Puzzles and Brainteasers, Set 3
It was a bit tough to get up for work this morning, but I did spend the two-week break well by relaxing and spending time with Mandy. It was nice to see my students' smiley faces, they are adorable, especially my 6th graders. They asked me what I did over the break, if I went anywhere, and if I watched the Rose Bowl last night. Of course I watched the Rose Bowl, silly — Oregon Ducks beat Wisconsin Badgers 45-38!! One student said that he was happy to return to school because he was bored at home.
My 8th grade geometry class, however, moaned and groaned about the below PS: Area of Quadrilateral that was due today. (They had three weeks to work on it!) It just makes me happy to learn that they struggle with a problem because I got them to think! I haven't graded them yet, so I don't know how the class did. But I will go over it with them in class tomorrow.
Area of Quadrilateral
In the figure show below, if the area of triangle BCF is 6 square units, the area of triangle BDF is 3 square units, and the area of triangle CEF is 2 square units, then what is the area of quadrilateral ADFE?
I gave this problem to my MathCounts elective class. They worked quietly on their own for 10 minutes, then we discussed it as a whole group. This problem is from NCTM Illuminations, a great resource!
Outside the Box
Complete the following steps.
- In the 4 x 4 grid below, choose a number in any cell. Circle it. Then cross out the other numbers in the same row or same column.
- Choose one of the nine remaining numbers, and circle it. Again, cross out the other numbers in the same row or same column.
- Choose one of the four remaining numbers, circle it, and cross out the other numbers in the same row or same column.
- Finally, circle the last remaining number.
- Add the four circled numbers together. What is the sum?
- Do this all over again by picking different numbers to circle. What is the sum? Can you explain why it happened?
My 6th graders got this fun problem.
Yokes on You!
If three hens lay four eggs in five days, how many days will it take a dozen hens to lay four dozen eggs?
If you need answers or solutions to any of the problems, please email me at email@example.com or leave a comment. Thank you!