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I am the Director of Professional Learning and Keep Indiana Learning at CIESC. I have taught high school and middle school math.

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7th Grade Mathematics

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I teach 6th grade math, including one section of high ability.

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Heather Spoljaric, Math Dept. Chair, teach Pre-Algebra & Algebra 1. Have taught high school math as well.

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6th grade math

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Create/implement a share and compare activity.

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Regain motivation utilizing more open-ended problems. Review and improve some of the better tasks I have used in the past.

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Put some higher level thinking problems as bell ringers in place of mixed review sometimes (maybe once a week?)

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Make a list of 5-10 good questions to use during lessons and use them regularly. Keep the questions on my desk so I can see them. :)

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Work on implementing math goal language in everyday conversation.

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I will ask more 'why' questions in class.

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I knew this... I can't believe my mind drew a blank on this. I visualize it in this way. The goal is to simplify the fraction so you have to multiply by the inverse/reciprocal in order to get a denominator of 1.

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So I made them into equivalent fractions with the same denominator and then divided across just like we multiply across. I don't know if really "explains" keep/change/flip but I can see this is an alternative strategy for sure.

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Also, can I just say that it's very obvious that my 6th graders DID NOT work in groups last year!!! They have no clue how to talk together, work through math, draw a fraction picture, etc. Rant over. Thanks for listening.

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Math nerd that I am, I tried to piddle around with the division problem Liz mentioned and prove K-C-F works.  I wanted to build on her idea of creating common denominators and see what happens....  No way that my reasoning will help my students, though.   I recreated "Fraction Islands" digitally and have been using it with my kids, and if I still have my sanity next week, I will continue using them with division.  My current plan is to have them visually see many examples with the islands like "4/5 divided by 1/3 equals 12/5" and hoping THEY will notice that flipping over the second fraction and multiplying always gives the answer they come up with using the islands.  But I am not sure if I will.  I have also taught the China method of getting common denominators in the past.  Decisions, decisions.....

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So I haven't looked into the visual reason as to why multiplying by the reciprocal works, but I can't believe I spaced the simple concept of making the denominator one, which is done by multiplying anything by its reciprocal. So mathematically, I now can back it up, but I'm still wanting a visual like with islands. I'll have to dig deeper into my abyss of old things ;)

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I chose the "mixing candies" task.  A learning goal attached to this activity could possibly be:  Students can solve an open-ended problem involving a system of linear relationships.  They may use graphing, substitution, elimination, visuals (2 balanced scales with tiles), data tables, or numerous other strategies to solve such problems.   The conceptual understanding is that we can use mathematical concepts to help us more easily work with (linear) patterns in real-world applications.

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I did the "Molly's Run" task. I think a learning goal for this activity could be:
Students will use a drawing to represent finding an equivalent ratio.
The big idea/concept for this task would be using equivalent ratios to solve realistic problems where they are looking for a missing part. Students could use a variety of strategies for doing this, one of which would be drawing a diagram/picture.

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I chose Molly's run task:

Learning Goal: Students will understand how to operate with rational numbers i.e. fractions in order to calculate the unit rate. They will be able to add, subtract, multiply, or divide in order to get a denominator of 1. Students will be able to explain why there are multiple ways to create a unit rate (or denominator of 1) when working with fractions.

I kind of tied a few of the 7th grade standards together on this one: computing rational numbers, calculating unit rate, and understand rational numbers on a number line.

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these were my attempts at solving and drawing to make sense of my answer

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I did Molly's Run.  I'm still struggling with this whole "Learning Goal" wording.  These are my learning goal and big ideas; I should probably elaborate a bit more:

Learning Goal:  Students will apply their knowledge of fractions to different situations.

Big Idea:  To conceptualize the use of fractions.

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Well, it's 10:30 on the night before we're supposed to zoom..... and my mind is broken. I feel like I've just been trying to keep my head above water with normal class stuff, and I've put our PD assignments WAY on the back burner. The only thing that is coming to my brain is something I stole from a Flocabulary video. A number times 1/2 is the same thing as dividing that number by 2. Since 1/2 is the reciprocal of 2, it shows that multiplying by the reciprocal works. I'm still not sure WHY it works.... but at least it gives one bite-sized example that they can conceptualize a little better before working with uglier fractions or mixed numbers.