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Mathematics in Elementary Education - Coggle Diagram
Mathematics in Elementary Education
Module 2
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:
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.
Module 1
Course Introduction
:
Notes
Required Materials
Base ten blocks: accurate, printed or purchased
Color counters: two varying shapes
Fraction manipulative
Homework Practice:
Complete all problems
Check answer key
Complete self-evaluation
Ploya's 4 Step Problem Solving Process
:
Notes
UnDevCarLo
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
Module 4
Building, Showing, and Solving Subtraction
Notes
Expanded form:
Expandable :check:
Efficient :red_cross:
Based in math :check:
Left-to-Right:
Begin with the left side to subtract all that you can until you can exchange for #s allowing you to subtract.
Expandable :check:
Efficient :green_cross:
Based in math :check:
Equal addends: Friendly numbers- #s ending in zero
Module 3
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 :check:
Efficient :red_cross:
Based in math :check:
Left-to-Right:
does not require that students rewrite the original problem
Expandable :check:
Efficient :check:
Based in math :check:
Friendly Numbers - Trading Off
: friendly #s end in 0
Expandable :check:
Efficient :check:
Based in math :check:
Scratch Method
Module 5
Build, Show, and Solve Multiplication
Notes
Expanded Form
: After expanding, multiply numbers up and down, then diagonally (vice-versa)
Expandable :check:
Efficient :red_cross:
Based in math :check:
Left-to-Right
: Each value in the first number is multiplied by each value in the second number
Fewer times students are required to rewrite problems, the better.
Expandable :check:
Efficient :check:
Based in math :check:
Area Model
: Similar to building the rectangle model, shorthand version of building rectangle model
Expandable :check:
Efficient :check:
Based in math :check:
Lattice
:
Expandable :check:
Based in math :red_cross:
Efficient :check:
Module 6
Show and Solve Division and Intro to Fractions
Notes
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