Leadership
2 Weeks
Math
Lesson Plan
Teacher: Math Teacher
Lesson Title: Leadership and Problem Solving
Grade: STEM Math IA
STRANDS
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. First, they will research the properties. Next, they investigate the algorithms of adding and
subtracting integers. Both of these 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 Multiplying and Dividing Integers. 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?” . 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
Objectives
Materials &
Resources
Instructional Procedures
Differentiated
Instruction
Assessment
(I can….)
1
I can explain
the
mathematical
practices.
I can use the
mathematical
practices to
help me solve
problems.
See Resource
Folder for the
following:
Word
Problems
Mathematical
Practice
Poster
Rubric for
Problem
Solving
Mathematical
Practices I
Can
Statements
Mathematical
Practices Four
Corners
Paper
Pencil
Materials for
Differentiated
Instruction –
Remediation:
Advanced
Organizer
Essential Question:
1. What are the mathematical practices?
2. How do I use them to help me solve problems?
Leadership and Problem Solving
Differentiated
Instruction –
Remediation:
Peer Tutoring
Set: 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 Grouping
to think, ask them to turn to their table and share their thoughts with their table.
Mathematical
Finally, we’ll discuss this as a whole group.
Practices Cubes
Teaching Strategy:
1. If problem solving is not on the list of leader qualities generated by the
Prompting
class, add that onto the list. Problem Solving is the ability to reason
during group
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.
work
2. 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.
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.
3. Give each table a complex word problem, such as The Checker Board
Problem (see Word Problems in resource folders). Have them use the Four
Corners organizer as they solve the problem. Ask that the students work
independently at first. When students have had enough time to process
the problem, ask the students to turn to their neighbors and discuss what
they have noticed.
Use of
Calculators
Use of an
Advanced
Organizer
Differentiated
Instruction –
Enrichment:
Use of the more
advanced word
problems.
Formative
Assessments:
Observations
Questioning
Ticket Out the
Door
Think-Pair-Share
Student response
to word problem.
Mathematical
Practices
Cubes
Summarizing Strategy: Ticket Out the Door: What are the mathematical practices?
How do they assist me with problem solving?
Calculators
Materials for
Differentiated
Instruction –
Enrichment:
Use some of
the more
advanced
word
problems.
2
I can simplify
expressions
using the
properties.
iPad
Essential Question: How to do simplify expressions using the properties?
"Math
Properties”
Math Properties
Set: Have students watch this video titled “"Math Properties" on TeacherTube.
Materials for
Differentiated Teaching Strategy:
Instruction –
 Ask students if they have heard of the properties we have in Math. Assign
Remediation:
table groups to research and teach the class about one of the following
Foldable (See
properties: Commutative Property of Addition, Commutative Property of
Resource
Multiplication, Associative Property of Addition, Associative Property of
Folder)
Multiplication, Identify Property of Addition, and the Identity Property of
Multiplication. Give groups 5 minutes to research and 5 minutes to come
Calculators
up with their presentation. Their presentation must include an example of
their property.
Materials for

Students will present. While students are not presenting, they are to take
Differentiated
notes. A foldable is available for students who need extra support. Ask
Instruction –
probing questions to enrich the students’ presentations.
Enrichment:

Show students examples of properties. Ask them to identify the property.
Simplifying
Algebraic
 After the presentations are over, ask students to multiply 12x24 in their
Expressions
head. Use these student answers to describe the distributive property.
Differentiated
Instruction –
Remediation:
Peer Tutoring
Formative
Assessments:
Grouping
Questioning
Prompting
Ticket Out the
Door
Use of
Calculators
Think-Pair-Share
Use of a
foldable
Foldable
Differentiated
Instruction –
Enrichment:
Simplifying
Algebraic
Observations
with the
Distributive
Property.
This problem can be done two ways.
12 × 24 = 12(20 + 4) = 12(20) + 12(4) = 240 + 48 = 288
or
12 × 24 = (10 + 2)24 = 24(10) + 24(2) = 240 + 48 = 288


After giving these two examples to the students, ask them what they
notice about the two methods. Ask them if they can describe the
distributive property.
Give the students some more examples of the distributive property. Ask
the students to simplify the expression using the distributive property.
Model a few examples for the students. Guide the students through some
examples. Allow the students to work collaboratively through some
examples. Finally, ask students to work independently through some
examples. The examples can include:
a. 15 × 34
b. 112 × 14
c. 125 × 28
d. Katelyn’s ballet class is performing a spring recital for which they need
3
butterfly costumes. Each fairy costume is made from 6 yards of fabric. Use
4
the Distributive Property to find the number of yards of fabric needed for 7
costumes. (Hint: a mixed number can be written as the sum of an integer and a
fraction.)
e. During a math facts speed contest, Jacob calculated the following
expression faster than anyone else in his class.
196 × 9
When classmates asked him how he was able to answer so quickly, he told
them he used the Distributive Property to think of the problem differently.
Write and evaluate an expression using the Distributive Property that would
help Jacob perform the calculation quickly.
Summarizing Strategy:
Expressions
with the
Distributive
Property.
Ask students to create their own multiplication problem and to use the distributive
property to simplify the expression
3
I can add
integers.
Two Color
Counters
Essential Question: How do I add integers?
Formative
Assessment:
Adding Integers
Differentiated
Instruction –
Remediation:
Peer Tutoring
Paper for
Foldable
Set: Watch the Khan Academy video on Absolute Value.
Grouping
Questioning
Prompting
Ticket Out the
Door
Use of
Calculators
Foldable
Rulers
Teaching Strategy:
Khan
 Pass out the paper to make a foldable. The students will be making a
Academy
shutter fold with four flaps. (For directions, please visit this website.) This
foldable will be used for a few days. The first flap is labeled with “Addition
video
with Like Signs”. The second is labeled with “Additional with Unlike Signs”.
The third is Subtraction. The last is for multiplication and division. Have
Materials for
students put the foldable to the side.
Differentiated
Instruction –
Remediation:
 Review with the students the concept of a zero pair. A zero pair is 1
positive and 1 negative combined creates zero. Make any clarifications
Calculators
that need to be made. Next, explain to the students how to use the
colored tiles (yellow is positive and red is negative).
Materials for
Differentiated
 Model adding with like signs for the students. Start out by modeling
Instruction –
positive addition, because this is something familiar for the students. Next,
Enrichment:
move on to negative numbers. Have the students model problems for
Adding
each other and for the class. The examples can include -1+-5, -2+-7, -4+-6.
When students have discovered the algorithm, have them write it in their
positive and
own words in the foldable. Also have students draw a picture to explain
negative
the algorithm.
Decimals.

After everyone understands the algorithm for adding like signs, move on to
Observations
Student created
examples
Differentiated
Instruction –
Enrichment:
Adding positive
and negative
Decimals.
unlike signs. Model problems for the students. These examples can
include -2+5, -7+3, 8+(-3), and 6+(-4). Have table groups create problems
for each other. Encourage conversations about what they are observing at
the tables. When students have discovered the algorithm, have them
write it in their own words in the foldable. Also have students draw a
picture to explain the algorithm.
Summarizing Strategy:
Students will write a Dear Teacher letter (See Resource Folder). This note will
include what they already know about integers, what they liked/disliked, and what
they are unclear about integers.
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 subtract
integers.
Subtracting
Integers
Two Color
Counters
Paper for
Foldable
Rulers
Essential Question: How do I subtract integers?
Differentiated
Instruction –
Remediation:
Peer Tutoring
Formative
Assessment:
Grouping
Questioning
Prompting
Ticket Out the
Door
Observations
Use of
Foldable
Materials for Subtracting Integers
Differentiated
Instruction –
Set: Watch this video on Subtracting Integers video.
Remediation:
Teaching Strategy:
Calculators
 Review with the students how to add using the two-color counters.
Mind Map
 Model subtraction with the students using the two color counters. Start
Flow Chart
out by subtracting with like signs, because this is familiar to the students.
These examples can include 5-2, 7-3, 3-5.
Materials for
 Next move on to negative numbers. Have students model problems for
Differentiated
each other and for the class. When students have discovered the
Instruction –
algorithm, have them write it in their own words in their own words in
Enrichment:
their foldable. Also have students draw a picture to explain the algorithm.
Adding
 If needed, model subtraction on a number line for the students as well.
positive and
Continue doing examples until all students can explain how to subtract
with integers. Have students work with their table groups.
negative
Summarizing Strategy: Write the directions to subtracting integers. Please include
Decimals.
examples in your explanation.
7
I can add and
subtract
integers.
ProblemSolving Rubric
Essential Question: How do I add and subtract integers?
Calculators
Mind Map
Flow Chart
Differentiated
Instruction –
Enrichment:
Adding positive
and negative
Decimals.
Differentiated
Instruction –
Remediation:
Positive or Negative Task
Positive or
Peer Tutoring
Negative
Set: Watch this video on Adding and Subtracting Integers.
Grouping
Prompting
Materials for
Teaching Strategy: Present the students with the “Positive or Negative” task.
Use of
Differentiated
Work through the task on his/her own. Encourage students to show as much detail
Calculators
Instruction –
in their problem solving. They may use the Four Corner organizer used on Day 1 of
Remediation:
Mind Map
this unit.
Flow Chart
Calculators
As student finish, pair the students up and ask them to critique each others’ work
Mind Map
using the problem-solving rubric. In addition, students should tell each other at
Differentiated
Flow Chart
least two things they liked about how the other students did the problem. When
Instruction –
they are done, they should thank each other.
Enrichment:
Materials for
Differentiated
Summarizing Strategy: Give the students an exit ticket that includes addition and
Adding and
Instruction –
subtraction of integer problems.
Subtracting
Enrichment:
Formative
Assessment:
Observations
Questioning
Ticket Out the
Door
Think-Pair-Share
Summative
Assessment:
Student Answers
to the Task.
Adding and
Subtracting
positive and
negative
fractions.
8
I can multiply
and divide
integers.
VCR or DVD
player
Video
Foldable
positive and
negative
fractions.
Essential Question: How do I multiply and divide integers?
Multiplying and Dividing Integers
Set: Play a fun and appropriate movie clip. Fast forward the clip and rewind the
clip at different speeds for comedic effect.
Teaching Strategy:
 Have students take out their foldable from last week. Review with them
what they learned last week.
Calculators
 Ask students to imagine a person who was walking (forward) at 2 steps per
Mind Map
second was videotaped. Have a student demonstrate this by walking
Flow Chart
across the front of the classroom for all students to see. We are now
pretending that we are watching the videotape.
Materials for
 If we pressed the forward button on the VCR and suppose that the forward
Differentiated
button speeds up the tape 3 times as fast as normal playing, how fast
Instruction –
would the person be walking/running now? (You can have someone
Enrichment:
demonstrate this, too.) The students will answer 6 steps per second. Write
Multiplying
down the multiplication example used to solve this problem: 2 x 3 = 6.
 If we pressed the rewind button on the VCR and suppose that the rewind
Decimals
button speeds up the tape twice as fast as normal playing as it runs
Multiplying
backwards, how fast would the person be walking/running now? The
students will answer 4 steps per second. Next, ask the students if the
and Dividing
person is running in the same direction? The answer is no; the person is
Fractions
running backwards now so we must use a negative sign in our answer to
indicate that the direction has changed. So the answer is –4. Write down
the multiplication example used to solve this problem: 2 x (-2) = -4.
 Suppose that the person who was videotaped was originally walking
backwards at 2 steps per second. Have a student demonstrate this by
walking backwards across the front of the classroom.
 If we pressed the forward button on the VCR and suppose that the forward
button speeds up the tape 3 times as fast as normal playing, how fast
Instruction –
Remediation:
Differentiated
Instruction –
Remediation:
Peer Tutoring
Grouping
Prompting
Use of
Calculators
Mind Map
Flow Chart
Differentiated
Instruction –
Enrichment:
Adding and
Subtracting
positive and
negative
fractions.
Formative
Assessment:
Observations
Questioning
Ticket Out the
Door
Think-Pair-Share



would the person be walking/running now and in what direction would
they be walking/running? The students will answer 6 steps per second
backwards.
Write down the multiplication example used to solve this problem
reminding the students that backwards must be indicated by writing a
negative sign with the number: -2 x 3 = (-6).
If we pressed the rewind button on the VCR and suppose that the rewind
button speeds up the tape twice as fast as normal playing as it runs
backwards, how fast would the person be walking/running now? The
students will answer 4 steps per second. Next, ask the students if the
person is running in the same direction? The answer is no; the person who
was running backwards has reversed and is now running forward. So the
answer is 4. Write down the multiplication example used to solve this
problem: -2 x (-2) = 4.
Have students turn to their table and discuss what this means. Have
students construct meaning of multiplying and dividing integers through
this. If there are students that need extra examples, use patterns in
function tables to show them the pattern. Once students have discovered
the algorithm, have them write it in their own word in their foldable and
draw a picture to explain the algorithm.
Summarizing Strategy: Ticket Out the Door: How do you, in your own words,
multiply and divide integers?
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
STANDARDS
Identify what you want to teach. Reference State, Common Core, ACT
College Readiness Standards and/or State Competencies.
1. 7.NS.1.d. Apply properties of operations as strategies to add and subtract rational numbers.
2. 7.NS.2.c. Apply properties of operations as strategies to multiply and divide rational numbers.
3. 7.NS.3. Solve real-world and mathematical problems involving the four operations with rational numbers.