Planning engageNY Math: Tips to Remix, Part 2

In case you missed it, you can read the first half of this blog here

Now that we have an understanding of the standard by doing the math and identifying the standard (see Part I), we are ready to move onto the remaining steps in the lesson planning process:



media-blogtwo2Step 3: Review the End Goal

Before customizing the lesson, I want to calibrate the level of rigor I am seeing on a variety of A.APR.1 assessment items. There are no questions on the Mid or End of Module Assessment directly related to this lesson, so we will look at the Exit Ticket, an item from the Regents Exam, and a non-calculator and calculator item from the Fall 2017 PSAT.

  • Exit Ticket:


In the exit ticket, students are asked if the sum of three polynomials will produce a polynomial. In the Teacher’s Lesson, the answer to this question is “yes”, but does this really demonstrate understanding?

The Teacher’s includes a Closing that directly relates to the student outcome:


The first question in the Closing may be an ideal supplement to the first question on the exit ticket.

  • June 2014 Regents Exam: This item requires students to substitute the expressions in for A and B, and accurately subtract the second quantity.


  • June 2016 Regents Exam: This item requires students to have the relevant vocabulary associated with polynomial expressions.


  • Fall 2017 PSAT Items: The no calculator question requires that students recognize function notation, distribute, perform the indicated operation, and combine like terms. The calculator question is relatively straightforward, requiring students to perform the indicated operation and combine like terms.

calc no calc 2In general, the questions require:

  • procedural fluency with adding or subtracting relatively simple polynomial expressions (3-4 different types of terms with the highest degree being 3)
  • conceptual understanding that adding polynomials results in another polynomial
  • knowledge of vocabulary associated with polynomial expressions

media-blogtwo9Step 4: Align & Assign

To better understand what the learning outcomes mean in relation to the standard and assessment, consider all of the lesson components and decide which outcome it’s best aligned to. This will give us an idea of:

  • the emphasis of each learning objective — are there multiple lesson components that align to the learning outcome? Some? None?
  • how the lesson components within a learning outcome build a cohesive sequence of learning?
    • ·  How does the complexity increase from one question to the next?
    • ·  Do I need to include strategic scaffolded supports so that students can access the learning outcome?
    • ·  Do I need to provide additional, meaningful practice so that students are able to master the conceptual demands and procedural fluency inherent in the outcomes? Just because students see or do something once does not mean that they have full command of that skill.

We also want to ensure the learning outcome is aligned to the end goal and that we are placing the right emphasis (time spent) on the learning outcome based & lesson components based on what students are expected to do on the end goal. This will also guide us to ensure the level of rigor of the end goal matches what we expect from students.

This leads into the final step, which is to rewrite the outcomes, if necessary.

media-blogtwo10Step 5: Rewrite Outcomes

Based on the end goal (Exit Ticket/Regents/PSAT), emphasis of lesson components and its relation to the standard(s), rewrite the learning outcome(s) to be specific, measurable and concise. In this lesson, there seems to be four different outcomes which I will write as the following objectives:

  • SWBAT relate polynomials to the system of integers
  • SWBAT define relevant vocabulary associated with polynomials
  • SWBAT understand that the sum or difference of two polynomials produces another polynomial
  • SWBAT add and subtract polynomials

These may not be perfect objectives and they may differ from others’ interpretation, but ultimately it is giving me ownership of discrete, measurable knowledge that I can hold my students accountable to by the end of the class period. It also makes conceptually and procedurally intentional objectives (relate, understand, define = conceptual, add = procedural).

So What Does This Look Like?

The following lessons are examples of all of the customizations I made as a result of going through this lesson planning process. To supplement the lesson, I used problems from eMathInstruction (Unit 7, Lesson 1: Introduction to Polynomials).

I broke this lesson into two separate lessons. This first lessons begins to relate the structure of polynomials to integers, and gives explicit practice on the many terms introduced in this lesson.

In the next lesson, I wanted to make the relationship of relating polynomial addition to integer addition intentional by providing several examples. The lesson concludes with students adding and subtracting polynomials.


After reading the lessons, what adjustments resonate with you? What would you do differently? Do the customized lessons meet the needs of students without compromising the rigor?

How are you already using this lesson planning process to customize your lesson? In what other ways are you customizing your lesson?

Feel free to share your thoughts or tips in the comment section below.


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