By: Fate Jacaban

Instrumentation in

Mathematics

PREPARED BY:JACABAN, FATE S.BSED MATH -IV

OUTLINE• Fraction wall• Number Line Wall• Algebra tiles• Gridline Wall• Geoboard• Pie• Platonic and Archemedean solids• Perimeter• Area• Surface area• Volume• Instrcutional Materials

FRACTION WALL

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.

HOW TO USE

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.

PEDAGOGICAL USE

• Basic operation on fractions

• Solving algebraic equations involving fractions

• Solving word problems involving fractions

NUMBER LINEWALL

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

HOW TO USE

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.

PEDAGOGICAL USE

• Introduction of integers

• Basic operations on integers

• Solving algebraic equations

ALGEBRA TILES

OBJECTIVE

This instructional material is made for the learners to:

• better understand ways of algebraic thinking and the concepts of Algebra.

HOW TO USE

Each tiles represents to a certain variable/ constant

x2

x

1

2X2 + x+ 3

See: http://mathbits.com/MathBits/AlgebraTiles/AlgebraTiles/AlgebraTiles.html

PEDAGOGICAL USE

• Concepts on Algebra basic operations on signed numbersSimple substitutionSolving equationsDistributive propertyRepresenting polynomialsBasic operations on polynomialsFactoring polynomialsCompleting the square

• Geometric figures on square and parallelogram

GRID LINE WALL

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

How to use

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

Pedagogical use

• Concepts of plane figures; area and perimeter

• Characteristics of polygons

GEOBOARD

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

How to use

• 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.

PEDAGOGICAL USE

Concepts of plane figures; area and

perimeter

Characteristics of polygons

PIE/ CIRCLE

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.

HOW TO USE

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

PEDAGOGICAL USE

• Concept of a circle; area and perimeter

• Relationship of a parallelogram and a circle

• Fraction

• Division of numbers

PLATONIC SOLIDSAND

ARCHIMEDEAN SOLIDS

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

HOW TO USE

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

PEDAGOGICAL USE

• 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.

PERIMETER

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

Let’s try!!!

Can you find the perimeter for this shape

12cm

5cm5cm

12cm

Answer

Add up all the length and width measurements:

12cm + 12cm + 5cm + 5cm OR 2 L + 2W 2(12) + 2(5) = 34cm!

AREA

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

• Diameterd=2r

• CircumferenceC=2πr

• AreaA=πr2

radius

diameter

Let’s Try !!!

Find the areas of the following parallelograms

125

6

13

5

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.

DIFFERENCE

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

SURFACE AREA AND VOLUME OF SOLID

FIGURES

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.

CUBE

SURFACE AREA

Total surface area:

6 (side) or 6(s) ² ²

Lateral surface area:

4(side) or 4 (s) ² ²

VOLUME

CUBE/SQUARE PRISM

V = s²H

The product of its height H and the area of its base s².

S

SH

RECTANGULAR PRISM

SURFACE AREA

Total surface area:

2(lb+bh +lh)

Lateral surface area:

2(l+b)h bl

h

VOLUME

V = lwh

The product of its length ,

width/base and height w

l

h

CYLINDER

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)

VOLUME

V = BhV= πr²h

The product of its base (πr²) and height (h)

h

b

TRIANGULAR PRISM

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

(1/3) Area of the Base x heightOr

(1/3) BhOr

1/3 x Volume of a Prism

b

h

CONE

SURFACE AREA

Total surface area of cone:

π r(s+r)

Lateral surface area of cone-

π rs

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)

SOLID FIGURES IN CEBU CITY

#solidfigselfie

HORIZON 101FRONT OF ST. THERESA’S COLLEGE (MANGO GATE)

IGLESIA NI CRISTO(GEN. MAXILOM AVE.)

OLD BUILDINGSENIOR CITIZEN PARK

MAGELLANE’S CROSS

VETERAN’S MONUMENT

PLAZA INDEPENDENCIA

OLD CANNONFORT SAN PEDRO

MARINERS’ COURTFRONT OF PIER 1

MIGUEL LOPEZ DE LEGAZPI MONUMENT

PLZA INDEPENDENCIA

INSTRUCTIONAL MATERIALS

Fraction wall

Number line wall

Algebra Tiles

Grid line Wall

GEOBOARD

Circle/Pie

GeometricFigures

THANKS!

Sources:

msjc.eduworldofteaching.comtaosschool.orgmarianhs.orgmathbits.com