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4th Grade 5th Grade 6th Grade 7th Grade Algebra Geometry Functions Probability & Statistics Calculus Linear Algebra Geometry 3D Financial Math Vector Calculus |
Number Sense
- Whole numbers in the millions
- Whole numbers and decimals to two decimal
- Round whole numbers through the millions
- When rounded solution
- Different interpretations of fractions
- Whole numbers in the millions
- Write tenths, hundredths, halves, fourths
- Fractions, decimals on number lines
- Relative position of positives
- Sum/difference positive decimals to two places
- Round 2-place decimals to 1 decimal
- Addition/subtraction of multi-digit numbers
- Multiply a multi digit number
- Solve problems involving multiplication
- Solve problems involving division
- Whole numbers break down in different wayss
- Know 2, 3, 5, 7, 11 are prime numbers
Algebra and Functions
Measurement and Geometry
- Measure the area of rectangular shapes
- Rectangles with same area and different perimeters
- Rectangles with same perimeter and different areas
- Solve problems involving perimeters and areas
- Linear relationships on graph paper
- Horizontal length is difference of x- coordinates
- Vertical length is difference of y- coordinates
- Parallel and perpendicular lines
- Radius and diameter of a circle
- Congruent figures
- Bilateral and rotational symmetry
- Right angle, an acute angle, and an obtuse angle
- Geometric solids (prisms, pyramids,...)
- Equilateral, isosceles, scalene triangles
- Different quadrilaterals
Probability and Statistics
Number Sense
- Manipulate very large and very small numbers
- Percents as a part of a hundred
- Positive integer powers of nonnegative integers
- Prime factors of all numbers through 50
- Number line: decimals, fractions, negative integers
- Operations with decimals, positive/negatives
- Division with positive decimals/long division
- Addition and subtraction of fractions
- Multiplication and division of fractions
- Solve problems with fractions
Algebra and Functions
Measurement and Geometry
Probability and Statistics
Number Sense
- Order positive and negative fractions, decimals
- Use ratios in different contexts
- Use proportions to solve problems
- Solve problems involving discounts
- Solve problems with operations of positive fractions
- Meaning of multiplication/division of positive fractions
- Solve problems with positive/negative integers
- LCM and GCD of whole numbers
- Estimation 1
- Estimation 2
Algebra and Functions
- One-step linear equations in one variable
- Write/evaluate an algebraic expression
- Order of operations and laws
- Solve problems manually or with calculator
- Convert units of measurement
- Understand meaning of rate
- Solve problems of rates, average speed, distance, time
- Use variables in expressions describing geometry
- Express symbolically relationships from geometry
- Commutativity of Subtraction/Division
- Associativity of Subtraction/Division
Measurement and Geometry
Probability and Statistics
- Range, mean, median, and mode
- Added data changes measures of central tendency
- Outliers affect on measures of central tendency
- Different measures of central tendency
- Compare data samples of a population
- Identify different ways of selecting a sample
- Analyze data displays
- Sampling errors and bias
- Identify/Evaluate claims based on data
- Possible outcomes for compound events
- Use data to estimate probability
- Represent probabilities as ratios, proportions, decimals
- Disjoint events, independent trials
- Independent and dependent events
Number Sense
- Rational numbers in scientific notation
- Operations with rational numbers
- Convert fractions to decimals and percents
- Rational and irrational number
- Convert terminating decimals to fractions
- Percentage of increases/decreases
- Simple and compound interest
- Negative whole-number exponents
- Use factoring to add/subtract fractions
- Rational exponent rules
- Powers/roots of perfect squares
- Absolute value of a number
Factoring
Linear Functions
Solve Systems Linear Equations
Quadratic Functions
Probability
- Concept of Instantaneous Rate
- Rate of Change
- Derivative of a Product of Two Functions (7)
- Differentiability and Continuity (2)
- Related Rates (2)
- Volume of a Solid by Plane Slicing (3)
- The number e, and derivatives of logs (4) (3x-2)e^x
- Derivative and Integral Practice Problems
- Differential Equations for Real World (15)
- Critical Points and Points of Inflection (11)
- Maxima and minima in Plane and Solid Figures (3)
- Volume of a Solid of Revolution - Cylindrical Shells (6)
- Length of a Plane Curve - Arc Length (10)
- Lengths and Areas for Polar Coordinates (2)
- Integration by Parts - a Way to Integrate Products (10)
- Rapid Repeated Integration by Parts (16)
- Points and Vectors in 3D
- Lines in 3D
- 3D Line Forms in 2D - Part 1
- 3D Line Forms in 2D - Part 2
- Line from Point and Vector
- Line through 2 Points
- Planes in 3D
- Plane through Point, Normal to Line
- Intersection of Line and Plane
- Line as Intersection of 2 Planes
- Distance from Point to Plane
- Angle between Line and Plane
- Gradients - Introduction
- 1D Gradient Vector Field of y=f(x)
- Ex 1: 2D Gradient Field - What do we see?
- Ex 2: 2D Gradient Field - What do we see?
- Ex 3: 2D Gradient Field - What do we see?
- Ex 4: 2D Gradient Field - What do we see?
- Vector Fields that are NOT Gradient Fields
- 3D Gradient Field - What do we see?
- Calculate the simple interest earned in 1 year on a deposit of $1,000 if the interest rate is 7%.
- Calculate the simple interest due on a 2-month loan of $2,000 if the interest rate is 5%
- The ordinary method for converting time from days to years is to use an average of ____ days in a month and 12 months in a year.
- The exact method for converting time from days to years is to use ____ days in a year.
- Calculate the simple interest due on a 60-day loan of $9,000 if the annual interest rate is 7%
- The simple interest charged on a 5-month loan of $2,000 is $58.33. Find the simple interest rate.
- Calculate the maturity value of a simple interest, 9-month loan of $2,000 if the interest rate is 8%.
- Calculate the maturity value using A = P(1 + rt) for a simple interest 9-month loan of $4,000. The interest rate is 6.75%.
- You deposit $2,500 in an account earning 9% interest compounded semiannually (i.e, twice a year). How much do you have in the account at the end of 1 year?
- You deposit $1,000 in an account earning 8% interest compounded semiannually (i.e, twice a year). How much do you have in the account at the end of 1 year?
- Calculate the compound amount when $500 is deposited in an account earning 8% interest, compounded semiannually, for 7 years.
- Calculate the compound amount when $1,000 is deposited in an account earning 5% interest, compounded daily, for 3 years.
- How much money should be invested in an account that earns 8% interest, compounded quarterly, in order to have $14,000 in 8 years?