Today's estimation dealt with a trip that was similar to yesterday's, just a different direction. Most students reasoned it was nearly the same distance.
The last 15 minutes of class yesterday students worked on the Rugs task from Inside mathematics. I used it last year, but this year I cut and paste the questions, along with important vocabulary and common misconceptions into the following Google slides:
In the first problem some students didn't understand "all the way around" meant it was asking for the perimeter. We also discussed multiple ways of looking at it and why 1 foot 6 inches is not 1.6 feet. One student in 5th period really understood the place value because he said that 1.6 feet means 1 and 6/10 feet, and there's not 10 inches in a foot. 1 foot 6 inches would have to be 1 6/12 or equivalent to 1 1/2 or 1.5 feet. Every year this is a main topic of discussion. I believe estimation prepared more students to be aware of this important concept.
In the second question, students had to manipulate the isosceles triangle to understand there were 2 right triangles inside of it. Fewer students imagined a rectangle with an invisible triangle on the top left and top right and found the side lengths that way. Students needed to understand perpendicular meant forming right angles. Some students looked it up in their text. I had them put their hands straight up to represent parallel lines. When you make a timeout, your hands intersect, are perpendicular, and form 2 right angles.
We also discussed converting all measurements to inches, or changing it into decimal feet. I wanted students to verbalize that they were using the pythagorean theorem since there was a right triangle. They also had to divide the base of the isosceles triangle by 2 to get the 2nd leg that was not the height. At least 3 students in each class recalled that isosceles meant a triangle with 2 equal sides, as well as 2 congruent angle measurements.
The 3rd problem dealt with circumference. Most students ignored that it said to give your answer in whole feet, so they did not round up. Also, some students interpreted the diameter as the radius because 2 pi r and the area formula were given. I pointed out that being given the area formula was a distractor.
Finally the last problem deals with a semi circular rug. Some students realized that was half a circle, so it wouldn't be half the circumference because you had to include the flat horizontal side.
|Defining perpendicular height.|
|Students focusing on giving good feedback.|
|I was impressed a student checked this book out from the library. I really want to read it now.|