80 Questions
What is the mathematical process of dividing a number into equal groups?
Division
What are the three main parts to a division problem?
Dividend, divisor, and quotient
What does 4 / 2 mean?
Separating 4 into 2 parts
What is the result of dividing a number by 1?
The number itself
When dividing by 10, what do you do?
Move the decimal point one place to the left
What is the value of a digit based on its location in the number?
Place value
What is a quotient?
The answer you get after dividing one number by another
What are compatible numbers?
Numbers that are close to the numbers in question yet can divide one another easily
What is the primary purpose of the Addition Property of Equality?
To maintain the equation true while solving for the variable
What is the result of multiplying a number by its reciprocal?
1
What is the best way to estimate the division problem 21/5?
Rounding the numbers to 20 and 5
What is an angle that measures exactly 90 degrees?
Right angle
What is the correct order of operations?
Parentheses, Exponents, Multiplication, Division, Addition, Subtraction
What is a common factor?
A number that is a factor of two different numbers
What is a polygon?
A closed, flat figure with at least three sides and angles
What is the term for a location in space with no length or width?
Point
What is the remainder in division?
The amount left over after dividing
What is the mean of a group of numbers?
The sum of the numbers divided by the number of numbers
What is the minimum number of sides a polygon must have?
Three
What type of angle is exactly 90 degrees?
Right angle
What is the purpose of lining up the decimal point when adding and subtracting money?
To avoid mistakes
What is the term for two lines that intersect at a right angle?
Perpendicular lines
What is a vertex?
A point where two or more lines or edges are connected
What type of polygon has equal sides and equal angles?
Regular polygon
What is the term for a straight series of points that extend in opposite directions infinitely?
Line
What is debt in the context of money?
Owing someone money for a purchase or service
What is the purpose of multiplying money by decimals?
To calculate tax rates and investment returns
What is the term for a part of a line that has two endpoints?
Line segment
What type of angle measures more than 90 degrees but less than 180 degrees?
Obtuse angle
What is the result of dividing a number by a divisor?
The quotient and the remainder
Where can vertices be found?
In both two-dimensional and three-dimensional shapes
What is a straight angle?
An angle that measures exactly 180 degrees
What is the most important thing to remember when multiplying money?
To line up your decimals appropriately
What is the key to dividing money by decimals?
To move the decimal point by an equal number of spaces to the right for both the dividend and the divisor
What is the purpose of the associative property in math?
To demonstrate that the order of numbers does not matter
What is the main idea behind the commutative property in math?
That the order of numbers does not matter
What does the Addition Property of Equality state?
That adding the same quantity to both sides of an equation produces an equivalent equation
How is the Addition Property of Equality used to solve equations?
By using the inverse operation to isolate the variable
Why is it important to review the answer to a money math word problem?
To make sure the answer makes sense based on the original question
What is the key to breaking down a money math word problem?
To use one of the strategies to help solve, such as estimation or CUBES
What is multiplication compared to division?
The opposite operation
What is the result of dividing a number by 10?
Move the decimal point one place to the left
What is the purpose of estimating quotients?
To get an approximate answer quickly
What happens when you divide a number by 1?
The answer is always the same number
What is place value?
The value of a digit based on its location in the number
What is the purpose of compatible numbers?
To make division problems easier
What operation is division the reverse of?
Multiplication
What happens when you divide a number by 100?
Move the decimal point two places to the left
What property of equality involves multiplying both sides of an equation by the same number?
Multiplication Property of Equality
What is the definition of a polygon?
A closed, two-dimensional figure with straight sides
What is the purpose of the Multiplication Property of Equality?
To balance equations
What is the definition of a vertex?
The location where two or more lines or edges are connected
What is the result of multiplying a number by its reciprocal?
1
What is the term for a location in space with no length or width?
Point
What type of angle measures more than 90 degrees but less than 180 degrees?
Obtuse angle
What is the term for a straight series of points that extend in opposite directions infinitely?
Line
What is the definition of a regular polygon?
A polygon with equal sides and equal angles
What type of angle measures exactly 90 degrees?
Right angle
What is the term for two lines that intersect at a right angle?
Perpendicular lines
What is the term for the process of identifying what data is available and what can be calculated using that data?
Solving a word problem
What is the definition of a straight angle?
An angle that measures exactly 180 degrees
Where can vertices be found?
In angles, plane figures, and three-dimensional shapes
What is the term for a part of a line that has two endpoints?
Line Segment
What is the minimum number of sides a polygon can have?
Three
What is the purpose of using compatible numbers when estimating a division problem?
To make the problem easier to solve
What is the result of dividing a number by its greatest common factor?
A whole number
What is the purpose of calculating the mean of a group of numbers?
To determine the average value
What is the purpose of multiplying money by decimals?
To calculate the tax rate
What is the result of subtracting money from a given amount?
Taking away money from a given amount
What is the purpose of using mental math when making and receiving change?
To make the calculation faster
What is the purpose of lining up the decimal point when adding and subtracting money?
To avoid mistakes
What is the term for owing someone money for a purchase or service provided?
Debt
When dividing money, what is the most important thing to remember regarding the decimal points?
To line up the decimal points correctly to avoid incorrect calculations.
What property of math allows us to add or multiply numbers in any order and get the same answer?
Commutative property
What is the purpose of using the strategy CUBES to solve a money math word problem?
To break down the problem into smaller parts and solve it step by step.
When multiplying money by decimals, what is the most important thing to remember?
To remember the dollar sign and the decimal point in the final answer.
What is the purpose of the associative property of math?
To allow us to add or multiply numbers in any order.
Why is it important to review the answer to a money math word problem?
To make sure the answer is correct and makes sense.
What is the purpose of the Addition Property of Equality in math?
To solve equations by adding the same quantity to both sides.
When solving a money math word problem, what should you do to break it down into manageable parts?
Use the CUBES strategy or estimation to break down the problem.
Study Notes
Multiplication and Division
- Multiplication is repeated addition
- Division is the opposite of multiplication, where we break apart or separate
- The three main parts of a division problem are:
- Dividend: the number being divided
- Divisor: the number by which we are dividing
- Quotient: the result of the division
Properties of Multiplication and Division
- Division is the reverse of multiplication
- Dividing by one equals itself
- When dividing by ten, move the decimal point one place to the left
- When dividing by 100, move the decimal point two places to the left
Estimating Quotients
- Use compatible numbers to estimate quotients
- Examples: 21 ÷ 5 ≈ 20 ÷ 5 = 4
Whole Numbers and Factors
- Whole numbers are counting numbers plus 0
- Factors are numbers that multiply together to get another number
- To find factors, use the multiplication table or divide the number systematically starting with 1
Factors and Common Factors
- Factors are numbers that multiply together to make a new number
- To find common factors, factor each number and compare them
- If they share any numbers, then they have common factors
Division in Math
- Division is the process of breaking up a number into equal groups
- Involves the word divide, meaning to break into groups of equal size
- Fact families are useful when dividing
- Example: 4 × 5 = 20, 5 × 4 = 20, 20 ÷ 5 = 4, and 20 ÷ 4 = 5
Long Division
- Steps for long division:
- Divide the digit of the dividend by the divisor
- Multiply the result with the divisor
- Subtract the result from the dividend being divided
- Bring the next digit of the dividend down to continue dividing
- The remainder is what is left over after the last subtraction
Mean (Average)
- The mean is the average of a group of numbers
- Calculated by adding all numbers and dividing by how many numbers there are
- Has many real-world applications
Money and Operations
- Review of adding and subtracting money
- Remember to line up decimal points
- Multiplying money by whole numbers and decimals
- Dividing money by whole numbers and decimals
Properties of Math Operations
- Associative property of addition and multiplication
- Commutative property of addition and multiplication
- Addition property of equality
- Multiplication property of equality
Solving Equations
- Use strategies like mental math, equations, and the order of operations (PEMDAS) to solve multi-step equations
- Remember to identify the variable and use the inverse operation to solve
Geometry
- Geometry deals with shapes, measurements, and relationships of points, lines, and angles
- Basic concepts: points, lines, line segments, rays, and angles
- Types of angles: acute, right, obtuse, straight, and reflex
- Properties of lines: perpendicular, parallel, horizontal, and vertical
Polygons
- A polygon is a closed, flat figure without curves, with at least three sides and angles
- Types of polygons: regular and irregular
- Examples: triangles, quadrilaterals, and more
Multiplication and Division
- Multiplication is repeated addition
- Division is the opposite of multiplication, where we break apart or separate
- The three main parts of a division problem are:
- Dividend: the number being divided
- Divisor: the number by which we are dividing
- Quotient: the result of the division
Properties of Multiplication and Division
- Division is the reverse of multiplication
- Dividing by one equals itself
- When dividing by ten, move the decimal point one place to the left
- When dividing by 100, move the decimal point two places to the left
Estimating Quotients
- Use compatible numbers to estimate quotients
- Examples: 21 ÷ 5 ≈ 20 ÷ 5 = 4
Whole Numbers and Factors
- Whole numbers are counting numbers plus 0
- Factors are numbers that multiply together to get another number
- To find factors, use the multiplication table or divide the number systematically starting with 1
Factors and Common Factors
- Factors are numbers that multiply together to make a new number
- To find common factors, factor each number and compare them
- If they share any numbers, then they have common factors
Division in Math
- Division is the process of breaking up a number into equal groups
- Involves the word divide, meaning to break into groups of equal size
- Fact families are useful when dividing
- Example: 4 × 5 = 20, 5 × 4 = 20, 20 ÷ 5 = 4, and 20 ÷ 4 = 5
Long Division
- Steps for long division:
- Divide the digit of the dividend by the divisor
- Multiply the result with the divisor
- Subtract the result from the dividend being divided
- Bring the next digit of the dividend down to continue dividing
- The remainder is what is left over after the last subtraction
Mean (Average)
- The mean is the average of a group of numbers
- Calculated by adding all numbers and dividing by how many numbers there are
- Has many real-world applications
Money and Operations
- Review of adding and subtracting money
- Remember to line up decimal points
- Multiplying money by whole numbers and decimals
- Dividing money by whole numbers and decimals
Properties of Math Operations
- Associative property of addition and multiplication
- Commutative property of addition and multiplication
- Addition property of equality
- Multiplication property of equality
Solving Equations
- Use strategies like mental math, equations, and the order of operations (PEMDAS) to solve multi-step equations
- Remember to identify the variable and use the inverse operation to solve
Geometry
- Geometry deals with shapes, measurements, and relationships of points, lines, and angles
- Basic concepts: points, lines, line segments, rays, and angles
- Types of angles: acute, right, obtuse, straight, and reflex
- Properties of lines: perpendicular, parallel, horizontal, and vertical
Polygons
- A polygon is a closed, flat figure without curves, with at least three sides and angles
- Types of polygons: regular and irregular
- Examples: triangles, quadrilaterals, and more
Review the basics of multiplication and division, including their relationship as reverse operations and how they can be applied to real-world problems, such as distributing cookies.
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