Standard #: MA.6.NSO.1.2

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

• MA.6.NSO.4.1
• MA.6.NSO.4.2
• MA.6.AR.1.1
• MA.6.AR.1.2
• MA.6.GR.1.1
• MA.6.GR.1.2
• MA.6.GR.1.3

 

Terms from the K-12 Glossary

• Integers
• Number Line
• Rational Numbers
• Whole Numbers

 

Vertical Alignment

Previous Benchmarks

• This is the first introduction to the concept of numbers having opposites.

http://flbt5.floridaearlylearning.com/standards.html

Next Benchmarks

• MA.7.NSO.2.1

 

Purpose and Instructional Strategies

In elementary grades, students plotted, ordered and compared positive numbers. In grade 6, students plot, order and compare on both sides of zero on the number line with all forms of rational numbers. This benchmark focuses on the comparison of quantities with opposite directions (one positive and one negative) and understanding what the zero represents within the provided context. In grade 7, students will use the concept of opposites when solving problems involving order of operations and absolute values. 

• A strong foundation in this skill can help students more efficiently solve problems involving absolute value, finding the distance between points on a coordinate plane, combining rational numbers as well as assessing the reasonableness of solutions.
• Within this benchmark, it is the expectation that students make informal verbal comparisons of rational numbers using “is greater than” or “is less than” or another comparison within context.
  • For example, when comparing the temperature in Chipley, Florida, which is 34°F, to Minneapolis, Minnesota, which is −4°F, one could say that it is warmer in Florida than Minnesota or that it is colder in Minnesota than Florida.
• Students can describe the relative relationships between quantities and include the distance between the values in their description, as this is a way of connecting and reinforcing the MA.6.GR.1 standard (MTR.2.1, MTR.7.1).
  • For example, if a shark is 7.5 meters below sea level and a cliff diver is standing on a cliff at a point that is 22 meters from the surface of the water, the shark is 29.5 meters below the cliff diver. The shark’s position can also be described as– 7.5 meters from the surface of the water if the surface of the water represents 0.

 

Common Misconceptions or Errors

• Students may incorrectly assign double negatives when describing relationships that are below zero.
  • For example, they may say the temperature is – 3 degrees below zero when they mean it is – 3 degrees from zero or it is 3 degrees below zero. In this same context, it is important for students to understand that identifying a value as negative indicates the position as being lower or colder than the neutral position of 0.
• Instruction provides many opportunities for students to share verbal descriptions (in written and oral forms) to better develop this skill (MTR.4.1, MTR.7.1).
• Students may experience difficulty when trying to create a number line and determining the meaning of 0 within the context. Instruction showcases drawing a picture of the context first and then connect it to the building of a number line.

 

Strategies to Support Tiered Instruction

• Instruction includes the use of a physical or digital number line to plot various values and to use their location on the number line to assist in comparing them. Instruction focuses on the generalization that the farther to the left a value is on the number line, the lesser the number.
• Teacher assists students with representing rational values in a real-world context, by first drawing a visual representation of the situation and labeling key features of the picture such as the “neutral” point of the visual (sea level, zero degrees, ground level, etc.), direction (above or below sea level, forward or backwards movement, etc.) and magnitude (the absolute value of the given quantity) of the given situation. Once a visual is drawn, the teacher or students create a corresponding horizontal or vertical number line to match the picture and the key features and then use the number line to write the correct rational number, paying close attention to the location of the point relative to zero.
  • For example, Jasmine is on a cruise and is going on a scuba diving excursion. Her elevations of 10 feet above sea level and 8 feet below sea level can be compared on a number line, where 0 represents sea level.

• Teacher provides opportunities for students to represent verbal descriptions of situations pictorially and on a number line. Students then restate the same situation using different vocabulary and check the reasonableness of the new situations by making connections back to the visual representation, number line, and meaning of zero in the context.
  • For example, Thomas’s football team lost 3 yards in their first drive while Derrek’s football team gained 5 yards in their first drive. The first drives for each team can be compared on a number line, where 0 represents the line of scrimmage for each play.

• Instruction includes providing students with opportunities to practice placing rational number cards on a provided number line. While placing the cards, students should share their thinking out loud while the teacher listens for reasonable estimations and assumptions for correct placement.
  • For example, if a student is placing a number card with −4$\frac{\text{3}}{\text{5}}$ on the number line, the student needs to know that $\frac{\text{3}}{\text{5}}$ is more than half, so to place the card, the student should be between −4 and −5, with the point closer to the −5. As more cards are added to the number line, the students may adjust the placement of other cards, if necessary, for more accurate estimates.
• Teacher and students co-create a list of common terms from contextual situations that may be used to describe positive or negative values.
  • Examples of this could include:

 

Instructional Tasks

Instructional Task 1 (MTR.4.1, MTR.7.1)Instructional Task 2 (MTR.5.1)