Grade 7 Math
General learning outcome: Students describe the characteristics of 3-D objects and 2-D shapes and analyze the relationships among them.
- Specific learning outcomes: Students perform geometric constructions, including perpendicular line segments, parallel line segments, perpendicular bisectors, and angle bisectors.
Grade 10-3 Math
- Demonstrate an understanding of angles, including acute, right, obtuse, straight and reflex, by drawing, replicating and constructing, bisecting, and solving problems.
In this hands-on project, students will construct a cardboard box that simulates common mitre joint angles used by carpenters when installing trim around windows and doors. By utilizing mitre, corner, and butt joints, students will develop their understanding of angles and precision in carpentry. Students can challenge themselves further by attempting more complex joints, such as octagonal corners. This project emphasizes the importance of accuracy and attention to detail—skills that are crucial for carpenters.
Joint types used in this project
- Mitre joint: A joint made by cutting two pieces of material at a 45-degree angle, allowing them to join to form a 90-degree corner. Commonly used in window and door trim.
- Corner joint: In this project, the corner joint refers to a vertical cut 45-degree mitre joint that wraps around the corner of the cardboard box. Corner joints are commonly used when wrapping an outside corner using baseboard trim.
- Butt joint: A simple joint where the end of one piece of material is placed against the surface of another piece. In this project, two butt joints are used in the bottom corners of the “door” part of the box. Used when connecting vertical door trim to baseboard trim.
- Octagonal joint: This joint is a variation of the mitre joint, created by cutting four pieces of material at 22.5 degrees. When joined together, these angled pieces form a 90-degree joint with eight sides, resembling an octagon. This type of joint is less common but is still used on uniquely shaped window trim.
Each of these joint types serves a specific purpose in carpentry and requires careful measurement and precise cutting to ensure a proper fit and a professional finish.
50–80 minutes, depending on group skill and box complexity.
- Mitre box
- 2 clamps
- Blank cardboard box
- 8 feet of fiberboard or other trim material
- Glue gun
- Extra glue sticks
- Table or desk to work on
- Watch accompanying videos.
- Gather all required materials and prepare workspaces for each group
- Assemble the cardboard box (10 minutes).
- Glue one side of the box at a time, ensuring 90-degree corners.
- Secure the mitre box to the table using clamps.
- Demonstrate how to cut the first 45-degree angle on the fiberboard.
- Measure and mark the fiberboard (5 minutes).
- Show students how to measure the distance from corner to corner and transfer it onto the fiberboard with a clean mark.
- Cut the second 45-degree angle on the fiberboard.
- Guide students in cutting the second angle in the mitre box, making sure the cuts face the correct direction.
- Check and glue the first piece (10 minutes).
- Instruct students to place the cut piece on the box to verify the length.
- Demonstrate how to secure the piece onto the box with glue, holding it for 15 seconds.
- Repeat steps for remaining pieces (30 to 50 minutes).
- Guide students as they cut and glue the remaining pieces, following the same process.
- Use the different joints on other sides of the box.
- Reflection and clean-up (5 minutes).
- Allocate time for students to reflect on their work and discuss challenges.
- Instruct students to clean up their workspaces and put away materials.
Practical Skill Assessment
- Observe students during the construction of their cardboard boxes, paying attention to their ability to accurately measure and cut angles, as well as their proficiency in assembling the mitre, corner, and butt joints.
- Assess the cleanliness and tightness of their joints, emphasizing the importance of precision in achieving a professional finish.
Reflection and self-assessment
Ask students to reflect on their experience and assess their own work. Provide guiding questions such as the following:
- How well do you think you measured and cut the angles?
- Did you encounter any challenges during the construction process? How did you overcome them?
- How satisfied are you with the overall quality of your joints and the appearance of your finished box?
- What would you do differently if you were to repeat this project?
Students who completed the 45-degree mitre joints, butt joints, and outside corner joints can try to accurately construct an octagonal mitre joint that uses four 22.5-degree cuts to get a 90-degree joint.
Colton Garner, Warren Anderson, Brody Forster