Lesson: Assessment

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Lesson Objective

Students demonstrate understanding throughout and at the end of unit

Lesson Plan


White Boards for each student

Dry Erase markers


Overhead Projector

Regular markers, colored pencils and/or crayons



Below are some techniques for assessing the progress and mastery of students throughout this lesson. These are routines that are used throughout my Algebra intervention class, so routines become very familiar to students. They are designed to inform and direct the teacher, to encourage student feedback, to provide frequent opportunities for success, and to eliminate testing failures due to learning disabilities or language differences rather than lack of understanding of the material.


8-12A 1.0 Students identify and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers, including closure properties for the four basic arithmetic operations where applicable:

A1.1 Students use properties of numbers to demonstrate whether assertions are true or false.


Formative Assessments:

Launch: Each class period starts with this “warm-up,” which contains review problems. Sometimes this is orchestrated to point students’ attention to skills that will be used in the upcoming lesson, but in general this activates prior knowledge and gives the teacher a quick sense of levels of retention. These should not be “stumpers,” students should feel like they know what’s going on. In cases where students make mistakes, other students should be called on to explain and then a similar problem should be presented so that students can succeed at that one and continue on a positive note. Present 3 problems that review recently acquired skills, provide 3-5 minutes for solving, solicit answers, guide student-led clarification if needed


Pre-Test: I give the same assessment with the same rules at the beginning of the unit as I plan on giving at the end of the unit. I have never had a student remember the questions or had this be a problem. This allows me to compare directly what they have learned, without having to allow for changes in formatting, level of complexity, or content of questions. This also gives me an opportunity to discover any faults in the assessment format early on, in case changes are necessary. (For example, I use “Algebra by Design” for most tests in this class, but there is an occasional mistake in the problems, so I have caught them by making up a master ahead of time and by having students pre-test.) In this unit, some students showed that they were able to guess an answer if digits were not too complex, but not that they could do the appropriate steps to find the answer. One student wrote out numbers in a format that looked, from a distant, like the steps to solving an equation, but in fact the numbers were nonsense. She didn’t understand which operations to do when, so she would just insert either the same or different numbers in places she felt like they should go. When I talked to her, she insisted that she had already learned and mastered this skill, but she was unable to talk me through her work on any problem. Most students had no strategy and wrote either nothing or wrote numbers willy-nilly under problems. Since some of these answers resembled 2 = 6, I knew that we needed to cement our understand of the = sign before working with equations.


Exit Tickets: Each class period ends with either a reflection or an exit ticket. Exit Tickets are half- or quarter-page problems that test exactly what was taught in the lesson. It is vital that they not contain any red herrings or additional complications. (For example, if you taught one-operation equations but didn’t specifically discuss negatives, don’t put a negative in the Exit Ticket problem, because some number of students will screw up on that part when in fact they have learned what you actually taught, which is the procedure for solving for a variable.) Use the same directions as in the lesson(assume students won’t read them) and the same template every time. Distribute these no more than 5 minutes before the class lets out, and collect them at the door or have a student collect them. They can be checked quickly. I just glance at each one and mark it either J or L. Some teachers give them back, but the intent is to be formative, so I keep mine in a binder. I also keep a list in the front of the binder with all students names and I check off when they got J on an exit ticket for a skill. I then quickly calculate a percentage for myself for the day, and this also allows me to quickly see who is falling behind or who might need more challenge.  If 80% or more of the class don’t pass your exit ticket, it simply means the lesson didn’t land. You can use this to plan a re-teach for the next day. In this case, it helps to try to see WHAT they did wrong, to see if you can target a specific misunderstanding.


Out of Five: At any point in any lesson, once this routine has been taught, you can ask your students to let you know how confident they feel about a topic. If you teach them to hold up 1 finger for “completely lost”. 5 for “totally get it,” and something in-between if they need more practice, you can quickly gauge whether to give another example or move on. This can also help if the class seems to have disengaged or if you’re not sure how many people share a problem with a struggling student.


Red/Greens: I made little tent-shaped items out of construction paper by gluing together a piece of red and a piece of green paper, and folding it over. This routine has the students put these on their desks, and flip to the green when they feel like they are ready for independent work on a skill. This  lets the teacher know when more explanation is needed or not.


Genius Questions: I have a strong theme of “genius” in my class, and Genius Questions is a part of that. I prepare a one-page transparency full of questions about once a week.  These are meant to be open-ended questions that require critical thought and a strong grasp of skills and concepts we have covered. This is a time I dedicate to the higher end of Bloom’s taxonomy. I offer “free spaces” to students who get one right, and those are used to excuse them from one problem of homework on their Bingo Card homework, a signature tool of mine.


White Board Quizzes and Games: See the section on games that provide increased exposure to a skill. White Board Quizzes are an impromptu time where you right example problems  on the overhead, students solve on their personal white boards, and hold up their answers. Sometimes this might be just for your information, so you might just make a mental note of the level of mastery and then move on. More often, I use this to reinforce student confidence, so I go around and point at everyone who has the right answer and say “GOOD! GOOD! GOOD!” and to students who have a wrong answer, I whisper a hint like “yeah, but there’s a negative, watch out…” This should be done when most of the class has mastered the skill. If that doesn’t appear to be the case, this transitions easily into additional modeling or student teaching.


Summative Assessments:

For most students, I use the “Algebra by Design” sheets as assessments for two reasons. One is that the formatting is easy to read and understand. I have not found that students are able to match the answers in the quilt square to the problem without understanding the skill, and even if they were, I do not award points with an accurate showing of work. Any test with just answers is handed back to the student for redoing or no credit. I am far more interested in their knowledge  of the process than in the correct answer, and this eliminates cheating. I do, however, have students spread out and I provide plenty of graph paper for scratch or showing work. Many students are used to graph paper (it’s all we use in my class, to help with visual organization) and prefer to copy the problems over and then work them. I also like the “Algebra by Design” series because it isolates skills, and that is vital when testing students with learning disabilities and language differences. Students know exactly what to expect on the test and no part of the test has the potential to confuse them by presenting the question in a different way. I also require that they do 5 problems on any sheet, and they may choose. Most students notice that the questions get progressively harder, but they frequently jump around. This is because many work very slowly and will get caught up for the whole testing period on one problem if they don’t feel free to move around. For a total of 20, I award 4 points per problem. This allows me to give, say, 3 points if they did every step right, but when reaching the answer they thought that 10-7 was 4 rather than 3. If I am testing equations, I am not presently concerned with subtraction skills, so I weight the grades away from peripheral mistakes. This is because my students have such uneven levels of skills and academic “potholes” in their mastery. These tests are also fun because when I hand them back, I can put a transparency up with all the correct answers, and students can color in the design and display their passed tests. This is part of the Math-positive culture I try to build in the classroom. There are also 2-3 versions for each skill, so you can mix to prevent cheating or offer re-takes while other students are coloring. 

Lesson Resources

Genius Questions.pdf  
AssessmentLesson.docx   Culture and Systems


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