Lesson 2.2 Think Throughs
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This year I started implementing what I call "Think Through" Problems into my Algebra class to push my students towards harder problems that have multiple avenues towards a solution. I got the idea after reading Jo Boaler's books Mathematical Mindsets and What's Math Got To Do With It? and exploring her site youcubed. Her books were inspirational, as they explained with examples, personal stories, math tasks, and prepares teachers and parents alike to work on ways to teach mathematics for a growth mindset. If you don't have time to read these books, now, then put them on your summer reading list, and you will not be disappointed.
What you do need to do now however is explore Jo Boler's website youcubed, and I will give you key places to start:
1. Watch this video of Jo Boaler & her students explaining the growth mindset in mathematics.
2. Check out her lessons from her Week of Inspirational Math There are four weeks of material, for any grade level, each lesson with a video, an activity, and an important message for students to believe in their abilities, embrace mistakes and enjoy tough problems.
3. Below are some of the tasks and activities I have used as Think Through problems for my 9th grade Algebra students from Boaler's Week of Inspirational Math & additional tasks:
1. Think Through #1: Finding a Pattern
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4. Two pipes are connected to a pool. One pipe can fill the pool in 20 hours, the other in 30 hours. How long will it take the two pipes together to fill the pool? *There is more than one way of solving this problem, any approach is welcome, but you MUST SHOW ALL YOUR WORK!!
5. Find the Secret Code, given the following clues: • It is between 8,500 and 8,800. • When multiplied by 8, the result is a whole number. • The digit in the hundreds place is ¾ the digit in the thousands place. • The sum of all digits in the number is 26. • The digit in the hundredths place is 200% of the digit in the tenths place. • There are no zeros in the decimal places.
a. What code numbers fit these clues?
b. Explain how you used all of these clues to find these possibilities.
c. Write one more clue so that there is only one possible code number.
References
Boaler, J. (2016). Mathematical mindsets: Unleashing students potential through creative math, inspiring messages, and innovative teaching. San Francisco, CA:
- Jossey-Bass & Pfeiffer Imprints.
Boaler, J. (2015). Whats math got to do with it?: How teachers and parents can transform mathematics learning and inspire success. New York: Penguin Books.
Boaler, J. (n.d.). Youcubed. Retrieved from https://www.youcubed.org/
Proceed to Next Lesson: Lesson 2.3 Embracing Mistakes