Transcript Manipulating Math - University of Georgia

Presented by Juli DeNisco
Crowder College AEL Director
Materials:
Yarn or String
Ruler
Calculator
Circular Object
Paper and Pencil
o
o
o
o
Wrap a string or yarn around a circular object.
Using a ruler measure the amount of string
Record this amount. This is Circumference
Next measure the diameter of the circle
Reminder for Teachers:
Pi = 3.14 or 22/7
The symbol for Pi looks like this
The idea of Pi is that the circumference of a circle
is approximately 3.14 times the diameter.
The formula for circumference is
distance (d)
circumference (C).
Seeking Patterns, Building Rules
Algebraic Thinking
McGraw Hill - EMPower
Collaboration Activity


Match the graphs, tables, equations and ads
Combine all phone plans into one graph


Complete Activity 2: It Would Depend on the
Person
Complete: Phone Plans Algebra
(Adult Numeracy Institute Handout)
Demystify Algebra Immediately
•I
can’t do Algebra
•I don’t understand why there are letters and number
“You can do algebra you just don’t realize it.”
_ + 5 = 12 …”what is it?”
“Yes, 7 + 5 = 12”
“In algebra we use a letter instead of a blank!”
x + 5 = 12
X
2
X
X
1
1
Positive
2
X
1
1
1
Negative
1
Solving Equations


Balance the equation.
What you do to one side of the equal sign, you must do the same to
the other side.
X +3 = 8
X
=
X+3
8
Solving Equations


Balance the equation.
What you do to one side of the equal sign, you must do the same to
the other side.
X +3 = 8
X
X
=
X=5
=
Solving Two-Step Equations
2x + 3 = 11
X
X
=
Solving Two-Step Equations
2x + 3 = 11
X
X
=
Solving Two-Step Equations
2x + 3 = 11
X
=
Virtual Algebra Tiles
X=4
X
Algebra Tiles Online
Using Algebra Tiles to Teach
Negative and Positive Computation
Online tutorials for teaching Neg and Pos with
Algebra Tiles
Math topics reviewed in this lesson:
o
o
o
o
o
o
o
Organizing Data with Charts and Tables
Converting Fractions, Decimals, and Percents
Finding the Mean and Median
Determining Probability
Finding Percentages
Graphing Data
Creating a Bar Graph and a Pie Graph
Organizing Data with Charts
YOUR BAG
COLOR
#
FRAC
CLASSROOM
DEC
%
COLOR
Blue
Blue
Brown
Brown
Green
Green
Orange
Orange
Red
Red
Yellow
Yellow
Total
Total
#
FRAC
DEC
%
Finding the Mean (Average) and Median
1. What is the average (mean) number of orange M&M’s in
this size bag?
2. What is the average number of blue M&M’s in this size
bag?
3. What is average number of yellow M&M’s?
4. What is that average number of brown M&M’s?
5. What is the average number of red M&M’s in the bag?
Probability
6. If you put all of the M&M’s in a cup and mixed
them up, what is the probability that you would
pick a red M&M?
7. If you put all of the M&M’s in a cup and mixed
them up what is the probability that you would
pick a blue M&M?
8. Under the same circumstances what is the
probability that you would pick a green M&M?
9. What is the probability you would choose a purple
M&M?
Finding Percentages and Median
10. Using the percentage of red from the Classroom Color
Chart what number of red M&M’s would you expect to
find in a bag of 300 M&M’s?
11. Using the percentage of green from the Classroom Color
chart what number of green M&M’s would you expect to
find in a bag of 300 M&M’s?
12.Using the percentage of blue from the Classroom Color
chart what number of blue M&M’s would you expect to
find in a bag of 300 M&M’s?
13. What is the median number of M&M’s in a ‘fun size’ bag?
Graphing Information

Use the information from YOUR BAG on the M&M’s
Color Chart. Put the information into the bar graph
in color.
Blue
Brown
Green
Orange
Red
Yellow
Graphing Relationships

STEP 1: Cut out colored bars and
tape end to end into bracelet.

STEP 2: Place the bracelet on paper
and trace the circle. Use the colors
to determine the size of each piece
of pie.

Arrange Squares

Trace Triangles

Measure Sides

Observe the
relationship between
sides and hypotenuse

Define Terms:

Right Angle

Sides

Hypotenuse
STUDENT TOOLBOX:
The Hypotenuse is always C.
It can be remembered as the C
for Cut across.

Plug in the
numbers and
SOLVE.
c² = a² + b²
 c² = 4² + 3²
 c² = 16 +9
 c² = 25
 Square root of 25 = 5
C = 5

Empower Series: Over, Around and Within
 Angles
 Perimeter
 Area
 Volume
 Similar shapes, scale and units of measure
 Surface area and volume
Geometry Sampler
http://empower.terc.edu/pdf/Over_Around_and_Within.pdf
Keeping Things in Proportion
Reasoning with Ratios
McGraw Hill
OBJECTIVES:
• Use the cross-product property as a tool to check that two ratios
are equal
• Distinguish between a true and a false proportion equation
• Use estimation to predict for more complicated numbers in
proportions
• Determine the missing number in a proportion
400
25
= 2,000
125
How could you test whether this proportion is true?
400
25
= 2,000
125
What is the relationship between 400 and 2,000?
Between 25 and 125?
400
25
= 2,000
125
What is the relationship between 400 and 25?
Between 2,00 and 125?
400
25
= 2,000
125
How could you test whether this proportion is true?
400
25
= 2,000
125
What is 400 divided by 25? What is 2,000 divided 25?

Set up a proportion with card set 1

Share final proportions with class
5
10
20

Set up a proportion with card set 2

Share final proportions with class

Complete Activity 1 Worksheet
76
123
251

All percent problems have four parts:
PART
WHOLE
%
100

The Part

The Percent

The Whole

100

15 is what percent
of 30?

15 x 100=1,500

1,500 / 30 = 50

X= 50%

15 is what percent
of 30?

15 x 100=1,500

1,500 / 30 = 50

X= 50%
Using a proportion box
Question: Last week Meredith traveled 125 miles on 5
gallons of gas. If she buys 12 gallons of gas
approximately how far will she be able to travel on her
next trip?
STUDENT TOOL BOX:
Note the relationship between the
percent box and the percentage box

1.
2.
3.
4.
What is 70% of 150?
PART
%
WHOLE
100
Place the known numbers in the
BOX
Use an X for the unknown
number
Multiply the numbers that are
diagonally opposite from each
other.
Divide the answer by the number
that wasn’t used.
150 X 70 =10,500
10,500 / 100 =105
X = 105
Using a proportion box
Answer:
125 X 12 = 1,500
1500 / 5 =300
X =300
Part
%
Whole
100
STUDENT TOOL BOX:
Note the relationship between the
percent box and the proportions box
Understanding the concept of subtracting a negative
number and changing both of the negative signs to
positive signs
•
•
Make cards with positive numbers from 1-9 on
one side and negative numbers on the back.
Also make a card with - on one side and + on the
back.
FLIP cards
-6 + (+5) = -1
Also written -6+5= -1
You will now move five
places in the positive
direction.
Plotting X-Y Coordinates

Sample Ship Box
Master Map has 10 ships

Sample Student Graph
HITS in RED
MISSES in BLUE
The horizontal axis is called the x-axis.
And the vertical one is the y-axis.
STUDENT TOOLBOX:
(X, Y) Z
Three ways to use the flashcards
Diameter
Quotient
Distance
through the
center of a
circle
Answer to
division
problem
Circumference Distance
around a circle
Complementary
Angles
Sum equals 90
Individual
or Partner - Students can match the cards
individually or with a partner. If used with a partner
they can see who can match the cards first.
Concentration
- Face the cards face down on a table. A
student turns over two cards. If they match the student
keeps the cards. If not, turn the cards over and let
another try. They will need to remember where the
cards are that were turned over. The student with the
most matches wins
Group –
Deal half the cards out to 4 or 5 students. The
teacher will hold up a card and the student
with the match gets the card. Another student
can steal the card by knowing the answer once
everyone has had a chance to try to match their
cards to it. If no one knows the answer it goes
back into the teacher pile. The student with the
most matches wins.
Free Financial Literacy online curriculum
From Wells Fargo Bank!
•
•
Free Interactive online program for students
HANDS ON BANKING
Free PRINTABLES – comprehensive lesson
plans and worksheets for kids, teens, young
adults and adults
•
DICE GAME
Practice Addition Skills
• Each player takes turns rolling dice. If you roll a double you
loss your turn. If you roll a snake eyes (2 ones) you loss
your entire bank.
• Add the two dice for points and total results
• First one to 100 wins!
•
Practice Multiplication Skills
• Use two sets of dice one set will represent one of the
numbers to be multiplied
• Multiply the total of first two dice times the total of the other
set of dice. If you roll a double you loss your turn. If you roll
a snake eyes (2 ones) you loss your entire bank.
• First player to 500 wins!
LINCS Website
The four LINCS regions have ANI-PD available:


ANI-PD is an intensive evidence-based
program in effective numeracy instruction for
adults.
http://www.mugginsmath.com/
Offers Math Manipulatives
Great videos on how to use manipulatives
•
•
http://www.fdic.gov/consumers/consumer/moneysmart/trainthetrainer.html
•
•
FDIC Money Smart Free Educational Materials
Train the Trainer tutorials for Teachers

CONTACT:
Juli DeNisco
AEL Director
Crowder College
601 Laclede Ave
Neosho, MO 64850
 417-455-5521
[email protected]