2. Pair off with another person, count the
number of triangles, explain the process,
and record the number.
2
3. Language through which most of
mathematics is communicated
Required course for high school
graduation
Gateway course for higher math
and science courses
Path to careers – math skills are
critical in many professions
3
4. Learn to value mathematics
Become confident in their ability to do
mathematics
Become mathematical problem solvers
Learn to communicate mathematically
Learn to reason mathematically
4
5. “Teachers must be given the
training and resources to
provide the best
mathematics for every
students”
-NCTM
5
6. Translate word problems into mathematical
symbols (processing)
Distinguish between patterns or detailed
information (visual)
Describe or paraphrase an explanation (auditory)
Link the concrete to a representation to the abstract
(visual)
Show fluency with basic number operations
(memory)
Maintain focus for a period of time (attention deficit)
Show written work (reversal of numbers and letters)
6
7. Solving problems
Visually representing problems
Processing problem
information
Self-monitoring
7
8. Language and communication
Processing
Attention
Organizational skills
Math anxiety
8
9. Instructional Strategies are
methods that can be used to
deliver a variety of content
objectives.
Examples:
Direct Instruction
Computer Assisted Instruction
9
10. Learning Strategies are
techniques, principles, or rules
that facilitate the acquisition,
manipulation, integration, storage,
and retrieval of information across
situations and settings
Examples: Mnemonics, Graphic
Organizers, Study Skills
10
13. CONCRETE: Uses hands-on physical
(concrete) models or manipulatives to
represent numbers and unknowns.
REPRESENTATIONAL or semi-
concrete: Draws or uses pictorial
representations of the models.
ABSTRACT: Involves numbers as
abstract symbols of pictorial displays.
13
20. Discover the sign
Read the problem
Answer or draw a
representation of
the problem using
lines, tallies, or
checks
Write the answer
and check
20
21. D iscover the variable
R ead the equation, identify
operations, and think about the
process to solve the equation.
A nswer the equation.
W rite the answer and check the
equation.
21
22. 4x + 2x = 12
Represent the variable "x“ with circles.
+
By combining like terms, there are six "x’s."
4x + 2x = 6x
6x = 12
22
23. Divide the total (12) equally among the circles.
6x = 12
The solution is the number of tallies
represented in one circle – the variable “x."
x = 2
23
24. The steps include:
Search the word problem;
Translate the words into an
equation in picture form;
Answer the problem; and
Review the solution.
24
25. Search: read the problem carefully,
ask questions, and write down facts.
Translate: use manipulatives to
express the temperature.
Answer the problem by using
manipulatives.
Review the solution: reread and
check.
25
26. More than & less than (duck’s mouth open
means more):
5 2
5 > 2
(Bernard, 1990)
26
27. O bserve the problem
R ead the signs.
D ecide which operation to do
first.
E xecute the rule of order
R elax, you're done!
27
29. PRE-ALGEBRA: ORDER
OF OPERATIONS
Parentheses, brackets,
and braces;
Exponents next;
Multiplication and
Division, in order from
left to right;
Addition and
Subtraction, in order
from left to right.
29
Please Excuse My Dear Aunt Sally
31. A graphic organizer is a tool or
process to build word knowledge by
relating similarities of meaning to the
definition of a word. This can relate
to any subject—math, history,
literature, etc.
31
32. Assist students in organizing and
retaining information when used
consistently.
Assist teachers by integrating into
instruction through creative
approaches.
32
33. #1 works with the figures
#2 asks questions
#3 records
#4 reports out
33
34. Differentiate the figures that
have like and unlike
characteristics.
Create a definition for each
set of figures.
Report your results.
34
35. GOs connect content in a meaningful way to
help students gain a clearer understanding
of the material (Fountas & Pinnell, 2001, as
cited in Baxendrall, 2003).
GOs help students maintain the information
over time (Fountas & Pinnell, 2001, as cited
in Baxendrall, 2003).
35
36. Heighten student interest.
Should be coherent and consistently
used.
Can be used with teacher- and
student- directed approaches.
36
37. 1. Provide clearly labeled branch
and sub branches.
2. Have numbers, arrows, or lines
to show the connections or
sequence of events.
3. Relate similarities.
4. Define accurately.
37
39. 1. Provide a partially incomplete GO for
students
2. Have students read instructions or
information
3. Fill out the GO with students
4. Review the completed GO
5. Assess students using an incomplete
copy of the GO
39
40. Teacher uses a GO cover sheet with
prompts.
Example: Teacher provides a cover
sheet that includes page numbers
and paragraph numbers to locate
information needed to fill out GO.
Teacher acts as a facilitator.
Students check their answers with a
teacher copy.
40
41. Framing the lesson
Previewing
Guided practice
Independent practice
Check for understanding
Peer mediated instruction
Simplifying the content or structure of the
GO
41
48. 48
Positive Integers
Numbers
What is it?
Illustration/Example
What are some
examples?
Properties/Attributes
What is it like?
Fractions
Compare and Contrast - example
Whole
Numbers Negative Integers
Zero
-3, -8, -4000
6, 17, 25, 100
0
54. Word = Category + Attribute
= +
Definition: A four-sided figure with four equal
sides and four right angles.
54
Square Quadrilateral
4 equal sides &
4 equal angles (90°)
56. 56
1. Word: semicircle 2. Example:
3. Non-example:
4. Definition
A semicircle is half of
a circle.
57. Divide into groups
Match the problem sets with the
appropriate graphic organizer
57
58. Which graphic organizer
would be most suitable for
showing these relationships?
Why did you choose this
type?
Are there alternative choices?
58
61. Addition Multiplication
a + b a times b
a plus b a x b
sum of a and b a(b)
ab
Subtraction Division
a – b a/b
a minus b a divided by b
a less b b) a
61
62. Use the following words to organize into
categories and subcategories of
Mathematics:
NUMBERS, OPERATIONS, Postulates,
RULE, Triangles, GEOMETRIC FIGURES,
SYMBOLS, corollaries, squares, rational,
prime, Integers, addition, hexagon,
irrational, {1, 2, 3…}, multiplication,
composite, m || n, whole, quadrilateral,
subtraction, division.
62
