Students are introduced to integers and rational numbers, extending the number line to include negative values, understanding the order of rational numbers, and interpreting them in context.
In Unit 4, sixth-grade students extend their understanding of numbers to include rational numbers. Prior to this unit, students have worked only with positive values, and their concepts of number lines and coordinate planes have been limited by these positive values. Students explore real-world situations that naturally connect to negative values, such as temperature, money, and elevation. The number line is a valuable tool that is referred to and used throughout the unit. Students use the number line to develop understanding of negatives, opposites, absolute value, and comparisons and inequalities (MP.5). They also discover the four-quadrant coordinate plane by intersecting two number lines at a 90-degree angle and representing locations using ordered pairs.
In elementary grades, students build and develop their sense of number with positive values. They use the number line as a tool to better understand whole numbers, fractions, and decimals. In fifth grade, students look at the first quadrant of the coordinate plane and represent locations using ordered pairs of positive numbers. In sixth grade, students build on and extend these concepts to include negative values.
In seventh grade, students will discover how to compute with rational numbers and what happens when the properties of operations are applied to negative values. The work they do in this sixth-grade unit is foundational of these seventh-grade concepts.
Pacing: 16 instructional days (13 lessons, 2 flex days, 1 assessment day)
This assessment accompanies Unit 4 and should be given on the suggested assessment day or after completing the unit.
reflection (of a coordinate point)
Extend the number line to include negative numbers. Define integers.
Use positive and negative numbers to represent real-world contexts, including money and temperature.
Use positive and negative numbers to represent real-world contexts, including elevation.
Define opposites and label opposites on a number line. Recognize that zero is its own opposite.
Find and position integers and rational numbers on the number line.
Order integers and rational numbers. Explain reasoning behind order using a number line.
Compare and interpret the order of rational number for real-word contexts.
Write and interpret inequalities to compare rational numbers in real-world and mathematical problems.
Define absolute value as the distance from zero on a number line.
Model magnitude and distance in real-life situations using order and absolute value.
Use ordered pairs to name locations on a coordinate plane. Understand the structure of the coordinate plane.
Reflect points across axes and determine the impact of reflections on the signs of ordered pairs.
Calculate vertical and horizontal distances on a coordinate plane using absolute value in real-world and mathematical problems.
Key: Major Cluster Supporting Cluster Additional Cluster