets,” and “R_____’s water bottle” (another student suggested this last item). The teacher announced that there was a short time left for the activity. Student P then took over as recorder and added: “family life script box” under the heading Items Filled to Capacity and “P_____’s house” under the heading Items Not Filled to Capacity.

When the teacher asked for examples of items the students had written down under Items Not Filled to Capacity, Student P raised her hand and said, “R_____‘s water bottle.” The teacher indicated that Student P had given a good example and wrote it down on the Smart Board under Items Not Filled to Capacity. She then asked Student P to justify her answer. Student P said that she had looked at the amount of water remaining in the bottle and had shaken the bottle to get a second confirmation that it was not filled to capacity.

(Slide #6) The next slide instructed: Estimate the capacity of the bag if we filled it with textbooks. The teacher asked the students to write this in their math communication notebooks and solve it for homework. She told the students that their answer should include pictures, numbers and words, in explanation. Students N and P both wrote down the instructions carefully. The teacher asked what else students could do to make their answers Level 4 quality. Student N raised her hand and suggested the importance of justifying the answer. She wrote down the guideline provided by the teacher that a Level 4 answer would include the use of appropriate math terms, such as capacity, total, textbook, container, units, and so on. Student P immediately began to answer the question in her notebook, however, she stopped and erased what she had written and filled the space with more of the teacher’s guidelines for answering the homework question.

In conclusion, this observation of two Level 3/4 female Grade 5 students revealed that both did an effective job of following along with the lesson during teacher instruction and class discussion. Students N and P worked effectively in a small group to experiment with capacity by filling a plastic bag to a desired capacity without ripping the material and to fill out a T-chart appropriately. They also communicated and co-operated well with each other. Students N and P both displayed Level 3/4 thinking and behaviour.

Student B and Student R Observations (Tony Cabral)

Level 3/4 Learners, Grade 5 males (student B = ELL)

The lesson study was conducted during a Grade 4/5 math lesson on capacity. This written report will look at the knowledge and understanding of two boys (Student B and Student R) as they work together to answer one key question: What is the capacity of a plastic bag if we filled it with notebooks? The students used the guess-and-check strategy as they took unused 40-page notebooks and tried to fit as many as possible into a plastic butcher bag. In this report, I will also take into consideration the possible impact that gender may have had on performance and thinking during this exercise. Student B and Student R have been identified by the classroom teacher as performing at Level 3 or 4. Additionally, Student B has been identified as an ELL, which may account for the fact that he rarely participated in class discussions and lessons. When Students B and R were assigned to be partners, Student R looked at Student B with hesitation and remained quiet. Later in the lesson, Student R asked the instructor, “Do we have to work with the same partner?” The students sat beside each other on a regular basis.

When the teacher asked the students to estimate how many notebooks would fit into the bag, Student B was very prompt with his written estimation that only 12 notebooks would fit. His partner, Student R, took longer to estimate, and his estimation was 15 notebooks. Interestingly, Student R did not write down an estimation until he saw Student B’s estimation. Furthermore, Student B wrote his estimation in a complete sentence, while Student R wrote only three words: “I think 15.” Student R took nearly double the time that Student B did to copy down the main focus question. Furthermore, the definition of capacity was written on the board, but neither student wrote down the definition in their math communication notebooks. Prior to conducting the study, we predicted that the boys would be forceful in trying to fit as many books as possible into the bag, potentially ripping the bag open accidentally. We also predicted that some of the boys would potentially be careless with the bags, stretching them out too much or ripping holes in them. This was not the case with Students B and R.

Contrary to our initial predictions, Students B and R were exceptionally careful as they placed the notebooks in the bag. They were especially mindful of not ripping the bag with the corners of the notebooks. At first, Student B laid the bag on the desk horizontally, while Student R placed the first notebook in it. Three notebooks later, Student R proposed that holding the bag open vertically and upright on his lap was a more effective strategy, and this allowed the books to slide in with ease. Student B carefully placed the books, one by one, into the bag. Student R emphasized his concern that they should be careful to ensure that the bag did not tear.

When it became difficult for Student R to slide the 24th notebook into the bag, Student B encouraged him to keep fitting more in. The students appeared to be somewhat preoccupied with how many notebooks other students at the table were able to fit in as they asked, “Did you put all of yours in?” It seemed as though Students B and R were competing to fit in more notebooks than their peers. Student B tried to stretch the bag a bit in order to accommodate the 25th book. Nevertheless, the students managed to avoid ripping the bag.

When the teacher declared that the allotted time was up, Student R was very eager to share with his classmates that he had managed to fit 25 notebooks in the bag. However, his partner (Student B) didn’t raise his hand to share the outcome. He seemed to be rather passive or shy and kept his fingers over his mouth when the students were given an opportunity to share their findings with the class. Student B never volunteered any answers throughout the entire math period. During conversations with his partner, his voice was barely audible as he spoke very softly.

When the teacher asked Student R, “Can you fit any more notebooks at the top of the bag in the empty space?” Student R replied, “Maybe.” (Pause.) “No, you can’t fit a book sideways at the top of the bag because the hole is too small.” Student R implied that the bag had reached its full capacity, which indicated that he did not entirely understand the concept of capacity. Furthermore, Students B and R did not take into consideration that the notebooks could have been folded, rolled or cut to fit the remaining space at the top of the bag.

When the teacher asked, “When did you know to stop filling the bag?” Students B and R did not raise their hands to volunteer an answer. Neither student answered the following question in their notebook: How do you know this is capacity? Justify your answer. (Slide #3)

(Slide #5) When it was time for the students to fill in other examples of capacity in the T-chart, Student B immediately began looking around the classroom for ideas and did most of the writing. The students were instructed to use their imaginations in order to list items filled to capacity on the left side and items not filled to capacity on the right. While Student B found objects not filled to capacity in the classroom, such as a garbage bin, water container, cupboard and pencil case, Student R looked around the room. On the left side of the chart, Student B recorded that Student R’s backpack was filled to capacity, although it was not. Overall, the boys had difficulty listing items filled to capacity. When asked why he placed the ocean in the Filled to Capacity column, Student R explained that it “has lots of water and comes upon shore sometimes.”

Throughout the lesson, Student R was very willing to share items listed in his T-chart as he eagerly extended his arm full length into the air for the teacher to notice. However, Student R did not volunteer to answer questions he was unfamiliar with, such as: Is this box of markers filled to capacity? It may have been the gaps between the markers that gave him doubts.

Although Student R raised his hand frequently to participate in the discussion, it was clear that he did not have the answers to several questions. The height he raised his hand indicated how sure he was of his answer. However, when Student R did not lift his elbow off the table while raising his hand, this seemed to indicate his uncertainty. For instance, when Student R was chosen to answer a question, he answered, “I forget.” This has been a pattern with this particular student on other occasions. However, Student R did answer correctly when he replied that capacity can be measured using “units” such as millilitres and litres. The teacher responded by saying, “Good thinking!”

When Student R was not selected to answer, he rested his head on the desk or played with his hair, as if to indicate that he was bored. It appeared as though Student R needed to be selected frequently to answer questions in order to remain alert.

In retrospect, the students’ responses during the activity did not seem to indicate a solid understanding of capacity. Students B and R may have needed to explore more examples of capacity in their T-chart, accompanied by more shared responses.