Update: see this reflection post with links to student work! http://joyceh1.blogspot.com/2015/12/day63reflectionblogpostsonymxb.html?m=1
 Go to http://www.blogger.com.
 Sign in to your school ID @millbraesd.org Google account.
 Create a blog. To see a video about this created by Mr. Sullivan, click here.
 Create a new post and copy and paste the following:
Write a stepbystep process for graphing directly from a rule. A student who has not taken this course should be able to read your process and understand how to create a graph. It may help you to think about these questions as you write:
What information do you get from your rule?
How does that information show up on the graph?
Where does your graph start?
How do you figure out the next point?
What should you label to make it a complete graph?
Title this entry “Graphing Without an x → y Table,” and label it with today’s date
5. To help you answer these questions, make up a rule and represent it with a table, graph, and tile patterns (Figures 0 to 3). Your "m" and "b" values should be different in the y=mx+b format. You should also show how m and b show up in each representation.
5. To help you answer these questions, make up a rule and represent it with a table, graph, and tile patterns (Figures 0 to 3). Your "m" and "b" values should be different in the y=mx+b format. You should also show how m and b show up in each representation.
6. Take a picture using the Chromebook camera or your phone of your graph, table, rule, and pattern work in your composition book to support your explanations. For extra help with this, click here.
7. Click send a tweet and send out a link to your blog post so a classmate can read it and give you feedback in the comments section. Make sure to use your first name and your period number after it.
8. Go to http://www.twitter.com and search for @joycemathletes. Find a person in our class who is also finished so you can read their post and give them at least 2 pieces of mathspecific positive feedback and 1 piece of CONSTRUCTIVE feedback that can help them improve their work that could be a suggestion or a question that should lead them to revise some of their work.
7. Click send a tweet and send out a link to your blog post so a classmate can read it and give you feedback in the comments section. Make sure to use your first name and your period number after it.
8. Go to http://www.twitter.com and search for @joycemathletes. Find a person in our class who is also finished so you can read their post and give them at least 2 pieces of mathspecific positive feedback and 1 piece of CONSTRUCTIVE feedback that can help them improve their work that could be a suggestion or a question that should lead them to revise some of their work.
9. If time, Graph your example rule in Desmos and provide a link to support your explanation. Read any feedback given on your post and improve your work.
This is a project that will be due next Friday so if you don't finish you can work on it at school or home. You need to at least have your first draft and a comment done by then, and if you don't tweet the link out, I can't give you credit. If you need help consult your notes, look at the building blocks listed below, and of course ask your classmates or myself questions!
The Common Core standard for this lesson is posted below, along with background knowledge you may or may not have in prior grades. I've listed some building blocks that will have more scaffolding involved later on.
This is a project that will be due next Friday so if you don't finish you can work on it at school or home. You need to at least have your first draft and a comment done by then, and if you don't tweet the link out, I can't give you credit. If you need help consult your notes, look at the building blocks listed below, and of course ask your classmates or myself questions!
The Common Core standard for this lesson is posted below, along with background knowledge you may or may not have in prior grades. I've listed some building blocks that will have more scaffolding involved later on.
Building Blocks of a Standard
Activity 2.15

__________________________________________________________________________________________________________________________________________________
Name:

Martin Joyce

Grade:

8

Year:

2015

8.F.4. Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
 
In the 6th grade students have experience with collections of equivalent ratios and the relationship between tables and graphs. In the 7th grade students worked with the proportional relationship y=kx where k is the constant of proportionality or unit rate.
Earlier in the year students have identified the parameters m and b in y=mx+b with m being the growth factor (rate of change) and b being the number of tiles in Figure 0 (initial value)

Building Blocks of a Standard

Notes

In a tile pattern the number of tiles added from one figure to the next is the growth factor, or m in y=mx+b.

Prompt students how can you make growth visible in tile patterns? (Shade growth of tiles added on)

In a tile pattern the number of tiles in Figure 0 is the parameter b in y=mx+b.

This figure is visible in all the other tile patterns, and especially Figure 1.

A table can represent a tile pattern with x representing the figure number, and y representing the number of tiles (dependent axis).

This is like keeping track of hours worked and money paid, except it’s not proportional. It does have a constant rate though.

A graph can represent the points from your table with the x axis labeled figure number and y axis labeled number of tiles.

Is it a discrete or continuous pattern? Even so, connect them to see the growth easier.

Once you know the growth factor, m, and number of tiles in Figure 0, you can substitute these parameters into the equation or rule y=mx+b.

y=mx+b color coded. M and B are labeled in each of the 4 representations of a pattern

On a graph, the growth factor, m, is represented on the growth triangle between 2 points on the graph while b is the coordinate (0,b) or the yintercept.

Draw right triangle using ruler between two consecutive coordinates. Label yintercept as an ordered pair, NOT just a number.

Next up is the Learning Goals and Success Criteria will be posted in relation to this.
Consider a class you are going to teach in the next two weeks. Using what you have learned, write a Learning Goal and Success Criteria for this lesson.
Learning Goal

Success Criteria

Understand that a figure number and it’s tile pattern can be entered into a table and help organize your information.
Understand that the slope triangle tells you the horizontal change is the increase in figure number and the vertical change is the increase in number of tiles (because of how the axes are labeled).
Understand that a tile pattern can be represented by a x/y table, graph, figure, and rule.

Students will construct a x y table of data where x represents figure number and y represents number of tiles.
Students will use this understanding to find other tile amounts for different figure numbers and then graph their data.
Students will use the parameters m, growth factor, and b, tiles in Figure 0, to write a rule in y=mx+b form.
Students will setup a coordinate plane with x and y axes labeled, intervals clearly marked using an appropriate scale (by 1’s, by 2’s, etc.)

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