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OUTLINE• Fraction wall• Number Line Wall• Algebra tiles• Gridline Wall• Geoboard• Pie• Platonic and Archemedean solids• Perimeter• Area• Surface area• Volume• Instrcutional Materials
OBJECTIVE
This instructional material is made for students to :• easily review on the basic concepts on
fractions• identify the basic skills in using fractions • solve algebraic operations with fractions and for mastery of any problems involving fractions.
The fraction table has two horizontal lines. The lower horizontal line is for the fractions (numbers) and the upper horizontal line is where students will put the number of blocks to be added, subtracted, multiplied or divided. These blocks are colorful rectangles.
• Basic operation on fractions
• Solving algebraic equations involving fractions
• Solving word problems involving fractions
This instructional material is made for students to master :
• the rules in solving basic operations on integers (the laws of signed numbers)
• Solving problems on integers.
OBJECTIVES
ADDITION To add a positive on the number line, move to the
right, towards the larger numbers. To add a negative on a number line you move to the left.
Simple ruleRule for adding integers with different signs:Subtract the absolute values of the numbers and the use the sign of the larger absolute value.
SUBTRACTION
To subtract a positive number, move to the left on the number line. This is the same thing that happens when we add a negative number.
SUBTRACTION
Subtract a negative number we need to move to the right.
Simple Rule:KEEP the first number the same. CHANGE the subtracting to adding. Then CHANGE the sign of the second number
MULTIPLICATION AND DIVISION
Multiplying is really just showing repeated adding. To add 2 three times. 2 + 2 + 2 = 6
MULTIPLICATION AND DIVISION
• With negatives.
Examples:-2 x 3 = -6
Add -2 three times. That means that -2 + -2 + -2 = -6.
MULTIPLICATION AND DIVISION
• Two Negatives
Examples:-2 x -3 = 6Meaning add -2 negative 3 times.
The negative symbol means "the opposite". So if there are two negative numbers/terms being multiplied then move to the .
SIMPLER RULES
Rule #1:If the signs are the same, the answer is positive.
Examples:
Rule #2:If the signs are different, the answer is negative.
Dividing integers are the same as the rules for multiplying integers.
Remember that dividing is the opposite of multiplying. So we can use the same rules to solve.
Rule #1:If the signs are the same, the answer is positive.
Rule #2:If the signs are different, the answer is negative.
OBJECTIVE
This instructional material is made for the learners to:
• better understand ways of algebraic thinking and the concepts of Algebra.
• Concepts on Algebra basic operations on signed numbersSimple substitutionSolving equationsDistributive propertyRepresenting polynomialsBasic operations on polynomialsFactoring polynomialsCompleting the square
• Geometric figures on square and parallelogram
This instructional material will help the learners :
• be introduced with the concepts of plane figures
• to master the skill in solving areas and perimeter of plane figures.
OBJECTIVES
The Geometry Grid Wall is composed of two areas. The upper area is to where the figure be pasted and the lower area is the grid area where a figure be drawn/ illustrated
This instructional material will help the learners :• be introduced with the concepts of plane
figures and its characteristics• to use concrete material on finding the area
and perimeter of plane figures• to master the skill in solving areas and
perimeter of plane figures
OBJECTIVES
• Geoboard consists of a physical board with a certain number of dots. If these dots are connected it will serve as the measurement of a certain side or the figure itself.
• The unit of area on the geoboard is the smallest square that can be made by connecting four nails:
• We will refer to this unit as 1 square unit.
• On the geoboard, the unit of length is the vertical or horizontal distance between two nails. Perimeter is the distance around the outside of a shape and is measured with a unit of length.
• Use a white board pen to draw a figure.
OBJECTIVESThis instructional material is made for
the students to:• solve for the area and circumference
of a circle • identify the relationship between a
circle and a parallelogram.
Each slices of the pie is detachable making it easy to explain the learners how to get the circumference and area of a circle.
Example: If the radius is 5 inches.
5 inches
In finding the relationship between a circle and a parallelogram
The radius of a circle is the height of the parallelogram and the base of a parallelogram is the circumference of a circle
• Concept of a circle; area and perimeter
• Relationship of a parallelogram and a circle
• Fraction
• Division of numbers
OBJECTIVES
The instructional material is made for the learners to:
• identify the concepts of solid figures; Surface area and volume; faces, edges and vertices
• recognize the relationship between platonic and archimedian solids
The instructional material is made with a pattern being followed.The following information are already given:• faces• edges•Vertices
Learners will investigate the surface area and volume of these figures as well as the relationship between Platonic and Archimedean solids. The figures made will serve as their basis for this investigation
• Concepts on plane figures and solid figures
• Surface area and volume of solid figures
• Mathematical investigations on the relationships of these solid figures
• Dice for various activities
OBJECTIVES
Define Perimeter and Area.
Illustrate the formulas on finding the perimeter and area of plane figures.
Find the perimeter and area of common plane figures.
The perimeter of any polygon is the sum of the measures of the line segments that form its sides. OR SIMPLY, the measurement of the distance around any plane figure.
Perimeter is measured in linear units.
Triangle
The perimeter P of a triangle with sides of lengths a, b, and c is given by the formula
P = a + b + ca
b
c
SQUARE
The perimeter P of a square with all sides of length s is given by the formula
P = 4s
s
s
s
s
RECTANGLE• The perimeter P of a rectangle with length l
and width w is given by the formula
P = 2L + 2W
W
L
W
L
Answer
Add up all the length and width measurements:
12cm + 12cm + 5cm + 5cm OR 2 L + 2W 2(12) + 2(5) = 34cm!
The amount of plane surface covered by a polygon is called its area. Area is measured in square units.
RECTANGLE
The area of a rectangle is the length of its base times the length of its height.
A = bh
HEIGHT
BASE
PARALLELOGRAM
• The area of a parallelogram is the length of its base times the length of its height.
A = bhWhy?
Any parallelogram can be redrawn as a rectangle without losing area.
BASE
HEIGHT
TRIANGLEThe area of a triangle is one-half of the length of its base
times the length of its height.A = ½bh
Why?
Any triangle can be doubled to make a parallelogram.
HEIGHT
BASE
TRAPEZOID
• Remember for a trapezoid, there are two parallel sides, and they are both bases.
• The area of a trapezoid is the length of its height times one-half of the sum of the lengths of the bases.
A = ½(b1 + b2)h• Why?
• Red Triangle = ½ b1h
• Blue Triangle = ½ b2h• Any trapezoid can be
divided into 2 triangles.
HEIGHT
BASE 2
BASE 1
Kite/Rhombus• The area of a kite is related to its diagonals.• Every kite can be divided into two congruent
triangles.• The base of each triangle
is one of the diagonals.The height is half of theother one.
• A = 2(½•½d1d2)
A = ½D1D2
d1
d2
DIFFERENCE
PERIMETER AREAThe perimeter of a plane geometric
figure is a measure of the distance
around the figure.
The area of a plane geometric
figure is the amount of surface
in a region.
Rectangle P = 2l + 2w A = bh
Square P = 2l + 2w A = bh
Triangle P = side + side + side
A = ½ bh
Parallelogram P = 2l + 2w A = bh
Trapezoid P = 2l + 2w
Circles C = 2∏r A = ∏r²
1 2
1( )2
A b b h
WORDS TO UNLOCK
SURFACE AREA
• The total area of the surface of a three-dimensional object
VOLUME
• is the amount of space enclosed in a solid figure.
SURFACE AREAthe amount of paper you’ll
need to wrap the shape
VOLUMEthe number of
cubic units contained in the
solid.
SURFACE AREA
Curved surface area 2 π rh
+area of the circle
2 π r2 0r
Total surface area: πrh +2 π r2
=2 π r(h+r)
SURFACE AREA
SA = ½ lp + B
Where l is the Slant Height and
p is the perimeter andB is the area of the Base
VOLUME
V = ⅓Bh V= ⅓ πr²h
where B is the area of the base and h is the height of the cone.
(1/3 the area of a cylinder)
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