Standard 6

Educators demonstrate a broad knowledge base and an understanding of areas they teach.

Over the last practicum I had started to work on the performance standards project: Proficiency benchmark trialing.  In this project, teachers are supposed to submit an analysis of student exemplars of curricular competency-based activities in terms of their numeracy and literacy skills. In this project we are analyzing the degree to which the numeracy and literary skills descriptors support the curricular competencies for the grade level.

TASK DETAILS
TASK TITLE	Bentwood Boxes
GRADE	8
LEARNING AREA(S)	Math 8
LITERACY and/or NUMERACY COMPETENCIES	Numeracy Apply -Represent visualization of the problem Apply- Develop a methodical plan of approach Solve- Solve the mathematical problem
CURRICULAR COMPETENCIES	List 1-3 curricular competencies to be developed and assessed Engage in problem-solving experiences that are connected to place, story, cultural practices, and perspectives relevant to local First Peoples communities, the local community, and other cultures Visualize to explore mathematical concepts
CURRICULAR CONTENT	Grade 8 – Constructing 3D objects with nets
TASK SUMMARY
Summarize task or include task as initially presented to students. Students are going to use blank poster paper to create nets for 3 boxes with no lids that can sit within each other. The added challenge is to use as much of the paper as possible. Students will demonstrate their understanding of the relationship of the sides of a nets and its 3D objects.

LEARNING STORY

CONTEXT

Describe any pre-learning that took place to prepare students for the task.   At this point in the course, we will have had an introductory lesson on nets. Students were able to start practicing physically cutting and folding 2D nets into 3D shapes (cubes). Students were able to practice visualizing folding 2D nets into 3D shapes (cubes and triangular prisms).Students have found that not all nets fold into 3D objects   This prior knowledge is going to allow students the skills to attempt to draw their own nets because they should understand how they come together into 3D shapes. Students will have the chance to be challenged by having to use their prior knowledge to allow them to compare the relative size of their nets so that the resulting boxes can nest.

PROCESS

Explain the steps taken to introduce the task, develop curricular or literacy/numeracy competencies, and how you assessed your students. Bentwood Boxes  (Mini Unit: Bentwood Boxes From FNESC)   -Bent wood bokes are a style of boxes made from Northwest Coast Peoples. -These boxes were use as a water tight boxes for storage and transportation of items that could get ruined or unusable if wet, or that were wet themselves. –For example, the Northwest Coast Peoples would use them to carry blankets, oolichan grease (grease from a small fish), tobacco, or other trade groups. -These boxes come in many shapes and sizes either for daily use and for gifts. There are some examples with amazing artwork carved into the wood and painted.   How are they made? -These boxes were made from one piece of cedar. -Harvesting from a cedar tree can be done in several ways, the first is cutting down the tree entirely and splitting it into planks, but you can also take a planks from a standing tree using chisels, wedges, and ropes. This way the tree doesn’t die. -The plank has kerfs carved in along the folding in such a way that it could be bent when softened by steam and then bent.   When the artist are harvesting the plank of wood they need to visualize the folding process so that they can minimize waste and only take what they need. How could visualizing the folding process help when harvesting cedar planks? Help the artist see the size and shape of the plank that is needed. – To help them determine how big or small of a box they can make. How might the artist visualize the folding process? –Nets  – what the side and base shapes will be and where they are placed.   We are going to be modeling a bentwood box using paper by creating nets for each box and then folding it into its 3D shape.   The challenge – in pairs (student choice) You are first going to design a net for a 3 bentwood boxes. You get 1 piece of graph paper for you to design your bent wood boxes. Then you will receive 1 piece  poster paper to create 3 boxes. 1 large, 1 med, 1 small. The small has to fit in the medium, and the medium into the large. The goal is to use as much of the paper as possible. AKA we want to have as little waste as possible. The boxes that we are making are not going to have lids either. As, traditional bentwood box lids are made separate.      Students will demonstrate their learning by: Drawing their own nets for a cube on the poster paper. Nets are going to have a base and 4 sides. Using a ruler to measure ensuring the sides are all the same length. Cutting out the nets Folding nets in to 3D shape Stacking the nets inside each other.   Assessment: Extending   -Creating 3 nesting non-square based boxes with no lids. – All sides need to align -Requires students to make a new shape of net than has been previously explored. -Students have to make the connection between the net only requiring 5 spaces as compared to previous day. -Used maximum amount of paper Proficient – Creating 3 nesting square-based box -All sides alignRequires students to make the same shape of net as yesterday, -Students have to make the connection between their nets requiring 5 spaces– Developing -Students may have made 3 boxes, -All boxes may not nest. -All sides may not align Beginning -Student have made 2-3 boxes that do not nest and may have lids. Emerging -Students require support in creating a net.

STUDENT A
TEACHER OBSERVATIONS AND STUDENT WORK
ASPECT: SUB-ASPECT	EVIDENCE OF PROFICIENCY AND RATIONALE
Insert aspect: sub-aspect(s) you assessed	Reference the observed anecdotal, conversational, or concrete examples of proficiency demonstrated by this student and why you believe it represents grade-level proficiency of this sub-aspect.
Apply: Represent visualization of the problem	Chooses an appropriate model(s) (e.g., concrete materials, diagrams, equations) to clearly represent the problem Students used the graph paper to design their nets. Students cut out their design as a model for their bentwood box.
Apply: Develop a methodical plan of approach	Uses mathematical reasoning to develop a logical and organized plan (an intentional sequence of steps with an end goal) that applies appropriate mathematical tools and/or strategies Students used the mathematical reasoning of scaling to determine the side length of the small, medium and large box compared to their model.
Solve: Solve the mathematical problem	Follows an effective and logical plan (an intentional sequence of steps with an end goal)  to solve the problem using tools/visuals/manipulatives as needed  Students had a plan of what tools were required to s to create their bentwood boxes.Students used rulers to measure the appropriate length sides of their boxes to ensure that the sides aligned when folded. Students used protractors to create square sides.

STUDENT B
TEACHER OBSERVATIONS AND STUDENT WORK
SUB-ASPECT	EVIDENCE OF PROFICIENCY AND RATIONALE
Insert aspect: sub-aspect(s) you assessed	Reference the observed anecdotal, conversational, or concrete examples of proficiency demonstrated by this student and why you believe it represents grade-level proficiency of this sub-aspect.
Apply:  Represent visualization of the problem	Students showed an extending ability to visualize the problem. They used the graph paper to design their nets that had a different base than square. Students ensured that the side walls and end walls of their net had the same height.
Apply: Develop a methodical plan of approach	Students used the mathematical reasoning of scaling of the graph paper to determine the side of squares required to create the small, medium and large box compared to their model.Students used the approach of creating their own sections of graph paper to ensure that each side had the right length.
Solve: Solve the mathematical problem	Students had a plan of what tools were required to s to create their bentwood boxes.Students used rulers to measure the appropriate length sides of their boxes to ensure that the sides aligned when folded. Students used protractors to create square sides.

Teacher Reflection

Following each lesson, spend some time considering the following questions in an effort to progress your learning about integrating, leading, observing, and assessing literacy and numeracy as they align with curricular competencies. Keep a record of your reflections for your debrief with your district or school team.

Compare and contrast your selection of proficient student work against the descriptors of literacy or numeracy proficiency. Do the descriptors accurately describe your concept of proficient work? What changes can be made to improve the accuracy of the descriptors?   Reflect on the applicability of the literacy or numeracy proficiency descriptors to your lesson’s learning area. Do the literacy/numeracy proficiency descriptors support or detract from the curricular competencies? How?

I felt that the wording of the numeracy descriptors of “represent visualization of the problem” and “develop a methodical plan of approach”  supported the curricular competency of “visualize to explore mathematical concepts”. Students in my class who were proficient in visualizing’s the mathematical concept of nets were able to use the graph paper to create a model of their bentwood box to represent the problem. I found that these students who were proficient made a model of the 3 different sized nets that they needed to make. To follow, they had to also visualize on their poster paper, where they were going to put their nets to maximize their paper use. So, at this point, the proficient students started to create a plan of to approach visualizing where they are going to place their nets on the poster paper. During this plan, the students had to use mathematical reasoning to determine how big their boxes could be so that they all fit on the paper, but also a plan as to how they are going to be able to create straight lines and 90-degree corners so that all the sides on the box would align.   I felt that the wording of the numeracy descriptors of “develop a methodical plan of approach” was also supportive of the curricular competency that students “engage in problem solving experiences that are connected to place, story, cultural practices, and perspectives that are relevant to local First Peoples communities, the local community, and other cultures”. The students who were proficient in taking in the values of local First peoples and the values of the Northwest Coast peoples where an individual only takes what they need were able to embody this in their application of the problem to the poster paper. Where the students tried to use all the paper that they could so that there was the least amount of waste. So, in this student had to develop a methodical plan of approach to maximize their paper use.   I felt that the wording of the solving  numeracy descriptor of “solve the mathematical problem” also supported the curricular competency that students “engage in problem solving experiences that are connected to place, story, cultural practices, and perspectives that are relevant to local First Peoples communities, the local community, and other cultures”. This numeracy descriptor described the say that students had to follow the plan that they can previously created in the visualization stage. In this case, Students had to execute their plan of what tools they needed to solve the problem, which in this case included rulers and protractors in order to create straight lines and square corners to create accurate nets. Students also had to ensure that they followed their plan of how they were going to scale their boxes to make a small, medium and large box. So, I felt that this execution of a plan was another way that students were engaging with problem solving experiences that are connected to place, story and cultural practices.   One thing that I think was missing from the solve and applying numeracy descriptors was mention of an iterative process. What I noticed throughout the students applying and solving the problem, was that as students who were at a proficient and extending level, they were refining their plan as they went.   In the future, I would like to use this lesson again, I would like to emphasize the role of the developing a methodical approach to plan and to execute their project. This may have helped students move from a beginning and developing level of to proficient, knowing what underlying thought process that they should be thinking of as they go through the challenge.