Problem solving for Grade Level 5
5.6.B Identify information that is given in a problem and decide whether it is essential or extraneous to the solution of the problem.
5.6.D Determine whether a problem to be solved is similar to previously solved problems, and identify possible strategies for solving the problem.
5.6.G Explain why a specific problem-solving strategy or procedure was used to determine a solution.
5.3.E Determine the formula for the area of a triangle by relating it to the area of a parallelogram.
Objective: Students will use strategies for finding the area of a triangle.
Math Words: Square root, Patterns, Area, Triangle, Rectangle
Give a sample questions to assess prior knowledge of finding the area of rectangles. Start by using grid sheets to ensure understanding of the basic concepts:
Lucy’s dad is building her a playhouse for her birthday. If the front wall of Lucy’s playhouse is made of plywood that is 10 feet by 10 feet, what is the square footage of that? Please show and explain your work. What is the square footage of the window and door in the illustration? Please explain your reasoning.
Ensure the students understand the concept of square feet:
Each square of the blocks represents a square foot of the playhouse.
Everyone pair up with your partner. You have a grid sheet with several triangles on it, so using whatever strategy you can come up with figure out how to find the area of the triangles.
After figuring the area of the triangles make the smallest rectangle possible around the triangles, and find the area of those rectangles.
Lucy’s dad needs to find out how much plywood to buy to build the front of the playhouse. The roof makes a triangle in front (shown below), so we will find the area of triangles and then find out how much plywood he needs to buy:
Enter your answers in the form below:
Now that you’ve worked through the problems and filled out the form get into your small groups and discuss your answers and reasoning. Consider these questions in your discussion:
- How was finding the area of a triangle different from finding the area of a rectangle?
- How was it similar?
- How were your group’s methods different? and which ones worked well?
- Did you see any patterns in your answers?
- Did the pattern work every time?