A number's digital root is a single digit value obtained by adding the digits of a number repeatedly until you are left with a one digit sum.
Ex) 23 --> 2 + 3 = 5 so 23 has a digital root of 5
85 --> 8 + 5 = 13 --> 1 + 3 = 4 so 85 has a digital root of 4
Kathy Collins, a Kim Sutton Associate, discussed digital root as a way to check divisibility, determine factors of a number, and a method to check whole number computation:
I can see using the digital root when teaching divisibility rules but was not a huge fan of using it to check whole number computation (especially the subtraction). The multiplication check would be my favorite because there was some fact practice incorporated.
Overall, neat concept, but probably not something that will have a huge place in my classroom.
Teaching Number Sense to iGeneration - Eric Milou
"This session will examine issues about whole numbers and rational numbers and the lack of students' sense making with such numbers. Participants will be engaged in strategies and activities using technology that can lead to building better number and fraction sense and to consider issues around curricular coherence"
Really fun and engaging speaker. Emphasized the use of technology. He started off by stating "Technology = Motivation" which I completely disagree with. Technology used effectively can absolutely be motivating to students, but simply using technology does not make something engaging. He did provide ways to use technology in effective, motivating, authentic ways though:
https://sites.google.com/site/emilou2010/ << Lessons, Games, Etc.
Seriously- overwhelming amount of resources which I have not even begun to really dig into:
Dan Meyer's 3 Acts
Andrew Stadel 3-Act Math Tasks
My plan is to organize these resources into the units and sequence I'm required to teach this summer so when I come to a unit, I already have a handful of ways to present problems to students and I don't have to spend tons of time searching.
The TEKS Process Standards: The Best TEKS of All - Robyn Silbey
To maximize student understanding of problems have them explain their plan for solving without using numbers.
Clueless- Unintended Consequences of Using Clues of Key Words - Cathy Seeley
- The best way to formatively assess a student is to listen to their problem solving process.
- There is a difference in solving word problems and solving mathematical problems posed with words.
- What students need for their future is as much about how they think as it is about what they know
- Their futures are in our hands and ours are in theirs
- Book recommendation: Mindset by Carol Dweck
- Resource: http://ccsstoolbox.org/
Building Powerful Numeracy: Fractions and Ratios - Pamela Harris
Probably my favorite session of the day. Such an energizing and engaging presenter!
- Math is figure-out-able!
Not memorizable. <<- When you sing cute songs and play cute games it supports this. - Look to most efficient strategies and buildproportional reasoning at the same time
- Teachers build own numeracy
- It’s about relationships
Among numbers to solve problems
Between teachers and students to build young mathematicians
Harris took us through problem strings to build relationships among numbers to solve problems. On this one...think about a clock:
- 30 minutes + 20 minutes = 50 minutes, 50/60, 6 equal sections of 10 minutes each, so 5/6
- students solve addition of fraction problems by understanding relationships in numbers, not by rushing to an algorithm that isn't built on conceptual understanding
- Develop relationships using naturally occurring denominators (think money /100 and clock /60) but continue to develop relationships- don't leave them here!
Quote from Harris, "Oh, that's going to be hard, so let's reframe it! No! If it is going to be hard then they need to confront it. Put the misconception in front of them!"
This session flew by and left my head spinning a little... definitely plan on purchasing this book though:
This session flew by and left my head spinning a little... definitely plan on purchasing this book though:
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