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Lesson 5-3: Question
Your action item for this lesson is to think of a learning goal coming up in the next few days or weeks and use our learning goal progression template to not only record the learning goal and notes about that lesson, but also record future knowledge or future learning goals that are connected to this one. They might be the learning goal for the next day or even a learning goal a month or so away in your long range planning.
Share your learning goals and any comments or questions you have here:
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38 Replies
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I wrote a long and detailed post but it wouldn’t post
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Sorry about that Rachael,
I see you sent that post to us by email. Thanks for that. Could you try posting it here again?
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Test!
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We have to do linear planning to help students be successful!
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New learning goal: 2.6(A) Model, create, and describe contextual multiplication situations in which equivalent sets of concrete objects are joined.
Future knowledge: Students will use their knowledge of multiplication to solve problems dealing with area of a planned garden.
Future knowledge: Students will use their knowledge of multiplication to create a wall with blocks. Students must know how many blocks they will need.
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I teach 8th grade and I really liked the popcorn lesson. My learning goals consists of knowledge that comes before those addressed in the lesson. If I were to go back 3 learning goals from those in this lesson I would start with:
1) Learn about coordinate plane/grid and ordered pairs and how to plot them, what does a point mean
2) Learn what is a linear function. What is it look like in a table, graph, and equation.
3) Learn about slope and y-intercepts
a) relationship of lines with the same slope and different y-intercepts
b) relationship of lines with same intercept and different slopes
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Since I have been teaching at my school for over 20 years, I have taught almost every high school math class and some middle school math classes that we offer. That allows me to really know where the grade 9 students I am teaching this year are heading!
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Our current unit for Geometry, this looks at the progression from potentially Grade 7 – 9 in these particular standards and how to build on prior knowledge.
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My learning goal is to get students to connect changing rates with the graphical representation.(Higer rate = steeper slope etc)
A future goal is to make connections to the various representations of a linear relation nd be able to change the equation to reflect the changing rate ot initial value
Another future goal would be to make the connection to linear systems.
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So, this week 11th graders will be working on basic matrix operations. Future goals would be representing and solving systems of equations, and eventually working with pretty complicated probability systems using matrices. Thinking about these future goals helps me deal with questions about why we do matrices at all: to do a lot of calculations efficiently.
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I just completed a unit with systems of linear and non linear equations. I really like the popcorn lesson for that as an activity, maybe even as an opener for the unit in my Honors 8 class. I ended up using another 3 act with the weights of glue sticks, pens and a few other items. The thing that I really like about the popcorn is that i focusses on rate and starting amount more. It seems like the popcorn one also gives a more open ended chance for students to strategize.
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What a great lesson. Glad you also like it! Best part is, we can often give students these types of problems upfront – without a video – and get much of the same benefit. Giving students a chance to think before being gifted an algorithm is so key. Nice work!
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New learning goal: Multiplying Decimals by Multiples of 10
Future knowledge & understanding: Dividing decimals by multiples of 10
Future knowledge & understanding: Estimate to multiply and divide decimals.
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Awesome. Have they already multiplied by tenths and divided by tenths? Could be a good precursor.
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I have attached an image of a Learning Goal Progression to progress from Graphing systems of equations to Graphing systems of inequalities and Linear Programming problems.
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With students just beginning proportions, close learning goals will be looking at proportional relationships on tables and graphs. If I do a 3 act task we can talk about the multiple representations students use. Goals that are further away are slope, linear relationships, and systems.
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Looking forward from learning about solving equations, it will be a natural progression to two-step and multi-step equations, and eventually getting to systems (both 2 and 3 equations) so it is easy to see where to focus on with this, in my opinion.
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Transition from area unit to Surface area and Volume chapter.
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This has made me realize I need to work on the vertical alignment of my 8th grade math classes with the HS. I know really well the classes below me. I don’t have a good feeling of what they will be needing and how those skills will prepare them.
I included a lesson on solving 8th grade style equations and how it will be leveraged later.
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I believe that starting the year off with exponents in 8th grade for students who are 2-3 grade levels below (have learning disability in area of math) is quite a big task. I am not sure this is where I want to start.
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I am noticing that pre-requisites are not linear and often encompass a wide range of strategies and concepts in other areas of Mathematics. I found an awesome site that does standard vertical and horizontal alignment for US Common Core standards at achievethecore.org. Although our state does not use the Common core standards, I feel this is a good starting point for looking forward and backward.
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Great resource share and notice about the non-linear progression of many math concepts. Math is certainly very complex making our jobs very challenging.
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I’m having a hard time coming up with the New Learning Goal and Future Learning Goals. Right now I’m working with 6-8th graders on Proportional Reasoning. I started with multiplication and division showing visual representation. We did Graduation Seats and Sowing Peas. I want to go into Proportional Reasoning and will do the Snow Shoveling driveway to move into fractions. I guess my issue is not know exactly what Proportional Reasoning consists of to write a learning goal. I haven’t taught middle school before so I’m unfamiliar with the standards.
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Getting familiar with the standards is key. Have you tried writing them out (or shorter versions of them) on stickie notes? This might help with organizing your order.
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Last section (5.2) I worked on thinking about adding and subtracting rational numbers. I’m trying to take a longer stride by focusing this time on multiplying and dividing, starting with integers.
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I think it’s so important to remember where students are going next. I teach in a school in which the vast majority of students are “behind” where they *should* be (and I imagine others do as well). It’s easy to skip things because they don’t seem important, but many times those skills will be built on in the next grade!
As a special ed teacher, I don’t often have students who have even met the grade-level standard, but I can see myself planning like this to help the high-flyers get there. I could plan for my “target” of what they will understand, and the grade-level standard can be the extension.
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I am going into another year of teaching statistics. As usual, students last year struggled the most with probability. This was the case everywhere and was even mentioned by the college board as the place where students struggled the most with the entire test in general. I focused on that unit for this.
I realize how important it is for students to really have a great grasp of the definition of probability, to see it as a chance process over a long period of time, in order to the understand why we use graphs and simulations to estimate probabilities. I think it is also the perfect place to build really great math moments.
I’m excited to give it a go.
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This reply was modified 8 months, 1 week ago by Jorgelina Corral. Reason: I don't know if my image is uploading. Not sure if it matters. I did map out some learning goals and future knowledge needed
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This reply was modified 8 months, 1 week ago by
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I think this is okay? I am having a hard time just filling 3 boxes because of how many extensions my students have from each starting point in my grade!
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There is no right or wrong here, but rather just thinking and reflecting on what you believe (currently) would fit well. As you do this more and more, you will naturally be refining your thinking.
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New Learning Goal: 1st Grade: Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of
comparisons with the symbols >, =, and <.I will be teaching K-2 and found this exercise to be very interesting and a great chance to dive into the standards that I need to gain familiarity with having taught upper elementary in the past. Student expectations of comparing numbers grows with their understanding of place value. Students ready to stretch could be given numbers beyond the grade level standards or perhaps be given fraction comparisons in grades 3 and 4 to stretch.
Prior Learning Goal: pre-K :
C. Compare numbers.
4. Count many kinds of concrete objects and actions up to ten, using one-to-one correspondence, and
accurately count as many as seven things in a scattered configuration. Recognize the “one more,” “one
less” patterns.
5. Use comparative language, such as more/less than, equal to, to compare and describe collections of
objects.Prior Learning Goal: K:
Identify whether the number of objects in one group is greater than, less than, or equal to the number
of objects in another group for groups with up to 10 objects, e.g., by using matching and counting
strategies.
7. Compare two numbers between 1 and 10 presented as written numerals.Future Learning Goal: 2nd Grade:
Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =,
and < symbols to record the results of comparisonsFuture Learning Goal: 4th Grade:
Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded
form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and <
symbols to record the results of comparisons. (up to 1 million) -
I have always felt it important to know where students are going. However, I will say it has been a struggle to find the time as an elementary teacher to understand more about the skills and understandings of Secondary School Math. I feel though even with a little investigation and then also a lot of the PD offered here @ MMM I am starting to gain more understanding for the extension of ideas past Grade 8. I really love too here how you took such a simple Krispy Kreme donut task that could prob start as early as Grade 2 and reached it all the way up to Secondary Math. This is definitely a goal of mine to continue to work on developing the capacity to do so.
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This lesson certainly made me think a lot more than the previous one as I am pretty comfortable with where they have been but I am not as well versed in where they are going. This is something I really need to consider more when I get back into the classroom as I am really unsure as to the progression for my first topic of proportional relationships. Given my time constraints to complete the materials before I lose access, I am planning to review the achievethecore.org site that was mentioned by another participant and see if that will shed some light on this for me. Thank you so much for stretching my thinking about my teaching.
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Grade 7, Unit on algebraic expressions and equations, but for the purpose of this module, I have been focusing on solving one-step equations and then two-step equations.
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I will be teaching Slope Intercept Form to my 8th Grade Math students. Once I teach this, we will go on to be able to write equations given different information and then on to Systems of Equations. This will involve graphing, writing equations and finding points of intersection through graphing, substitution, and elimination.
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I’ve got a linear intro coming up and have been trying to think through the progression towards quadratics. This helps to begin seeing the steps that we might take towards that learning goal.
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This reply was modified 4 months ago by Craig Polzen.
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This reply was modified 4 months ago by
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This is helpful to think through the progression towards quadratics from my intro to linear relations.
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As a middle school math teacher (elementary/middle school degree) its been helpful to me to have two other middle school math teachers with secondary degrees, it helps immensely to see the importance of some topics that I otherwise may not see value in.
New Learning Goal:
8.EE.C.8 Analyze and solve pairs of simultaneous linear equations.
Future Knowledge and Understanding:
A.REI.C.5 (Algebra 1)
Prove that, given a system of two equations in two variables, replacing one equation with the sum of that equation and a multiple of the other produces a system with the same solutions.
A.REI.C.6 (Algebra 1)
Solve systems of linear equations exactly and appropriately focusing on pairs of linear equations in two variables.
A.REI.D.7 (Algebra 1)
Solve a simple system consisting of a linear equation and quadratic equation in two variables algebraically and graphically.
A.REI.D.11 (Algebra 1)
Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x).
(I actually have a document from one of the special education teachers in my building that lays out the prerequisites for each math standard at every grade level. it is very helpful to identify why students struggle with current content!)
