DETAILED LESSON PLAN: AVALANCHE RESCUE TRAINING · MidSchoolMath Lesson Plan: Avalanche Rescue Training 1 Geometry 5.G.A.1 Use a pair of perpendicular number lines, called axes, to

MidSchoolMath Lesson Plan: Avalanche Rescue Training 1

5.G.A.1Geometry

Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that

the names of the two axes and the coordinates correspond (e.g. x-axis and x-coordinate, y-axis and y-coordinate).

The coordinate plane is the basis for many concepts in future mathematics, such as visualizing equations and scatter plots. During Avalanche Rescue Training, the students are part of the Ski Patrol training for avalanche rescues. The trainers explain the set-up of the coordinate grid as being part of the Beacon system worn by the patrol and used to help guide the avalanche dogs to the victim's location. The data provided is a numberless grid showing the location of the "victim."

DETAILED LESSON PLAN: AVALANCHE RESCUE TRAININGWhere is the victim in relation to you?

Prerequisite Standards• 3.NF.A.2

Lesson Plan OverviewLesson Length: 4 Days

English Language Learners: Some students may have difficulty understanding the terms used regarding the Avalanche Rescue Transceiver (ART), specifically “grid” and “plane.” Discuss these terms so students understand them as mathematical terms in this type of real-world situation.

Standards for Mathematical PracticeMP7: Look for and make use of structure.On Day 1, during the Immersion and Data & Computation phases, students will relate the structure of horizontal and vertical number lines to the coordinate plane as they devise a system to locate victims of an avalanche.

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Common MisconceptionsSometimes students reverse the points when plotting them on a coordinate plane. They count up first on the y-axis and then count over on the x-axis.

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Cluster Connection

Direct Connection: In Avalanche Rescue Training, students will use ordered pairs on a coordinate plane to understand how to locate a person buried in snow in relation to their current location. Cross-Cluster Connection: This activity connects 5.G to 6.NS, 7.RP, 8.EE, 8.G and 8.F as it provides students with the foundation necessary for future work with the coordinate plane as it relates to graphs of proportional and non-proportional relationships, functions and transformations.

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Cluster Heading: Graph points on the coordinate plane to solve real-world and mathematical problems.

VocabularyCoordinate plane: A two-dimensional number line, split into four quadrants by the x-axis and y-axis; used to plot points, lines and figures.X-axis: The horizontal number line running through the center of the coordinate plane. Y-axis: The vertical number line running through the center of the coordinate plane. Origin: The intersection of the x and y-axes on the coordinate plane; located at (0, 0).Quadrants: The four regions of a coordinate plane, as divided by the x and y-axes.Ordered pair: Two numerical coordinates (x, y), specifically ordered, to locate or name a point on a coordinate plane.

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5.G

.A.1

Ava

lan

che

Res

cue

Trai

nin

g


5.G.A.1Geometry

KevinSimpson

GladysGraham

MeganLeBleu

Practice Printable

Instruction at a Glance Clicker Quiz

Full-sized Answer Key available in printed Teacher’s Guide

Gladys: Consider allowing students to grapple with how best to communicate the location of a point on the coordinate plane before teaching them about it. Try giving them just the major axes, with no grid lines, and ask them to communicate where a particular point is. Once there is a major need for grid lines to improve communication, then give them the additional structure. See what structure or method they use intuitively to describe the location of a point.

Kevin: Use the number line to help the students understand that, just as points on a number line can be located by their distance, the coordinate system can be used to locate and plot points.

Megan: Use this standard to emphasize the importance of precision. Make sure students understand the effects of switching the order of coordinates.

AVALANCHE RESCUE TRAININGWhere is the victim in relation to you?

5.G.A.1

Use a pair of perpendicular

number lines, called axes, to

defi ne a coordinate system, with

the intersection of the lines (the

origin) arranged to coincide with

the 0 on each line and a given

point in the plane located by using

an ordered pair of numbers, called

its coordinates. Understand that

the fi rst number indicates how

far to travel from the origin in

the direction of one axis, and the

second number indicates how far

to travel in the direction of the

second axis, with the convention

that the names of the two axes

and the coordinates correspond

(e.g., x-axis and x-coordinate, y-axis

and y-coordinate).

About this standard

Date PeriodName

MidSchoolMath Avalanche Rescue Training 1 of 2

The victims are located at these coordinates:

A B C D

E F G H

JI

(2, 8) (6, 12)

(9, 10) (3, 14)(11, 3)(4, 0)

(5, 4) (8, 2)

(0, 5) (8, 6)

The Ski Patrol is once again training for avalanche rescues. This time they have placed ten patrol members in various places as victims.

Write the coordinates of each of the ten locations so that the dog can locate and rescue them all.

APPLYING THE STANDARD

Label each part of the graph.

Plot and label each point on the graph.

Put an X in the box next to each TRUE statement.

X

X

X

X

X

X

• Origin• x-axis• y-axis• Scale on the x-axis: 1 - 11• Scale on the y-axis: 1 - 11


Date PeriodName

How might this standard appear on a test?

The x-axis and y-axis intersect at the origin.

The x-axis and y-axis intersect at 10.

The x- and y- coordinates are used to locate points on a coordinate plane.

The x- and y- axes are parallel number lines.

x- and y-coordinates are always written: (x, y).

The x- and y- axes are perpendicular number lines.

The coordinates of the origin are (0, 0).

The point (3, 5) is located 3 units above the origin and 5 units to the right of the origin.

The point (5, 2) is located 5 units to the right of the origin and 2 units above the origin.

• A (6, 0)• B (7, 5)• C (4, 3)• D (0, 9)• E (8, 8)• F (10, 7)• G (2 , 5)• H (5, 10 )• I (9 , 3 )

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23

12

12

Check out my worked example:Point J on Page 1


5.G.A.1

MaterialsAvalanche Rescue Training Immersion videoChart paper/Interactive whiteboard

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Procedure1. Play the Immersion video to the whole class.

2. Restate the question and keep it visible: Where is the victim in relation to you?3. Use the Think-Pair-Share protocol. Ask students: “What do we need to know?"

Think-Pair-Share Ask students to think individually about what information they need to know and make some notes (≈ 1-2 min). Tell students to pair with a partner and discuss their notes (≈ 2 min). Finally, facilitate whole-class by cold-calling on students to share their strategies on an interactive board (≈ 2 min).

MaterialsCopies of Avalanche Rescue Training Data Artifact, one per student •

Procedure1. Distribute the Data Artifact to each student.2. Invite students to work individually or with a partner to arrive at a solution.3. Observe students at work (avoid confirmation of the solution). Look for opportunities to clarify vocabulary, identify student strategies or work samples to be shared, and ask students questions to further their thinking.

• What information are we given? • What information is missing? • What do we already know about graphs or number lines that can help us? • What do we know already know about cardinal directions? • What are some way you could communicate to someone else exactly where the victim is?

As a warm-up, tell students to log into their account and access Test Trainer Pro. Specify the domain in which you would like students to work (preferably a different one than the prior day) and also the length of time you wish students to work (not a number of items). It is important to remind students to work out the math using paper and pencil when necessary and to look at their feedback.

Test Trainer ProAllow 7 to 10 minutes

Lesson Plan Day 1

The Math SimulatorTM

Allow 12 minutes

Immersion1

Allow 20 minutes

Data & Computation 2


5.G.A.1Lesson Plan Day 1, cont'd.

MaterialsAvalanche Rescue Training Resolution video•

Procedure

4. After determining students are nearing ‘sufficient’ progress, either consider using an additional teaching protocol, or ask students to provide a thumbs up/middle/down to indicate readiness to see the Resolution video. You may grant students additional work time, if necessary.

Here are examples of statements you might make to the class:

1. Play Resolution video to the whole class, and have the students mentally compare their solutions as they watch.2. After the video, prompt students with the following questions:

• What did you do that was the same? • What was different? • What strategy do you think was more efficient? Why? It is not always necessary for students to respond. The questions can simply be used to cue thinking prior to instruction.

Let’s review the problem from Avalanche Rescue Training. Remember we were trying to locate someone stuck under the snow from an avalanche.

We learned that a coordinate plane is a grid made from a horizontal number line (the x-axis) and a vertical number line (the y-axis). Both of these lines intersect at a right angle at the origin, forming 4 quadrants. For now, we will just focus on quadrant I.

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Allow 14 minutes

Resolution3

Teacher InstructionAllow 6 to 8 minutes

Answer: The victim is located and rescued at the point (7, 9).

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Let’s look at another example.

The origin is where the two number lines meet at 0, so it is plotted at (0, 0).To plot any point or locate any point, we use an ordered pair (x, y), with the x-coordinate always coming first and the y-coordinate always coming last.If we have the ordered pair (10, 5), it tells us that the point is located at the intersection of x = 10 and y = 5. If we had the ordered pair (5, 10), the point would be in a different location, at the intersection of x = 5 and y = 10. So the order is very important.

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How many points are shown on the grid? [11]Which point is directly on the y-axis? [K] What are its coordinates? [(0, 5)]Which point is directly on the x-axis? [F] What are its coordinates? [(5, 0)]Which point is farthest away from the origin? [D]Which point is located at (5, 4)? [A]

Now if you notice on the previous grid, all points landed on the exact intersection of two whole numbers. But do they always? No.We can use decimals and fractions for ordered pairs, too. They just might not be very precise, depending on the grid.



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Let’s look at two other points on a coordinate plane. •

••••

What would you say are the coordinates for point G? [(3, 1.75)]What would you say are the coordinates for point H? [(5.5, 5.25)] Would you say these are exact coordinates or estimated coordinates? Why? [These are exact coordinates because the scale of the graph is precise enough to show exact values, and the points land on exact intersections.]

Let’s look at these same two points on a different coordinate plane.

Notice that the points don’t land on an exact intersection of the grid.What would you say are the coordinates for point G? [(3, almost 2) or (3, 1.7), etc.]What would you say are the coordinates for point H? [(5 1/2, a little over 5) or (5 1/2, 5.3), etc.]Would you say these are exact coordinates or estimated coordinates? Why? [These are estimated coordinates because the scale of the graph isn't precise enough to show exact values.]


5.G.A.1

Materials• Copies of Avalanche Rescue Training Practice Printable, 1 per student

Practice Printable/Exit TicketAllow 16 minutes



Lesson Plan Day 2

Procedure1. Assign the Simulation Trainer to all students.2. Tell students to navigate to the Simulation Trainer assignment.3. Have students work individually to start.4. Consider using varied protocols that include peer teaching.5. Use Progress Monitoring on the Teacher Dashboard to determine which students are having difficulty. Provide individual help when necessary.

Materials• Avalanche Rescue Training Simulation Trainer• Student Devices• Paper and Pencil• Student Headphones

Allow 25 to 35 minutes

The Math SimulatorTM

Simulation Trainer




5.G.A.1



















and y-coordinate).

About this standard

Date PeriodName



A B C D

E F G H

JI

3. Sort the Practice Printables based on student self-assessment and professional teacher judgment of accuracy of the response. This sorting can be used for grouping students for differentiation of instruction the following day.

Procedure

1. Distribute copies of the Practice Printable. Have students work through the front page.

2. Exit Ticket: Ask students to rate their personal understanding of the problem on a scale of 1 to 3.

1 = I need more help 2 = I need more time, yet mostly understand 3 = I’ve got this! Have students put the number on their Practice Printable and turn them in.


5.G.A.1

Differentiation PlanRemediation

Meet with students who were unsuccessful on the Exit Ticket in a small group. Consider using

whiteboards to work through problems on the Practice Printable together.

Practice

Students who completed the Exit Ticket but need more practice should spend the class period

completing the Practice Printable. Encourage them to confirm strategies and solutions with each

other. Any additional time remaining should be spent getting started on the Student Reflection.

Enrichment

Students who demonstrated confident mastery on the Exit Ticket can finish the Practice Printable and spend the remaining time getting started on the Student Reflection or completing the following

activity:

• Have students create a picture on a coordinate grid.

- List the ordered pairs of the points that need to be plotted to complete the mystery picture on a

separate sheet of paper.

- Trade with a partner.

Practice PrintableAllow 26 minutes

MaterialsAvalanche Rescue Training Practice Printable•

Procedure1. Group students according to the prior day's Exit Ticket evaluation.2. Redistribute previous copies of the Practice Printable and implement the Differentiation Plan as they finish the Practice Printable. Encourage them to show their work.3. Collect completed Practice Printable.

Lesson Plan Day 3



Don't forget to assign my worked example!



Date PeriodName

My visual representation and title are attractive

and relevant to the story. I put extra

effort into my work.

My math drawing shows complete

understanding of the math concept.

I clearly described how the math is used in the story and used

appropriate math vocabulary.

My multiple choice question is original and directly relates

to the math concept. I have the correct

answer.

My multiple choice question directly

relates to the math concept. I have the

correct answer.

My visual representation and

title are mostly attractive and

relevant to the story. I put good effort into

my work.

My visual representation and title are somewhat

attractive. I only put a little bit of effort

into my work.


title aren’t attractive. I put very minimal


I did not make it clear how the math is used

in the story and/or didn’t use math

vocabulary.

My multiple choice question doesn’t use

the math concept.

I didn’t include a visual representation

or title.

I didn’t include a mathematical

drawing.

I didn’t explain how the math is used in

the story.

I didn’t include a multiple choice

question.

Visual Representation

Exceeds Expectations

4Meets

Expectations

3Nearing

Expectations

2Does Not Meet Expectations

1Incomplete

0

MathematicalDrawing

Math-StoryNarrative

Multiple Choice Question

MidSchoolMath

STUDENT REFLECTION This will help you with in-depth understanding.

Rubric:

Instructions:1. Draw a visual representation of the story. Include a title.

2. Create a mathematical drawing (tables, graphs, equations, figures, etc.) that shows the math used in the story.

3. Write a brief narrative that describes how the math was used in the story.

4. Using an example from your life, create a multiple choice question using the math concept. Circle the correct answer.

5. Use the rubric to grade yourself by circling how you did in each category. Turn this in with your Student Reflection.

Examples:

Student Reflection

I described how the math is used in the

story and used some math vocabulary.

I tried to describe how the math is used

in the story and/or used limited math

vocabulary.

My math drawing shows basic


My math drawing shows limited


My math drawing shows little to no



relates to the math concept, but I have

the incorrect answer.

Materials• Copies of Student Reflection rubric, 1 per student• White Paper• Colored Pencils

Procedure1. Available in the Student Reflection lesson on Teacher Dashboard, print and distribute the rubric. Discuss requirements with students.2. Distribute white paper and colored pencils to students.3. Have students begin the Student Reflection by sketching a draft. They will have additional time the following day to complete it.

Student ReflectionAllow 20 minutes


5.G.A.1Lesson Plan Day 4



Clicker QuizAllow 30 minutes

MaterialsAvalanche Rescue Training Clicker Quiz Student DevicesPaper and Pencil

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•

1. Ask students to log into their account and access Virtual Clicker. 2. Open the Clicker Quiz, whole class. 3. Prompt students to enter the quiz code on their device. 4. Launch quiz. 5. For each question: a. Show question and give students time to work. Consider using various protocols (i.e., students work individually, work with a partner, or maybe they have to agree with an entire table). b. Click “Vote,” and students will have 10 seconds to enter a response. c. Analyze class distribution. Decide whether more teaching is necessary, either a mini-lesson from you or by having students share strategies. d. Click “>” to advance to the next question. e. You may either then “Skip” the question or repeat steps a through e.

Procedure


Procedure1. Students continue working and complete their Student Reflections.2. Consider having a Gallery Walk when they are complete, using the I Wonder…, I Notice… protocol and sticky notes.

Gallery Walk (16-20 min)Display student work (such as Student Reflections) on classroom walls. Assign groups with tasks focused on

specific details (such as identifying different ways to solve a problem) and/or larger patterns (such as general

misconceptions). Tell groups to walk around, complete their task (≈ 8-10 min), then prepare and report brief

remarks to the class with their broader “a-ha” and “why” understandings (≈ 8-10 min).

I Wonder . . . , I Notice . . . (8-10 min)Following a completed whole-class assignment, set ground rules for peer critique, including being thoughtful,

specific, helpful and joining in (≈ 1 min)! Choose a student to be “the originator” who is tasked to explain his or

her approach and solution to a problem (≈ 2 min), while other students listen only. Then ask other students to

ask “the originator” clarifying questions or comments that start with ‘I wonder’ and ‘I notice’ (≈ 5-6 min).

Date PeriodName

My visual representation and title are attractive

and relevant to the story. I put extra


My math drawing shows complete


I clearly described how the math is used in the story and used

appropriate math vocabulary.

My multiple choice question is original and directly relates

to the math concept. I have the correct

answer.


relates to the math concept. I have the

correct answer.


title are mostly attractive and

relevant to the story. I put good effort into

my work.

My visual representation and title are somewhat

attractive. I only put a little bit of effort

into my work.


title aren’t attractive. I put very minimal


I did not make it clear how the math is used

in the story and/or didn’t use math

vocabulary.

My multiple choice question doesn’t use

the math concept.

I didn’t include a visual representation

or title.

I didn’t include a mathematical

drawing.

I didn’t explain how the math is used in

the story.

I didn’t include a multiple choice

question.

Visual Representation

Exceeds Expectations

4Meets

Expectations

3Nearing

Expectations

2Does Not Meet Expectations

1Incomplete

0

MathematicalDrawing

Math-StoryNarrative

Multiple Choice Question

MidSchoolMath

STUDENT REFLECTION This will help you with in-depth understanding.

Rubric:

Instructions:1. Draw a visual representation of the story. Include a title.

2. Create a mathematical drawing (tables, graphs, equations, figures, etc.) that shows the math used in the story.

3. Write a brief narrative that describes how the math was used in the story.

4. Using an example from your life, create a multiple choice question using the math concept. Circle the correct answer.

5. Use the rubric to grade yourself by circling how you did in each category. Turn this in with your Student Reflection.

Examples:

Student Reflection

I described how the math is used in the

story and used some math vocabulary.

I tried to describe how the math is used

in the story and/or used limited math

vocabulary.

My math drawing shows basic


My math drawing shows limited


My math drawing shows little to no



relates to the math concept, but I have

the incorrect answer.

• Student Reflections from Day 3• White Paper• Colored Pencils• Sticky Notes

Materials

Student ReflectionAllow 20 minutes


AVALANCHE RESCUE TRAININGArtifact 1




5.G.A.1



















and y-coordinate).

About this standard

Date PeriodName



A B C D

E F G H

JI

APPLYING THE STANDARD

Label each part of the graph.

Plot and label each point on the graph.

Put an X in the box next to each TRUE statement.

• Origin• x-axis• y-axis• Scale on the x-axis: 1 - 11• Scale on the y-axis: 1 - 11

• A (6, 0)• B (7, 5)• C (4, 3)• D (0, 9)• E (8, 8)• F (10, 7)• G (2 , 5)• H (5, 10 )• I (9 , 3 )


Date PeriodName

How might this standard appear on a test?

The x-axis and y-axis intersect at the origin.

The x-axis and y-axis intersect at 10.

The x- and y- coordinates are used to locate points on a coordinate plane.

The x- and y- axes are parallel number lines.

x- and y-coordinates are always written: (x, y).

The x- and y- axes are perpendicular number lines.

The coordinates of the origin are (0, 0).

The point (3, 5) is located 3 units above the origin and 5 units to the right of the origin.

The point (5, 2) is located 5 units to the right of the origin and 2 units above the origin.

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12

Check out my worked example:Point J on Page 1

Documents

DETAILED LESSON PLAN: AVALANCHE RESCUE TRAINING · MidSchoolMath Lesson Plan: Avalanche Rescue Training 1 Geometry 5.G.A.1 Use a pair of perpendicular number lines, called axes, to