Mathematics in Elementary Education
Module 2
Module 1
Course Introduction:
Notes
Required Materials
Ploya's 4 Step Problem Solving Process:
Notes
UnDevCarLo
Module 4
Homework Practice:
Module 3
Building, Showing, and Solving Addition in Base Ten and other bases.
Notes
In base ten, a single unit is equal to 1, a single long is equal to 10 units, and a single flat is equal to 10 longs or 100 units.
We can assume that any number written without script, is in base ten.
When working with bases not including base ten, the base tells you how many blocks you need to make a full group.
5/10 Frames:
Complete all problems
Check answer key
Complete self-evaluation
Base ten blocks: accurate, printed or purchased
Color counters: two varying shapes
Fraction manipulative
Look back: does the answer make sense?
Understand the problem: break it down into parts
Develop a plan: use prior knowledge to brainstorm steps
Carry out the plan
Students should fill in the 5 frame (anchor) first
One object per one square
When students are drawing diagrams, units should be represented with dots, longs as vertical lines, and flats will be drawn as squares.
Addition: Alternative Algorithms
Notes
Components of a "good" algorithm:
Expandable
Efficient
Based in mathematical properties
Expanded Form: write each number showing the value of each Place Value
Expandable ✅
Efficient ❌
Based in math ✅
Left-to-Right: does not require that students rewrite the original problem
Expandable ✅
Efficient ✅
Based in math ✅
Friendly Numbers - Trading Off: friendly #s end in 0
Building, Showing, and Solving Subtraction
Notes
Expanded form:
Expandable ✅
Efficient ✅
Based in math ✅
Scratch Method
Module 5
Build, Show, and Solve Multiplication
Module 6
Show and Solve Division and Intro to Fractions
Notes
click to edit
Notes
Expanded Form: After expanding, multiply numbers up and down, then diagonally (vice-versa)
Left-to-Right: Each value in the first number is multiplied by each value in the second number
Area Model: Similar to building the rectangle model, shorthand version of building rectangle model
Expandable ✅
Efficient ❌
Based in math ✅
Fewer times students are required to rewrite problems, the better.
Expandable ✅
Efficient ✅
Based in math ✅
Expandable ✅
Efficient ✅
Based in math ✅
Lattice:
Expandable ✅
Based in math ❌
Efficient ✅
Module 7
Building Fractions
Working with fraction manipulatives
Area Model: : Ex. "Fraction" of the area of the white circle is red.
Linear Model: Ex. "Fraction" of the length of the green line is marked/colored in
Set Model: Ex. "Fraction" of this set are pink circles.
Understanding the parts of a fraction
Numerator: Number of pieces/things that are present
Denominator: Size of those pieces/things
Module 8
Left-to-Right: Begin with the left side to subtract all that you can until you can exchange for #s allowing you to subtract.
Equal addends: Friendly numbers- #s ending in zero
Expandable ✅
Efficient ❌
Based in math ✅
Expandable ✅
Efficient ❎
Based in math ✅