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Math and Geometry Tools

Starting from Math

These math activities are intended for intermediate students; however, they can be modified for students of any grade. The lessons focus on building students' number concepts, extending computation fluency, and introducing math concepts while building a connection with the natural environment.

Map

1

Shape Shifting

Using natural objects, students can practice single transformations (slide/translation, flip/reflection, turn/rotation) though making a game.

2

Land Surveyors

Students will practice measuring perimeter and area using standard units. Through this activity, students have the opportunity to explore a small area of the natural environment in depth.

3

Shape Shelters

Using natural materials, students will strengthen their understanding of 2D and 3D shapes through building shelters. 

Shape Shifting

Curricular Competencies

Math

  • Model mathematics in contextualized experiences

  • Develop, demonstrate, and apply mathematical understanding through play, inquiry, and problem solving

  • Visualize to explore mathematical concepts

  • Develop and use multiple strategies to engage in problem solving

  • Communicate mathematical thinking in many ways

  • Use mathematical vocabulary and language to contribute to mathematical discussions

  • Represent mathematical ideas in concrete, pictorial, and symbolic forms

  • Reflect on mathematical thinking

Science

  • Demonstrate curiosity about the natural world

  • Observe objects and events in familiar contexts

  • Generate and introduce new or refined ideas when problem solving

Physical Education

  • Develop and apply a variety of fundamental movement skills in a variety of physical activities and environments

  • Apply a variety of movement concepts and strategies in different physical activities

  • Apply methods of monitoring exertion levels in physical activity

  • Develop and demonstrate safety, fair play, and leadership in physical activities

Materials: ​

  • sidewalk chalk

​

  1. Gather students outside on the blacktop with sidewalk chalk.

  2. Ask students to choose a small objects from nearby (e.g. pinecones, short sticks, leaves, rocks, etc).

  3. Draw out a grid (like grid paper, 10x10 squares or larger

  4. Using the object, trace it onto the grid. Translate/slide, rotate/turn, and reflect/flip the object to a new spot on the grid. Trace the final spot of the transformed shape. Write down the steps (sequence) of how you go to that spot (e.g. transform two left, flip horizontally, transform two down, rotate right).

  5. Trade grids with a partner, see if they can follow your steps to transform your natural object to its new spot on the grid.

  6. Discuss: What strategy did you use to transform your object? If you changed your object, how would that change your sequence?

 

Extensions: 

  • PE Game: gather students in an open area, outline a large rectangle using cones (or use the gym walls if playing indoors). The teacher will call out directions - left (run to the left boundary), right (run to the right boundary), up (run to the top boundary), down (run to the bottom boundary), translate (slide on the spot), rotate (turn to face the other direction), reflect (stand back to back with another player). As the teacher calls out, the last person to do the action will be out and help make calls.

Land Surveyors

Curricular Competencies

Math

  • Model mathematics in contextualized experiences

  • Develop, demonstrate, and apply mathematical understanding through play, inquiry, and problem solving

  • Visualize to explore mathematical concepts

  • Develop and use multiple strategies to engage in problem solving

  • Communicate mathematical thinking in many ways

  • Use mathematical vocabulary and language to contribute to mathematical discussions

  • Represent mathematical ideas in concrete, pictorial, and symbolic forms

  • Reflect on mathematical thinking

Science

  • Demonstrate curiosity about the natural world

  • Observe objects and events in familiar contexts

  • Generate and introduce new or refined ideas when problem solving

English Language Arts

  • Exchange ideas and perspectives to build shared understanding

  • Use writing and design processes to plan, develop, and create texts for a variety of purposes and audiences

  • Communicate in sentences and paragraphs, applying conventions of Canadian spelling, grammar, and punctuation

Art

  • Choose artistic elements, processes, materials, movements, technologies, tools, techniques and environments using combinations and selections for specific purposes in art making

  • Create artistic works collaboratively and as an individual using ideas inspired by imagination, inquiry, experimentation, and purposeful play

  • Connect knowledge and skills from other areas of learning in planning, creating, interpreting, and analyzing works for art

Materials: ​

  • clipboards

  • worksheets

  • pencils

  • tape

  • rulers

​

  1. Take students outside to an open area.

  2. Demonstrate perimeter and area using students: ask two students to lie down in a line. Ask two more students to lie in a line vertically to the students already lying down, forming a vertex (corner). Ask 4 more students join the square/rectangle to complete the shape. 

  3. Ask: What shape do you see? (square/rectangle). What is the perimeter (in students) of this shape? (2+2+2+2=8 students). If all the students were the same height, what would the area be? (2x2=4 students).

  4. Explain that students will be mapping out an area (smaller than 30cm x 30cm) in pairs. Hand out clipboards, worksheets, pencils, tape, and rulers.

  5. Review boundaries. Ask each group to find their own small area. Use tape to map out this area. Measure the perimeter and area of the area. Sketch and label the natural beings in this area.

  6. Early finisher options using the back of the sheet: write about why they chose this spot, any observations, or a reflection about the activity.

  7. Bring the class back together, have students share what their land survey looked like: what natural beings did you notice? How did focusing on one small spot change your perspective?

  8. Go back to your spot and clean up the tape in your area.

 

Extensions: 

  • Game: Using the the area you surveyed as a reference, draw 5 natural objects onto graph paper within a 20 x 20 box. Label each axis: 1,2,3, etc. on the X-axis and A,B,C, etc. on the Y-axis. With a partner, play a battleship-type game using the natural objects in your field. Players take turns guessing spaces, either hitting or missing the natural objects. For example: partner 1 guesses 2A. Partner 2 says hit. Both partners mark down the hits and misses on their grid. Play until one player has found all 5 objects.

  • Go back to the spot you mapped, journal about the space other beings that share that space. How do you notice interconnectedness?

  • Draw/paint a detailed picture of the space you surveyed. Include the art elements (shapes, lines, colours, etc.) present in the space.

Shape Shelters

Curricular Competencies

Math

  • Model mathematics in contextualized experiences

  • Develop, demonstrate, and apply mathematical understanding through play, inquiry, and problem solving

  • Visualize to explore mathematical concepts

  • Develop and use multiple strategies to engage in problem solving

  • Communicate mathematical thinking in many ways

  • Use mathematical vocabulary and language to contribute to mathematical discussions

  • Represent mathematical ideas in concrete, pictorial, and symbolic forms

  • Reflect on mathematical thinking

Science

  • Demonstrate curiosity about the natural world

  • Observe objects and events in familiar contexts

  • Generate and introduce new or refined ideas when problem solving

English Language Arts

  • Exchange ideas and perspectives to build shared understanding

  • Use writing and design processes to plan, develop, and create texts for a variety of purposes and audiences

  • Communicate in sentences and paragraphs, applying conventions of Canadian spelling, grammar, and punctuation

Art

  • Choose artistic elements, processes, materials, movements, technologies, tools, techniques and environments using combinations and selections for specific purposes in art making

  • Create artistic works collaboratively and as an individual using ideas inspired by imagination, inquiry, experimentation, and purposeful play

Materials: ​

  • 3D shape nets (rectangular prism, triangular prism, and square prism)

  • string/tape

​

  1. Bring students outside to a space with sticks and branches.

  2. Demonstrate how nets (opened/flattened 3D shapes) fold up to make a 3D shape.

  3. Divide students into groups of 3-4. Assign a prism to each group (rectangular prism, triangular prism, or square prism).

  4. Ask each group to construct their prism shelter using natural materials (sticks or small branches work best) and tape/string to secure vertices. The prisms can be small or large. Remind students to reference the paper nets when building.

  5. When prisms are complete, do a gallery walk as a class to view each prism shelter. Discuss: what was your process for building the prism? Is there anything you would change about it? Would this be a good shelter (for humans or animals)?

  6. Deconstruct the prisms or keep them intact to continue imaginative play.

 

Extensions: 

  • Challenge students with building different or more complex prisms (pentagonal and hexigonal prisms)

  • Write about the shelter you built from a non-human perspective. For example: as a bear, what would you think if you came upon this structure. Is it a suitable habitat? Is there anything you would change about it?

  • Sketch how it would look if a non-human lived in the shelter.

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