Teacher: 6 th Grade Teacher
Lesson Title: Holiday Traditions and Geometry
STRANDS
Grade: STEM Math IA
The Number System and Geometry
LESSON OVERVIEW
MOTIVATOR
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.
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
Objectives
(I can….)
Materials &
Resources
Instructional Procedures Assessment Differentiated
Instruction
1

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”

3 I can use rational expressions of irrational numbers to compare the size of irrational numbers, locate them approximat ely on a number line
Square Roots
Notes”
“Squares and
Square Roots
Ball Toss” instructions
“Koosh” ball
Materials for
Differentiated
Instruction –
Remediation:
“Memory
Work for
Squares and
Square Roots”
“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 of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions?
Estimating Square Roots
Set: Show Art Benjamin video “Lightning Calculation and other Mathemagic “ to inspire students when they see that the human brain is capable of squaring numbers more quickly than a calculator!
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.
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 their answer choices upon completion of the matching activity. To connect this lesson to
Differentiated
Instruction –
Remediation:
Students should visit http://www.m
athisfun.com/s quareroot.html
to learn a trick for estimating the square root of imperfect squares.
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”
Materials for
Differentiated
Instruction –
Remediation:
Internet
Materials for
Differentiated
Instruction –
Enrichment:
Internet previous standards, teacher will ask students to explain which types of numbers have rational square roots and which have irrational square roots.
Summarizing Strategy: Students will complete the exit ticket “Imperfect Square
Approximation.”
“Square Roots Approximation Assignment” will be assigned for homework
4 I can determine if a number is rational or irrational.
6 different colors of construction paper
Scissors
Glue
Markers
Materials for
Differentiated
Instruction –
Remediation:
Graphic
Organizer (See
Resource File)
Essential Question: How do I determine which number set a number belongs to?
Rational vs. Irrational
Set: Show the students this comic.
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:
Students should visit http://www.ixl.
com/math/gra de-8/evaluatevariableexpressionsinvolvingsquares-andsquare-roots to be challenged with variables.
Has Activity.”
Summative
Assessment:
“Square
Roots
Approximatio n
Assignment”
Differentiated
Instruction –
Remediation:
Prompting
Grouping
Graphic
Organizer (See
Resource
Folder)
Differentiated
Instruction –
Enrichment:
Have students discover how
Formative
Assessment:
Foldable
Ticket Out the Door
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.
7.
Further examples that can be use are -6,
2
3
, -0.44444444444…, 𝜋 ,
12
4
, and
−15
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”
“Exponent
Rules Notes”
“Exponent
Rules Group
Work”
“Exponent
Rules Graphic
Organizer”
“Exponent
Rules
Homework”
Materials for
Differentiated
Instruction –
Remediation:
“Need More
Support Group
Work”
Differentiated
Instruction –
Enrichment:
“Need More
Challenge
Group Work”
Essential Question: How do I apply the properties of integer exponents to generate equivalent numerical expressions?
Exponent Rules
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.
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 –
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
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 x
2
=p, where p is a positive rational number.
Opening
Activity”
I can evaluate square roots of small perfect squares.
the form x
2
=p, where p is a positive rational number?
2.
How can I evaluate square roots of small perfect squares?
Solving Equations with 𝒙 𝟐
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.
x 2 =25
2.
x 2 +10 =14
3.
x 2 -5 =76
4.
3x 2 = 108
5.
2x 2 +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 describe the
Pythagorean
Theorem.
Station 1: (See
Resource
Folder)
Station 2: (See
Resource
Folder)
Station 3: (See
Resource
Folder)
Graph Paper
Scissors
Square Tiles
Materials for
Differentiated
Instruction –
Remediation:
Calculator
Materials for
Differentiated
Instruction –
Enrichment:
What’s Your
Angle,
Pythagoras?
By Judy Ellis
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.
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.
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.
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
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.
Formative
Assessment:
Station
Activities
Ticket Out the Door
Summative
Assessment:
Homework
Assignment

8 I can use the
Pythagorean theorem to solve problems.
Jane’s TV (See
Resource File)
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
Essential Question: How do I use the Pythagorean Theorem to solve problems?
Lesson Title: Pythagorean Theorem
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.
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?
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.
Differentiated
Instruction –
Remediation:
Allow students to use a calculator
Allow students to use Algebra
Tiles
Questioning
Grouping
Prompting
Differentiated
Instruction –
Enrichment:
Allow students to do Between the Lines Level
D task and present on that instead.
Formative
Assessment:
Informal observations
Questioning
Student
Responses to
Jane’s TV
Performance
Assessment:
Between the
Lines
Summative
Assessment:
Homework

9
10
Summarizing Strategy:
Ticket Out the Door: Pythagorean Theorem Exit Slip (See Resource Folder)
Practice problems will be assigned for homework.
Project Day 2 – refer to Unit Plan
Topic – Gallery Walk

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.