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Turn and talk to your partner to tell them a story about what might have happened. Which would make the colored circles harder to use when playing the game. Seems like lots of you want to check in with your partner? Can someone just get us started with something they noticed? What I realized was that these 4th graders had a lot of experience with finding factors, but only two factors.
The 7 and the 8 basically switched places and the answer stayed the same. Alina: 7 times 80 is the same as 8 times 70 because they are both like copies of 7 x 8. Let me ask a different question: do you have a story if I do this? The next part of the string was: Then, something happened and I had bought 8 cups. Eller led a notice and wonder on the first 20 numbers, then , and then the kids had time to explore the charts on their own.
And those circles are the key to mathematizing the game, I think. They groaned when I put a 10 on the chart under the cups of coffee, possibly a sign that they were invested in the context with me. In Realistic Mathematics Education RME , we think about how particular mathematical models are worth investing in, because they shape how kids think about mathematics.
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That is where I think the colored circles have a really interesting and concrete role to play as a possible model for the deep structure of numbers as factors. Okay, sounds like you are saying we might need to modify some of the contexts to make them fit the numbers here, but that it can be done. Who understands what Franky is saying and can build on his idea? The number line, for example, is not just a visual, but a tool that offers certain affordances in HOW you think about operations and pretty much all of mathematics.
To think of 60 not as the pairs of numbers that multiply, but the core factors, the prime factors, that is something that is challenging to represent in a way that it becomes intuitive for kids. I wanted the number string to call attention to how the prime factors were related, so that kids could see the connections between related multiples. And we have 7 tables of 8 people each, thanks to Rodney. Jackie: So 7 packs of gum with 80 sticks is, like, not really a thing. My students now know they have been invited into a world where maybe we can have a garage with cars, or I can spend an entire day just on coffee runs, and we can wonder about how many stairs we have climbed.
But I could write an entire post about the difficulties of representing the associative property with number lines or arrays. A number string is a beautiful way to call attention to mathematical patterns, since we do one problem at a time, and we focus on developing our collective noticing of emerging patterns. And finally, we have 7 packs of 8 sticks of gum, thanks to Imani. But you could have 80 packs of gum with 7 sticks in it.
I decided to focus on multiples of 5, since that would allow everyone to engage in thinking about the model, while feeling comfortable with the facts. Turn and tell your partner about your context, and then listen to find out about theirs.
After a short turn and talk, I solicit at least three different stories, being sure to record each of them on chart paper. David: So instead of 7 tables of 80 people, you could have 80 tables of 7 people. We start pretty simple, with the basic- how do these colors work-problems. Hector: Yeah, so before you had 8 people at a table and now you have 80 people at a table.
Wondering what a number string looks like in a classroom? With problems with more than two factors, I explored if kids rearranged the factors to multiply, like if they decided to do 2 x 3, then 6 x 5, or did 2 x 5, then multiplied by 3. I know you are working on some decimal operations and today I brought a number string to help us all think about those problems.
You can share something you and your partner talked about. These students have a wonderful classroom teacher, Hayley Roberts, who does number strings regularly with the students as part of a rigorous, inquiry-based mathematics curriculum. I thought this might make it more explicit for those kids. Hayley is off camera in Part 1 leading the students in a mathematics mindfulness exercise. On the second slide, I went for another equivalence example, this time with 2 x 3 x 5 and 6 x 5. Since you are  graders, you already know many contexts that we could use. Students in this class had done lots of number strings with the open number line for addition and subtraction, as well as the array as a model for multiplication.
It seemed to work well in this group, since our discussion was mostly about strategies, not answers. There was some great conversation on the relationship between the two.
I recommend a turn and talk for the second to last problem, which is the stumper last problem of a string, challenging, and has multiple ways to solve here. Here is the Google Slide of the string with animations. Today, that will be your job — to give us some stories that could help us make sense. On the previous day, the number string had been a multiplication doubling and halving string on the open number line.
Our discussion was around how kids dealt with multiple factors, some rearranging using the associative property. I have some ideas for other number strings that would build off the game: division could be very interesting, and perhaps repeating 2s for students to think about what patterns emerge when we multiply 2 x 2 x 2 x 2 x 2.
Before you watch, you might want to anticipate how 4th graders might solve these problems, and how Rachel will represent strategies on the open number line. Alina, let me try to capture your idea for all of us to make sense of…. Do we need new stories for thinking about this one? Is the dollar sign helping anyone else to make up a story? Kristina: Yep, what about 7 packs of gum and you spent. And in this class, I give myself permission to teach what would be considered K-5 mathematics.
My students who are the least ready for 6th grade material are also assigned to a numeracy class, in addition to their regular 6th grade math class. Marlene, will you share what you and Mariama were talking about? So, does that help you to find the answer to 8 times. Are you all convinced the 70 cents 8 times is. What we found, as a school community, was that this approach was not working, and just not enough. Justin: Basically you could make a story where you were buying any cent thing and for some reason you needed 7 of them.
Marlene: But now you have 8 candy bars and they each cost 70 cents. Instead, our goal is to get them to do 8th grade math by 8th grade. Originally, we tried to teach them grade level content, and scaffold the work by re-teaching or reviewing topics like double-digit multiplication or generating equivalent fractions. To address the challenge, our approach has been to take the long view: we are not too concerned with getting them to do 6th grade math in 6th grade.
When they enter my school in 6th grade, most of my students are 3 to 4 years below grade level.
Rodney: I know that cents is the same as 5 dollars and 60 cents. At my school, located in East New York I am really struggling to help students access grade-level content. With just a bare number ratio table, my kids would not have found their way out of this misconception. When my entire class tried to convince me that since cars would have tires, 99 cars would have , I knew I had a problem. Recently with my students, though, I came to really appreciate the power of story as a referent for kids.
An even bigger issue was that the context never seemed to be taken up by students during independent work or when the problems got more complex. To be honest, I was slow to come to the idea of loving context in number strings — the numbers were so beautiful on their own! It sounds like none of us have a great story for this problem — mini-sharks, tables, money, nothing. What do you think is true about the answer, even if you are not totally sure what the answer is? Review Materials. A major focus of this course is the cell — its structure and function, cell transport and cellular energy, and how cells divide.
This is one of over 2, courses on OCW. Comment goes here. This idea is on fire in my standard bio. Drop us a note and let us know which textbooks you need. You can use this course at any To promote genetics education from K and beyond, ASHG sponsors a number of education programs throughout the year. Gregor Mendel Responsible for the Laws We've been pioneering the use of technology in science education for twenty years. Early Ideas About Heredity A.
Use the code given in class and follow the power point to download your honors bio textbook: We will download the textbook together during our next class! Take this mobile-friendly course to review the concepts that are typically taught in high school biology classes. Welcome to Ms. In genetics, anecdotal evidence from practitioners of high school life science teacher e-mails and listserv communications and direct evidence collected through these 2 years of ASHG-sponsored nationwide essay contests suggest that genetics is an area where many high school students harbor multiple misconceptions and significant misinformation.
Its members have expertise in genetics content, science education, and teaching, including substantial expertise with high school curricula and pedagogy. The quiz below is designed to test just how much you know about genetics. This feature will provide a comprehensive set of tools enabling our website visitors the ability to experience interfaces that are most accessible and usable to their needs. Miller, and I am very excited to engage my students in biology—the study of life.
Discover the natural world with this collection of free biology worksheets for middle school and high school students on botany, ecosystems, and the human body. And for students enrolled in AP courses, the end of the year is particularly challenging. The West Seneca Central School District is committed to ensuring that all materials on our website are accessible to all users.
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Scientists use many different organisms to study diseases in humans. The method is described in a paper Genes are functional segments of DNA molecules which stores genetics information in cell nucleus. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. I have created this site to offer students, parents and biology teachers resources such as lecture notes, powerpoints, worksheets and animations to help everyone better understand the themes and The human genes hold a lot of things that scientist are still trying to figure out.
Language arts is organized into four English courses that are correlated to state standards and include writing practice, vocabulary building, reading comprehension and communication skills. We break down the processes of everything from bacteria to blue whales. Teacher, High School Computer Science. Genetics Here you'll find a wealth of resources and information aimed at helping educators bring genetics, bioscience and health alive in the classroom.
Some basic biology class topics might include cellular structure and functions, evolution and natural selection, heredity and genetics and ecosystems.
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