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?
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.
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)
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
-7-5 12 3 4 6-1 0 0 13 9-11 2-2 -1 1
-3-3 8-8 -4 6-1 14-5 7-5 -6 10-9 2-4
2-6 9-6 -9 1-4 -9 3-3 9-8 0 0-5 5
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 -15-20 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.
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.
Ordering and Comparing Integers Record and Average Temperatures in VA (Lesson 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.