Math EU’s and EQ’s
Multiplication and Division 1: Number Puzzles and Multiple Towers
Enduring Understandings:
Students will understand that...
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Numbers are sorted and classified into groups based on their factors.
Prime factorization is the DNA of a number: each number can be built by only one unique combination
of prime factors.
Essential Questions:
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Have we found all of the possible factors of a number? How can we be sure?
What is another equivalent multiplication combination? How is it related to the others?
Addition, Subtraction and the Number System: Thousands of Miles,
Thousands of Seats
Enduring Understandings:
Students will understand that...
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With the right strategy, I can subtract faster than a calculator.
Landmark numbers make subtracting mentally much easier.
Using place value and groups of ten, there is no limit to how high numbers can go.
Essential Questions:
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What is the best way to break large numbers apart in order to subtract or divide?
What is the best strategy for computing?
How will I explain my computation strategy in an understandable way?
Fractions and Percents 1: What's that Portion?
Enduring Understandings:
Students will understand that...
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The relationship a part of a group has to the whole group can be quantified.
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Numerical data is relative; fractions express relationships, and the size or amount of the whole group
matters.
Every fraction has a unique place on the number line.
To add or subtract fractions, a common whole is needed.
Pieces don't have to be congruent to be equivalent.
To compare fractions, the size of the whole group must be the same
Essential Questions:
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What is the relationship between the part and the whole?
How can I best represent this numerical relationship to my audience?
What is the point of reference for the data (the size of the whole group)?
2-D Geometry and Measurement: Measuring Polygons
Enduring Understandings:
Students will understand that...
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Sometimes shapes are exactly the same (congruent) and other times they look the same but one is
bigger or smaller than the other (similar).
In similar figures, length and area grow or shrink proportionally, but the angles always remain
congruent.
When a figure grows, its area grows at a faster rate than its sides and perimeter.
Essential Questions:
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What are the attributes and characteristics I can use to identify and describe it?
What similar attributes should I use to classify and organize these objects?
Is this the only way to organize them?
Decimals, Fractions, and Percents 2: Decimals on Grids and Number
Lines
Enduring Understandings:
Students will understand that...
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Every fraction can be written as a decimal number.
Decimals have place values related by groups (powers) of 10.
Strategies for adding, subtracting, multiplying, or dividing decimals are the same strategies we have
always used with whole numbers.
Essential Questions:
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In this situation, what's the best way to communicate this quantity? Would it be better to represent it
as a fraction or a decimal?
Multiplication and Division 2: How many People? How Many Teams?
Enduring Understandings:
Students will understand that...
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In order to estimate multiplication or division with big numbers, I need to start by computing left to right.
Strategies for division always require me to multiply.
Multiplication and division are inverse operations
Repeated additions can be regrouped
Essential Questions:
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Can I figure this out in my head and explain it to someone else, or do I need to write it down to keep
track of my thinking?
Is there a quicker way?
How can I improve my thinking in order to avoid grabbing a pencil or a calculator?
Data Analysis and Probability: How Long Can You Stand on One Foot?
Enduring Understandings:
Students will understand that...
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The type of data being presented usually reveals the type of graph or chart I should use.
The way an idea (or data) is presented influences the audience.
The likelihood of an event (such as snow tomorrow or that a sports team will win) can be represented
with numbers.
Any event will either always happen, never happen, or is likely to happen at some degree in between.
Essential Questions:
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What do I need to share with my audience to help them see the trends of the past and predict other
relationships?
How should I represent the data and relationship so that it is most helpful and understandable for
others?
How likely is it?
What decisions should I make based on the chances of certain events happening?
What factors influence the likelihood that an event will happen?
3D Geometry and Measurement: Prisms and Pyramids
Enduring Understandings:
Students will undertand that...
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Complex things can best be measured and evaluated by breaking them into their most basic,
understandable pieces.
Every object in our world can be measured and quantified using it's dimensions of length, width, and
height.
Essential Questions:
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What are the most basic, familiar pieces I can break this thing into in order to better understand it?
Will these objects hold the same amount of water? Will they be made from the same amount of plastic
or cardboard?
Is there a better shape?
Patterns, Functions, and Change: Growth Patterns
Enduring Understandings:
Students will understand that...
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Any data in a table can be graphed on a coordinate grid.
A table shows how a few quantities in a situation are related; a graph helps visualize how more of the
quantities are related; but an arithmetic expression is the best, because it can be used to find the value
of one quantity if I know the other quantity
Essential Questions:
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What is the relationship between these two situations?
What is the best way to predict what will happen in two situations in the future?
How should I represent the relationship so that it is most helpful and understandable for others?