Feliks Zemdegs (@Fazrulz) set a new Rubik's Cube World record at the POPS Open 2016 on December 11th. Even with this time, however, he did not win the competition. The winner is determined by a trimmed mean. Five times are recorded and the fastest and slowest are removed and the middle three are averaged. Trimmed means are used to score a number of sports and competitions such as diving and snowboard halfpipe. As a class activity, I would encourage students to guess what the World Record fastest time for solving a Rubik's Cube is. After some guessing, I would let them watch the video of Feliks solving the Rubik's Cube and have them estimate his time to the nearest hundredth of a second. As in many Estimation180 tasks, you might ask students to make a guess that they know is too fast and a guess that they know is too slow in order to establish a reasonable range for their estimates. (Note: You may want to download this video and shorten it. Since the title of the video includes the record time, you might give away the answer by showing the video from YouTube.) 4.73 seconds is really fast! How fast you say? As Anne Haensch stated, "That’s faster than you can say 'Hey Feliks, can you solve this Rubik’s Cube in under 5 seconds?'" You'll see in the video, when he turns the camera around, that the recorded time is actually 4.737 seconds. The official rules from the World Cube Association state that timed results are measured and truncated (not rounded) to the nearest hundredth of a second. These times are measured using a Stackmat timer and are accurate to 0.001 seconds. It was recently pointed out in a tweet from Matthew Oldridge (@MatthewOldridge) that there are few places in life where the thousandths digits are used. One of the places where people do see this is on gas pumps. The amount of fuel that you pump is shown to the thousandths of a litre (0.001 L is equal to 1 mL). This is a pretty small amount... just 1/5 of a teaspoon or about 20 drops (the size of a drop depends on the fluid and the dropper, but 20 drops in an mL is generally a good estimate). Using a photo like the one below, you might ask your students what they know about the price of gas for this sale.
To help students being introduced to decimal place value and operations, I created two variations of a game that can be played using either dice or a deck of number cards. Students either roll a die or draw a card to complete decimal numbers with the goal of creating the largest number. The links to the google docs of these handouts are below (https://goo.gl/vuNluM and https://goo.gl/oIUWSr) Nova Scotia Mathematics Curriculum Outcomes Math at Work 12 S01  Students will be expected to solve problems that involve measures of central tendency, including: mean, median and mode; weighted mean; trimmed mean. Math at Work 12 M01  Students will be expected to demonstrate an understanding of the limitations of measuring instruments, including precision, accuracy, uncertainty, and tolerance, and to solve problems. Grade 7 N02  Students will be expected to demonstrate an understanding of the addition, subtraction, multiplication and division of decimals to solve problems (for more than onedigit divisors or more than twodigit multipliers, the use of technology is expected). EL
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