Estimating Perimeter on Grid Paper
Grade 7 students in Big Ideas Math Advanced 2 (Chapter 13: Circles and Area) learn to estimate the perimeter of curved and composite figures on grid paper using the approximation that diagonal segments are approximately 1.5 units each, while horizontal and vertical segments are exactly 1 unit.
Key Concepts
When estimating perimeter on grid paper: horizontal and vertical segments = $1$ unit each, diagonal segments ≈ $1.5$ units each.
Common Questions
How do you estimate perimeter on grid paper in 7th grade?
Count horizontal and vertical segments as 1 unit each. Estimate diagonal segments as approximately 1.5 units each. Add all segment lengths for the total estimated perimeter.
Why are diagonal segments approximately 1.5 units on a grid?
Diagonal segments cross grid squares at angles, making them longer than 1 unit. The 1.5 approximation accounts for this extra length from the Pythagorean theorem (sqrt(2) is approximately 1.414).
How accurate is the 1.5 unit diagonal estimate?
It is an approximation. The exact diagonal length for a 45-degree segment is sqrt(2) approximately 1.414, so 1.5 slightly overestimates.
What chapter in Big Ideas Math Advanced 2 covers estimating perimeter on grid paper?
Chapter 13: Circles and Area in Big Ideas Math Advanced 2 (Grade 7) covers estimating perimeter on grid paper.
When would you use this grid estimation method?
Use this method to estimate the perimeter of irregular or curved shapes drawn on coordinate grids where exact formulas cannot easily be applied.