MidSchoolMath 1

Finding the distance between positive and negative numbers is used in many instances, so exposing students to real world representations is crucial for their current understanding and future learning. During Avalanche Pits, members of the Taos Ski Patrol, will dig snow pits to calculate the temperature gradient (TG), which is the difference between the temperatures in the upper and lower layers of the snow. The greater the temperature difference between the layers, the greater the likelihood of an avalanche. Students are to rank the avalanche areas from most to least dangerous. The data provided is an image displaying the upper and lower temperatures for each high-risk area.

LESSON: AVALANCHE PITSHow would you rank the avalanche areas from most to least dangerous?

Avalanche Pits

Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real world contexts.

The Math SimulatorTM

ImmersionPlay Avalanche Pits Immersion video, whole-class. Restate the question: How would you rank the avalanche areas from most to least dangerous?Facilitate classroom discussion; ask students: "What do we need to know?"

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2 Data & ComputationPrint the Data Artifact and distribute to students. Allow students work time. Ask students: "Does your answer make sense?"Consider using a sharing protocol leading to mathematical insights and/or highlighting misconceptions. Allow students to revise their work.

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3 ResolutionPlay Avalanche Pits Resolution video, whole-class. Prepare and give brief lecture (Teacher Instruction).

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Download the Detailed Lesson PlanAvailable on the Teacher Dashboard

+ Simulation TrainerAssign the Simulation Trainer.Use protocols that encourage students to help each other.Use Progress Monitoring to access real-time data for the classroom.Provide individual help for students who are not making progress.

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(Use student headphones.)

7.NS.A.1cThe Number System

MidSchoolMath Avalanche Pits

Clicker QuizLaunch the Clicker Quiz, whole-class.

7.NS.A.1cThe Number System

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Gladys: It can be confusing to know when to just subtract versus when to find the absolute value of the difference. When there is context to find the distance between two numbers, the absolute value of the difference should be calculated.

Kevin: You may need to remind students that subtracting a positive number means moving in the negative direction, and subtracting a negative number means moving in a positive direction. Keep connecting this to the idea of adding the additive inverse.

Megan: Continuing to use number lines may be helpful for students as they tackle this standard.

KevinSimpson

GladysGraham

MeganLeBleu

Ex. Clicker Quiz #2Standard Math Procedures

Instruction at a Glance

1 Set up a subtraction problem.

600 – (-150)

600 + 150 = 750

|750| = 750 feet

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Add the additive inverse.

Find the absolute value of result, since the question asked for distance.

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AVALANCHE PITSWhich avalanche area is the most dangerous?Kate and Vitt have been asked to help the Santa Fe Ski Patrol determine whether some of their slopes are at risk for an avalanche. They will dig avalanche pits in high-risk areas and then measure the temperature of the upper and lower layers. The diff erence between the layers is called the Temperature Gradient (TG). Areas with the largest diff erence are at a higher risk for avalanche.

Based on the given information for each location, determine the temperature gradient to decide which avalanche area is the most dangerous.

7.NS.A.1c

Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their diff erence, and apply this principle in real world contexts.

About this standard

Date PeriodName

MidSchoolMath Avalanche Pits 1 of 2

The most dangerous slope is ___________________.

APPLYING THE STANDARD

Mt. Everest is the highest point in the world at about 8850 meters above sea level. Dead Sea Shore is the lowest point on dry land at about 418 meters below sea level. What is the diff erence of the heights of the two points?

1)

Subtract.2)

Evaluate for p = -16.2 and q = -21.3)

MidSchoolMath Avalanche Pits 2 of 2

Date PeriodName

How might this standard appear on a test?

64 – 89a)

p – qa)

-9.7 – (-18.6)b)

q – pb)

-113 – 208c)

-p – qc)

4 – 7d)

p – (-q)d)

At 12:30 p.m., the temperature at Taos Ski Valley was 16°F. At 12:30 a.m. the next morning, the temperature was -4°F.

6)

What was the diff erence in temperature?a)

The temperature after 12:30 a.m. decreased by 0.25°F every half hour. What was the temperature at 2:30 a.m.?

b)

The temperature after 12:30 a.m. decreased by 0.25°F every half hour. What was the temperature at 2:30 a.m.?

c)

a – b = 21 m – n = -15 4) 5)

Write this diff erence using two positive numbers.

Write this diff erence using two positive numbers.

a) a)

Write this diff erence using one positive number and one negative number.

b) Write this diff erence using one positive number and one negative number.

b)

Write this diff erence using two negative numbers.

c) Write this diff erence using two negative numbers.

c)

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Check out my worked example #2a

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