Lesson 1

Equivalent Expressions - Formative Assessment Lesson Day 1 of 3

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SWBAT generate equivalent expressions using numeric notation, words, input/output tables, and area models.

Big Idea

Through an engaging hands-on activity students develop a sense of equivalence as an essential skill in solving equations that begin with expressions.

Previous Preparation

5 minutes

If you have never used a formative assessment lesson (classroom challenge) from the Mathematics Assessment Project then you really need to begin with some extensive planning.  These lessons are wonderful and I try to use at least one in every unit because they are so effective at uncovering student misconceptions and then helping me to modify instruction to address those misconceptions.  I put a time of five minutes on this section but that is misleading.  The time spent on this section will be outside of class and could add up to two or three hours of preparation.

Lesson LinkClick here

When you click on the lesson link you will see a page full of very valuable information on how to use these lessons.  These lessons are very effective when you are very prepared and they are very ineffective when you are trying to "wing-it."  You need to read all the materials (the PDF is a packet of teacher instructions and student resources.)  This lesson requires cards for the collaborative activity, which you will begin in roughly two days.  This means you need to be copying and cutting cards before you begin the activity.  I use parent volunteers, aids, office staff, and when desperate students to help cut cards and manage the prep time required.  The card sets to be copied (one set for every group) are located on pages S-2 through S-5.  I usually paper clip each sheet of cards together and place all clipped sets into a large manila envelop.  You want to keep each "type" of card set separate because you give students cards at different times.  So for example, the cards on page S-2 would be cut as one sheet for each group.  I would cut one sheet apart and clip that one sheet with a paper clip (blank cards and all) and then put them in a large enveloped labeled set A.  The cards sets on page S-3 would be copied and cut separately and clipped and placed inside a different envelop labeled as set B.  All this cutting and labeling needs to be completed prior to the day you begin the activity. 


Lesson Pre-Assessment

15 minutes

Today begins the process of implementing a formative assessment lesson (classroom challenge) from the Mathematics Assessment Project.  These classroom challenges involve three parts, a pre-assessment, a collaborative activity, and a post assessment.  The goal of pre-assessment is to uncover student misconceptions.  The questions are non-routine so students must think critically to answer and thus incorrect ideas surface immediately.  You should expect wrong answers as a means of learning more about your students.  When you click on the lesson link you will see a page of information about the lesson and I highly recommend you read this material if you are unfamiliar with classroom challenges.  The lesson PDF is linked at the bottom of the page.  Click on the PDF and scroll down to page S-1.  Page S-1 is the student pre-assessment.  Copy this pre-assessment for every student as your learning check today.  Page T-2 of the teacher resources fully explains administering the pre-assessment.

Each student is given his/her own copy and should work alone.  You can clarify the directions of the assessment but do not help students with the questions even though they are sometimes difficult.  Tell students before you pass out the papers that this is a pre-assessment for an activity that they will be completing in a few days and some questions may be difficult but do their best to answer every one.  This is not a grade but will give you valuable information about what students know and what they still need to figure out before the unit exam.  Say whatever you need to so students are not panicked but also so they work diligently and do no give you papers full of IDK.  Allow about 10-15 minutes to complete. 

Before I begin to discuss analyzing student pre-assessments, let me say that giving the pre-assessment on the same day as framing the lesson and starting the cooperative activity is not ideal.  If you have an extra day before today in which you have about 15 minutes to administer the pre-assessment, then I recommend that option.  One of the purposes of the pre-assessment is to help you group students productively before they begin the cooperative activity.  This lesson is the first lesson in the unit, so you may not have time to give the assessment in advance but it is better to group students prior to beginning the cooperative activity.

When you gather the pre-assessments from today, you will need to review these overnight before the next day.  Analyzing the pre-assessment is essential in planning the collaborative activity.  Over night you will review the work looking for two things:  common student misconceptions in order to generate some guiding questions and to group students homogeneously.  When misconceptions surface, and they will, your plan is to find the common group level misconceptions and write some guiding questions that will help students to think about their understanding.  This may sound like a difficult task but if you look at page T-3 of the lesson plan PDF you will common student misconceptions that research has proven often occur with this lesson and then some suggested guiding questions.  You can use this page to help you get started.  

You want to create about four to five class level guiding questions that will be used throughout the activity.  You also want to begin grouping students for the card match activity.  I recommend grouping students homogeneously.  When looking through the pre-assessments (Do not grade these and begin to mark questions wrong or right!!!!!  Only assess them for misconceptions - ink pens down!)  Pair students together who seem to struggle with the same concepts.  You want students to work productively and at the same pace through the card activity.  You do not want one student to carry the other but instead for them to work to learn together.  If I have students who struggled to complete any questions correctly then I might choose to make these students into a group of three instead of a pair so there will be more support during the activity and these groups are where I focus the majority of my time and feedback.  Begin tonight to look over pre-assessments and group students for the activity ahead.



Framing the Lesson

15 minutes

To see this part of the lesson unfold, watchClassroom Video: Developing a Conceptual Understanding

Framing the collaborative activity is one of the most important steps in preparing students for a productive struggle through the activity instead of a frustrating struggle.  These activities are unique and card match activities such as this one; usually have several sets or layers of cards.  Framing the lessons prepares students’ minds for the work ahead and clarifies the types of questions they will be working with today.   Do not turn the framing of the lesson into a lecture period where you go ahead and re-teach the misconceptions and then the activity becomes the guided practice after your lecture.  These activities are strong and research based.  The activity is designed to do the re-teaching for you of common misconceptions uncovered through researching thousands of students who have completed this assessment before your class.  Do worry about your students and try to make it easier by either re-teaching or modifying the cards.  It is natural to worry about your students when you see mistakes but believe me from experience, your students can handle more rigorous tasks than you think. 


The script for framing the lesson is laid out in detail on page T-4 in the teacher guide.  You will need white boards for all your students.  Heavy page protectors or even binders with clear plastic overlays work great with dry erase markers as well.  Frame the lesson according to the written plan.

Beginning the Collaborative Activity

20 minutes

To see this part of the lesson unfold, watchClassroom Video: Discourse and Questioning

Again, ideally you would give the pre-assessment before today and already have students working in permanent groups.  If you must give the pre-assessment on the same day as the activity, then allow students to work in temporary groups you create to the best of your ability.  It works best to group students together who have similar strengths and weaknesses.

Pages T-4 and T-5 of the teacher resources clearly explain how to begin the collaborative activity by first matching card sets A and B together.  In the first matching activity students are matching algebraic statements to algebraic expressions.  There are several blank cards because students will be asked to create correct matches for any card that is without a printed match.  Be aware that many students begin to match all the blank cards together and write their own statments and expressions that pair.  You may want to warn students ahead of time that a blank card will never match to another blank card.  An empty card will always have at least one part already printed.  


Closing the Lesson

5 minutes

To see this part of the lesson unfold, watch: Classroom Video: Organizational Systems

This is the first day of the activity and students have not yet been properly paired according to pre-assessment data.  Therefore, I recommend telling students to make their own key for the matches they and their partner created today.  the cards are labeled with identifying marks: word cards are labeled with W# and expression cards are labeled with E#.  I would warn students that tomorrow they will be regrouped with a permanent partner so it is important to make a key of all their matches so everyone has notes to begin working again tomorrow.  Store all the cards in small envelops according to my Storing Small Manipulatives.