Modern Living
Two Weeks
Math
Lesson Plan
Teacher: 6th Grade Teacher
Grade: STEM Math IA
Lesson Title: Holiday Traditions and Geometry
STRANDS
The Number System and Geometry
LESSON OVERVIEW
Summary of the task, challenge, investigation, career-related scenario, problem, or community link.
During this unit, as students are exploring the costumes and traditions of communities around the world in Social Studies, they will be looking at the communities of
numbers we have in Math. We will be discovering the Real Number System. Students will juxtapose irrational numbers and rational numbers, and will investigate how to
estimate irrational numbers. Finally, students will be applying their irrational number knowledge through discovering the Pythagorean Theorem. A connect with Science
will be created through incorporating the use of the Pythagorean Theorem when creating electrical circuits. Students will be expected to reflect in written form through
the entire unit.
MOTIVATOR
Hook for the week unit or supplemental resources used throughout the week. (PBL scenarios, video clips, websites, literature)
As our unit is looking at holiday traditions of different countries, students will watch a video on how to make a holiday wreath using two-dimensional geometric figures.
This video is titled DIY Geometric Wreath (see Resource Folder). This video will allow students to see the connection between our holidays and Geometry.
DA
Y
1
Objectives
(I can….)
Materials &
Resources
Instructional Procedures
Differentiated
Instruction
Assessment
Project Day 1 – refer to Unit Plan
Topic – Gallery Walk
2
I can square
a number.
I can find
the square
root of a
number.
I can apply
squares and
square roots
to real
world
problems.
Internet
TV or Smart
Board for
display
“Square
Numbers”
video
“Square Roots
Video”
“Think I’m
Square
Squares and
Square Roots”
video
“Understandin
g the
Exponent 2”
activity page
“Perfect
Squares and
Essential Question: How can I square a number? How can I find the square root of a number?
How can I apply squares and square roots to real world problems?
Perfect Squares and Square Roots
Set: Show “Square Numbers,” “Square Roots Video,” and/or “Think I’m Square Squares and
Square Roots” to promote interest in the lesson and introduce the topic.
Teaching Strategy: Ask students to complete “Understanding the Exponent 2.” Discuss answers
and mend students’ understanding as necessary. Use “Perfect Squares and Square Roots Notes”
to guide the lesson. Get students up and moving in the “Squares and Square Roots Ball Toss.”
With answers fresh on their minds, students should complete “Memory Work for Squares and
Square Roots.”
Summarizing Strategy: Ask students for an exit ticket explaining why the word “square” is used
to describe this type of math. Students should also list all of the perfect squares that they
already have memorized.
“Perimeter Area Squares Square Roots” will be assigned for homework.
Differentiated
Instruction –
Remediation:
Students will
use “Perfect
Squares and
Square Roots
Notes” and
“Memory Work
for Squares and
Square Roots”
as needed.
Differentiated
Instruction –
Enrichment:
Try to add two
prime numbers
to obtain the
perfect squares
between 4 and
50.
Formative
Assessment:
“Understandi
ng the
Exponent 2”
Performance
Assessment:
“Squares and
Square Roots
Ball Toss”
Summative
Assessment:
“Perimeter
Area Squares
Square
Roots”
Square Roots
Notes”
“Squares and
Square Roots
Ball Toss”
instructions
“Koosh” ball
Materials for
Differentiated
Instruction –
Remediation:
“Memory
Work for
Squares and
Square Roots”
3
I can use
rational
expressions
of irrational
numbers to
compare
the size of
irrational
numbers,
locate them
approximat
ely on a
number line
“Perfect
Squares and
Square Roots
Notes”
Internet
TV or Smart
Board for
display
“Square Roots
Approximatio
n Lesson
Activity.”
“Estimating
Square Roots
Notes”
“Square Roots
Essential Question: How can I use rational expressions of irrational numbers to compare the size Differentiated
Instruction –
of irrational numbers, locate them approximately on a number line diagram, and estimate the
Remediation:
value of expressions?
Students
should visit
Estimating Square Roots
http://www.m
Set: Show Art Benjamin video “Lightning Calculation and other Mathemagic “ to inspire students athisfun.com/s
quarewhen they see that the human brain is capable of squaring numbers more quickly than a
root.html to
calculator!
learn a trick for
estimating the
Teaching Strategy: Ask students to complete “Square Roots Approximation Lesson Activity.”
Discuss and correct as necessary. Use “Estimating Square Roots Notes” to guide the instruction. square root of
imperfect
Get students involved in “I Have Who Has Activity.” For initial practice students will complete
“Match Square Root Approximation to Number Line.” Teacher will ask a few students to explain squares.
their answer choices upon completion of the matching activity. To connect this lesson to
Formative
Assessment:
“Square
Roots
Approximatio
n Lesson
Activity”
“Imperfect
Square
Approximatio
n”
Performance
Assessment:
“I Have Who
diagram,
and
estimate the
value of
expressions.
Approximatio
n Assignment”
previous standards, teacher will ask students to explain which types of numbers have rational
square roots and which have irrational square roots.
Materials for
Differentiated
Instruction –
Remediation:
Summarizing Strategy: Students will complete the exit ticket “Imperfect Square
Approximation.”
“Square Roots Approximation Assignment” will be assigned for homework.
Internet
Materials for
Differentiated
Instruction –
Enrichment:
Internet
4
I can
determine if
a number is
rational or
irrational.
6 different
colors of
construction
paper
Scissors
Essential Question: How do I determine which number set a number belongs to?
Rational vs. Irrational
Set: Show the students this comic.
Differentiated
Instruction –
Enrichment:
Students
should visit
http://www.ixl.
com/math/gra
de-8/evaluatevariableexpressionsinvolvingsquares-andsquare-roots to
be challenged
with variables.
Has Activity.”
Differentiated
Instruction –
Remediation:
Formative
Assessment:
Foldable
Prompting
Ticket Out
the Door
Summative
Assessment:
“Square
Roots
Approximatio
n
Assignment”
Grouping
Glue
Graphic
Organizer (See
Resource
Folder)
Markers
Materials for
Differentiated
Instruction –
Remediation:
Graphic
Organizer (See
Resource File)
Teaching Strategy:
Create a “Types of Numbers” foldable. This will summarize all the types of numbers into one
neat book. Here are the steps for the foldable.
Differentiated
Instruction –
Enrichment:
Have students
discover how
Informal
Observations
Responses to
questions.
Summative
Assessment:
Homework
Materials for
Differentiated
Instruction –
Enrichment:
Have students
discover how
to write a
repeating
decimal as a
fraction.
1. Using 1/8 of piece of construction paper, make a small book. On the outside cover, title
it “Whole Numbers”. Inside of the book, have students write the definition of whole
numbers and draw a number line illustrating the whole numbers.
2. Using ¼ of a piece of construction paper, make a small book. On the outside cover, title
it “Integers”. Inside of the book, have students write the definition of integers and draw
a number line illustrating the integers. Leave space to glue the whole number booklet
inside of the integers, because the Whole Numbers are part of the Integer Set.
3. Using ½ of a piece of construction paper, make a small book. On the outside cover, title
it “Rational Numbers”. Inside of the book, have students write the definition of rational
numbers and show some examples of positive and negative rational numbers. Leave
space to glue in the Integer booklet, because the integers are part of the rational
numbers.
4. Using a ½ sheet of construction paper, make a small book. On the outside cover, title it
“Irrational Numbers”. On the inside of the booklet, define irrational numbers and give
some examples. Nothing will be glued inside of this booklet.
5. Using a whole sheet of construction paper, make a small book. On the outside cover,
title it “The Real Number System”. On the inside of the booklet, define the Real Number
System and glue both the Irrational and the Rational booklets.
6. To use this foldable, students start with all of the rational number booklets open. When
they are given a number, for example -10.5, they start with innermost booklet. Students
will ask themselves, is -10.5 a whole number? The answer is no. They close the booklet.
Next, is -10.5 an integer? The answer is no. They close the booklet. Is -10.5 a rational
number? The answer is yes. Since Rational and Real Number are the open booklets, 10.5 is Rational and Real.
2
12
−15
7. Further examples that can be use are -6, , -0.44444444444…, 𝜋, , and
3
4
5
8. Allow students to create examples for each other within their groups.
Summarizing Strategy: Writing. Create an analogy in the following format –
LIGHT:DARK::WHITE:BLACK that compares the relationship between two sets of numbers to a
relationship between two things in the students' lives. Then write a short paragraph to explain
the analogy.
Practice problems will be assigned for homework.
to write a
repeating
decimal as a
fraction.
5
I can know
and apply
the
properties
of integer
exponents
to generate
equivalent
numerical
expressions.
“Exponent
Rule Opening
Activity”
Essential Question: How do I apply the properties of integer exponents to generate equivalent
numerical expressions?
“Exponent
Rules Notes”
Set:
Begin by showing students the “Exponent Rule Opening Activity”. Have students try to name
each piece of the expressions. Have students share their answers and discuss which labels they
think are correct. Make sure the students understand which answers are correct, and continue
to use that terminology throughout the lesson.
“Exponent
Rules Group
Work”
“Exponent
Rules Graphic
Organizer”
“Exponent
Rules
Homework”
Materials for
Differentiated
Instruction –
Remediation:
“Need More
Support Group
Work”
Exponent Rules
Teaching Strategy:
Students will look at the “Exponents Rules Notes”. This will also be projected for the class to see.
The teacher will go through each rule, having the students fill in the blanks with the appropriate
formulas. This will also give the chance to show students several examples of each type of rule.
After the students have gone through the notes with the teacher, the students will be placed in
heterogeneous group of 3-4. They will then work together to complete several different types of
exponent mathematics problems using the “Exponent Rules Group Activity.”
Summarizing Strategy:
As a summarizing strategy, have the students fill out the Exponent Rules Graphic Organizer. Let
students share and discuss what they have put in the graphic organizer. Make sure that these
answers are correct, and the students understand the difference between the rules.
Practice problems will be assigned for homework.
Differentiated
Instruction –
Enrichment:
Differentiated
Instruction –
Remediation:
Peer Tutoring
Heterogeneous
Grouping
“Need More
Support Group
Work” will be
available for
students in
need of
remediation
Differentiated
Instruction –
Enrichment:
Peer Tutoring
Heterogeneous
Grouping
“Need More
Challenge
Group Work”
will be
available for
students in
need of
enrichment
Formative
Assessment:
Teacher
observations
of opening
activity
Performance
Assessment:
“Exponent
Rules Group
Activity”
finished
product
Summative
Assessment:
Exit Ticket
“Need More
Challenge
Group Work”
6
I can use
square root
“Square Root
Property
Essential Question:
1. How can I use square root and cube root symbols to represent solutions to equations of
Differentiated
Instruction –
Formative
Assessment:
and cube
root
symbols to
represent
solutions to
equations of
the form
2
x =p, where
p is a
positive
rational
number.
I can
evaluate
square roots
of small
perfect
squares.
Opening
Activity”
2
the form x =p, where p is a positive rational number?
2. How can I evaluate square roots of small perfect squares?
Solving Equations with 𝒙𝟐
Set:
Begin the by having the students complete the “Square Root Property Opening Activity.” This will
ask students square several different numbers. Students will begin to see that there is a pattern.
Opposite numbers have an equivalent square. Have students discuss how this is happening, and
if the pattern will hold true for all integers and their opposites. This will also be a great
opportunity to show the students why the calculator does not always give the correct answer if
you do not put your negative values in correctly.
Teaching Strategy:
After students have discovered that each integer and it’s opposite have equivalent squares, then
show the students the Square Root Property:
• Square Root Property: If c is a positive number and if x2 = c, then x =√c or x =-√c.
(This can be
written as one answer as ±√c.)
Walk students through each of the steps to solving using the square root property.
1. Isolate the variable on one side of the equation.
2. Take the square roots of both sides
3. Square root property says you will have a positive and negative root as a solution.
Go through several examples with the students so they have see different scenarios that could
come up.
1. x2=25
2. x2 +10 =14
3. x2 -5 =76
4. 3x2= 108
5. 2x2 +13 = 213
Have students go to this website and see how much money (fake) they can win by finding square
roots!
Summarizing Strategy:
Remediation:
For students in
need of
remediation,
the website
allows students
to have
multiple
choices when
answering
questions, let
them know
when they
have made a
mistake and
allow them to
work at their
own pace.
Differentiated
Instruction –
Enrichment:
For students in
need of
enrichment,
this website
challenges
their
knowledge and
allows students
to move at
their own pace.
This gives them
the ability to
deepen their
understanding.
Teacher
observations
of opening
activity
Performance
Assessment:
Final product
from class
examples
Summative
Assessment:
Exit ticket
As an exit ticket, have students answer:
1. How many solutions will you get when you take the square root of a number? Why?
2. Name a profession in which square roots are often used.
7
I can
Station 1: (See
describe the Resource
Pythagorean Folder)
Theorem.
Station 2: (See
Resource
Folder)
Station 3: (See
Resource
Folder)
Graph Paper
Scissors
Essential Question: What is the Pythagorean Theorem?
Task Proving the Pythagorean Theorem
Set: Have a word splash on the board that includes the following words: right triangle, right
angle, leg of a triangle, and hypotenuse. Ask students to discuss these words with their table
groups.
Teaching Strategy:
Explain to the students that we are going to be doing Math Stations today. Go over student
behavior expectations as we go through each of the stations. There are three stations. The
stations are described below. Depending on how big your classes are, you may need to have
more than one station for each activity. Students should be in groups of 2-4, with the best size
being 3. Each of the stations will lead the students to discovering the Pythagorean Theorem.
Square Tiles
Station 1: Have students do Example 1 (See Resource File). Students are cutting paper to prove
that the area of Square A and Square B are equal to Square C.
Materials for
Differentiated
Instruction –
Remediation:
Station 2: Have students do Example 2 (See Resource File). Students are cutting paper to prove
that the area of Square A and Square B are equal to Square C.
Calculator
Materials for
Differentiated
Instruction –
Enrichment:
What’s Your
Angle,
Pythagoras?
By Judy Ellis
Station 3: Students will discover Pythagorean Triples. (See Resource File).
Bring the students back together to discuss what they discovered as they went through the
stations.
Summarizing Strategy: Ticket Out the Door: What was the most important thing that you
learned from today’s station?
Practice problems will be assigned for homework.
Differentiated
Instruction –
Remediation:
Grouping
Prompting
Formative
Assessment:
Station
Activities
Ticket Out
the Door
Calculator
Peer Tutoring
Reduce the
Number of
Stations
Differentiated
Instruction –
Enrichment:
Have the
students read
What’s Your
Angle,
Pythagoras?
By Judy Ellis
and ask them
to present
what
Pythagoras
found.
Summative
Assessment:
Homework
Assignment
8
I can use the
Pythagorean
theorem to
solve
problems.
Jane’s TV (See
Resource File)
Essential Question: How do I use the Pythagorean Theorem to solve problems?
Lesson Title: Pythagorean Theorem
Between the
Lines Level C
(See Resource
File)
Materials for
Differentiated
Instruction –
Remediation:
Calculator
Algebra Tiles
Materials for
Differentiated
Instruction –
Enrichment:
Between the
Lines Level D
Set: Watch “Origami Proof of the Pythagorean Theorem” (See the Resource Folder).
Teaching Strategy:
1. Use the video above to review the Pythagorean Theorem with the students.
2. Hand-out Jane’s T.V. (See Resource Folder). Give the students some private think time about
this problem. This contains two types of problems. One has a missing a and the other with a
missing c. Bring the class in for a discussion on how to solve these two problems. Ask students
to juxtapose how to solve the two problems.
Differentiated
Instruction –
Remediation:
Allow students
to use a
calculator
4. After giving students some private work time, ask students to share their generated ideas
with their groups. During this time, the groups should share and model their ideas, compare
solutions, and focus their discussion on the key ideas of this problem. The groups should come
up with a plan to proceed with the task.
As groups work on this task, the teacher monitors students’ progress through asking assessing
and advancing questions. The teacher may also select examples to periodically share, discuss,
and analyze with the entire class. These examples may show different solution paths to the
same task, different representations, errors, or misconceptions.
5. Assign each group a triangle to present to the class. They may use their iPads during their
presentation. They must explain how they found their missing sides and what their final area is.
After each presentation, groups can discuss how they found their answers.
Informal
observations
Questioning
Allow students
to use Algebra
Tiles
Student
Responses to
Jane’s TV
Questioning
Grouping
3. Handout the Between the Lines Level C task. Allow student to explore the task on his/her
own. This will allow students to generate their own solutions. During this time, assist students
in generating solutions. Ask students assessing and advancing questions. These questions can
include:
How do you find the lengths of the side that are drawn horizontally or vertically through dots?
How do find the lengths of the sides that are drawn at diagonals through dots?
How would you prove this is a right angle?
What would happen if they triangle does not include a right angle? Is there a way to create a
right angle within the triangle to find missing sides?
Formative
Assessment:
Performance
Assessment:
Prompting
Differentiated
Instruction –
Enrichment:
Allow students
to do Between
the Lines Level
D task and
present on that
instead.
Between the
Lines
Summative
Assessment:
Homework
Summarizing Strategy:
Ticket Out the Door: Pythagorean Theorem Exit Slip (See Resource Folder)
Practice problems will be assigned for homework.
9
Project Day 2 – refer to Unit Plan
Topic – Gallery Walk
10
Project Day 3 – refer to Unit Plan
Topic – Gallery Walk
STANDARDS
Identify what you want to teach. Reference State, Common Core, ACT
College Readiness Standards and/or State Competencies.
8.NS.2. Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate
the value of expressions.
8.EE.A.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions.
8.G.6. Explain a proof of the Pythagorean Theorem and its converse.
8.G.7. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two- and three-dimensions.