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5-8 Math

6th Grade Math - Explore LessonOverview

Planner: McNickle/MitchellUnit: Unit 3 – Rational NumbersDay/Title: IA1, L26 “Comparing and Ordering, Day 2” (Real World Contexts)CCSS: CCSS.Math.Content.6.NS.C.7.b

Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write -3 oC > -7 oC to express the fact that -3 oC is warmer than -7 oC.CCSS.Math.Content.6.NS.C.7.cUnderstand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of -30 dollars, write |-30| = 30 to describe the size of the debt in dollars.CCSS.Math.Content.6.NS.C.7.dDistinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than -30 dollars represents a debt greater than 30 dollars.

STAMP: Previously we knew how to compare rational numbers by using the number line Now we know how to compare rational numbers in a real world context:

Comparing the size/magnitude (such as debt) requires that you consider absolute value.

Comparing a location, elevation, or worth requires that you consider value.

PrepareObjective: SWBAT write, interpret, and explain statements of order for rational numbers

in real-world contexts.

IA 1 L 26 (Rational Numbers) 1

http://www.corestandards.org/Math/Content/6/NS/C/7/d/

http://www.corestandards.org/Math/Content/6/NS/C/7/c/

http://www.corestandards.org/Math/Content/6/NS/C/7/b/

5-8 MathExplore Exemplar


5-8 MathExit Ticket Exemplar:


5-8 MathIA Alignment:


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Upcoming for IA2 There is a hot air balloon floating 20 feet above a lake. There is a scuba diver that is

swimming at a depth of 30 feet. Who is further away from the surface of the water?a) The hot air balloon is farther away from the surface because |−30|<|20|b) The scuba diver is farther away from the surface because |−30|>|20|c) The scuba diver is farther away from the surface because −30>20d) The hot air balloon is farther away from the surface because −30<20

Harold is part of the way up a hill, at a point that is 800 feet above sea level. Kerry’s location represents the opposite of Harold’s location. Which statement best describes Kerry’s location?a) Kerry is standing next to Harold.b) Kerry is at the top of the hill, at a point 1,600 feet above sea level.c) Kerry is scuba diving 800 feet below sea level.d) Kerry is in a rowboat at sea level.

Previous Learning:

Yesterday, students practiced using a number line to compare and order rational numbers. They know that they should not only consider the absolute value (or magnitude) of the numbers, but also the position/location of the numbers on the


5-8 Mathnumber line. They should know that numbers further to the left on the number line have less value, and numbers to the right on the number line have more value.

Relevant Math Knowledge:

From the CCSS Progressions Document:With the introduction of negative numbers, students gain a new sense of ordering on the number line. Whereas statements like 5 < 7 could be understood in terms of having more or less of a certain quantity – “I have 5 apples and you have 7, so I have fewer than you” – comparing negative numbers requires closer attention to the relative positions of the numbers on the number line rather than their magnitudes. Comparisons such as -7 < -5 can initially be confusing to students, because -7 is further away from 0 than -5, and is therefore larger in magnitude. Referring back to contexts in which negative numbers were introduced can be helpful: 7 meters below sea level is lower than 5 meters below sea level, and -7 degrees Fahrenheit is colder than -5 degrees Fahrenheit. Students are used to thinking of colder temperatures as lower than hotter temperatures, and so the mathematically correct statement also makes sense in terms of the context.

Key Vocabulary:

Elevation, locationDepth, altitudeDebt, value, worthAbsolute value, valueInequalityShallow/deep

Annotation & Organization Strategies:

If a number line is not provided, students should draw one to help them visualize the location of the numbers in relation to each other and in relation to zero. If a number line is given, they should mark it up with the information from the problem.

Students use of CUBS today will be incredibly important, as they will be deciphering word problems.

Materials: LP, worksheetsCalculators: NoneHomework: Comparing & Ordering, Day 2

Mix It Up

Launch (1-5 minutes)Activate Foundational Knowledge (1-5 min):

To activate foundational knowledge today, students will explore a real-world context in which the values are all positive. Then, we’ll repeat a similar activity in which the values are all negative, so students can draw comparisons between the two scenarios.

I’m so excited for today’s lesson because we’ll get to explore some interesting real-world contexts! Let’s start with a quick warm-up on a situation involving aircrafts. Read it for us please.There are two parts – your job in part A is to what? Your job in part B?Awesome- coming around to see how you show and explain how you know for each part. Four minutes – go!

TW show-call correct work for part A (answer = helicopter), such as: Inequality statement, 43/4 < 14 1/3 < 14.5 Vertical number line showing jet is below propeller plane is below

helicopter


5-8 Math Statement describing that helicopter has largest absolute value, therefore

furthest distance from zero, therefore highest elevation

TW show-call correct work for part B (answer = helicopter), such as: Inequality statement, |43/4| < |14 1/3| < |14.5| Vertical number line showing jet is below propeller plane is below

helicopter Statement describing that helicopter has largest absolute value, therefore

furthest distance from zero

NOTE: the answers to both of these questions will be the same. Since this is a set of positive numbers, the number with the greatest value (elevation) also has the greatest absolute value (distance from sea level).

Key Takeaway:For this set of positive numbers, the number with the greatest value also has the greatest absolute value.

Challenge (1 min):

Let’s see who can tackle our next real world situation – in today’s Explore!

ID the Task and Name the Parameters (1 min):

Read the task to yourselves. Same idea as in Part 1 – which item has the highest elevation & which

item is furthest from sea level. I’m excited to see how you show and explain how you know!

Bright Line (< 1 min):

4 minutes – go!

Monitor the Explore (5-10 minutes)Aggressively Monitor: Procedural Lap

TW set environment [Set timer, play classical music, get clipboard and pen in hand; scan the room

to ensure students on task.]

Procedural Lap (1-2 minutes) [Start with faster mathematicians, then monitor slower problem-solvers.] Name the laps:

o I’m coming around to check your M & O in MOLE.

Anticipated Error Prompts# of

Students Making Error

1. M in MOLE incorrectly: Does not circle numbers; underlines too much or too little information; does not mark up the problem at all

Look at our MOLE chart. How do we mark-up questions?

What should you do to numbers?

We don’t want to underline too much information (TW erase all underlines). Underline only important information.

2. O in MOLE incorrectly: Look at our MOLE chart.


5-8 MathDoes not organize the workspace

How do we organize our workspace for this unit?

Where is your number line? Have you marked up your

number line? Aggressively Monitor: Conceptual Lap

Conceptual Lap (4-6 minutes) Name the lap and work the clock: These are recommendations, but can be adjusted to meet the data needs in

your classroom. Explore Laps I am coming around to see how you determine who has the highest elevation. I am coming around to see how you determine who is farthest from sea level.



1. Does not convert all of the numbers to the same format to compare.

How could you rewrite the numbers to compare them efficiently?

What steps do you need to rewrite an improper fraction as a decimal?

2. Thinks number with greatest absolute value (most negative) has greatest value

Draw a number line. Where on the number line are the

numbers with a higher “elevation”?

Are we thinking about value or absolute value in this part? How do you know?

3. Thinks number with greatest value also has greatest absolute value

Draw a number line. Where is sea level in this scenario? Are we thinking about value or

absolute value in this part? How do you know?

Discuss (6-8 minutes)Chart the Error

[Collect student work samples (two strategies) prior to the start of discourse.]

Evaluate Narrow the focus: “Let’s take a look at how each scholar [zoom in to the area

of difference].” “Evaluate these two answers,” poll the room “Who agrees with student A?

Student B?” Turn and talk: then re-poll the room to see who has changed their thinkingDiscuss the Work Chart the Error

o Call on students with incorrect and then correct answero Build consensus by calling on multiple students to share outo Teacher confirms and crosses out incorrect strategyo Ask students to name the error

ORIA 1 L 26 (Rational Numbers) 8

5-8 Math Chart for Connections

o Call on student to explain why strategy A is correct, then call on student for strategy B

o Compare and contrast these two responses. Why do those differences matter?

o Build consensus by calling on multiple students to share outo Teacher confirms that both strategies are correct

Name a Key Takeaway For Chart the Error, ask students to explain the correct work and annotate

the work while they speak For Chart for Connections, ask students to name the benefits/limitations to

each strategy and when/why you would use each one and annotate the work while they speak

T&T to generalize the rule: “How can we generalize these ideas into one sentence to apply to all …?”

Teacher charts the key takeaway while students state it in their own words Use the same color marker to write the key takeaway and to highlight the

exemplar work

1. Does not rewrite the numbers all in decimal format to compare.Error Correct Answer

−854 , <20.15, <20 ½

Name the Error: Does not rewrite the numbers all as decimals to compareClose the Gap: In order to accurately compare a set of fractions and decimals, rewrite them in the same format.

2. Thinks number with greatest absolute value (most negative) has greatest value (part A)

Error Correct Answer

Great White (-21.25) has highest elevation

Blue shark (-20.15) has highest elevation

Name the Error: Thinks number with greatest absolute value (most negative) has greatest valueClose the Gap: Negative numbers which are closer to zero have the most value because they are furthest right (or uppermost) on the number line. We


5-8 Mathuse the actual value to compare locations.

3. Thinks number with greatest value also has greatest absolute value (part B)


-20.15 = farthest from sea level

-21.25 is farthest from sea level

Name the Error: Thinks number with greatest value also has greatest absolute valueClose the Gap: Negative numbers with a greater value actually have a smaller absolute value, because they are closer to zero. We use absolute value to compare distances.

Restart Name the lap to close the gap. TW use the close the gap language from the most recent error charting to name the next lap.

Note: Restart with the Explore task until completed. Transition to the IP once students have completed the Explore task. Continue to monitor/discuss throughout all student work time as multiple cycles may be needed.

Monitor the IP (15-20 minutes)Aggressively Monitor: Procedural Lap

TW set environment [Set timer, play classical music, get clipboard and pen in hand; scan the room

to ensure students on task.]

Procedural Lap (1-2 minutes) [Start with faster mathematicians, then monitor slower problem-solvers.] Name the laps:

o I’m going to be checking your M and O in MOLE.



3. M in MOLE incorrectly: Does not circle numbers; underlines too much or too little information; does not mark up the problem at all

Look at our MOLE chart. How do we mark up questions?

What should you do to numbers?

We don’t want to underline too much information (TW erase all underlines). Underline only important


5-8 Mathinformation.

4. O in MOLE incorrectly: Does not organize the workspace

Look at our MOLE chart. How do we organize our workspace for this unit?

Where is your number line? Have you marked up your

number line? Aggressively Monitor: Conceptual Lap

Conceptual Lap (4-6 minutes) Name the lap and work the clock: These are recommendations, but can be adjusted to meet the data needs in

your classroom. Independent Laps I am coming around to check how you are interpreting and choosing the best

answer for each mild question. I am coming around to check how you are interpreting and choosing the best

answer for each medium question.



1. Does not interpret “depth” to mean negative value

What is the difference between depth and altitude?

If something has a depth, is it above or below zero?

If something has an altitude, is it above or below zero?

2. Answer choice does not match the comparison symbol which is given

Read the inequality statement we were given in the text. [T should point to instructional signage posted at the front of the room]

The answer choice we pick needs to correspond with that statement. This value is [less than/greater than] this value.

3. Compares values instead of absolute values

If you are measuring the size of someone’s debt, should you consider the value or absolute value of that number?

If you are measuring someone’s worth, should you consider the value or the absolute value of that number?

Discuss (6-8 minutes)Chart the Error

[Collect student work samples (two strategies) prior to the start of discourse.]

Evaluate Narrow the focus: “Let’s take a look at how each scholar [zoom in to the area

of difference].” “Evaluate these two answers,” poll the room “Who agrees with student A?

Student B?” Turn and talk: then re-poll the room to see who has changed their thinkingDiscuss the Work


5-8 Math Chart the Error

o Call on students with incorrect and then correct answero Build consensus by calling on multiple students to share outo Teacher confirms and crosses out incorrect strategyo Ask students to name the error

OR Chart for Connections

o Call on student to explain why strategy A is correct, then call on student for strategy B

o Compare and contrast these two responses. Why do those differences matter?

o Build consensus by calling on multiple students to share outo Teacher confirms that both strategies are correct

Name a Key Takeaway For Chart the Error, ask students to explain the correct work and annotate

the work while they speak For Chart for Connections, ask students to name the benefits/limitations to

each strategy and when/why you would use each one and annotate the work while they speak

T&T to generalize the rule: “How can we generalize these ideas into one sentence to apply to all …?”

Teacher charts the key takeaway while students state it in their own words Use the same color marker to write the key takeaway and to highlight the

exemplar work

1. (Question 1) Does not interpret “depth” to mean negative valueError Correct Answer

a) A depth of 12.4 feet is lower than a depth of 14.9 feet

b) An altitude of 12.4 meters is lower than an altitude of 14.9 meters

Name the Error: Does not interpret “depth” to mean absolute valueClose the Gap: A depth indicates a location below zero, which must have a negative value. An altitude indicates a location above zero, which has a positive value. We use the value of the number to compare locations.

2. (Question 3) Answer choice does not match the comparison symbol which is given


c) Nine feet below sea level is higher than two feet below sea level

b) A person at a depth of 9 feet is lower than a person at a depth of 2 feet

Name the Error: Answer choice does not match the comparison symbol which is givenClose the Gap: Our real-world story must match the comparison symbol given in the text. < means less than, underneath, lower, colder, less value. > means greater than, above, higher, more value.


5-8 Math

3. (Question 7) Compares values instead of absolute valuesError Correct Answer

a. Frank’s debt is less than Bruce’s.|-45.30|<|-5|

b. Bruce’s debt is less than Frank’s.|-5|<|-45.30|

Name the Error: Comparing values instead of absolute valuesClose the Gap: When you compare the size (magnitude) of something such as debt you need to compare absolute values.

Restart Name the lap to close the gap. TW use the close the gap language from the most recent error charting to name the next lap.

Stamping the UnderstandingStamping the Understanding(5 min):

Prompt towards the big idea:Recap the work: Over the course of today, we have come to some big ideas.

Stamp it-use the best prompt to get to the big idea: Let’s synthesize our learning in one place. How does today’s new learning connect to what we already know about

comparing rational numbers? Take 2 minutes – everybody writes, Go!

Chart it: TW show call one scholar’s written response that synthesizes all of their

thoughts of today’s lesson.

Evaluate: Are we missing anything? TW revise/edit with missing components or better mathematical language. TW record STAMP:

Previously we knew how to compare rational numbers by using the number line Now we know how to compare rational numbers in a real world context:

o Comparing the size/magnitude (such as debt) requires that you consider absolute value.

o Comparing a location, elevation, or worth requires that you consider value.

Exit Ticket (5-7 minutes)Exit Ticket(5-7 min)

[TW start timer counting backwards from 5 minutes and place on doc cam large enough for all scholars to see.]TW say: Scholars, you have 5 minutes to complete the Exit Ticket. You will show your work and use MOLE. Go!


5-8 Math


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