Grade 1 - Models and Repeated Addition

Grade 5, Creating an organized list, using student-generated formulas to calculate surface area

Grade 3, Creating drawing representations of rectangular prisms and labelling the side measures

Grade 5, using the surface area formula

Grade 3, creating models

Grade 2, Creating models and counting each square to calculate area

Grade 2, creating models, counting each side

Grade 2, Creating Nets based on Visualization, Counting each face

Grade 2, Beginning to demonstrate understanding for Surface area ofrectangular prisms

Grade 7, Creating drawings, demonstrating understanding of surface area

Grade 7, Demonstrating understanding for factors, creating drawings

Grade 7, Creating an organized list and student-generated algorithm,calculating area of each face

Grade 3, Visualizing Arrays, creating models, counting each face tocalculate surface area

Grade 3, Creating nets based on visualization

Grade 3, creating drawings of prisms, demonstrating understanding forsurface area

KG, creating models demonstrating conservation of number

KG, creating structures, demonstrating understanding of the conceptthat some arrangements are the same

KG, creating models, composing and decomposing numbers

KG, Creating models, beginning to demonstrate understanding of arrays

Creating structures with the given cubes

Grade 1, creating drawings, demonstrating understanding of arrays

Grade 1, Creating Structures

Grade 3, creating nets

Grade 5, creating models and drawing faces

Grade 5, using a formula for surface area

Grade 5, creating models and counting each face

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Grade 5, creating an organized list and student-generated algorithms

Grade 5, using formulas for surface area

7. Using Patterns and Formulas to Calculate Surface Area

At this stage, students are using the patterns in their t-charts and formulas for surface area to calculate the surface area. They are applying their understanding of factors and the relationship between factors of a number and volume of a rectangular prism. They are clearly justifying why a certain chosen prism will have the smallest surface area.

6. Creating Labelled Charts, Looking for Patterns, Using Student-Generated Algortihms

At this stage, students are creating labeled charts to record all possibilities. They are looking for patterns and using these patterns efficiently to calculate surface area of the prisms, using their own algorithms. They are beginning to demonstrate their understanding of factors in generating all possibilities. They are visualizing using an appropriate representation in the form of models, diagrams or by making connections.

5. Creating an Organized List and Student-Generated Algorithms

At this stage, students are creating an organized list to record the models of rectangular prisms of a given volume. They are applying their understanding of rectangular prisms and their congruent faces in problem-solving contexts by beginning to create their own algorithms to calculate the surface area.

4. Creating Nets based on Visualization

At this stage, students are visualizing rectangular prisms of the given volume by making connections and estimating to make arrays. They are beginning to demonstrate an understanding for surface area and are making connections between area of a rectangle and surface area of the faces of a rectangular prism. They are representing their models by creating nets of the rectangular prisms.

3. Visualizing Arrays, Tracing/Drawing Faces, Creating Models and counting for surface area

At this stage, students are visualizing an array using the given cubes. They are creating rectangular prisms. They are tracing and/or drawing faces of the prisms they have created and using some simple counting strategies to count the number of units on each face.

2. Drawing/ Tracing Faces

At this stage students are using the given number of cubes to create models of the chocolate bars. They are tracing or drawing faces.

1. Creating a Structure

At this stage, students are creating a structure with the given cubes. They are experimenting with the material and trying a variety of arrangements, not necessarily in the form of rectangular prisms. Some students are demonstrating understanding for the big idea that the shape or arrangement of the structure does not change the volume. Some students are composing and decomposing the given number.

School-Wide Numeracy Prompt, An Overview

The numeracy team is attempting to record our journey of working with the school-wide numeracy prompt electronically. We will be using this platform to try and create a school-wide Bansho of student work from KG to Grade 8. We are hoping that you can post a couple of samples of student work in the tags appropriate to your students. This will create a landscape of learning/trajectory for student thinking in the context of this problem which can then be used in other problem-solving contexts in your classrooms or even for co-creating criteria in other math contexts.

School Success Goal
If we teach students to visualize in numeracy (both the question and their solution) then students will be better able to communicate their thinking in Numeracy.

Task
KG: Chocolate bars have pieces. How many pieces are in this chocolate bar (12 linking cubes attached)? Can you design a chocolate bar that looks different but has the same number of pieces?
GRADE 1: Rearrange a chocolate bar, 32 or 16 cubes long in a different shape.
GRADE 2: How many possible ways can you make a rectangular prism using 16 or 32 linking cubes? How many units of wrapping would each rectangular prism need?
GRADE 3: Use 36 linking cubes to create rectangular prisms. What is the best way to package the chocolate using the least amount of packaging?
GRADE 4-8: You have 36 linking cubes which represent the total volume of a chocolate bar. The Eco team would like to use as little as possible wrapping to create minimal waste. Your task is to work with the 36 linking cubes to find all possible formats for the chocolate bar in order to reduce waste. For shipping and storage purposes, the final product must be in the form of a rectangular prism.