General Information
Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Absolute Value
- Integers
- Number Line
- Rational Number
- Whole Number
Vertical Alignment
Previous Benchmarks
- This is the first introduction to the concept of absolute value.
Next Benchmarks
Purpose and Instructional Strategies
In elementary grades, students plotted positive numbers on a number line and related addition of positive numbers to distance on a number line. In grade 6, students determine and compare absolute values. In grade 7, students will use the concept of opposites when solving problems involving order of operations and absolute value.- All values within this benchmark are limited to integers since students do not perform operations on negative rational numbers until grade 7.
- Instruction includes making connections in absolute value problems to direction and distance, or speed. This benchmark connects to finding the distance between two points on a coordinate plane with the same x- or y-coordinate.
- Instruction within absolute value contexts are not limited to distances, temperature and finances. Other situations could arise from a predetermined amount, or zero point, and then measuring above or below that amount (MTR.7.1).
- For example, Leah eats on average 1200 calories in a day. On Wednesday, her caloric intake was 400 calories different than her average. What are her possible caloric intakes on Wednesday?
- Students should progress from solving problems using a concrete number line to solving problems abstractly. Students should represent equations with a visual model to illustrate their thinking. This will allow for students to solidify the abstract concept through a pictorial representation. When students understand both methods and how they connect, students are often able to think more flexibly and reason through challenging problems successfully (MTR.2.1, MTR.5.1).
- Instruction includes the use of technology, including calculators.
Common Misconceptions or Errors
- Students may incorrectly state the absolute value of a negative number has a negative value. Instruction includes opportunities for students to talk about absolute value as distance in real-world scenarios (MTR.7.1).
- For example, the odometer on my car reads 92,500 miles when I leave my house to drive 89 miles to Grandma’s house. When I get to Grandma’s house, the odometer reads 92,589 miles. When I turn around and drive home, which is the opposite direction, will my odometer count backwards and read 92,500 again when I get home, or will it read 92,678 miles?
- Students may incorrectly assume distance is only referring to physical traveling between locations, such as walking, biking or driving. However, if we plot two values on a number line, this can also represent distance because we are determining how far away two points or values are from each other (MTR.3.1).
Strategies to Support Tiered Instruction
- Teacher provides instruction to reinforce the concept of absolute value being the distance of a number from zero.
- For example, students plot integer values that represents temperature on a number line and then record the number of units from zero.
- Teacher provides instruction for utilizing the absolute value symbols within the order of operations and refers to them as groups symbols.
- For example, when evaluating −|6|, first apply the absolute value of 6, then apply the factor of −1 to result in a solution of −6, so that−|6| = (−1)(|6|)= (−1)(6)
= −6.
- For example, when evaluating −|6|, first apply the absolute value of 6, then apply the factor of −1 to result in a solution of −6, so that
- Instruction for comparing absolute values of integers includes the use of pictorial representations or number lines to model the comparison and the use of key features of the model to discuss the problem, using contextual language when provided.
Instructional Tasks
Instructional Task 1 (MTR.2.1, MTR.7.1)
Instructional Items
Instructional Item 1*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.