Grade 4 math
Guiding question: In what ways can angles be described?
Learning outcome: Students determine and express angles using standard units
Skills and procedures:
- Measure an angle with degrees using a protractor
- Describe an angle as acute, right, obtuse, or straight
- Estimate angles by comparing to benchmarks of 45°, 90°, 180°, 270°, and 360°
Guiding question: In what ways can geometric properties define space?
Learning outcome: Students analyze and explain geometric properties
Skills and procedures:
- Identify relationships between the sides of a polygon, including parallel, equal length, or perpendicular, by measuring
Guiding question: How can area characterize space?
Learning outcome: Students interpret and express area.
Skills and procedures:
- Determine the area of a rectangle using multiplication
- Solve problems involving area of rectangles
In this hands-on project, students will construct a cardboard box that simulates common mitre joint angles used by carpenters when they’re 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 examine the features of parallel and perpendicular lines and the roles of each when working with angles. 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 finishing carpenters.
Each group will need the following:
- Mitre box
- Two clamps
- Blank cardboard box
- Speed square
- 8 feet of fiberboard
- Glue gun and extra glue sticks
- Table or desk to work on
- Watch accompanying videos.
- Gather all required materials and prepare workspaces for each group.
- Suggested group size is 2–4 students per group.
- NOTE: Glue guns are extremely hot. Student supervision is suggested.
Types of joints
- Mitre joint: A joint made by cutting two pieces of material at a 45-degree angle, allowing them to join together 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. These 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. These joints are used when connecting the vertical door trim to the baseboard 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.
- Set up workspaces for each group and make sure all materials are ready.
- Assemble the cardboard box by instructing students to glue one side of the box at a time, using speed squares to ensure 90-degree corners. Next, clamp the mitre box and prepare fiberboard. Then, secure the mitre box to the table using clamps. Demonstrate how to cut the 45-degree angle on the fiberboard by placing the fibreboard in the mitre box and the saw in the 45-degree slot. This is for the mitre joint or corner joint. Remember to take a full cut with the saw.
- Measure and mark the fiberboard. Show students how to measure the distance from one corner of the box to the other corner and transfer that measurement onto the fiberboard with a clean mark. Depending on the student body, they may need assistance on how to use and read a tape measure. Cut the second 45-degree angle on the fiberboard. Guide students in cutting the second angle in the mitre box, ensuring the cuts face the correct direction. This can be done by placing the fibreboard against the box in the direction the fibreboard will be going.
- Check and glue the first piece. Instruct students to place the cut piece on the box to verify the length and check to ensure that the two 45-degree angles make a 90-degree angle. This can be done visually or using a tool like a speed square. Demonstrate how to secure the piece onto the box with glue by holding it for 15 seconds.
- Repeat the steps for the remaining pieces by guiding students as they cut and glue the remaining pieces, following the same process.se keywords like parallel and perpendicular when placing the fibreboard pieces on the box.
- Allow students to reflect or lead students in a reflection of the activity. Clean up.
Practical skill (Observational checklist)
- Observe students during the construction of their cardboard box, 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 students’ joints, emphasizing the importance of precision in achieving a professional finish.
Self-assessment (EXIT SLIP)
- 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?
Whole CLASS OR Group discussion
- Facilitate a group discussion where students can share their successes, challenges, and lessons learned from the project.
- Encourage students to ask questions, seek advice from their peers, and provide constructive feedback on each other’s work.
- Evaluate their ability to articulate their thoughts, actively listen to others, and engage in collaborative problem-solving.
- Administer a written assessment to gauge students’ understanding of key concepts related to angles, measurement, and different types of joints used in carpentry.
- Include questions that require students to solve angle-related problems, identify the correct joint for given scenarios, and explain the steps involved in constructing a mitre joint.
- 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, resembling an octagon. While these types of joints are less common, they’re still used on uniquely shaped window trim.
- Calculation of area: Students can calculate the area of the various rectangles that were created.
Colton Garner, Brody Forster, Warren Anderson