Transcript GACE Math Review Study Session Presented By: Tonya Clarke and Joe E.

GACE Math Review Study
Session
Presented By: Tonya Clarke and Joe E. Hart
[email protected]
[email protected]
Website: http://www.heritagekids.info/5.htm
GACE Early Childhood Education 001, 002
Web site www.XAMonline.com
GACE Math Review Study
Session
Sample Content Area Exercise
Page 3 -4
Overview
The Language of Math
 Math Concepts and Skills: Numbers and
Mathematical Operations
 Math Concepts and Skills: Geometry
 Math Concepts and Skills: Algebra
 Math Concepts and Skills: Data Analysis
 Problem Solving
 Instruction Strategies

The Language of Math
http://www.amathsdictionaryforkids.com/
 http://www.mathwords.com/
 http://www.harcourtschool.com/glossary/
math2/index_temp.html
 Dictionary Sheet Kaplan p330-331

Instructional Strategies

Model Lesson on Multiplication
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
1. Multiplication story (Initial Focus – Get their attention)
2. Model with Concrete Objects
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Use connecting cubes to make rectangular arrays
Commutative property of Multiplication
3. Guided Practice with Pictures
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

Draw pictures of actual objects
Draw pictures of circles and dots
Number Sentence
factor
 4 x 6 = 4 groups of 6
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Factor X Factor = Product factor
4. Independent or group work
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

Product
Memorization (Flash cards)
What are things that come in 6’s? (connect to life)
5. Summarize
Instructional Strategies

Concrete to Abstract

Hands-on materials
Base-Ten Blocks
 Counting Bears
 Tiles
 Counters
 Judy Clocks
 Play Money
 Fraction Bars

Instructional Strategies

Deductive reasoning
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Proceeds form the general to specific.
Inductive reasoning

Proceeds from specific to general.
Instructional Strategies
Instructional Strategies

Different ways to different answers
Encourage mathematical conservations
 Accept mathematically sound explanations
 Develop the use of mathematical journals to
springboard mathematical conversations

Math Concepts/Skills: Operations

1. Comparing
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2. Ordering
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greater than (>), less than (<), equal to (=)
Greater than or equal to( ), less than or equal to ( )
alligator, Pacman, abc order
3. Estimating

educated guess, about, rounding, benchmarks
Math Concepts/Skills: Operations
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Rounding
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Number Lines
Steps:
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Underline the place
Look next door
5 or less, the underlined # stays the same
5 or more, the underline # goes up 1

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Ex. 32. 8 rounds to 33, Ex. 32. 4 rounds to 32
Nearest ten, hundred, thousand, ten thousand,
dollar, dime, nickel, tenth, hundredth
Math Concepts/Skills: Operations
•
Estimate
•


Rounding
Benchmark numbers
4. Place Value

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Up to the hundred thousands
and to the hundredths
987,654.321
Expanded Notation/Form

Ex: 5,621 = 5,000+600+20+1
Math Concepts/Skills: Operations
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5. Prime and Composite Numbers
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Prime numbers only divisible by themselves and 1
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Composite numbers have more than two factors
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10 = 1 X 2 X 5
36 = 1 X 2 X 2 X 3 X 3
6. Multiples
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Numbers that can be created by multiplication
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1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53,
59, 61, 67, 71, 73, 79, 83, 89, 97, 101
4, 6, and 12 are multiples of 2
7. Factor
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Number that can be created by division
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1, 2, and 3 are factors of 36
Math Concepts/Skills: Operations
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8. Fractions

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1
4
Equal parts of a whole
Identify by pictures first
Numerator (top number) tells the parts being
examined (shaded, unshaded, etc)
Denominator (bottom number) tells the
number of parts in all
Math Concepts/Skills: Operations

9. Adding Fractions

Like denominators
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Add only numerators
1
2
3


4 4
4
Unlike denominators

Find least common multiple of the denominator
1 2 2 2 4 1
    
4 8 8 8 8 2
Math Concepts/Skills: Operations

10. Subtracting Fractions

Same Denominators

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Subtract numerators
2
1
1


4
4
4
Different Denominators

Find least common multiple of the denominator
2 2 4 2 2 1
    
4 8 8 8 8 4
Math Concepts/Skills: Operations
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
11. Equivalent
Fractions
12. Simplifying
Fractions

Divide by greatest
common factor
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5/35 = 1/7
24/49 = 4/7
1 2 3 10
  
2 4 6 20
5
55 1


35 35  5 7
Math Concepts/Skills: Operations

13. Multiplying Fractions

Multiply numerators and denominator
4 6
24
 
5 7
35

Can simplify first
4 5
45
11 1




10 20 10  20 2  5 10

14. Dividing Fractions

Multiply by the inverse
4 5 4 20 4  4 16
   

5 20 5 5 1  5 5
Math Concepts/Skills: Operations
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15. Mixed Numbers
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Adding
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5 34  6 18  5 86  6 18  1178
Subtracting

11 78  5 34  11 78  5 86  6 18
Math Concepts/Skills: Operations
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16. Decimals
1/10 = 0.1
 1/100 = 0.01
 1/1000 = 0.001
 ¼ = 0.25, 1/2 = 0.5, ¾ = 0.75
 4/4 = 1.0

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17. Percentages

0.25 = 25%, 2.45 = 245%
Math Concepts/Skills: Operations
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18. Properties of Numbers and Number
Systems
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Commutative (Addition and Multiplication)
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When the order of 2 factors is changed the product is the
same (this also works for addition)
5 x 7 = 7 x 5,
5+7=7+5
35 = 35,
12 = 12
Associative (Addition and Multiplication)

When multiplying 3 or more factors, any of the two factors
can be multiplied, and the remaining factors may then be
multiplied without changing the product ( this also works
for addition)
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(3 x 4) X 5 = 3 x (4 x 5),
12 x 5 = 3 x 20,
(3 + 4) + 5 = 3 + (4 + 5)
7+5=3+9
Math Concepts/Skills: Operations

Distributive
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When multiplying the sum by a number is the same as
multiplying each addend by the number and then adding
the products

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Identity
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When multiplying any factor by 1, the product is the other
factor (when adding any number to 0 the sum is the other
number)
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
3 x (4 +2) = (3 x 4) + (3 x 2)
3 x 6 = 12 + 6
18 = 18
1 x 5 = 5,
0+5=5
Property of Zero

When multiplying any factor by 0, the product is 0
Math Concepts/Skills: Operations
M
A
T
H
O
1a
2a
3a
4a
5b
6b
17a
18a
16e
7a
8a
1b
9c
15b
9a
10a
11b
5e
3c
11a
12a
13a
14a
15a
16b
Math Concepts/Skills: Operations
M
A
T
H
1a=B
2a=B
3a=B
6b=A
17a=D 18a=D 16e=A
7a=D
8a=D
1b=E
9c=D
15b=B
9a=C
10a=B
11b=C
5e=D
3c=A
11a=C
12a=A
13a=B
14a=C 15a=D 16b=C
4a=A
O
5b=A
Math Concepts/Skills: Geometry
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19. Metric System
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Length/Distance
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mg, g, kg
Length/Distance
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in, ft, yd, mi
Capacity
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mL, L
Mass

20. Customary
System
mm, cm, m, km
Capacity
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c, p, q, gal
Weight

oz, lb, ton
King Henry Drove My Dumb Cat Mad
i
e
e
e
e i
l
c
k
c
n l
l
t
a
i
t l
i
o
i i
Math Concepts/Skills: Geometry

Measurement
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22. Perimeter
perimeter
The distance around a figure
Example:
2 cm + 3 cm + 3 cm = 8 cm
The perimeter of this figure is 8 centimeters.
Math Concepts/Skills: Geometry

Measurement

23. Area
area
The number of square units needed
to cover a surface
Example:
The area is 9 square units.
Math Concepts/Skills: Geometry

Measurement

24. Volume
volume
The measure of the amount of space a solid figure occupies
Example:
The volume of this figure is 24 cubic units.
Math Concepts/Skills: Geometry
Measurement
 25. Time

Elapsed Time
 Time to minute

elapsed time
The amount of time that passes
between the start of an activity and
the end of that activity
Example:
Math Concepts/Skills: Geometry
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Measurement
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26. Temperature
degree Celsius (°C)
A metric unit for measuring
temperature
degree Fahrenheit (°F)
A customary unit for measuring
temperature
Math Concepts/Skills: Geometry
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Geometric Figures
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Plane Figures
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27. Circle
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diameter (2r), radius, circumference (pi x d), C ÷ d = 3.14
(pi)
circumference
The distance around a
circle
diameter
Example:
Example: diameter
A line segment that passes through the center
of
a circle and has its endpoints on the circle
Math Concepts/Skills: Geometry

Geometric Figures

Plane Figures
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28. Quadrilateral
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
polygons with 4 sides and 4 angles
trapezoid, parallelogram, rectangle, rhombus, square
Quadrilaterals
(A figure bounded by four distinct line segments)
Parallelogram
Trapezoid
(opposite sides congruent and parallel)
(One pair of opposite sides
parallel)
Rectangle
Rhombus
(4 right angles)
(All sides are congruent)
Square
(4 right angles and 4 congruent sides)
Math Concepts/Skills: Geometry

Geometric Figures

Plane Figures
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29. Triangles
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isosceles- 2 congruent sides
scalene- each side different
equilateral- all congruent sides
isosceles triangle
scalene triangle
A triangle with two congruent sides
A triangle with no congruent sides
equilateral triangle
A triangle with three congruent sides
Example:
Example:
Example:
Math Concepts/Skills: Geometry
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Geometric Figures
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Plane Figures
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29. Triangles

right, acute, obtuse classified by angles
right triangle
A triangle with one right angle
Example:
acute triangle
A triangle in which all three angles are acute
Examples:
obtuse triangle
A triangle that has one obtuse angle
Example:
Math Concepts/Skills: Geometry

Geometric Figures
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Plane Figures
30. Solid Figures

cone, pyramid, sphere, square pyramid, rectangular prism,
cube (nets)
Math Concepts/Skills: Geometry
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31. Similarity

same shape, same angles, same ratio of
side lengths
Figures with the same shape but not necessarily the same size
Example:
Math Concepts/Skills: Geometry

32. Congruence

same size and shape
Math Concepts/Skills: Geometry

33. Transformations of Plane Figures
slide- move to side – translation
 flip – across line – reflection
 turn –move around a fixed point - rotation

translation
reflection
rotation
Math Concepts/Skills: Geometry
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Angles and Rays
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34. Ray
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35. Angle



part of a line that has one endpoint and goes on forever in
one direction; named by its endpoint and one other point
on the ray
two rays that have the same endpoint; named by vertex
and one point on each ray or just the vertex
acute (less then 90), obtuse (more than 90), right (exactly
90)
36. Tools for measuring: measured with protractor
Math Concepts/Skills: Geometry

37. Line Relationships

Point


Line



straight path in a plane; has no end; named by any two
points on the line
Line segment


identifies a location on an object; named by a letter
part of a line between two endpoints
Plane

flat surface with no end; named by any three points on
a plane
Math Concepts/Skills: Geometry

Perimeter


P = s1 +s2 +s3 + s4
Area
A = s1 x s2
 A=LxW
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Volume

length x width x height
Math Concepts/Skills: Geometry

Hollywood 2’s
Math Concepts/Skills: Algebra

38. Patterns
1, 2, _, 4
 13, __, 39, 52, __, 78


39. Order of Operations

Please Excuse My Dear Aunt Sally
Parenthesis
 Exponents
 Multiplication/Division
 Addition/Subtraction

Math Concepts/Skills: Algebra
52 + 7 x 4 – (4 +22) =
 40. Find errors:

4 x (5 ÷ 1) + 3 =
 20 ÷ 1 + 3 =
 20 ÷ 4 = 5

Math Concepts/Skills: Algebra
•
41. Balanced Equations
•
Must do the same action to both sides
•
•
•
•
4+x= 9
4-4+x=9-4
x=5
42. Inequalities
•
•
9>4+2
9 < 1 +11
Math Concepts/Skills: Algebra

43. Graphs

Ordered Pairs (x, y)
x = horizontal axis
 y = vertical axis
 Over Rover

Math Concepts/Skills: Algebra

Quizdom Game
Math Concepts/Skills: Data Analysis

44. Graphs

Pictographs
Math Concepts/Skills: Data Analysis

44. Graphs
Pictographs
 Bar Graphs

Math Concepts/Skills: Data Analysis

44. Graphs
Pictographs
 Bar Graphs
 Tally Tables
 Frequency Tables

Math Concepts/Skills: Data Analysis

44. Graphs
Pictographs
 Bar Graphs
 Tally Tables
 Frequency Tables
 Line graphs

Math Concepts/Skills: Data Analysis

44. Graphs
Pictographs
 Bar Graphs
 Tally Tables
 Frequency Tables
 Line graphs
 Circle Graphs

Math Concepts/Skills: Data Analysis

Probability
45. most likely, least likely, certain
 46. mean (average)
 47. mode (result that occurs the most)
 48. median (the middle data result)
 49. range (first to last result of data)

Mean = 3+10+5+5+2 = 25/5= 5
Median =1, 2, 3, 5, 5, 9 = middle number is between 3 and
5 = average of 3 and 5 = 4
Mode = 5
Problem Solving

50. Strategies

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Real life situations
Work Backward
Draw a Picture
Act It Out (use manipulatives)
KWHA (What I Know, What I Want to Know, How I
Will Solve It, Answer)
Use a Formula
Groups (How would you work the problem?)
Assessment
Quizdom Review
 Tests
 Performance Assessments
 Math Journals
 Create Your Own Problem


Are you smart enough to be a 5th Grade
Teacher? (Teaching Math)
Written Assessment
Review Sample page 3-4
 Kaplan p 343-344
