Elementary Math 280
Week 11
Exam #2
- Alt Algorithms- Subtractions
- Expanded Form
- Equal addends= add same number to both sides to make friendly number on Take Away side
- Order to teach the multiplication table and why?
- Red (64%), Green (24%), Yellow
- 1's, 2's, 10's, 3's, 9's, Doubles, 4's,6's,7's,8's
- Previously learned skip counting
- Division
- Repeat Subtraction
- Upwards Division
- Building and showing integers
- Add/Subtract using Tiles
- Use Keep Change Change and diagram to solve
- Multiply- Show and solve
- Parts of a fraction and comparing fractions with reasoning's
- Rules of multiplication
- Same signs = +
- Different signs = -
- Divisibility rules
MindMap
Weeks 7-10
Week 10
Review for Exam #2
Mindmap Project #1
- Summarize Weeks 7- 10
- Give ways to solve
Fractions intro to Algorithm
Addition
- whole numbers: just add them
- mixed numbers and a mixed number: Add whole numbers first, Next Find same denominator; Last add fractions
Subtraction
- whole number from a fraction: Make whole number into mixed fraction using same denominator; Then subtract
- mixed number and mixed number: subtract whole numbers first; find same denominator; last solve
Whole number + fraction = combine
Whole number - fraction = take one from whole number put in form a fraction (same denominator as other fraction); Then subtract the fractions. New whole number carries over
Solving Fractions
- what you do to the numerator you have to do to the denominator
- denominators must be the same
- No cross multiplying need
- Always must equal 1 EX: 10/10; 1/1(both Numerator and denominator is the same number
Ex: _5_*_3__ +_8__* _2_
8 * 3 + 12 * 2
_ _15_+ 16_= 31_
24 + 24 = 24
= 1 _7
24
Comparing Fractions
- Compare: >,<,=
- > is greater than
- > is less than
- Anchor Fractions- fractions that we know
- like 1/2-compare fraction to "is it more than 1/2"
Fractions Intro
- Numerator- Number of Pieces
- Denominator- Size of Pieces
- No need to use terms like improper fraction
By Jackie Shipman
Week 9
Solving Subtraction and Multiplication/Division
Subtraction:
- is the same as adding the opposite
- Use KEEP-CHANGE-CHANGE then use Hector's Diagram
Ex: -43-20
K C C
-43+(-20)
-- - =-63
Multiplication and Division
Rules
- Same signs = +
- Different signs = -
- EX:
25(-60) Different signs = -
Build and Show Subtraction/ Multiplication
Build: use 2 color counters
red is negative other color is positives
Subtraction:
- start with first number __ take away___
- example 4-7 = 4 pos take away 7 pos- add a zero bank
ooooooo
ooo =-3
Multiplication:
- first number is group. number in ( ) = how many in groups
- ex: -3 (-2) = take away 3 groups of 2 neg
oooooo= 6
oo/oo/oo=0
Show: draw a diagram
use + and - signs
Subtraction:
- -2-5= 2 neg take away 5 pos
+++++ =
- - - - - - - =-7
Multiplication:
- state it correctly
- ___ groups of ___
- EX: -4 (2) = Take away 4 groups of 2 pos
++/++/++/++/ =0
- - - - - - - - =-8
Week 8
Solving Adding Integers
- Hectors Method-two signs on top of the largest number; 1 sigh on top of the smaller.
- Circle one from from each number
- The sign not circled reminds what sign the answer will be
- different signs =subtraction
- same signs = addition
Build and Show Integers-Add
Integers: any numbers that are positive and negative
- build is to show with materials.
- use 2-color counters
- Red is negative and always on bottom
- yellow is positive and always on top
- add a zero bank
- 1 positive with 1 negative = zero
- Show- use symbols
- + stands for positive
- - stands for negative
EX: show 4 using 10
+ + + + + + + + +
- - - - -
Divisibility Rules
Divisibility Rules:
2's- Even numbers
3's- sum of the digits are divisible by 3
4's- the last 2 digits are divisible by 4
5's- last digit is a 5 or 0
6's- if 2 and 3 works then 6 works
8's- if last 3 digits are divisible by 8
9's- the sum of the digits are divisible by 9
10's- last digit is 0
no rules for 7
Week 7
Division Alt Algorithms: Repeat Subtraction and Upward Division
- number divided into how many groups
- long division- have to be able to estimate, then multiply, next subtract and bring it down and know what to do with remainders *not a good method* Must know times tables
Repeated subtraction
- use what they know
- answer ends at the bottom
- don't have to know any special skills
- get close to the number without going over
Upwards division
- write it as a fraction- (the way you read it)
- Separate numbers
- solve left to right
- write the subtraction by the nu mbers
- the remainder is at the numerator and it stays, then move the denominator up below numerator
Multiplication Alt Algorithms: Expanded Form, Left to Right, Lattice
- Expanded Form: separate for place values, then multiply ame place values, then add together
- Left to Right: multiply starting with the left side using place value, then add answers together
- EX: 47*53
4 7
X 5 7
2000
350
120
+ 21
2491
- Lattice: draw the lattice box with diagonal cuts. Write one number on top and the other number on the right and multiply. Last add the numbers diagonally
multiplication Automaticity
- Finding area
- Timed test: ineffective because of the stress and pressure that they put on our students (does not access long term memory) hurt self image
- times test teach automaticity
- use flash cars-(make your own) focus on the group you are working on
- Tricks do not work
- teach times tables in order Red (64%), Green (24%), Yellow
1's, 2's, 10's, 3's, 9's, Doubles, 4's,6's,7's,8's
Alternative Algorithm-Subtraction-Expanded Form and Equal Addends
- Expanded Form: expand each place value and then subtract across
EX: 278-57
200+70+8 200+60+18
- 0 +50+7 - 0 +50+7
200+10+9 = 219
- Equal Addends: Add an equal amount to both numbers( turn the
EX: 134-56
134 + 4 = 138
-56 + 4 = - 60
78
Spiraling Content
- Revisit previously learned content throughout a semester
- Used to reinforce material
- So students cant forget anything
- Reminds of old content
- Gives students a chance to learn the content over a matter of weeks instead of teaching all at once and the students forgetting the content
Week 15
Mindmap part 2
weeks 11-15
Scientific Notation
Three Parts of Scientific Notation:
- first number always between 1 and 10
- always times 10
- has exponent (e^-1 is a decimal)( e^+ is a big number)
positive exponent = number bigger than 1
negative exponent = decimal
Example:
4.25 x 10^-4 = small number
0.000425
1.63 x 10^7 = big number
16,300,000
Week 14
Order of Operation
Forget- (PEMDAS)
G- Groups
E- Exponents
M/D or D/M- multiplication and division left to right
A/S or S/A- Subtraction and Addition left to right
Exponents:
(-4)^2=(0-4)^2=16
-(4)^2=0-(4)^2=-16
-4^2=0-4^2=-16
-(-4)^2=0-(0-4)^2=-16
Week 13
Solve Decimals
- estimate
- line up whole numbers
- place decimal based on estimate
Multiply Decimals
- estimate- make sure the answer makes since
- multiply without decimals
- look at your estimate to place the decimal
Subtract Decimals
draw
Add Decimals
Draw one square and divide based on place value
- 0.1 = separate into ten
- 0.24 = separate into 100
Next color or shade the first decimal
Then shade the second decimal in
bigger decimals:
- estimate= does the answer make since
- write it out, line up whole number
Show Decimals
draw squares and equally divide the squares
Week 12
Dividing fractions
Always estimate first
- do the backwards C for mixed numbers= take the denominator and times the whole number then add the product to the numerator
- Keep Change Flip
15 / 18 15 X 10
22 10 22 18
k c f
3. Factor each numerator and each denominator
3*5 2*5
15 X 10
22 18
2*11 6*3
4. Use funky 1's= cross out on numerator with equal denominator
5 X 5 = 25
11 6 66
Multiply Fractions
Always estimate first
Numerator times numerator= numerator
Denominator times Denominator = demoninator
Build and Show fractions
Build- use fraction tiles or circles
Show- Draw a box and separate it into the number of squares marked by the denominator
Add fractions- will have 3 squares- first 2 will be perpendicular
Subtraction will have 2 squares
Multiplication will have 1 square- separate with perpendicular lines
