Unit 4 – Operations with Integers – 6th grade
5E Lesson Plan Math
Grade Level: 6th grade
Subject Area: Math
Lesson Title: Unit 4 – Operations
Lesson Length: 10 days
with Integers
THE TEACHING PROCESS
Lesson Overview This unit bundles student expectations that address identifying
a number, its opposite, and its absolute value, and representing and modeling
integer operations fluently, including standardized algorithms. According to the
Texas Education Agency, mathematical process standards including application, a
problem-solving model, tools and techniques, communication, representations,
relationships, and justifications should be integrated (when applicable) with
content knowledge and skills so that students are prepared to use mathematics in
everyday life, society, and the workplace.
During this unit, students examine number relationships involving identifying a
number, its opposite, and absolute value. Previous work with number lines
transitions to the understanding that absolute value can be represented on a
number line as the distance a number is from zero. This builds to the relationship
that since distance is always a positive value or zero, then absolute value is
always a positive value or zero. Although students have been introduced to the
concept of integers, this is the first time students are exposed to operations with
negative whole numbers, which is a subset of integers. The development of
integer operations with concrete and pictorial models is foundational to student
understanding of operations with integers. Forgoing the use of concrete and
pictorial models as a development of integer operations could be detrimental to
future success with computations involving negative quantities, such as negative
fractions and decimals. The use of concrete and pictorial models for integer
operations is intended to be a bridge between the abstract concept of operations
with integers and their standardized algorithms. It is expected that once the
concept of integer operations has been sufficiently developed and connected to
the standardized algorithms, students should add, subtract, multiply, and divide
integers fluently.
Unit Objectives:
Students will…
 examine number relationships involving identifying a number, its opposite,
and absolute value
 represent absolute value on a number line as the distance a number is from
zero.
 develop integer operations with concrete and pictorial models
 develop and connect integer operations to standardized algorithms
 add, subtract, multiply, and divide integers fluently
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Unit 4 – Operations with Integers – 6th grade
Standards addressed:
TEKS:
6.1A- Apply mathematics to problems arising in everyday life, society, and the
workplace.
6.1B- Use a problem-solving model that incorporates analyzing given information,
formulating a plan or strategy, determining a solution, justifying the solution, and
evaluating the problem-solving process and the reasonableness of the solution.
6.1C- Select tools, including real objects, manipulatives, paper and pencil, and
technology as appropriate, and techniques, including mental math, estimation, and
number sense as appropriate, to solve problems.
6.1D- Communicate mathematical ideas, reasoning, and their implications using
multiple representations, including symbols, diagrams ,graphs, and language as
appropriate.
6.1E- Create and use representations to organize, record, and communicate
mathematical ideas.
6.1F- Analyze mathematical relationships to connect and communicate
mathematical ideas.
6.1G- Display, explain, and justify mathematical ideas and arguments using
precise mathematical language in written or oral communication.
6.2B- Identify a number, its opposite, and its absolute value.
6.3C- Represent integer operations with concrete models and connect the actions
with the models to standardized algorithms.
6.3D- Add, subtract, multiply, and divide integers fluently.
ELPS:
ELPS.c.5B - write using newly acquired basic vocabulary and content-based
grade-level vocabulary
ELPS.c.4F - use visual and contextual support and support from peers and
teachers to read grade-appropriate content area text, enhance and confirm
understanding, and develop vocabulary, grasp of language structures, and
background knowledge needed to comprehend increasingly challenging language
Misconceptions:
 Some students may think the absolute value is the opposite of a number
rather than the distance of the number away from zero (e.g. A student may
think that the absolute value for 5 is -5, but -5 is actually the opposite.)
 Some students may forget to attach the sign of the integers to the sum or
difference when adding or subtracting integers.
 Some students may have difficulty rewriting subtraction problems involving
integers as the addition of an opposite.
 Some students may think that subtracting a negative integer from a
negative integer always results in a difference of a negative integer.
 Some students may think that multiplying a negative integer by a negative
integer results in a product that is negative.
 Some students may think that dividing a negative integer by a negative
integer results in a quotient that is negative.
Page 2 of 17
Unit 4 – Operations with Integers – 6th grade
Vocabulary:



Absolute value – the distance of a value from zero on a number line
Fluency– efficient application of procedures with accuracy
Integers – the set of counting (natural numbers), their opposites, and zero
{n,…, 3, 2, 1, 0, 1, 2, 3, ..., n}. The set of integers is denoted by the symbol
Z.
Related Vocabulary:
Addend, Ascend, Compare, Credit, Debit, Deposit, Dividend, Divisor, Factor, Gain,
Like signs, Loss, Opposite, Positive, Product, Profit, Quotient, Sum
List of Materials:
Day 1
 PowerPoint
 Day 1 Notes
 Task Cards
 Integers at Sea
Day 2
 Red and yellow construction paper
 Video “Number Line Dance”
 Two color counters or red and yellow squares cut from construction paper
 Handout – Adding Integers with Models
 Handout – Adding Integers with Number Lines
Day 3
 PowerPoint – Adding Integers
 Integer Foldable
 Handout - Integer practice without models
 Handout - Homework – Magic Sum and Word Problems
 Exit ticket
Day 4
 Video “Khan Academy” Subtracting integers
 Handout – Subtracting Integers with a Number Line and counters
 Video – You tube – how to teach subtracting models
Day 5
 Video – You tube – Subtracting integers song
 Video – “Khan Academy part 2” Why subtracting a negative is a positive
 Handout - Subtracting Integers
 Handout - Homework – Subtracting Integers practice and word problems
 Exit Ticket
Day 6
 Video – Modeling Multiplying Integers
 Handout for the video
 Handout – Discovery Activity
 Video – Multiplying Integers
 Video – Why negative times a negative is a positive?
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Unit 4 – Operations with Integers – 6th grade
 Handout – Homework Multiplication Magic and word problems
 Exit Ticket
Day 7
 Counters, red and yellow pencils or red and yellow construction paper
(choose one)
 Handout – Division of Integers
 Handout – Discovery rules for dividing integers
 Video – “Dividing Integers” by The Khan Academy
 Handout - Homework – Dividing Integers with word problems
 Exit Ticket
Day 8
 Handout – Extending Integers
Day 9
 Handout – Integer Practice
Day 10
 Performance Indicators
INSTRUCTIONAL SEQUENCE
Phase 1 – Engage the Learner
Integers – Opposites – Absolute
Value
Day 1 Activity 1:
Have two students stand back to back. Tell the students to take 5 steps forward.
Illustrate this situation with a number line on the board starting with zero.
What’s the teacher doing?
What are the students doing?
The teacher is directing the students to
illustrate a human number line and
questioning the class.
The students are answering questions
and thinking about the human number
line.
Questions:
 What integer is represented by
student A and student B? (5, -5)
 Are the integers the same on the
number line? (No, these are
called opposites)
 What integers would be
represented if the students took
ten steps? (-10, 10)
 How far from zero is Student A
and Student B? The students
are the same distance from zero
if they both took five steps or if
they both had taken ten steps.
This is called Absolute Value.
Page 4 of 17
Unit 4 – Operations with Integers – 6th grade
Absolute value is the distance
from zero.
Integers – Opposites – Absolute
Value
Phase 2 Explain/Explore
Day 1 Activity 2:
Show the power point explaining integers, opposites and absolute value.
thMathIntegersandAbsolutValuesPowerpoint.ppt
After showing the PowerPoint have students complete the notes for integers.
Then have students create 5 real-life situations where integers are used. After
students have had a chance to create examples they will share their situations
with a partner and trade examples to figure out what integer is represented by the
situations.
Day 1 Activity 3:
Task card activity: Depending on the amount of time left, you can have the task
cards posted around the room and have students complete all twenty cards or you
can have students choose 4, 8, or 10 etc. to complete. This activity could be
completed with partners or independently. (See Handout)
Day 1 Activity 4:
Exit Ticket: What was important in today’s lesson? Why?
Homework or Classwork Activity: Students will complete Integers at Sea for
homework or classwork, if time allows.
What’s the teacher doing?
The teacher is going over the
PowerPoint slides with students to
define integers and absolute value.
What are the student’s doing?
Students are listening and reading the
slides from the PowerPoint. Then
students are creating examples and
interpreting situations.
Questions:
 How would you interpret the word
“loss”? (positive or negative)
 How would you interpret the word
“deposit”? (positive or negative)
 How would you interpret the word
“withdrawal”? (positive or
negative)
 Is the number “0” positive or
negative? (neither)
 What is the relationship between
Page 5 of 17
Unit 4 – Operations with Integers – 6th grade

a number, its opposite and its
absolute value?
How can positive and negative
numbers be represented in realworld problem situations?
(temperature, money, etc.)
Activity 3: The teacher is walking
around the room and helping students
as needed.
Activity3: Students are working
problems found on task cards.
Activity 4: Students will complete a
number line activity by drawing
examples using real-life situations.
(Integers at Sea)
Phase 3 Engage the Learner
Adding Integers
Day 2 Activity 1:
Give ½ the students a sheet of red construction paper and the rest of the class a
yellow sheet. Tell the students that red means negative and yellow means
positive.
Have the students model -4 + 2 by facing each other, red on one side and yellow
on the other. One red cancels out one yellow so how many are left? What color
is left? Based on this example what is the sum of -4 + 2?
Day 2 Activity 2:
Teach your students the Integer RAP – watch the video on the teaching channel to
learn the dance moves (http://www.alexkajitani.com/videos.html) or
(https://www.teachingchannel.org/videos/math-teaching-techniques)
Student part:
Negative to the left,
Positive to the right.
It’s the number line dance.
I could dance all night.
What’s the teacher doing?
The teacher is facilitating the integer
model with students and asking
questions.
The teacher is asking questions about
the video and having the students
describe how integers are used in
everyday situations.
What are the students doing?
Students are modeling positive and
negative numbers.
Students are learning the number line
dance and discussing how integers are
used in real-life situations.
Page 6 of 17
Unit 4 – Operations with Integers – 6th grade
Phase 4 Explain/Explore
Adding Integers
Day 2 Activity 3:
(See Handout) Have the students complete examples of adding integers with two
color counters or red and yellow squares and then discuss what happens when
you add two integers together. Does adding a positive plus a positive result in a
negative or positive answer? Does adding a positive plus a negative give you a
positive or negative answer? (it depends) Does adding a negative plus a negative
result in a positive or negative solution? In the solution 3 plus -1 the sum is +2 but
3 plus -5 the sum is -2 why is one sum positive and the other sum negative? In
order to answer this question use models to illustrate the relationship between
positives and negatives.
(See Handout) Have students complete examples using a number line. What do
you notice about the number line when you add a negative and a negative
number? What happens when you add two opposites on the number? What
happens when you add 9 + -3 on the number line?
What’s the teacher doing?
What are the students doing?
Questions:
 Does adding a positive plus a
positive result in a negative or
positive answer? (positive)
 Does adding a positive plus a
negative give you a positive or
negative answer? (it depends)
 Does adding a negative plus a
negative result in a positive or
negative solution? (negative)
 In the solution 3 plus -1 the
sum is +2 but 3 plus -5 the sum
is -2 why is one sum positive
and the other sum negative?
 What do you notice about the
number line when you add a
negative and a negative
number? (it moves to the left)
 What happens when you add
two opposites on the number
line? (always equals 0)
 What happens when you add
9 + -3 on the number line?
(positive 6)
 How are concrete and pictorial
Students will complete examples with the
counters.
Students will complete examples using a
number line.
Page 7 of 17
Unit 4 – Operations with Integers – 6th grade
models used with integer
operations (e.g., number lines,
two-color counters, etc.)?
Phase 5 Explain/Explore/Elaborate
Adding Integers
Day 3 Activity 1:
Explore:
AddingIntegersTutorial.pptx
Show the PowerPoint with adding integers. Have a class discussion about
adding integers and create a foldable for integer operations. Complete only the
adding integers portion today.
http://everybodyisageniusblog.blogspot.com/2012/07/integer-foldable.html
(See handout)
After students have practiced adding integers with models have them try a few
problems with larger numbers such as -97 + -36, -97 + 36, and 100 + -24. How do
you solve problems that are too large to use a model? Simply ask yourself: Do
you have more positives or negatives? How many more positives or negatives do
you have? By having the students asking these two questions, students will not
need a model to determine the answer.
Explain: Exit Ticket: What generalization can be made about the sum of two
integers with the same sign? When adding integers, if a pair of addends has the
same sign, then the sum will ………………….. What generalization can be made
about the sum of two integers with opposite signs? When adding integers, if a pair
of addends has the opposite signs, then the sum will ……………………
Elaborate: Homework: Students will practice adding integers “Magic Sum” and
word problems. (See Handout)
What’s the teacher doing?


What generalization can be
made about the sum of two
integers with the same sign?
(pos. + pos. = pos., neg. + neg.
= neg.)
What generalization can be
made about the sum of two
integers with opposite signs?
(the sign will be same as the
What are the students doing?
Students will complete adding integers
with and without models.
After solving several problems with and
without models students will make
generalizations about adding integers.
Page 8 of 17
Unit 4 – Operations with Integers – 6th grade

number with the largest
absolute value)
Does the problem have more
positives or negatives? How
many more positives or
negatives does it have?
Phase 6 Engage and Explore
Subtracting Integers
Day 4 Activity 1:
Engage:
Watch the video on subtracting integers and discuss. Students may question that
subtracting a negative is the same as adding a positive and that is where the
second video from “Khan Academy” has a great explanation. See Day 5’s lesson
for the other video.
https://www.khanacademy.org/math/pre-algebra/negatives-absolute-value-prealg/add-subtract-negatives-pre-alg/v/adding-and-subtracting-negative-numberexamples
Day 4 Activity 2:
Explore:
(See Handout) Students will practice solving subtraction problems using a number
line and make generalizations at the conclusion of this activity.
Students will model subtraction of integers using counters. See this video for help
on showing students how to model subtraction of integers. The counter example
starts 4 minutes into the video. https://www.youtube.com/watch?v=Va_CiPK49vU
What’s the teacher doing?
What are the students doing?
The teacher is having a class
discussion after watching the video
and answering student questions.
The teacher goes over examples of
subtracting integers on a number line
and with models (counters).
 How is subtraction related to
addition? (they are opposites)
 What generalization can be
made about the difference of
two integer numbers with
opposite signs?
Students are watching the video and then
solving subtraction of integers with
models. (number lines and counters)
Page 9 of 17
Unit 4 – Operations with Integers – 6th grade
Phase 7 Engage, Explore, Explain,
Subtracting Integers
Elaborate and Evaluate
Day 5 Activity 1:
Engage:
Watch the videos and discuss.
https://www.youtube.com/watch?v=5f0rF4m9TGY
https://www.khanacademy.org/math/pre-algebra/negatives-absolute-value-prealg/add-subtract-negatives-pre-alg/v/why-subtracting-a-negative-equivalent-toadding-a-positive
Use the foldable from yesterday to complete only the subtracting integers portion.
http://everybodyisageniusblog.blogspot.com/2012/07/integer-foldable.html
Day 5 Activity 2:
Explain/Explore:
(See Handout) Students will complete the engage problems by solving as many
problems as they can in three minutes and look for a pattern between problems.
As they complete the problems they should notice a pattern to help solve the
remaining problems. Once students have completed the problems have a class
discussion about the type of problems they see and how to solve them. Some
students may be able to create rules for subtracting integers based on the
examples. After the brief discussion, go over the examples by rewriting them as
addition problems and adding the opposite integer following the subtraction
symbol, and then applying the rules for adding integers. Students will then select
equivalent problems.
Elaborate:
Homework: Students will practice subtracting integers with and without models.
Students will also incorporate word problems involving integers.
Evaluate:
Exit Ticket: How is subtracting integers related to adding integers?
What’s the teacher doing?
The teacher is playing the videos and
answering student questions. The
teachers will facilitate the lesson and
guide students to rewrite integer
problems as addition problems.
 How can you change a
subtraction problem to an
addition problem? (by adding
the opposite)
 How is subtracting integers
related to adding integers? (it is
the same as adding once you
What are the students doing?
Students are watching the video and
asking questions.
Students will complete a pattern of
problems and practice rewriting
subtraction problems as addition
problems. Students will compare
expressions to find equivalent problems.
Students will practice subtracting integers
with and without models for homework.
Students will explain in written form how
subtracting integers and adding integers
are related.
Page 10 of 17
Unit 4 – Operations with Integers – 6th grade

add the opposite)
What generalizations can you
make about subtracting
integers?
Phase 8 Engage, Explore, Explain
Multiplying Integers
etc.
Day 6 Activity:
Engage:
Students will watch the video of modeling multiplication with integers. While they
are watching the video have them follow along by setting up the models on their
paper and coloring the models. Pause the video as the students work. (See
Handout) https://www.youtube.com/watch?v=Gk4QhK3KMq4
Explain/Explore:
Once students have practiced with models they will complete the handout with
experimental practice and discover the rules for multiplying integers. After
students have drawn conclusions for multiplying integers show the video.
https://www.khanacademy.org/math/pre-algebra/negatives-absolute-value-prealg/mult-div-negatives-pre-alg/v/multiplying-positive-and-negative-numbers
Then show “Why a negative times a negative is a positive”.
https://www.khanacademy.org/math/pre-algebra/negatives-absolute-value-prealg/mult-div-negatives-pre-alg/v/why-a-negative-times-a-negative-makes-intuitivesense
Students should complete the multiplying integers part of their foldable.
Elaborate: Homework: Students will practice multiplying integers with word
problems. (See Handout)
Evaluate:
Exit Ticket: What generalization can be made about the product or quotient of
two or more integers with no negative signs or an even number of negative signs?
What generalization can be made about the product or quotient of two or more
integers with one negative sign or an odd number of negative signs?
What’s the teacher doing?
Engage Activity
The teachers is walking around the
room watching the students create
models from the video and pausing
the video as necessary.



What are the students doing?
Engage Activity
The student are following the video and
creating models from the video and
coloring them onto their paper.
How do you model -5 x 2?
How do you model -2 x -5?
How do you model -2 x 5?
Page 11 of 17
Unit 4 – Operations with Integers – 6th grade

How do you model 5 x 2?
Explain/Explore Activity
Allow time for students to complete
the activity. Monitor and assess
student pairs to check for
understanding. Facilitate a class
discussion to debrief student
solutions.
 What generalizations can be
made about multiplying
integers? Answers may vary.
The product of two positive
integers is always positive; the
product of two negative
integers is always positive; the
product of a positive integer
and a negative integer is
always negative; etc.
Explain/Explore Activity
Students will complete the handout with
experimental practice and discover the
rules for multiplying integers. After the
conclusions have been made show
students the video for multiplying
integers.
Evaluate:
Students will complete an exit ticket and
work on homework.
Phase 9 Engage, Explore, Explain
Dividing Integers
etc.
Day 7 Activity:
Engage/Explore:
Facilitate a class discussion about using two-color counters to model division
problems. Instruct students to replicate the model with two-color counters, create a
sketch of the model with pictures of the two color counters or (–) and (+), and
record an equation to represent the model in their math journal.
Ask:
How would you model 8 positive counters in 4 groups? (I would separate 8
positive counters equally in 4 groups with 2 positive counters in each group.)
What equation would you record to represent this model? (8 ÷ 4 = 2)
What multiplication equation would you use to verify the quotient for 8 ÷ 4 =
2? (4 • 2 =8)
How would you model the equation 8 ÷ 2 = 4? (I would separate 8 positive
counters equally into 2 groups with 4 positive counters in each group.)
Page 12 of 17
Unit 4 – Operations with Integers – 6th grade
What multiplication equation would you use to verify the quotient for 8 ÷ 2 =
4? (2 • 4 =8)
How would you model 8 negative counters in 4 groups? (I would separate 8
negative counters equally in 4 groups with 2 negative counters in each group.)
What equation would you record to represent this model? ((−8) ÷ 4 = (−2))
What multiplication equation would you use to verify the quotient for (−8) ÷ 4
= (−2)? (4 • (−2) = (−8))
How would you model the expression (−8) ÷ 2? (I would separate 8 negative
counters equally into 2 groups with 4 negative counters in each group.)
What multiplication equation would you use to verify the quotient for (−8) ÷ 2
= (−4)? (2• (−4) = (−8))
How would you model the opposite of 8 positive counters in 4 groups? (I
would separate 8 positive counters equally into 4 groups with 2 positive counters
in each group and then flip the counters over to the negative side.)
Page 13 of 17
Unit 4 – Operations with Integers – 6th grade
What equation would you record to represent this model? (8 ÷ (−4) = (−2))
What multiplication equation would you use to verify the quotient for 8 ÷ (−4)
= (−2)? ((−4) • (−2) = 8)
How would you model the expression 8 ÷ (−2)? (I would separate 8 positive
counters equally into 2 groups with 4 positive counters in each group and then flip
the counters over to the negative side.)
What multiplication equation would you use to verify the quotient for 8 ÷ (−2)
= (−4)? ((−2) • (−4) = 8)
How would you model the opposite of 8 negative counters in 4 groups? (I
would separate 8 negative counters equally into 4 groups with 2 negative counters
in each group and then flip the counters over to the positive side.)
What equation would you record to represent this model? ((−8) ÷ (−4)= 2)
What multiplication equation would you use to verify the quotient for (−8) ÷
(−4) = 2? ((−4) • 2 = (−8))
How would you model the expression (−8) ÷ (−2)? (I would separate 8 negative
counters equally into 2 groups with 4 negative counters in each group and then flip
the counters over to the positive side.)
Page 14 of 17
Unit 4 – Operations with Integers – 6th grade
What multiplication equation would you use to verify the quotient for (−8) ÷
(−2) = 4? ((−2) • 4 = (−8))
Explain/Explore #1:
Instruct student pairs to complete problems on the Division of Integers handout.
Allow time for students to complete the activity. Monitor and assess student pairs
to check for understanding. Facilitate a class discussion to debrief student
solutions.
Ask:
What generalizations can be made about dividing integers? Answers may
vary. The quotient of two positive integers is always positive; the quotient of two
negative integers is always positive; the quotient of a positive integer and a
negative integer is always negative; etc.
Explain/Explore #2:
Once students have practiced with models they will complete the handout with
experimental practice and discover the rules for dividing integers. After the
conclusions have been made show students the video for dividing integers.
https://www.khanacademy.org/math/pre-algebra/negatives-absolute-value-prealg/mult-div-negatives-pre-alg/v/dividing-positive-and-negative-numbers
Students should complete the final part of their foldable.
Elaborate: Homework: Students will practice dividing integers with word problems.
Evaluate:
Exit Ticket: What generalization can be made about the product or quotient of
two or more integers with no negative signs or an even number of negative signs?
What generalization can be made about the product or quotient of two or more
integers with one negative sign or an odd number of negative signs?
What’s the teacher doing?
Engage Activity
Facilitate a class discussion about
using two-color counters to model
division problems.
What are the students doing?
Engage Activity
Students will replicate the model with
two-color counters, create a sketch of the
model with pictures of the two color
Page 15 of 17
Unit 4 – Operations with Integers – 6th grade
counters or (–) and (+), and record an
equation to represent the model in their
math journal.
Explain/Explore Activity
Allow time for students to complete
the activity. Monitor and assess
student pairs to check for
understanding. Facilitate a class
discussion to debrief student
solutions.

Explain/Explore Activity
Student will complete the discovery
worksheet to create rules for dividing
integers.
How are multiplication and
division related? Answers
may vary. They are inverse
operations; a multiplication
problem involves factor x factor
= product. A division problem
involves the product from a
multiplication problem
(dividend) divided by 1 of the
factors (divisor) which will equal
the other factor (quotient); etc.
Phase 10 Elaborate
Evaluate:
Students will complete an exit ticket and
work on homework.
Integers Operations
Day 8 Activity 1:
Elaborate 1:
Students apply integer rules to solve equations with more than 2 numbers and
real-life problem situations.
Place students in pairs and distribute handout: Extending Integers to each
student. Instruct student pairs to complete the handout. Allow time for students to
complete the activity. Monitor and assess student pairs to check for
understanding. Facilitate a class discussion to debrief student solutions.
Day 9 Activity 1:
Elaborate 2:
Handout (optional): Integer Practice may be used as additional practice, as
needed.
What’s the teacher doing?
Monitor and assess student pairs to
check for understanding. Facilitate a
class discussion to debrief student
solutions.
What are the students doing?
Students apply integer rules to solve
equations.
Phase 11 Evaluate
Integers Operations
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Unit 4 – Operations with Integers – 6th grade
Day 10 Activity:
Assess student understanding of related concepts and processes by using the
Performance
Indicator(s) aligned to this lesson.
What’s the teacher doing?
What are the students doing?
The teacher monitors students and
walks the room to ensure students are
on task.
Students are demonstrating their
knowledge by completing the
performance indicator.
Page 17 of 17