Intermediate School Mathematics

Goals

1. Facility in using negative rational numbers
2. Facility with basic mathematical expressions
   1. Ability to create mathematical expressions of real world situations
   2. Ability to interchange equivalent mathematical expressions
   3. Working ability to recognize real world relationships in mathematical expressions
3. Facility in using variables for unknown values
4. Working ability with basic mathematical sentences
   1. Knowledge of the properties of equality
   2. Ability to manipulate equations
   3. Ability to solve basic equalities
   4. Ability to manipulate inequalities
   5. Ability to express reali world relationships in mathematical sentences
5. Ability to apply basic formulas to solve practical problems
6. Working ability with advanced counting techniques

Previous: elementary. Next: secondary.

Objectives

• Adding and subtracting rational numbers
  • Explain negative numbers as distances below zero
  • Explain negative numbers as combining distance and direction
  • Explain negative numbers as deficits to be made up
  • Calculate the sums of integers
  • Demonstrate the equivalence of subtraction and adding negatives
  • ☆ Explain negative numbers as a way to complete the concept of subtraction of rational numbers
• Multiplying and dividing rational numbers
  • Identify the properties of -1
  • Express negative numbers as the product of a positive number and -1
  • ☆ Express multiplication by -1 as the reversal of a physical interpretation of number
  • Calculate the product of two integers
  • Calculate the product of two rational numbers
• Mathematical expressions
  • Explain a mathematical expression as a sequence of operations
  • Explain a mathematical expression as a number
  • Identify the order of operations implied by a mathematical expression
  • Explain the use of parentheses to alter the order of operations
  • Identify changes to the order of operations permitted by communitivity
  • Simplify a mathematical expression involving a single type of operation
  • Simplify a mathematical expression involving a multiple types of operation
  • Expand integers, decimal fractions, and mixed numbers into mathematical expressions
  • ☆ Explain a parenthesized quantity as a number
  • ☆ Explain an expression containing a quantity as a nested set of operations
  • Express repeated multiplication using exponents
  • Calculate the value of a number raised to an integer power
  • Define roots as the inverse of powers
  • Find integer roots of natural numbers
  • Identify natural numbers which lack specific integer roots
  • ☆ Explain exponents as a method to simplify expressions
  • ☆ Demonstrate exponent arithmetic by using the definition of exponents
• Unknowns (variables)
  • Explain a mathematical expression containing an unknown
  • Write a mathematical expression containing an unknown
  • Express a real or imagined situation using an unknown
• Equations
  • Explain equality in terms of a physical analogy
  • Explain equality in terms of identity of value
  • Express equality using a simple equation
  • Illustrate the properties of equality
  • Express a real world relationship using an equation
  • Express a relationship using an equation with an unknown
  • Explain or illustrate the concept of solving an equation
  • Solve a simple equation with one unknown and an addition
  • Solve a simple equation with one unknown and a multiplication
  • Solve a simple equation with one unknown and both addition and multiplication
  • Use the distributive property to rewrite an expression into an equivalent form
  • Use the distributive property to solve an equation
  • Interpret the solution of an equation in a real world situation
  • ☆ Use the definition of multiplication and the commutivity of addition to prove distributivity
• Formulas
  • Explain a formula as an equation
  • Apply a formula and known value to convert units
  • Apply a formula and known values to calculate perimeter
  • Apply a formula and known values to calculate area
  • Apply a formula and known value to calculate tax [such as sales tax]
  • Create a formula for a real or imagined situation
• Inequalities
  • Identify the symbols representing inequality [< ≤ ≥ >]
  • Represent an inequality using a visual pisture or diagram
  • Explain or illustrate the concept of solving an inequality
  • Solve a simple inequality with one unknown and an addition
  • Solve a simple inequality with one unknown and a multiplication
  • Solve a simple inequality with one unknown and both addition and multiplication
  • Interpret the solution of an inequality in a real world situation
• Counting revisited
  • Compute the average [mean] of a list of values
  • Demonstrate that the average times the number of values is the same as the sum of the values
  • Describe a real life situation using an average
  • Discriminate between appropriate and inappropriate uses of averages
  • Demonstrate simple probability based on counting
  • Calculatea the probability of simple random tasks
  • Illustrate one-to-one correspondence with physical objects
  • Illustrate one-to-one correspondence between numbers and objects
  • Demonstrate that there are as many multiples of an integer as counting numbers
  • ☆ Demonstrate that there are as many counting numbers as integers

May, 2014