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 Dear Parents and Caregivers, Thank you for supporting your child to achieve success in school. We value your input and active participation in your child’s education. These letters are designed to help you understand the work your child brings home and the academic expectations of Arizona’s College and Career Ready Standards. Your child is developing the necessary skills and knowledge to help them compute, think, and reason mathematically. This letter is about integers in grade 6. End-­‐of-­‐year goals In sixth grade, students will be introduced to the concept of positive and negative integers and absolute value. They find, position, and compare rational numbers using a number line diagram, plot coordinates on a 4-­‐quadrant coordinate grid, and create models to help solve real-­‐world mathematical problems involving rational numbers. Vocabulary: •
Absolute value: The distance of a number from zero on the number line; absolute value is always positive. •
Axis: a reference line from which distances or angles are measured on a coordinate plane •
Ordered pair: A pair of numbers that give coordinates of the location of a point on a coordinate plane e.g. (4 , 6), (-­‐3, 2) •
Coordinate plane (sometimes called a coordinate grid): a 2-­‐dimensional system that describes location of a point by its distance from two intersecting, usually perpendicular straight lines called axes •
Integer: Whole numbers and their opposites (…-­‐2, -­‐1, 0, 1, 2, …) •
Negative number: numbers that are less than zero; the opposite of a positive number •
Positive number: numbers that are greater than zero •
Rational number: a number that can be expressed as a ratio of two non-­‐zero numbers (e.g. 2, , -­‐6.6,) •
Whole number: any of the numbers 0, 1, 2 and so on Models for Integers Some real-­‐world examples of integers are: • Debits or credits with money (positive or negative cash flow) • Above or below zero temperature (positive or negative degrees) • Gain or loss of yards in football (positive or negative yardage) Zero (0) is neither positive nor negative. Number lines and the coordinate plane Positive and negative numbers can be shown on a number line. negative zero positive 2 and -­‐2 are opposites. and Absolute value is the distance a number is from zero. The symbol for absolute value is . The (absolute value of negative 2) and 2 is 2 2, because each number is located two spaces away from zero on the number line. Mesa Public Schools/Grade 6/Coordinate Planes/2013 Authorization to reprint or disseminate must be granted by Mesa Public Schools (February-­‐2014). are opposites. 4.5 and -­‐4.5 are opposites. Opposites have a sum of zero. Students can use a coordinate plane to model the location of a point using ordered pairs. Ordered pairs can have both positive and negative numbers. The origin point on the plane is (0, 0), where the x-­‐ and y-­‐axes intersect. When plotting an ordered pair, the first number indicates the horizontal coordinate and the second number indicates the vertical y-­‐axis coordinate. •
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To plot the ordered pair (3, 4), start at the origin (0, 0) and move three spaces horizontally to the right along the x-­‐axis. Then move four spaces up vertically along the y-­‐axis. The intersection of these two lines is the location of the ordered pair. To plot the ordered pair (-­‐4, -­‐2), start at the origin and move four spaces horizontally to the left along the x-­‐axis. Then move two spaces down vertically along the y-­‐axis. The intersection of these two lines is the location of the ordered pair. (3, 4) x-­‐axis (-­‐4, -­‐2) (0, 0) will also use the coordinate plane to solve problems involving area. They may plot coordinates of 2-­‐
Students dimensional polygons, such as rectangles and trapezoids. They can use these coordinates to find the lengths of the sides and the area of the polygon. They also can represent the reflection of a point across either the x-­‐axis or the y-­‐axis. Plot these ordered pairs: (2, 1); (5, 1); (2, 3); (5, 3) What polygon is formed? (a rectangle) What is the length of each side? (length = 3 units, height = 2 units) What is the area of the polygon? 2
(6 square units or 6 units.) How to help at home •
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What are the coordinates of the reflection of (-­‐4, 2) across the x-­‐axis? (-­‐4, -­‐2) (-­‐4, 2) -­‐(4, -­‐2) Ask your child to identify real-­‐world examples of negative numbers. Watch these videos about coordinate planes from LearnZillion. http://learnzillion.com/lessonsets/344-­‐understand-­‐and-­‐plotting-­‐points-­‐on-­‐coordinate-­‐planes • Remember, making mistakes is a part of learning. Mesa Public Schools/Grade 6/Coordinate Planes/2013 Authorization to reprint or disseminate must be granted by Mesa Public Schools (February-­‐2014).