In seventh grade, the students applied their knowledge of ratios, proportions, and scale to a project where they had to produce a scaled version of a regular playing card. The purpose of the project was to have the students apply their understanding of proportions to a real task and for students to develop an appreciation for the feature on tablets and phones where they can just pinch to enlarge and/or shrink a map or image. These are seemingly simple features that require a great deal of mathematics to make functional and accurate.
I like this project because there are many ways for students to customize their experiences and provide differentiation. They could add difficulty in the value of the card, the suit, the scale factor, and whether or not they did the whole or just part of the card. Artistic ability is not required to succeed on this assignment, but it is an opportunity for those who have an interest in artistic expression to share their interest. It brings a little color and fun to the walls of the classroom!
Friday, March 17, 2017
Sixth grade is moving into an exciting part of the year where we move from computation to more conceptual work. We are reviewing the concept of ratios with a hands-on activity with a box of Froot Loops.
Students were asked to estimate the total number of Froot Loops in the 12.2 oz box of Froot Loops. The box was divided up amongst the students and they had to catalog and count each color. The students made adjustments to their estimates for the full box and made estimates for the total number of each color in the box. We briefly discussed this as a way to do sampling to estimate the total box of Froot Loops.
I took this opportunity to show the class the power of spreadsheets. We used Google Sheets to collect our class data. Then we used formulas for sum to find totals of each color and for each student. We applied our knowledge of fractions and percents to turn the totals into percents. They also saw the power of the spreadsheet to generate a bar graph of our data. The class was curious to compare their data to previous years data sets and made interesting observations. Students reflected upon their experience and saw how using ratios was helpful in refining their estimating. They were happy because they enjoyed ingesting their data set after we were done!
Thursday, February 2, 2017
We have entered the world of rational numbers in 6th grade. We are working on building our fluency with different representations of fractions: moving between fractions, decimals, and percents. A perennial question that emerges, "Is 0.99999 (repeating) the same as 1?"
This year, I asked the class to tell me what they thought before any explanation was given. There was a clear majority who felt like 0.9999... was not equal to one. There was heated debate and we had to work on how to speak to each other so we could understand the other's point of view. We recognized that repeating the same response is not going to help someone see another point of view. The challenge is finding another way to explain it help someone see from a different perspective.
We capped off the discussion by watching the ViHart video (above). There is a lot of information to take in and unpack, but there are some very convincing arguments. For homework, the class was asked to reflect on where they stand on the questions now. Many students found reasons to change their thinking and a few are steadfast in their belief that 0.9999.... is not equal to one.
Sunday, January 29, 2017
Wednesday, January 25, 2017
As introduced in the post, Snapshot: 8A Barbie Bungee Jump, the eighth grade applied their knowledge of linear functions to a Barbie bungee jump challenge. The intent of the project was to provide a real world application of linear functions to ground student understanding. Students were divided into groups of two or three to do some introductory experimentation with a Barbie, up to three rubber bands, and a meter stick. Here are all the bungee jump groups with their test Barbie and company name.
Groups plotted their data two ways: by hand and using the an online regression tool. Using their math skills they drew a line of best fit and did their best to estimate the slope of the line. Once they had their calculations figured out, they plotted their data on regression tool and it gave them a linear equation. They had to figure out what the slope and y-intercepts represented in this scenario and use these data points to decide how many rubber bands to add to their bungee rope.
We had to wait patiently for a dry day to perform our bungee jumps. Jump day was thrilling. They students made their initial jumps and then modified their numbers one last time. Here are some photos from jump day.
We experimented with filming and photography of the event. There were a couple of GoPros and lots of iPhone footage. Our favorites were the slow-motion jumps taken from the ground.For our final jump, we had all Barbies jump simultaneously. It was a great way to make a direct comparison of all the bungee cords.
Student reflection and feedback gave me insights into how to improve upon this activity. Fun was had by all and we made math come to life!
Thank you to all the people who shared their Barbies for us to use and to B. Hansen for the great video clips.
I found this brief article insightful. I have always felt that math anxiety does not just materialize but comes from messages that children receive that they should be anxious. It is helpful to know that this is one source. The next step is figuring out how to address parent math anxiety so they do not pass it onto their children.
One resource I recommend to parents is YouCubed.org by Dr. Jo Boaler. She provides many practice tools and suggestions to help students learn math in ways that do not produce math anxiety.