Unit 1 · The Number System & Roots
Trap a square root between consecutive integers, then refine with decimals.
To estimate √40, note 6² = 36 and 7² = 49. So 6 < √40 < 7. Since 40 is closer to 36 than to 49, √40 is a little more than 6.3.
An integer that is the square of an integer.
Example: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.
Try the prompt first. The steps stay folded until you ask to see them.
Between which two consecutive integers is √70?
Watch for
Using (n/2)² instead of nearby perfect squares
Estimation needs the closest integer squares, not half the number.
Fix: Memorize perfect squares through 15² = 225.
Submit each answer to check it. The key is not shown until you do.
The area of a square-shaped garden is 324 square feet. What is the length, in feet, of each side of the garden?
What is the solution for x in the equation x³ = 125?
The area of a square-shaped garden is 324 square feet. What is the length, in feet, of each side of the garden?
Build a perfect-square flash ladder from 1² through 12².
Estimate ∛30 using 3³ = 27 and 4³ = 64.
Sentence starters · Notice and Wonder · Three Reads · Think-Pair-Share · Compare and Connect · Math Talk · Stronger and Clearer Each Time