MTH211 Foundations of Elementary Math 1

the one percent

Fun with whole numbers.

MTH211
Notes on Whole Numbers
Fall 2019

Table of Contents

§ 3.2 Addition and Subtraction

Math Activity 3.2: Playing with Blocks

Addition with base-ten blocks
22 plus 23 sum of 55

Math Activity 3.2: Playing with Blocks

Subtraction with base-ten blocks

36 - 23 means, what do you get if you take 23 away from 36?

So, start with 36:

36 in base-ten blocks

Now, take away 23:

36 take away 23 in base-ten blocks

That leaves 13!

Main topics
  • Addition Models
    • set model
    • number line model
  • Addition Properties
    • closure
    • Commutative
    • Associative
    • identity
  • Addition Algorithms
    • standard (right to left, regroup)
    • Expanded
    • Lattice
    • Hindu (left to right)
  • Inequality
  • Subtraction Models
    • Take-away
    • Compare
    • Missing Addend (what do I add?)
    • number line
  • Subtraction Algorithms
    • Standard (right to left, rename)
    • Equal Additions
    • Hindu (left to right)
    • Complements
    • Subtract up
    • low stress
  • Approximations and Estimations
    • Front end
    • Compatible numbers

§ 3.3 Multiplication

Math Activity 3.3: Multiplication as Area
an array of squares, 23 by 12, with rows 10 tall and 2 tall, and columns 10 wide, 10 wide, and 3 wide.

Main Topics
  • Multiplication Models
    • Groups of
    • Repeated Addition
    • Area
    • Array
    • Cartesian Product
  • Factors
  • Products
  • Partial Products
  • Algorithms
    • Repeated addition
    • Expanded
    • Regrouping (Standard)
    • Hindu (left to right)
    • Lattice
  • Properties
    • Closure
    • Commutative
    • Associative
    • Identity (one)
    • Distributive property of multiplication over addition
  • Estimation

§ 3.4 Division and Exponents

Math Activity 3.4: Division Models

Check out section 3.4 of the book, Division and Exponents. There are 2 models listed:

1. The Set Partition Model (sharing concept)

2. The Repeated Subtraction Model (measurement concept)

For each of these illustrate and explain 42/3. Your illustrations should be similar to those in the book for Example D, 48/4.

Main topics
  • Definition of division:
    If n÷d=q, then q⋅d=n
    6÷2=3 since 3⋅2=6
  • Division Models
    • Set Partition
      Split 6 into 2 groups. How many are in each group?
      6 is 2 groups of 3, set Partition model for division
    • Repeated Subtraction
      How many groups of 2 are in 6?
      6 is 3 groups of 2, repeated subtraction, aka groups in
    • Missing Factor (aka what do I multiply by?)
      6÷2=□ means square xx 2 = 6
  • Division Algorithms
    • Repeated Subtraction
    • Grouped Repeated Subtraction
    • Scaffolding
    • Long Division
    • Short Division
  • Division Algorithm Theorem
    For any whole numbers n and d, with divisor d!=0, there are whole numbers q and r such That
    • n=d*q+r
    • 0≤r<d
  • Division with zero
    • 0//3=0
    • 3//0 is undefined
    • 0//0 is indeterminate
  • Equal quotients
    70-:20=7-:2=3 1/2
  • Approximate quotients and compatible numbers
    31-:16~~30-:15=2
  • Rounding and front-end estimation
    723-:215~~700-:200=7-:2=3 1/2
  • Exponents
    • b^0=1 show pattern
    • b^1=b show pattern
    • a^n*a^m=a^(n+m)
    • a^n/a^m=a^(n-m)
    • (a^n)^m=a^(n*m)
    • (a*b)^n=a^n*b^n
    • (a/b)^n=a^n/b^n
  • Scientific Notation
  • Order of Operations
    1. Parentheses (inside)
    2. Exponents
    3. Multiplication OR Division (left to right)
    4. Addition OR Subtraction (left to right)

Chapter 4: Number Theory

§ 4.1 Factors and Multiples

Math Activity 4.1: ?

§ 4.2 Greatest Common Factor and Least Common Multiple

Math Activity 4.2: ?