a. Make tables of equivalent ratios relating quantities with whole-number measurements, find
missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables
to compare ratios.
b. Solve unit rate problems, including those involving unit pricing and constant speed. For
example, if it took 7 hours to mow 4 lawns, then, at that rate, how many lawns could be
mowed in 35 hours? At what rate were lawns being mowed?
c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the
quantity); solve problems involving finding the whole, given a part and the percent.
d. Use ratio reasoning to convert measurement units; manipulate and transform units
appropriately when multiplying or dividing quantities
6.MP3 Construct viable arguments and critique the reasoning of others
The Learning Objective: Graph the relationship of two different units
Quote of the Day: “All my life I’ve been playing up, meaning I’ve challenged myself with players older, bigger, more skillful, more experienced - in short, better than me.’ First she played with her older brother. Then at ten, she joined the eleven-year -old boys’ team. Then she threw herself into the number one college team in the United States. ‘Each day I attempted to play up to their level...and I was improving faster than I ever dreamed possible.” - Mia Hamm
Agenda:
The Assessment: The homework, partner practice. I circumvented the room as students were doing the homework.
Homework: Page 51-52 problems 1-10 in the textbook.
My Glass Half-Full Take: This lesson on the surface looks like I did nothing to prep or involve myself. I used the book for notes and for the actual homework. The fact is that I did work quite hard to find the right questions to ask to make sure students were understanding the basics of the objectives and I poked a little harder with the other questions I asked. I list them in the next topic.
I'm not a huge fan of using the book. I think it's boring usually, but we have them for a reason. Teaching graphing without the book involves a good deal more labor from me and the students in terms of writing the graph, labeling the axis, etc. There are more important places to deposit my time during the school day and I think I spent my time worrying about what questions to ask. Perhaps next year I could spice up the actual lesson.
Questions to Provoke Learning: During the jumpstart: What graph do you think starts out making the most paperclips? What graph do you think doesn't change the speed that it adds paperclips to the chain? What graph starts out slow and then gets faster? Why do you think that it's possible in real life to start out fast clipping paperclips and then slow down? Why do you think it's possible in real life to start out slow clipping paperclips and then speed up? What graph is closest to a machine? Why would a machine sometimes not be Graph A?
During the ratio table review: How can we get from 6 to 4 using division and multiplication? Is there more than one way to get there? If 5 DVDs cost $60, how much money does 3 DVDs cost? How does the unit rate help solving this problem?
During the coordinate plane introduction: What axis is the x-axis? Which is the y-axis? How can we remember which is which? How do we find a given point (what comes first the x coordinate or the y coordinate)? How do we remember this? Why do we connect the dots in some graphs and some graphs leave the dots unconnected? How can we compare two different ratios that measure the same units? How can a ratio be described in words?
There's a lot of questions there. And I asked every one of those today. Could every student answer everyone correct tomorrow. I doubt it. In fact I think there isn't a single student that could answer every single one of these questions, but many of them go outside of the objective and were simply asked to ensure that I was differentiating and pushing the thinking of students that were quick to accomplish the objective.
One Thing to Do Differently: The question that asked the students to describe the pattern of a given table or ratio was answered with vagueness. I wanted students to use units in their answer. Many would simply state, "The pattern is going up by 4 each time." I would follow up by asking 4 what? It's imperative that students state 4 minutes per page rather than 4 pages per minute, so that they would not specify at all was wrong to me. In one class I even forewarned students I was going to ask the same question three times (this particular question about describing the pattern). I ended up asking it five because the students asked the question the third and fourth times couldn't answer after hearing valid answers two times before. It's essential to make sure all students are as detailed as possible in giving a description of a pattern.
Link of the Day: America needs to encourage discovery in learning. Harvard is. There are days where I believe I am lacking here. Today might have been one although I really think the jumpstart got students thinking before I taught them anything.
The Learning Objective: Graph the relationship of two different units
Quote of the Day: “All my life I’ve been playing up, meaning I’ve challenged myself with players older, bigger, more skillful, more experienced - in short, better than me.’ First she played with her older brother. Then at ten, she joined the eleven-year -old boys’ team. Then she threw herself into the number one college team in the United States. ‘Each day I attempted to play up to their level...and I was improving faster than I ever dreamed possible.” - Mia Hamm
Agenda:
- Jumpstart with graphing ratios
- Review the homework from ratio tables
- Review yesterday's exit ticket
- Coordinate plane vocabulary kinesthetic activity
- Guided Practice
- Partner Practice
- Students begin their homework (and in one class finish)
The Assessment: The homework, partner practice. I circumvented the room as students were doing the homework.
Homework: Page 51-52 problems 1-10 in the textbook.
My Glass Half-Full Take: This lesson on the surface looks like I did nothing to prep or involve myself. I used the book for notes and for the actual homework. The fact is that I did work quite hard to find the right questions to ask to make sure students were understanding the basics of the objectives and I poked a little harder with the other questions I asked. I list them in the next topic.
I'm not a huge fan of using the book. I think it's boring usually, but we have them for a reason. Teaching graphing without the book involves a good deal more labor from me and the students in terms of writing the graph, labeling the axis, etc. There are more important places to deposit my time during the school day and I think I spent my time worrying about what questions to ask. Perhaps next year I could spice up the actual lesson.
Questions to Provoke Learning: During the jumpstart: What graph do you think starts out making the most paperclips? What graph do you think doesn't change the speed that it adds paperclips to the chain? What graph starts out slow and then gets faster? Why do you think that it's possible in real life to start out fast clipping paperclips and then slow down? Why do you think it's possible in real life to start out slow clipping paperclips and then speed up? What graph is closest to a machine? Why would a machine sometimes not be Graph A?
During the ratio table review: How can we get from 6 to 4 using division and multiplication? Is there more than one way to get there? If 5 DVDs cost $60, how much money does 3 DVDs cost? How does the unit rate help solving this problem?
During the coordinate plane introduction: What axis is the x-axis? Which is the y-axis? How can we remember which is which? How do we find a given point (what comes first the x coordinate or the y coordinate)? How do we remember this? Why do we connect the dots in some graphs and some graphs leave the dots unconnected? How can we compare two different ratios that measure the same units? How can a ratio be described in words?
There's a lot of questions there. And I asked every one of those today. Could every student answer everyone correct tomorrow. I doubt it. In fact I think there isn't a single student that could answer every single one of these questions, but many of them go outside of the objective and were simply asked to ensure that I was differentiating and pushing the thinking of students that were quick to accomplish the objective.
One Thing to Do Differently: The question that asked the students to describe the pattern of a given table or ratio was answered with vagueness. I wanted students to use units in their answer. Many would simply state, "The pattern is going up by 4 each time." I would follow up by asking 4 what? It's imperative that students state 4 minutes per page rather than 4 pages per minute, so that they would not specify at all was wrong to me. In one class I even forewarned students I was going to ask the same question three times (this particular question about describing the pattern). I ended up asking it five because the students asked the question the third and fourth times couldn't answer after hearing valid answers two times before. It's essential to make sure all students are as detailed as possible in giving a description of a pattern.
Link of the Day: America needs to encourage discovery in learning. Harvard is. There are days where I believe I am lacking here. Today might have been one although I really think the jumpstart got students thinking before I taught them anything.
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