WhatKidsNeedToKnow.html

Prerequisite knowledge and related concepts

How to read tables and graphs
Multiplication
- Multiplication facts (1-10)
- Factors of numbers (list the factors)
- Prime numbers
- Prime factorization of numbers (use a factor tree, show expanded form only)
- Exponents (integer exponent, integer base)
- Prime factorization of numbers (exponent form and expanded form)
- Common factors of two or more numbers (lists, and prime factorization table using the bridge analogy)
- Greatest common factor (GCF) of two or more numbers
- Multiples of numbers
- Common multiples of two or more numbers
- Lowest common multiple (LCM least common multiple) of two or more numbers
Fractions
- Ratios, rates, and unit rates
- Conversion factors
- Converting between different units of measure
  - Customary to Customary
  - Metric to Metric
  - Metric to Customary and Customary to Metric
- Proportions
- Scale drawings and models
- How to add and subtract fractions with and without common denominators
- How to multiply and divde fractions
Ways to represent numbers and compare them
- How to convert between fraction, decimal, and percent forms of a number
- How to convert numbers from scientific notation to decimal form
- How to convert numbers from decimal form to scientific notation
- How to compare and order numbers in fraction, decimal, and percent form
Absolute value and opposite of a number
Perfect squares and perfect cubes
Roots (square and cube)
Irrational numbers
Pythagorean theorem and its converse

Algebra knowledge and related concepts

Operations with numbers
- How to add and subtract positive and negative numbers
- How to multiply and divide positive and negative numbers
- The distributive property to get rid of grouping symbols
- The distributive property to pull out a common factor
- Associative property of addition and Associative property of multiplication
- Commutative property of addition and Commutative property of multiplication
- Identity property of addition and Identity property of multiplication
- Inverse property of addition and Inverse property of multiplication
- Order of operations
Factoring numerical expresions and variable expressions
- Using prime factors in expanded form
- Using prime factors in exponent form
Greatest Common factor of variable expressions
Least Common Multiple of variable expressions
Adding, subtracting, multiplying, and dividing fractions containing variable factors
Operations with variables
- How to evaluate variable expressions
- How to write variable expressions from their verbal descriptions
- How to distinguish between an expression, an equation, and an inequality
- How to evaluate formulas (area and perimeter of rectangles, squares, trapezoids, parallelograms, triangles)
- How to evaluate formulas (area and circumference of circles)
- How to find area and perimeter for shapes made of combinations of basic figures (tirangles, rectangles, squares, circles)
Equations & Inequalities
- How to test if a given number is a solution of an equation
- How to combine like terms
- How to solve one-step equations
- How to write one-step equations from their verbal description
- How to test if a given number is a solution of an inequality
- How to solve one-step inequalities
- How to write one-step inequalities from their verbal description
- How to solve two-step equations
- How to write two-step equations from their verbal description
- How to solve two-step inequalities
- How to write two-step inequalities from their verbal description
- How to solve multi-step equations (distributive property, variables on both sides, combine like terms)
- How to solve equaqtions with fractions in them ( 1 step, 2 step, and multi-step)
How to solve percent problems
- How to write numbers in percent form
- How to find the percent of a number
- Given percent and base find part
- Given base and part find percent
- Given part and percent find base
- How to find commission and commission percent
- How to find discount and discount percent
- How to find the percent of increase or decrease
- How to find simple interest, interest rate, and time
- How to find compound interest
Laws of exponents
- Product of Powers
- Power of a Power
- Power of a Product
- Power of a Quotient
- Quotient of Powers
- How to multiply and divide numbers in scientific notation
Monomials and Powers
- Power of a product
- Power of a power
- Power of a quotient
- Combinations of all 3 rules
Polynomials in one variable
- Identifying a polynomial
- Classifying polynomials by number of terms
- Simplifying a polynomial
- Writing a polynomial in standard form
- Evaluating polynomial expressions
- Finding the opposite of a polynomial
- Adding and Subtracting Polynomials
  - Using algebraic expressions
  - Using area models
- Finding the product of a monomial and a polynomial
- Finding areas and volumes of shapes with side lengths expressed in polynomial form
- Binomial multiplication
  - Using the distributive property to multiply binomials
  - Using FOIL to multiply binomials
  - Squaring a binomial
Coordinate Plane and related concepts
- How to plot points in the coordinate plane
- How to read the coordinates of a point in the coordinate plane
- How to find the distance between two points in the coordinate plane
- How to find the midpoint of two points in the coordinate plane
- How to make scatter plots
- How to make a best fit line for a scatter plot (if possible)
- How to determine correlation from a scatter plot
- Definition of a function
- Writing a function from an input-output table
- Putting an equation into function form
- How to graph an equation/function (1st, 2nd, and 3rd degree) in a coordinate plane using an input-output table
- Finding the x and y intercepts of an equation
- Graphing an eqution using its x and y intercepts
- Slope of a line
- How to find the rise and run of an equation (slope of the line) from its graph
- How to determine if slope is positive, negative, zero, or undefined (graphically and numerically)
- Slope-intercept form of an equation
- Graphing an equation in slope-intercept form given the slope and y-intercept
- Finding the slope and y-intercept from the graph of a linear equation
- How to write the equation of a line in slope-intercept form given its graph
- Using slope as the rate of change in real-life problems
- How to graph a linear inequality
- How to test if a point is a solution to a linear inequality given the graph of the inequality
- Solving systems of equations by graphing and finding the point of intersection
- Solving systems of inequalities by graphing and finding the common shaded area
- Solving square root equations

Geometry Concepts Plane and Solid

Plane geometry
- Constructions with a compass and straight edge
  - angles
  - angle bisector
  - segment bisector
- Using protractors
  - reading angle measures
  - drawing angles to specific measures
- Parts of a circle
- Area and Circumference of Circles
- Points, lines, planes
- Parallel lines, perpendicular lines, skew lines
- transversals
- corresponding angles
- vertical and adjacent angles
- Angles
  - parts of angles (rays, vertex)
  - naming angles (a number, vertex, 3 points)
  - single angle classification
    - reflex
    - obtuse
    - right
    - acute
  - angle pair classification
    - complementary
    - supplementary
- Polygons
  - Regular and irregular polygons
  - Congruent and similar polygons
  - Area and perimeter of polygons
  - Area and perimeter of shapes made from combining simple polygons and parts of circles (rectangles, triangles, trapezoids, semicircles, quater circles)
  - Effect on area and perimeter of a polygon when all sides are multiplied by a scale factor
  - Effect on area and circumference of a circle when the radius is multiplied by a scale factor
  - Triangles (3 sides)
    - obtuse
    - right
    - acute
    - scalene
    - isosceles
    - equilateral
  - quadrilaterals (4 sides)
    - parallelograms
      - squares
      - rectangles
      - rhombus
    - trapezoids
    - kites
  - pentagons (5 sides)
  - hexagons (6 sides)
  - heptagons (7 sides)
  - octagons (8 sides)
  - nonagons (9 sides)
  - decagon (10sides)
  - dodecagon (12 sides)
  - n-gons (n sides)
- Reflections across a line
- Translations in the plane
Solid Geometry
- Find surface area and volume of solid shapes made from cubes
- From a picture of a solid made from cubes determine the number of cubes used
- Nets
- Point out the edges, vertices, and faces of polyhedrons
- Lines in space: coplanar, parallel, perpendicular, skew
- Prisms
- Surface area of a prism
- Volume of a prism (rectangular solid)
- Cylinders
- Surface area of a cylinder
- Volume of a cylinder
- Volume of a cone
- Volume of a pyramid
- Voulme of a sphere
- Similar Solids