Using Numbers to Predict the Future

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Objective

SWBAT use patterns and the measures of tendency to make numerical predictions.

Big Idea

Students will calculate weighted averages. Students will use the properties of "9" to predict the value of a mystery number.

Do-Now

10 minutes

This lesson is planned to fall during our school's homecoming week. There will be many exciting school pep rallies and celebrations held throughout this time, so there is a huge feeling of energy and enthusiasm felt from both teachers and students. Even though today's activities deviate away from our normal Algebra Curriculum, they are still math based, and will give students a place to channel the high energy from the events.

Our Do-Now will be a writing activity. When students enter the room, a prompt will be written on the board:

 

  • Write a poem or a haiku about Algebra. Be creative! 

 

After 5 minutes students will share their responses, and the class will then vote on which was the best. Students will be completing this activity on construction paper, and I will display them in the hallway for the rest of the building to enjoy.

Group Activity: Weighted Averages

35 minutes

My students take 8 different classes throughout the year, all with different class requirement and grading schemes. Students receive syllabi during the first week of school stating these class guidelines, but have misplaced it soon there after. There is great confusion amongst them why one homework assignment can increase their overall grade by 20 points in one class, but only 2 points in another.

This Presentation and Handout review weighted averages, giving students the tools they need to better understand the math behind their grades. The majority of this lesson should be completed as a whole group. Students can work individually or in pairs on Slides 17 - 21.

This portion of class will close with the discussion questions on Slide 22 and Slide 23.

Group Activity: Magic Math

35 minutes

This activity is a lot of fun, and one of my favorite activities to complete with students. Using the Flash Mind Reader, students will explore the properties of the number nine. This website should be displayed in the front of the room when the activity begins.

I begin by making a large bet with the entire class. I will say, "This website is magic, and it can read your mind." My students will laugh at this notion, of course, so I will then up the stakes, "If it reads your mind incorrectly, the entire class will have NO homework for an entire month!" 

We will then begin using the website. The following instructions should be given aloud to students:

    1. Pick a number between 10 and 99.
    2. Add both digits together.
    3. Subtract the sum from your original number.
    4. Take this final number and look up the symbol on the chart.
    5. Concentrate on your symbol!

I will then click on the Magic Eight Ball on the Flash_Mind_Reader screen. The magic eight ball will yield the symbol that students choose in Step 4. The class will be in absolute awe, and insist on repeating this process multiple times in an attempt to prove my conjecture wrong. Eventually, the students will usually accuse me of rigging the website, and will send a class representative to the board to take over the operation of the mouse. Much to their surprise, the website will continue to guess the correct symbol every time.

After about 5 minutes of fun, I will challenge the class to figure out why this works. Students will break apart into groups of 2-3, and will use a laptop or tablet to play around with the website some more. I will encourage students to record their observations as they go along, and to write down all of their work.

I will circulate around the classroom as students are working, but will be careful not to give students any formal hints or guidance. Students will problem solve in groups until the end of the class period. I usually have at least one group who can figure out how the website works, but if no students are able to solve the riddle before class ends, I will assign this task as an extra credit challenge to be completed on their own. 

This activity is much more rewarding for the students if they are able to "crack the code" completely on their own.

 

Teacher's Note (Spoiler Alert!): Any time you add the numbers of a two-digit number and then subtract that sum from the original number, there are only 9 possible answers. If you examine the number key on the website, these nine numbers will always be of the same symbol. Even though the other numbers change with each click, the multiples of nine will always stay the same.