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Lesson 53: Question
Serina Signorello updated 1 month, 1 week ago 39 Members · 44 Posts 
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:

The learning goal I’m working on is solving one step equations. Future learning goals will be writing a onestop equation (and eventually more complex ones) from a situation, Solving two step, multistep, variable on both sides, with distributive property equations, representing the equation in different ways — words, tables, graphs. There are more, but I think this is a good start.


I need to better understand where students are going in 8th and beyond.

I chose to look at proportional reasoning in grade 8.

I am going to use the same learning goal that I use for Lesson 2 “Know Where Your Students Come From.” THe learning goal will be students will be able to Completely factor quadratic expressions into product form. As I stated in the previous lesson there are a lot of previous understandings that are required to support students to meet the learning goal, but factoring quadratics is laying to foundation to future learning as well. The first is finding the roots for your quadratic when solving for x. Preliminary to the Quadratic Formula students will solve for x using the factors. Next, students will use the roots to find where the parabolic graph will cross the xaxis. But if we go even further with division of polynomials, the factoring will help cancel out common factors from the dividend and divisors.
I do like the idea of creating a situation that we can keep going back to for all the future knowledge so the students will experience the progression of math are you go from one learning goals to another. I think that allows the students who are in that master stage in learn can see how what they already know connects to what they do not know.

My leaarning goal coming up is solving a multistep equation. I will have these students next year in 8th grade and I want them to start thinking about how changing the coefficient and constant change the problem. For example i nthe shotput problem, changing the coefficient has a greater affect on the situation because there are multiple sticks but changing the constant has only the effect o the one part. Also, moving the constant to the front of the sitautian shows the commutative property (cycle back) and the idea of inital value (stretch forward). So next year when we are introdiucing linear functions we could go back to this task and extend our thinking from coefficient and constant to slope and yintercept.

Love how you’ve taken a problem based unit and extended the context to help you address some more specific content expectations. Nice work!


Following on from the multiplicative goal. My students’ future goals:
Solve word problems involving multiplication and division
Use a table or similar organiser to record methods used to solve problems
Explore the use of brackets and the order of operations to write number sentences
Perform calculations involving grouping symbols without the use of digital technologies
 This reply was modified 7 months ago by Jaana Gray.

I heavily relied on the strand overview chart in the new math curriculum.
 This reply was modified 6 months, 1 week ago by Michelle Grebe.

Nothing wrong with that! Every time you participate in this type of thinking, you’ll learn something new about the curriculum and feel better prepared for the next time you plan to teach a unit! Nice work.

New learning goal. Find the algebraic formula of an affine or lineal function, from the information given in a proble situation.
Future knowledge. Automate y=mx+n from a graph and vice versa.
Future knowledge. Solve sistems of linear equations.


I’ve not taught math in 10 years, so while much seems the same, much has changed! (no textbooks, for one!)
I am carefully looking at the new curriculum to ensure that I try to cover what’s there. What I have found is that with last year’s closure (and some general mathphobia with my group) that where they were coming from is much further back than I anticipated. So, that has led to us cycling back a lot, to ensure that previous ideas are clearer before we forge too far ahead and create more anxiety. For example, place value and order of operations were not as clear in my students’ minds as I would have thought, so we’ve had to do some simpler tasks to cover those.

My learning goal for 5.2 was to ID place value in a 3 digit #. So, to stretch that (in my class, I call this a sneaky peek … and I shut the door so that nobody knows that these students are learning this stuff because they aren’t supposed to learn this stuff until they are in 2nd or 3rd grade!) So, my “stretch” goal could involve ID place value of a 4 digit number, or perhaps counting on or back from a number by 10s, 5s, 2, 100s.

Third Grade multiplication and division In the last discussion I talked about teaching multiplication of 2, 3, 4, 5 and 10 this lessons will build into distributive property and communicative property when teaching multiplication and division of 6, 7, 8, and 9. If students understand and can explain multiplication and division of these numbers and how to use the distributive property they will be able to multiply larger numbers in the fourth grade.

Learning Progression

@anthony.waslaske you could possibly explore finding the side length of squares as an application of irrational numbers to “get around” the district sequencing. That way when you bump into the pythag theorem students have already been introduced to the main operation that pythag uses.


When I am teaching place value, I need to keep in mind that this is followed by addition and subtraction with regrouping. So students need to develop an understanding of movement within place value.

Using the learning goal progression template, proportion relationship will be my area of exploration with my students. The prior knowledge of a progressive multiplication will be exploited.
Students will then be mediated to take advantage of the pattern to drive the generation of an equation related to proportional relationship.
My wonder now would be to find a way to help student generate a graph of a proportional relationship with minimum assistance from me.

It is so helpful to view what others have come up with after watching the videos. Not only does it help me get new ideas, but it also helps me build and improve on what I have come up with on my own. My chosen topic was Solving OneStep Equations. From there, students move to solve OneStep Inequalities, TwoStep Equations & Inequalities, then Solving MultiStep Equations & Inequalities.
I like the ‘formality’ of the Progression templates as well because they serve as an organizational tool, a reminder of what you should be doing when planning lessons, and they force you to think deeper about the math.

In this response I am going to build on the same Safety Net Standard for fourth grade that I used in our lesson 5.2.
LEARNING GOAL: Compare two fractions with different numerators and different denominators and represent the comparisons using the symbols < , =, >.
FUTURE KNOWLEDGE AND UNDERSTANDING:
Represent and solve addition and subtraction of fractions with equal denominators using objects and pictorial models that build to the number line and properties of operations.
Relate decimals to fractions that name tenths and hundredths
I believe that if I build students’ understanding of the relative sizes of fractions with different numerators and denominators without jumping to the “crossmultiplying trick,” they would be much more ready for solving problems, and then making the connection to decimals, especially if some of my “different denominators” in the Learning Goal are tenths and hundredths.

I have used the same Standard that I used for Lesson 52. I also used achievethecore.org as a resource for this progression


I’ve been using Desmos and Camtasia Studio to create Notice and Wonder activities for Grade 12 Advanced Functions. An example is at https://youtu.be/irbdUKWZy74 – feel free to have a look and let me know what you personally notice and wonder – would be interesting feedbacl for me.
I’ve now created other Advanced Functions tasks relating to secants (average rate of change) to tangents (instantaneous rate of change), about 8 of these activities now.
What I do to make these is start Camtasia Studio, start the Desmos animation after about 10 seconds (allows for titles to be added), and run the animation (sometimes starting and stopping different Desmos animations in a predetermined sequence). I’m not adding any audio in the interest of witholding information.
 This reply was modified 3 months ago by Peter Gehbauer.

Apply properties of operations as strategies to multiply and divide. Examples: If 6 x 4 = 24 is known, then 4 x 6 = 24 is also known. (Commutative property of multiplication.) 3 x 5 x 2 can be found by 3 x 5 = 15, then 15 x 2 = 30, or by 5 x 2 = 10, then 3 x 10 = 30. (Associative property of multiplication.) Knowing that 8 x 5 = 40 and 8 x 2 = 16, one can find 8 x 7 as 8 x (5 + 2) = (8 x 5) + (8 x 2) = 40 + 16 = 56. (Distributive property)
Future Learning:
Multiply onedigit whole numbers by multiples of 10 in the range 10 – 90 (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of operations.
Multiply a whole number of up to four digits by a onedigit whole number, and multiply two twodigit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.


In the last section, I was starting with basic fractions and building to have students perform basic operations with fractions. This will lead to students being able to use exponents with fractions and finally for them to recognize that rational expressions with variables follow the same rules as those with fractions.

Both of my posts showed up so I hope this one can be deleted.
 This reply was modified 2 months, 3 weeks ago by Linda Andres.

My rates lesson initial learning goal is for students to identify and simplify a rate, comparing the number of mice caught to a time period. (Video of barn mice being caught in humane trap.)
Future knowledge & understanding: create a table of values, graph the values and ultimately create an equation with 1 variable.

I will use the same example of adding/subtracting fractions with unlike denominators, that I did in the last lesson as my new learning goal.
For future knowledge and understanding: it would be great to start working with word problems where students are provided the answer and need to create a question, they can be provided part of the info (to pique curiosity) and come up with notice/wonder questions to ignite extended learning, etc.
I could even look further in the future and have students solve realworld and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. (which is a 6th grade standard.)

When teaching integer operations they learn to add, subtract, multiply, and divide positive and negative numbers. This will begin their journey into operations of all rational numbers, solving algebraic equations, and balancing a checkbook in financial literacy. Students tend to struggle understanding how adding two negative numbers will make a “larger” negative number, which has a lesser value.

Using the Same Goal from 52 – Solve for Unknowns with Angle Relationships
Future Knowledge and Understanding: Students will notice through exploration and conjecturing that there are an infinite number of triangles that can be created that have the same exact angle measurements and those triangles are therefore similar to each other and not necessarily congruent.
Future Knowledge and Understanding in HS Geometry: Students will work to Prove and apply theorems about lines and angles. Theorems include but are not restricted to the following: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.
Looking at the progression of these concepts helps me understand their importance as well as how important this concept is foundationally for their future math success.

My learning goal is to develop proportional reasoning skills by placing students in learning activities that will promote them to discover/apply proportional reasoning to complete the task. I will begin with rich tasks that focus on fractions, so students can apply/review/learn addition/subtraction/multiplying/dividing with fractions so they feel comfortable with fractions. Next I would move on to tasks like popcorn pandemonium to promote proportional thinking. As students explore tasks like this and more I hope to help students become confident problem solvers.

Typically at the beginning of the year with my 6th graders we study finding the greatest common factor and least common multiple. It can be a sticky point for a lot of them. I really like the planting flowers task to move forward, but I’m hoping to figure out a way to teach GCF and LCM better. It appears to hold people back with ratios and rates as well as computation with fractions.

Learning Goal – Growing the Idea of Compound Interest from:
Total Cost = Price (1+ Percentage Increase)**Percentage Increase at the store means TAX

For my 8th grade unit 3 will be solving linear equations with rational coefficients. Looking at the worksheet:
Future Knowledge and Understanding includes: Analyzing and solving pairs of simultaneous equations.
After that: future knowledge and understanding includes: Use of functions and applying linear equations in geometry including volume of cylinders, cones, and spheres.

Progression is to create functions with the use of parameters – then onto drawing composite shapes – which leads to the summative of coding a diagram using composite shapes of their own creation.

A third grade learning goal is to represent and solve problems using multiplication and division with whole numbers. In 4th grade they have to use all four operations to solve problems with whole numbers. Then this goes into understanding the place value system and in 5th grade using the operations to solve problems including multidigit whole numbers and decimals to the hundredths place. This activity is really helpful as a lot of teachers don’t consider the progress of where students are coming from and where they are going. It really helps to stimulate vertical alignment between grade levels as well which benefits the students’ progression of learning.
 This reply was modified 2 months ago by Vanessa Weske.


In grade 7 we start seeing algebraic expressions and equations as well as linear equations. These are all knew knowledge which will be worked and grown upon. In grade 8 students dive deeper into this content for more linear equations and complex equations. It is nice to keep this in mind to point out and explore how these things might develop with hints or extensions for stronger students.

Great points. Also worth noting that while students may not have prior experience with algebraic equations, they do “see” numeric equations for many years prior. Starting there and working your way slowly towards algebra can be super helpful. Using boxes or blanks for the variable might help.


Learning Goal: Zeros of a Linear function. Students will extend their understanding of x and y intercepts to zeros of a function. Future Learning: They can use zeros and yintercepts to graph functions. As they learn about quadratic functions they will be asked to find zeros of a function. Also, as they move to Algebra II, they will be dealing with functions that can have more than two zeros.