I have been trying the Whole30 Program for about 15 days now, and it's definitely challenging to avoid all of the foods on the "non-compliant" list. The only food I am really missing is peanut butter/peanuts. The reasoning for not eating peanuts, basically, is this: as a legume, peanuts have lectin (a protein structure that may be hazardous to humans), which is highly resistant to digestion and toxic to animals (when raw). All legumes have lectin, but it's usually destroyed during heating. In peanuts, it isn't destroyed, and lectins then fool your gut lining into letting them into the bloodstream by mimicking the structure of other proteins. Undigested proteins shouldn't be released into the body, so the result is inflammation in the body.
Instead of eating peanut butter, the authors/founders of the program suggest sunflower butter, which they say is very similar to peanut butter. I finally picked some up today, and I really like it! Since the Whole30 does not include eating bread of any kind, I had the sunflower butter with an apple. It is very creamy, so it was easy to spread on the apple and would be easy to spread on any bread/toast (when/if I eventually eat that again). I definitely like it better than the almond butter I had been using.
Last week, we started discussing factoring, mostly with numerical expressions. It's 6th grade, it's the first time students are factoring, and it's the first time I've taught factoring. I know how to factor, but I wasn't really sure how to best explain it so it would be easy for the students to understand. When I learned to factor something like 18x + 24, we just thought of the GCF and divided both numbers by it. Maybe we listed out the factors to find GCF if the terms were large numbers, but that was it and I don't remember thinking it was that difficult (it was a while ago, though!). However, I didn't learn to factor in 6th grade.
So not knowing what to expect, I used a video clip from our math series to start with, as well as a PowerPoint from the series. The PowerPoint explanation/examples connected to the Distributive Property, but not well enough for the students to really understand the connection. When they tried a few problems on their own, some students were still confused. So, I showed them what I remember being taught (find the GCF and divide the terms by it). They thought this was much more simple, but we only had time for one or two additional examples before the period was over, so I knew we'd need to continue the next day. This was good, because it gave me more time to consider what approach might be best. The video and PowerPoint weren't great, but the dividing idea seemed to make sense to them.
As I had been walking around during this instruction, I noticed many of the students were using the ladder method to find the GCF. I noticed that the numbers at the bottom of the ladder end up being the numbers that go in the parentheses when the GCF is "removed" from the expression. This idea might be really obvious to those of you that regularly teach factoring, but I hadn't seen factoring presented in this way. I searched online to see if I could find it, and I couldn't. I spoke to a few teachers and they hadn't seen it before either, but they liked it.
Here's what I mean: With the expression 18 + 24, the 18 and 24 are side by side on the ladder, and we see that they can both be divided by 3. So, we divide them both by 3 to get 6 and 8. 6 and 8 can both be divided by 2, so we do that and end up with 3 and 4 on the bottom of the ladder. To write to the factored form of 18 + 24, we take the 3 and 2 from the left and multiply them to get 6 (GCF). This GCF goes on the outside of the parentheses. The 3 and 4 on the bottom of the ladder are the factors that remain when the GCF is removed from 18 and 24, and these go inside the parentheses, so the factored form is 6(3 + 4).
When I presented this to the students the next day, they thought it made so much more sense, and that it was so easy. It seems particularly helpful for students who don't know all their facts that well, or for when a GCF might not be as easy to think of (like GCF of 42 and 56 is 14 - most of them think it's 7, but the ladder method helps them to determine that it's 14).
I made a notes sheet to help them remember the steps. Feel free to download it if you'd like to use it.
I haven't done a Workin' On It Wednesday in a while!
I hope what you're working on is going well!
I've been working on eating clean and weight training, have started an Instagram account, and have been putting a lot of thought into factoring using the ladder method (about which I have a different blog post that I'm working on).
I don’t know about you, but I love my workouts. They do so
much for me, mentally and physically, and I really miss them when things come
up that cause me to skip them. I miss them so much that I often get up at 4:30
am to be sure I get some workout in, just in case my day ends up having other plans for
Why is it important for teachers to work out? These are my top 5 reasons:
1) Exercise is a great stress reliever! How many
days do you come home stressed out over the events of the day? Still thinking about things that kids (or parents, or administrators) did that got you worked up? Do you bring
that stress home with you or leave it at school? I know I have trouble leaving
it at the door, but if I can go jump on the treadmill or the elliptical and
pound that stress out using my body, my mind definitely becomes more free.
2) Working out can renew your energy level for the rest
of the day, especially if you can do it right after school. I usually have some
grading (or planning) that I bring home, or I need to help my daughter with homework during the evenings; when I take that exercise time right after school, I get recharged for the evening.
3) It helps you avoid snacking!! I don’t know about you, but when
I get home, I feel like eating EVERYTHING I can get my hands on, (and until lately some of those foods haven't been very healthy!) If I work out, I don't have the same snacking urges.
4) Creativity! Research shows that exercise helps memory and stimulates creativity. It's a great time to run lesson/activity ideas through your mind; somehow that extra physical activity gives your brain the boost to make those lessons more engaging/exciting/interesting!
5) Sleep better! What teacher doesn't need to get good sleep?
Who else loves their workouts??
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There are times during the school year when
I think I spend too much time on a math topic….not because the kids seem bored
with it or anything like that, but because I have to get so many concepts
covered that I’m afraid I’ll run out of time; so spending more time than
I’m “supposed to” occasionally stresses me out. But most of the time, I’m glad I spend so much
time on concepts, even though I appear to be “behind” when talking with other
teachers about “where we are.” When I say that I spend more time, it’s not that
I make the students do worksheet after worksheet; instead, we practice/interact
with the same skills in different ways, as I’m sure you do. For example, before
the holiday break, we worked on finding the GCF. In the past, most of the students
had only been taught one method to find GCF - by listing out the factors. I
taught the students the prime factorization method and the ladder method
(personally, I LOVE the ladder method, for most sets of numbers). Then we had the holiday break. So on our first day back, we briefly reviewed the methods and then I had
the students partner up (using the equivalent expressions partnering cards!)
and write short paragraphs to explain each method (and include their own
examples). That took most of the math class (after our warm up and
reviewing….only a 40 minute class). The following day, with the same partners, the students
started their GCF Footloose, which included listing of factors, finding GCF of
given numbers, and quite a few GCF word problems. The students in the first class period didn’t even get half-way
through the Footloose cards, and I started thinking, “Oh, no, now we have to
use another day to finish this tomorrow…or maybe we shouldn’t finish, just move on.” BUT, as I
listened to my students’ discussions, class after class, I decided that we
definitely needed to finish the next day. And I definitely need to continue to spend
the same amount of time on topics that I have been spending, in all the
different ways I employ. Their discussions with and comments/advice to each other
were such a confirmation that spending this time is best for my students.
As they worked, I heard them finding factors of larger numbers by testing
divisibility rules (without me advising them to!), using
different methods to
confirm answers, helping one another by pointing out one another’s mistakes
(politely) – which means they can identify mistakes in work! I was so impressed
with their ability to communicate about how to complete a problem or how to
communicate disagreement with apartner.
I was impressed that they turned to each other for help and really tried to
figure out the answer before asking me. I was impressed with their increased use of math language! I love to walk around and listen to
them. I have my students work together quite often in the time that I spend on topics, and their discussions are continually improving, as are their collaborative thinking skills. Is the extra time I spend on topics worth it? Absolutely!
What do teachers need? What's the first thought that comes to your mind? I'm so curious to know the first thought that crosses your mind when asked that question (as a current teacher or former teacher). Will you leave your thoughts in the comments below? Whatever comes to mind first....!
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