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Key Terms

100

Define what a BMU and MU is

Basic measuring unit (BMU): The quantity that is assigned the numeral “1”

Measuring units (MUs): Quantities that are used to measure other quantities

200

What are the definitions of procedural fluency and strategic competence

•Carrying out mathematical procedures, Solving the equation

•the ability to use multiple strategies to solve a math problem

300

Define Conceptual understanding (extra explain how it will apply to your future classroom)

•idea, definition, principles, The why behind it

entails teaching children not only how to do something but also why they should do it. Through conceptual understanding, children can see the bigger picture that underlies all math topics and exercises, allowing them to think in a fluid way, use their math skills in a variety of contexts, and utilize higher-order thinking skills

400

Define Quantity and numeral. Explain the difference

Quantity is an amount of stuff (ex. Length of a board, Volume of water in a glass, Weight of a penny, Amount of lambs in a field)

Numeral, which refers to the symbol(s) used to designate the amount of stuff.

Ancient Numeration System

100

What system is most like ours?

Hindu- Arabic

200

Name the numeration systems

Tallies, Egyptian, Roman, Babylonian, Hindu-Arabic

300

List the all of the properties for all numeration systems

Subtractive, Positional, Multiplicative, Place Valued, Zero, Additive:

• Additivity-of-symbols

• Additivity-within-place-values

• Additivity-across-place-values

400

Define all of the Numeration Properties

Additive: Additivity-of-symbols: Each symbol in a numeral represents a specific part of the quantity. Additivity-within-place-values: Within each place value, add up the face value of each symbol to get the total face value for that place. Additivity-across-place-values: Determine the amount that is represented in each of the place values and then add all of these amounts to get the total value of the numeral. 

Subtractive: When the first of two consecutive symbols stands for a smaller amount than the second, subtract the value of the first from that of the second to get the value of the combination.

Positional: The position of the symbol affects the value of the symbol.

Multiplicative: Use of a symbol or position to indicate that a particular symbol is multiplied by some constant.

Place Valued: The value of a symbol is a function of its place in the numeral. The places represent measuring units.

Zero: Designates “no groups” of a particular measuring unit

Story Problems

100

What are the two categorizations of story problems?

1.) Actions that take place in the story (four types)

2.) Missing whole Missing part

200

List the types of addition and subtraction story problems and write the attached number sentence

Join Story Problem, Part- part Whole Story Problem, Take Away Story Problem and Comparison Story Problem

p+p=W

W-p=p

300

List the types of multiplication and division write the attached number sentence

Repeated Addition, Rectangular Array/Area, Multiplicative comparison, Combinations

a x b= c

Repeated Subtraction and Partition model of division (Equal Sharing)

c/b=a

c/a=b

400

Annalise is looking for a new outfit. She has 6 different tops and 7 different bottoms to choose from. She wants to see all the possible outfits she can create using one top and one bottom. How many outfits can Annalise create? What type of story problem is this? Identify a, b, c, write number sentence and part whole diagram.

a = 6 tops

b = 7 bottoms

c = ? total outfits

Number Sentence 6 x 7 = ?

Story Problem Type Combinations

Part whole diagram

Models

100

Explain the beginning process of modeling an operation

Define a, b, and c

Write the number sentence and part-whole diagram (depending on operation)

Define the model representations of smallest to largest numerals within equation

200

Model 10-7.4=?

2.6

300

Model 3.2÷8=? and 1.44÷0.12=? Explain what division type you used and why?

Partitioning & then Repeated Subtraction

400

Model 1.3 x 0.2 with base 4

0.32

Operations

100

What are the 3 types of algorithms (there is one bonus one) and define them?

• Invented algorithms: algorithms that children come up with in their own or different then the standard one
• Intermediate: algorithms that emphasize place value concepts, and that are generally taught prior to the standard algorithms
• Standard: most commonly taught algorithms; often the most efficient algorithms. These algorithms do not generally reiterate/develop place value concepts
• Buggy Algorithms- students try to mimic the teacher-taught algorithms but they are not correct

200

Using the chip model -5-4=? Depict the answer two different ways (name the type)?

Take Away and Missing Addend (adding up)

300

Define the operations (addition, subtraction, multiplication, and division)

type of operation that results in the sum of two or more numbers. There is a sign to represent the operation addition, called a plus sign, which is a +.

Subtraction is a type of operation that results in finding the difference between two numbers. The sign to represent the operation subtract is called a minus sign and it looks like this -.

Multiplication is a type of operation that requires you to add in equal groups, multiplication results in a product. The sign that represents the operation multiplication can be called the multiplication sign and it looks like this ×. 

Division is the operation that is opposite to multiplication, it involves breaking a number down into equal parts. The sign that represents the operation division is simply called a division sign and looks like this ÷.

 

400

Find the value of 4.23 +1.1 with base 5

10.33