Grade 3 · Separate covering from boundary distance · 219 of 750
Separate covering from boundary distance: width: 5; height: 15
A rectangular plan for a classroom activity measures 5 units across and 15 units high. Find the original perimeter and area, explain the calculation, and check a related question.
Try the question, use a hint when you need one, and compare your reasoning with the worked solution. The animation starts with this chapter’s values; changing its controls explores a new case.
01 · Make a prediction
Your practice question
A rectangular plan for a classroom activity measures 5 units across and 15 units high. First find the original perimeter and area. Then answer: Increase the width by one unit while keeping the height fixed. How much does the perimeter increase?
Use this scratch space or work on paper. Your notes stay on this page and clear when you leave. Answers are for self-checking; they are not automatically graded.
A starting point
Perimeter is the complete boundary distance. Opposite sides of a rectangle are equal, so add both widths and both heights. Area instead measures the interior covering.
Work through the reasoning
Step 1
Identify the quantities and the task
A rectangular plan for a classroom activity measures 5 units across and 15 units high. The first task is to find the original perimeter and area. Perimeter is the complete boundary distance. Opposite sides of a rectangle are equal, so add both widths and both heights. Area instead measures the interior covering.
Step 2
Calculate the original result
P = 2(5 + 15) = 40; A = 75. The full boundary is 40 length units, while the area is 75 square units. These quantities answer different questions.
Step 3
Complete the follow-up calculation
Increase the width by one unit while keeping the height fixed. How much does the perimeter increase? It increases by 2 units because both horizontal sides grow by one. The new perimeter is 42.
The answer
P = 2(5 + 15) = 40; A = 75. The full boundary is 40 length units, while the area is 75 square units. These quantities answer different questions. Follow-up: It increases by 2 units because both horizontal sides grow by one. The new perimeter is 42.
Compare the method as well as the result. A different valid method may reach the same answer. Keep exact values until the last step when the question asks for rounding.
02 · Explore the model
See the mathematical relationship move.
Use Play, Pause, and the timeline to inspect the construction. Reset restores the question’s original settings. The displayed assumptions describe where this model applies.
Watch the relationship
PausedHD animation studio
From experiment to screen.
Present a crisp Canvas scene, save a full-HD image, or capture your model as a silent video.
The mathematical idea
A rectangular plan for a classroom activity measures 5 units across and 15 units high. Perimeter is the complete boundary distance. Opposite sides of a rectangle are equal, so add both widths and both heights. Area instead measures the interior covering. The full boundary is 40 length units, while the area is 75 square units. These quantities answer different questions.
P = 2(5 + 15) = 40; A = 75
03 · Reflect and transfer
Explain what changes and why.
Trace the boundary without jumping across the interior. Pause at a corner and identify which lengths have already been counted. Explain which quantity changes and which relationship stays valid. Use the starting values again before checking your written answer.
This is a distinct guided scenario using a reusable mathematical model. Similar-looking diagrams can represent different given values and conclusions; they are not different mathematical theories.