1. “Know and understand are not synonyms.”
Essential Questions
“Know and understand are not synonyms.”
Wiggins and McTighe,
Understanding by Design

2. “Understanding is always fluid, transformable into a new theory.”
What we want students to be able to do is to take information and skills and apply them in new situations rather than “spewing back the particular fact, concepts, or problem sets that were taught.”
Wiggins and McTighe
Understanding by Desigh

3. “How does one go about determining what is worth understanding amid a range of content standards and topics?” Wiggins and McTighe, 1989 p.10
BEFORE you do your lesson plans, ask yourself, “What do I really want these student to know? What is the core nugget of knowledge that, when they are 32 years old and have forgotten most of what they have learned, will allow them to function in real life situations?”

4. An essential question:
is a provocative question designed to engage student interest and guide inquiry into the important ideas in a field of study.
does not have one “right” answer
is intended to stimulate discussion and rethinking over time
raises other important questions
When using more than one, essential questions can be differentiated to meet student needs.

5. An essential question
“is an intellectual linchpin. A linchpin is the pin that keeps the wheel in place on an axle. Thus, a linchpin idea is one that is essential for understanding – without it a student cannot go anywhere” (71).

6. Topic – Martin Luther King
Example:
Topic – Martin Luther King
What events and people influenced MLK to become a leader in Civil Rights?
How did MLK change the world today?
What techniques did MLK use to persuade the world that his ideas were important?
How did MLK’s leadership and philosophies influence the US position?

7. Two Types of essential questions:
Topical – can be answered by uncovering a unit’s content. They stay within the bounds of the topic. They can be answered as a result of in-depth inquiry. Ex: After reading Merchant of Venice, answer the question: Is Shakespeare prejudice?
Over-Arching – Point beyond a unit to a larger, transferable idea. May link a topic to other topics and subjects. Ex: What in Shakespeare’s plays make them “classic” literature?

8. What makes a human/country civilized?
Unit – Middle Ages
Truth vs Fantasy: the feudalism, knights, castles, religion. What was the Middle Ages really like?
Unit – Renaissance
How did the music and art of the time influence the politics?
Unit – Holocaust
What factors contributed to this society that still exist today?

9. Three types of knowledge
Good to know; knowledge worth being familiar with; covered in class
Essential, important to know; uncovered in class
Enduring knowledge; has understanding beyond the classroom; student come to the realization

10. How is electricity helpful
Grade 4
Unit:
Electricity;
Reports
Knowledge worth being familiar with; facts covered in class
Vocabulary: protons, electrons, friction, volts, etc.
Lightning facts
A circuit is a continuous loop of energy and motion.
Parts of a circuit
How has electricity
changed the world?
How is electricity an
energy source in
my world?
How is electricity helpful
and harmful
Static
electricity
is caused by
friction/
transfer of
electrons
3 types of circuits:simple;
series;
parallel
Make up of a
molecule
Schematics
Enduring knowledge:
These have value beyond the classroom.
Student come to the realization.
There are different energy sources
and they all produce electricity
Knowledge and skills important to know. These are uncovered in class.

11. Knowledge worth being familiar with; facts covered in class
Grade 8
Unit: Role of
Government
Reports/
Persuasive
Knowledge worth being familiar with; facts covered in class
Vocabulary: self-interest, government, democracy, law, etc.
Federal/
state/
local
Why national parks were created
Enduring knowledge:
These have value beyond the classroom.
Student come to the realization.
Whose job is it
to solve America’s
problems?
Choose a national
park – Whose
job is it to preserve
this park?
Names and locations of national parks
How a law
Is made
The enduring
knowledge
question may
embed the facts learned in the other
parts of the circle.
What is the difference between government and committed group?
length of
terms of
office
Knowledge and skills important to know. These are uncovered in class.
Background – growth of industrialism

12. embed the facts learned in the other
High School
Unit: Holocaust:
Reports/Persuasive/
Project
Knowledge and skills important to know. These are uncovered in class.
Nazi philosophy; fascism; totalitarian government; racism; anti-Semitism
Leaders
Courage to Care: Warsaw Ghetto; Denmark; Avenue of the Just
Enduring knowledge:
These have value beyond the classroom.
Student come to the realization.
Progression of laws
How do individuals,
groups, towns,
and countries make a
difference? How can
we make a difference?
Difference between bias, prejudice, discrimination
Events
The enduring
knowledge
question may
embed the facts learned in the other
parts of the circle.
Preparing for obedience: propaganda, role of education, indoctrination of people
Knowledge and skills important to know. These are uncovered in class.

13. Your turn: Work in grade-level or subject matter groups
Pick a topic/subject
Write at least 3 essential questions

14. What about essential questions in math?

15. A Sampling of Questions Assessing the Enduring Understanding of Fractions
How can you tell if a fraction equals ½ ?
How can you tell if a fraction is less than ½ ?
How can you tell if a fraction is greater than ½ ?
Is 11/15 more than ⅔ or less than ⅔ ? How do you know?
Write a fraction whose value is greater than ½ but whose denominator is more than 50. How did you do this?
If the numerator of a fraction is 102 what denominator will give it a value of ½ ? Explain your reasoning.
If the denominator of a fraction is 102 what numerator will give it a value of ½ ? Explain your reasoning.
What is the relationship of the numerator and denominator of a fraction if the value of the fraction is ½ ?
(A variety of questions such as the ones above can be asked with the subject referring to fractions whose values are ⅓, ⅔, ¼, ¾, ⅛, etc.)
What does it mean to find a fractional part of a number?
What does it mean to find ⅝ of a number?
What does it mean to find ⅝ of 60?
If ⅔ of a number equals 60, how do we find the number? (Tell me how! You do not need to tell me the answer!).
Why is ¼ of 48 less than ⅓ of 48?
Why is ⅓ of a number more than ¼ of the same number?

16. When you square a proper fraction, why is the product smaller than the original fraction?
When you multiply two proper fractions why is the product always less than either of the two original fractions?
What math operation (or operations) are involved in finding 1/5 of a number?
What math operation (or operations) are involved in finding 3/4 of a number?
Why does 5/50 not equal 1/25 ?
What does it mean when we say that something has grown by 10% ? (Describe the result by describing the important math operations.)
What does ½ of ⅔ mean? Use the “Concept of Fraction” to represent (draw) it.
What does ¾ of ½ mean? Draw a representation of this calculation.
Explain why ½ of ¾ means the same thing as ¾ of ½ . Draw a representation of both.
Explain why there is no such thing as the “smallest fractional part of a number”.
When you divide by a fraction why do you always multiply by the reciprocal of the fraction?
Which is greater: 75% or 0.8 ? Explain how you know.
Given any two fractions with the same numerator, how can you tell which fraction is larger?
Given any two fractions with the same denominator, how can you tell which fraction is larger?
Find ⅔ of 3/5. Use the definition of a fraction to show why this is true.
Multiply: ⅔ x 3/5. Use the definition of a fraction to show why this is true.
Which is larger, ⅔ of a number or 3/5 of the same number? How do you know?
Add: ⅔ + 3/5 . Why is the answer not ⅝ ? Use the definition of a fraction to show how you got your answer.

18. Questions About These Conceptual Questions
Which of these would you consider to be essential questions? Which of these would you emphasize at your grade level?
How many of your students would be able to answer a “good number” of these?
Can all of your students answer a fair sampling of (grade appropriate) questions like these?
How many of your students would rather just be able to “get the right answer” (by copying……by “getting helpful hints” from others….. by memorizing algorithms, etc. and would rather not answer the part of the question that involves explaining their thinking?

20. A Sampling of G.L.E.s Involving Fractions
M3:1 Demonstrates conceptual understanding of rational numbers with respect to positive fractional numbers (benchmark fractions: a/2 , a/3 , a/4 , a/6 , a/8, where a is a whole number greater than 0 and less than or equal to the denominator) as a part to whole relationship in area and set models where the number of parts in the whole is equal to the denominator;
M3:2 Demonstrates understanding of the relative magnitude of numbers by comparing or identifying equivalent positive fractional numbers (a/2 , a/3 , a/4 where a is a whole number greater than 0 and less than or equal to the denominator) using models, number lines, or explanations.
M5:1 Demonstrates conceptual understanding of rational numbers with respect to positive fractional numbers (proper, mixed number, and improper) (halves, fourths, eighths, thirds, sixths, twelfths, fifths, or powers of ten [10, 100, 1000]) using models, explanations, or other representations*.
*Specifications for area, set, and linear models for grades 5 – 8: Fractions: The number of parts in the whole is equal to the denominator, a multiple of the denominator, or a factor of the denominator.
M5:2 Demonstrates understanding of the relative magnitude of numbers by ordering, comparing, or identifying equivalent positive fractional numbers within format (fractions to fractions) in context using models or number lines.
M7:1 Demonstrates conceptual understanding of rational numbers with respect to percents as a means of comparing the same or different parts of the whole when the wholes vary in magnitude (e.g., 8 girls in a classroom of 16 students compared to 8 girls in a classroom of 20 students, or 20% of 400 compared to 50% of 100); and percents as a way of expressing multiples of a number (e.g., 200% of 50) using models, explanations, or other representations.*
M7:2 Demonstrates understanding of the relative magnitude of numbers by ordering, comparing, or identifying equivalent rational numbers across number formats.
Note: after 6th grade the word “fractions” does not appear in the G.L.E.’s except to refer to exponents with fractional bases (in 7TH grade).

21. Interpreting the G.L.E.s (and communicating to students)
Is it clear to you what the standards are at your grade level?
Would you know if each of your students had achieved the standard?
Would your understanding of the standards be compatible with those of the teachers in the grades immediately below and above your grade?
Does a majority of the time allotted to your teaching of this standard address the enduring understanding (the bull's-eye) for this standard?
Do the students know what is expected of them (conceptually) when they study fractions in your class?
Is it difficult for many of your students to progress with your curriculum because they are lacking the conceptual foundation from previous
class?

22. Only a person who has questions can have knowledge.” Gadamker, 1994