Grade 5 Visions Math Integers Preassessment

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1 Name Grade 5 Visions Math Integers Preassessment 1) In your own words, what is an integer? 2) Give an example of an integer. Use an integer to represent each situation. 3) You rollerbladed 70 yards 4) The temperature dropped 3 degrees 5) You earned $25 in interest in your bank account 6) A painter lost 4 paintbrushes 7) A dog lost 6 pounds Name the opposite of each integer. 8) 16 9) ) 0 11) 23 12) -54 Compare using < or >. 13) ) ) ) ) 34 17

2 18) What is the absolute value of -74? 19) Write a short explanation that describes this situation: 20) What do you think of the situation below? How would you determine if it is good or bad?

3 5 th grade Math Friday, 3/19/10 Integers and Absolute value (Lesson taught during the same period that the integer preassessment was administered) What students should know and be able to do at the end of the lesson: Understand the meaning of the term integer and be able to give an examples of them Explain the concept of absolute value Apply their understanding of absolute value to a number line game requiring them to determine the winner based on the distance walked Instructional time 1 hour Key content 6.5 The student will identify, represent, order, and compare integers. Process/Skills Reasoning Comparing Addition Materials/Resources Example sample space problems Whiteboards and markers Class/homework of Practicing with Tree Diagrams and the Counting Principle Document camera Instructional Strategies/Sequence Visual representations Cooperative learning Modeling 1) Tap students prior knowledge of integers by referring to the vertical number line and asking about the kinds of things they discussed with Mrs. Colorado earlier in the year about positive and negative numbers. a. Are there numbers less than zero? b. What happens as we get further away from zero on the number line?

4 2) Give students the Integer Preassessment. Be sure to emphasize that it is NOT for a grade and is only to give me a better idea of what they already know about integers. In fact, they could look on it as a way of showing how their learning grew since they will be taking an integer quiz on Tuesday. (2:45) 3) Display a hand-drawn horizontal number line on the document camera to model how positive and negative integers are represented on a number line. Define integers as positive whole numbers and negative whole numbers. Another way of saying this is (display definition): Integers: The set of positive whole numbers, their opposites, and zero. Have students copy the definition in their math journals and give an example of one in the next column. Explain how students first learned about counting numbers (1, 2, 3 ) which are positive integers, and how the negative integers are their opposites. Model how opposites would be the same distance from zero on the number line (e.g., -4 and +4). This is intuitive since positive and negative are opposites. Opposites: Two numbers that are the same distance from zero on the number line Have students copy the definition and give an example of two opposites in the next column. Ask when we use negative integers in the real world (to talk about temperature, weather, losing yards in football, making a withdrawal from the bank) Draw -4 and ask how many students wondered what this was on the preassessment. Elicit input as to what it might be. Explain that the lines are the absolute value sign. They tell us how far the number is from zero. The lines essentially mean to ignore the negative sign in the lines. Positive numbers can also be written with absolute value signs around them, though the number would be the same with or without them.

5 Provide the definition, and have students copy it with an example of the sign beside of it: Absolute value: A number s distance from zero on the number line (3:05) Introduce the Exploring Integers game as a way to practice with finding students way around the number line using positive and negative integers. Explain that the goal is to be the first to move a total of 30 spaces. Demonstrate how this will require that students record on a whiteboard how many spaces they moved altogether. (3:15) Closure/Extension Pose the scenario of why using absolute value would be beneficial: If we were interested in how far someone rode their bike for logging how many miles they rode, it wouldn t matter if they went 12 miles north and 8 miles south in the opposite direction. Discuss when else we might disregard the sign in front of a number (total number of people who lived in a town during a given year, including those who moved away before the end of the year)

6 Integer Definitions and Examples Term Definition Example Integers Opposites Absolute value The set of positive whole numbers, their opposites, and zero. Two numbers that are the same distance from zero on the number line A number s distance from zero on the number line Integer Definitions and Examples Term Definition Example Integers Opposites Absolute value The set of positive whole numbers, their opposites, and zero. Two numbers that are the same distance from zero on the number line A number s distance from zero on the number line

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10 5 th grade Math Friday, 3/22/10 Comparing and ordering integers Instructional time 1 hour Key content 6.5 The student will identify, represent, order, and compare integers. Materials/Resources Whiteboards, markers, & socks Colored ½ index cards with average and record VA temperatures Copies of VA temperature assignment for students 1) Go over homework (until 2:35) 2) Model how to compare numbers on a drawn number line (e.g., -4 and 2). Point out misconception that on the left side of the number line, the larger a number s amount, the greater it is (e.g., -5 and -3) 3) Have students practice 3 examples with whiteboards of comparing integers after first plotting them on number line -5 and 7-5 and and -18 Pose hypothetical of What if we had -7 and 2? (until 2:45) Introduce sequencing integers with example of Jeopardy! contestants who have -400, -200, and 300 points during the first round. Write sequencing.

11 Introduce VA temperature assignment on document camera. Students may work alone or with others at their table if they need help. Reinforce that they can use ½ index cards with the temperatures in them if they need extra reinforcement. (end explanation at 2:55, let students work until 3:05) Closure/Extension Check temperature assignment together. Go over corrections of and expectations for preassessment.

12 Ordering and Comparing Integers Record and Average Temperatures in VA (Classwork) Record Low Temperatures: Richmond: -12 F (January 1940) Norfolk: -3 F (January 1985) Williamsburg: -7 F (January 1985) Average January Temperatures: Richmond: 28 F Norfolk: 33 F Williamsburg: 29 F 1) Place the record low and average temperatures for these cities on the number line. 2) Write the temperatures from least to greatest. 3) Compare the average January temperature of Richmond with Norfolk s record low temperature. 4) Compare Williamsburg and Richmond s record low temperatures.

13 Name Grade 5 Visions Math Integers Quiz (11-1 and 11-2) 1) In your own words, what is an integer? 2) Give an example of an integer. Use an integer to represent each situation. 3) You drove 125 miles 4) Your obese rat lost 9 ounces 5) Your friend lost 17 marbles 6) You earned $32 for mowing your neighbor s lawn 7) The temperature dropped 6 degrees Name the opposite of each integer. 8) 61 9) ) 0 11) ) -4,517 Compare using <, >, or =. 13) ) ) ) )

14 18) What is the absolute value of -63? 19) Write a short explanation that describes this situation: 20) What do you think of the situation below? How would you determine if it is good or bad?

15 Reflection on Pre and Postassessment Results and Lessons Following the Preassessment I created and gave a preassessment on integers to the ten 5 th grade students in my cooperating teachers pullout class for math. What follows are the preassessment (which was not graded; the percentage represents what the students would have received had the assessment been for a grade), two lesson plans directly following the preassessment, the postassessment, and one students results on both the pre and postassessment. The preassessment was very revealing to me in that it demonstrated what little students background knowledge and experience students had with integers. I am cognizant that before giving a preassessment of any kind, it is always best to elicit students prior knowledge and/or preteach minimally so that students do not take the assessment cold. I took about five minutes to reference a class number line to ask the class what they had learned about the kinds of numbers on it (positive numbers and negative numbers) with their teacher this year and last year. Students generally knew that you can have positive and negative numbers. When I asked what happened to numbers as one went up or down the number line, students generally knew that numbers decreased as they became negative and increased as they became positive. I asked if they knew what an integer was. One student read the textbook definition ( whole numbers, their opposites, and zero), while many said that they had never heard this definition before or knew what it meant. As soon as students saw the preassessment, they began giggling and the room was filled with a chorus of I don t know! as many expressed relief that the preassessment would not be counted for an actual grade. Many wondered aloud, What are those lines next to the numbers? in reference to the absolute value signs. It took the students less than 10 minutes to complete the preassessment, because if they did not know how to answer a question I told them that they could leave the question blank, or write a question mark. Although the scores among the 10 students

16 ranged from 28% to 76%, all students answered all of the items that asked them to name a number s opposite. This quick observation that I made formatively as students completed and turned in their assessments informed me that I would not need to teach about opposite numbers during either of my integer lessons and could reference them only briefly as students knew how to provide examples of them when prompted to do so. I spent most of the first lesson talking about absolute value since no students knew what this concept meant. Because students knew the relationship between numbers moving to the left and to the right of zero on a number line and whether they increased or decreased, I used this prior knowledge to teach students about how to make reasonable judgments about the overall qualitative outcome of a scenario. The last two questions on the preassessment had asked students to create hypothetical descriptions for scenarios posed on a number line. Only one of the students provided a response for the first of these two items, which simply stated, I moved ahead eleven spaces. I provided an example of another scenario this might represent (e.g., earning money) and discussed others with the students. During the lesson following the preassessment, I focused on ordering and comparing integers, which further reinforced the introduction to absolute value I provided to students in the following lesson because we explored instances when the absolute value of a number could impact whether it was greater or less that the number to which it was being compared. All students improved their score on the postassessment. The range of scores on the postassessment was 88% to 100%. Responses revealed that there was still some confusion regarding the concept of an integer. Two students, for example, had responses that stated integers were positive and negative numbers, but did not include zero. Despite this misunderstanding, the students were able to compare integers and determine their absolute value correctly, which demonstrates a

17 conceptual misunderstanding that does not interfere with their math skills, but nonetheless needs to be addressed. The students had many creative interpretations for the final two open-ended questions that illustrated they had internalized the concept that whether a positive or a negative change on a number line can be considered good or bad depends on the situation and what is being lost or gained. A major strength of my assessments is that they required demonstration of student knowledge across several cognitive levels aside from comprehending the definition of an integer, it asked students to make value judgments about situations, which afforded the students flexibility in their responses. Because two students misinterpreted the start and endpoints on the number line for the second to last object (which was hand-drawn), I realized that this was a weakness of the assessment that I would need to delineate more clearly in the future. Overall, the assessment effectively revealed to me the extent of students understanding of integers both before and after my instruction. Results of One Student s Pre and Postassessments The following student s results on the pre and postassessments I wrote and administered for integers are representative of the growth most students demonstrated in this area of study. He verbally expressed that he did not know much, if anything, about integers, though he made gains in their understandings following the two lessons I taught on integers. The graded preassessments were returned to students on Monday after they had taken the preassessment on Friday and received instruction about integers on both Friday and Monday. The student s name has been removed to maintain confidentiality.

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