Digital Leadership
Math
Lesson Plan
Teacher:
Math Teacher
Lesson Title:
Leadership and Problem Solving
STRANDS
Grade:
6th Grade
The Number System
LESSON OVERVIEW
Summary of the task, challenge, investigation, career-related scenario, problem, or community link.
A good leader is also a good problem solver. Students will be exploring the Number System through problem solving. First, students will review the Mathematical
Practices as problem solving tools. An emphasis will be placed on the similarities of the Mathematical Practices and the Scientific Method. Students will also
communicate how they came to their answers through writing.
Next, students will begin their exploration of rational number operations. Students will investigate decimal operations. This will get students ready for the Ship the
Chip project. In this project, students will work through the Engineering Design Process to design a package in which to ship a potato chip. Students will be required to
calculate the cost of creating and shipping their potato chip package. This requires students to do the operations using rational numbers.
Finally, students will begin their investigation of LCM and GCF. Through this exploration, students will investigate the history of technology. Specifically, they will
research how much faster a computer is now than it was during various different periods of time.
MOTIVATOR
Hook for the week unit or supplemental resources used throughout the week. (PBL scenarios, video clips, websites,
literature)
Watch “Are You a Leader?” (See Resource Folder). This video is an inspirational video that illustrates that leaders can come from any walk of life. Students will discuss
the character traits of a good leader. Problem Solving is an essential trait of a good leader. Math’s contribution to leadership is problem solving. Students will use their
problem solving skills to create their shipping container for “Ship the Chip”.
DAY
1
Objectives
(I can….)
I can explain
the
mathematical
practices.
Materials &
Resources
Word
Problems (See
Resource
Folder)
Mathematical
Practice
Poster (See
Resource
Folder)
Rubric for
Problem
Solving (See
Resource
Folder)
Mathematical
Practices I Can
Statements
(See Resource
Folder)
Instructional Procedures
Leadership and Problem Solving
Differentiated
Instruction –
Remediation:
Peer Tutoring
Set:
Grouping
Teaching Strategy:
 Explain to the students that we are starting the leadership unit. Ask the
students to think about the qualities of a good leader. After giving them
some time to think, ask them to turn to their table and share their
thoughts with their table. Finally, we’ll discuss this as a whole group.
Mathematical
Practices Cubes
Essential Question: What are the mathematical practices? How do they assist me
in problem solving?


Pencil
If problem solving is not on the list of leader qualities generated by the
class, add that onto the list. Problem Solving is the ability to reason
through a problem and generate solutions to the problem. It’s not a skill
only found in Math. It’s a valuable skill to have in life.
Introduce the Mathematical Practices. Many of the students should
already know about the Mathematical Practices, but it’s good to review
them. Use the Mathematical Practice I Can Statements to help the
students make sense of the standards.
Ask students to compare and contracts the Mathematical Practices with
the Scientific Method. Discuss the similarities and the differences.
Mathematical
Practices Four
Corners (See
Resource
Folder)
Paper
Differentiated
Instruction
During this time, introduce the Mathematical Practices Four Corners
graphic organizer. This is a tool help them keep their work organized as
they are solving problems.

Give each table a complex word problem, such as Jane’s Aquarium. Have
them use the Four Corners organizer as they solve the problem. Ask that
the students work independently at first. When students have had
Prompting
Use of
Calculators
Use of an
Advanced
Organizer
Differentiated
Instruction –
Enrichment:
Use of the more
advanced Word
Problems.
Assessment
Formative
Assessments:
Observations
Questioning
Ticket Out the
Door
Think-Pair-Share
Materials for
Differentiated
Instruction –
Remediation:
Advanced
Organizer (See
Resource
Folder)
enough time to process the problem, ask the students to turn to their
neighbors and discuss what they have noticed.
Summarizing Strategy: Ticket Out the Door: What are the mathematical practices?
How do they assist me with problem solving?
Mathematical
Practices
Cubes (See
Resource
Folder)
Calculators
Materials for
Differentiated
Instruction –
Enrichment:
Use some of
the more
advanced
Word
Problems (See
Resource
Folder).
2
I can add,
subtract,
iPads
Essential Question: How do I add, subtract, multiply and decimals?
Differentiated
Instruction –
Formative
multiply, and
divide
decimals.
Create a list of
at least 30
expressions
that include
add,
subtracting,
multiplying,
and dividing
decimals.
Materials for
Differentiated
Instruction –
Remediation:
Expressions
with just 1
place past the
decimal or
only whole
numbers.
Decimal Operation Tournament
Set: Watch a Review on Operations with Decimals.
Teaching Strategy:


Materials for
Differentiated
Instruction –
Enrichment:
Word
Problems
involving
Decimal
Operations


Give students a multi-digit multiplication problem and a multi-digit division
problem. Both problems should include decimals. Have the students
work out the problems on their own. Once they have completed the
problems, ask the students to compare their results with their table
groups. If there is a disagreement, students are to re-work the problem
together. Ask for volunteers to AirPlay their work onto the television.
Explain to the students that we are going to be playing a game. The game
is called the Decimal Tournament. The game goes as follows:
a. The students will work as a table group. They will decide on the order
students will go. They must stay in that order. Only one person per
table will be asked to answer the question at a time. They will always
go in the pre-determined order.
b. Using your iPad, AirPlay a decimal problem. The students can begin
working as soon as the problem is displayed. The first team to raise
their hands, will get to AirPlay their work. The only answer that will
count will be from the student whose turn it currently is. If the team
that raises their hands gets it correct, they get 1 point. If they get it
wrong, they get -1 point.
c. All students should be working out all of the problems. In the event
that all of the groups do not answer the question correctly, the other
students will have an opportunity to answer it.
d. Continue the tournament until everyone has had a few turns.
Discuss any difficult problems as they arise. Ask probing questions to
assist students in understanding.
In order to hold students accountable for the tournament, collect the work
Remediation:
Think-Pair-Share
Grouping
Questioning
Prompting
Use of a
Calculator
Peer Tutoring
Limit the
number of
places after the
decimal place to
1 or return to
whole number
operations.
Differentiated
Instruction –
Enrichment:
Use word
problems during
the game
instead of
expressions.
Assessments:
Observations
Ticket Out the
Door
Student responses
to the game.
for all of the problems that we worked out during the game.
Summarizing Strategy:
Write a set of directions for adding and subtracting decimals, multiplying decimals,
and dividing decimals.
3
I can multiply
and divide
decimals.
Reasoning
about
Multiplication
and Division
and Place
Value
Materials for
Differentiated
Instruction –
Remediation:
Calculator
Materials for
Differentiated
Instruction –
Enrichment:
Reasoning
about
Multiplication
and Division
and Place
Value Part 2
(See Resource
Essential Question : How do I multiply and divide decimals?
Reasoning about Multiplication and Division and Place Value
Set: Watch: Solving a Problem, Make a Plan from The Teaching Channel.
Teaching Strategy:
1. Present the students with “Reasoning about Multiplication and Division
and Place Value”. Answer any questions the students may have. Allow
students to work independently, gathering their ideas on how to solve this
problem. After giving students adequate time to work on their own, have
them turn to their table and discuss ideas. Ask probing questions in order
to stimulate student thinking.
2. Have students work together to fill out the Four Corner graphic organizer
(See Resource Folder) for this problem. When they complete the problem,
each person in the group will use the rubric (See Resource Folder) and the
“I Can Statements” (See Resource Folder) to evaluate the end product.
3. After students have answered the questions on this task as a group, ask
each student to recreate this problem on their own with different
numbers. Students are to write their new problem out on a piece of paper.
(Students are to answer their own questions on another sheet of paper.
These will be stapled together at the end of class to be turned in.)
4. Ask students to exchange papers with another student and they will
workout the problems of the other student.
Summarizing Strategy: Ticket Out the Door: Turn in the problems you made and
the answers to your questions. Please explain your reasoning to your questions.
Differentiated
Instruction –
Remediation:
Think-PairShare
Grouping
Formative
Assessments:
Observations
Questioning
Ticket Out the
Door
Think-Pair-Share
Questioning
Prompting
Use of a
Calculator
Peer Tutoring
Differentiated
Instruction –
Enrichment:
Reasoning
about
Multiplication
and Division
and Place Value
Part 2 (See
Resource
Performance
Assessment:
Student response
to task.
Folder)
Folder)
4
Project Day 1 – refer to Unit Plan
Topic – “Ship the Chip”- Leadership
5
Project Day 2 – refer to Unit Plan
Topic – “Ship the Chip”- Leadership
6
I can find the
GCF of two
Materials for
Differentiated
Essential Question: How do I find the GCF of two whole numbers less than or
equal to 100?
Differentiated
Instruction –
Formative
whole
numbers less
than or equal
to 100.
Instruction –
Remediation:
Calculator
Materials for
Differentiated
Instruction –
Enrichment:
GCF with
Algebraic
Expressions
Set: Watch this video on Finding GCF Using the Ladder Method.
Teaching Strategy:
 Ask students to define the word factor. Let them think about it for a short
time. Then let them pair with their tablemates, and then ask for a
volunteer to share the definition of factor.
 Next asked students what the Greatest Common Factor is. Discuss the
definition. Ask them what the Greatest Common Divisor is. This is sort of
a trick question because GCF and GCD are actually the same thing.
 Pass out paper to do a foldable. We will be doing a shutter fold with 4
flaps. We will only be working with the top two flaps. The bottom two
flaps will be filled in a later lesson. Ask the students to label the top left
flap as GCF List Method.
 Inside the flap, ask the students to copy down an example as you teach
them how to do the list method of finding the GCF of two numbers.
a. GCF (12, 18).
b. List all of the factors of 12. (1,2,3,4,6,12)
c. List all of the factors of 18. (1,2,3,6,9,18).
d. Find the greatest factor they have in common. In this case, it’s 6.
 Continue to give students examples. First model for the students, then
guide the students, then allow the students work collaboratively, then ask
the students to work independently.
 Ask the students to write GCF Ladder Method on the top right flap.
 Inside the flap, ask students to copy down an example as you teach them
how to do the ladder method of finding the GCF of two numbers.
a. GCF (24, 36)
b. Write the numbers inside an upside down division box as shown
below:
c. Ask the students to identify a number that is a factor of both. For
example, let’s say a student identifies the factor of 4 that divides into
Remediation:
Think-PairShare
Grouping
Questioning
Prompting
Use of a
Calculator
Peer Tutoring
Differentiated
Instruction –
Enrichment:
GCF with
Algebraic
Expressions
Assessments:
Observations
Questioning
Ticket Out the
Door
Think-Pair-Share
Foldable
both evenly. Record the 4 on the outside of the box, and record the
quotients below as shown:
d.
Ask the students to identify a factor of both 6 & 9. A student might
say that 3 is a factor of both 6 & 9. Record the 3 and the quotients as
shown.
e. Ask the students if there is a common factor for both 2 & 3. Once the
class agrees that there is not one (other than 1), inform the class that
we have reached the endpoint. The GCF can be found by multiplying
the numbers on the left hand side, as shown below:
f.

7
I can find the
LCM of any
Materials for
Differentiated
By multiplying 4 x 3, we find that the GCF of 24 & 36 is 12. This
method works regardless of the numbers chosen by the students. For
example, you could have started with a 2 as a common factor rather
than 4, and the result would have been the same.
Continue to give students examples. First model for the students, then
guide the students, then allow the students work collaboratively, then ask
the students to work independently.
Summarizing Strategy:
Have the students write a paragraph explaining what a GCF is, and describe a
method to find the GCF of a pair of numbers. Provide them with an example as a
guide.
Essential Question: How do I find the LCM of any two whole numbers less than or
equal to 12?
Differentiated
Formative
two whole
numbers less
than or equal
to 12.
Instruction –
Remediation:
Calculator
Materials for
Differentiated
Instruction –
Enrichment:
LCM and
Algebraic
Expressions
Set: Kiara baked 30 oatmeal cookies and 48 chocolate chip cookies to package in
plastic containers for her friends at school. She wants to divide the cookies into
identical containers so that each container has the same number of each kind of
cookie. If she wants each container to have the greatest number of cookies
possible, how many plastic containers does she need?
Have students collaborate to find the answer. Discuss what students found. This
will serve as a review of GCF.
Teaching Strategy:
1. Review with the students the term “Multiple”. How is it different than
“Factor” (since the two terms are often confused)? . Let them think about
it for a short time. Then let them pair with their tablemates, and then ask
for a volunteer to share the definition of factor.
2. Next asked students what the Least Common Multiple is. Discuss the
definition.
3. Ask students to pull out their foldables from the previous day.
4. Have students label the bottom left flap as LCM List Method. Inside of the
flap, have students copy down an example as you teach them how to find
the LCM of two numbers.
a. LCM (4, 12)
b. List all of the multiples of 4: 4, 8, 12, 16, 20, 24, 28…
c. List all of the multiples of 12: 12, 24, 36…
d. The least number the two have in common is the least common
multiple.
5. Continue to give students examples. First model for the students, then
guide the students, then allow the students work collaboratively, then ask
the students to work independently.
6. Ask the students to write LCM Ladder Method on the bottom right flap.
7. Inside the flap, ask students to copy down an example as you teach them
how to do the ladder method of finding the LCM of two numbers.
8. This is done the same way as listed in GCF, expect when we finish, we
multiply all of the numbers listed on the outside of the ladder. For
example:
Instruction –
Remediation:
Think-PairShare
Grouping
Questioning
Prompting
Use of a
Calculator
Peer Tutoring
Differentiated
Instruction –
Enrichment:
LCM and
Algebraic
Expressions
Assessments:
Observations
Questioning
Ticket Out the
Door
Think-Pair-Share
Foldable
LCM (24, 36) = 4 × 3 × 2 × 3 = 72
9. Continue to give students examples. First model for the students, then
guide the students, then allow the students work collaboratively, then ask
the students to work independently.
Summarizing Strategy:
Have the students write a paragraph explaining what a LCM is, and describe a
method to find the LCM of a pair of numbers. Provide them with an example as a
guide.
8
I can use GCF
and LCM to
solve a
problem.
Bake Sale (See
Resource
Folder)
Materials for
Differentiated
Instruction –
Remediation:
Calculator
Materials for
Differentiated
Instruction –
Enrichment:
Essential Question: How can I use GCF and LCM to solve problems?
Think-PairShare
Formative
Assessments:
Bake Sale Task
Working with a
group.
Observations
Questioning
Ticket Out the
Door
Think-Pair-Share
Set: Review GCF and LCM Using the Ladder Method Video (See Resource Folder).
Questioning
Teaching Strategy: Present the students with “Bake Sale” (See Resource Folder).
Give the students some time to read through and understand the question.
Answer any questions the students have about the problem. Allow students to
work independently. After giving students adequate time to being the problem on
their own, ask students to talk with their table groups to see what they have
discovered.
Differentiated
Instruction –
Remediation:
Use a calculator
Have students work together to fill out the Four Corner graphic organizer (See
Resource Folder) for this problem. When they complete the problem, each person
Differentiated
Performance Task:
Student response
to the task.
Ask students
to come up
with their
own LCM and
GCF
problems.
in the group will use the rubric (See Resource Folder) and the “I Can Statements”
(See Resource Folder) to evaluate the end product.
Instruction –
Enrichment:
Summarizing Strategy: Ticket Out the Door: How did your knowledge of GCF and
LCM help you solve this problem?
Ask students to
come up with
their own LCM
and GCF
problems.
9
Project Day 3 – refer to Unit Plan
Topic – “Ship the Chip”- Leadership
10
Project Day 4– refer to Unit Plan
Topic – “Glogster Reflection”- Leadership
1.
STANDARDS
Identify what you want to teach. Reference State, Common Core, ACT
College Readiness Standards and/or State Competencies.
6.NS.2 Fluently divide multi-digit numbers using the standard algorithm.
6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
6.NS.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12.
Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common
factor. For example, express 36 + 8 as 4 (9 + 2).