Teaching Mathematics Strategies

7/29/2019 Teaching Mathematics Strategies

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Prepared by:

LETICIA L. LAYUG

ERL DELA VEGA

Sitero Francisco Memorial National High School

Mapulang Lupa National High School

BLOCK MODEL APPROACH IN

SOLVING PROBLEMS


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BUILDING MATH CONCEPTS

USING VISUAL MODELS

Below are pictures of blocks that model the terms in Algebraic Expressions.

Algebraic Expressions

Constant 1 x y

5x5 5y

xy x2 y2

2y22x22xy


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Example

y2 2xy 5x 2y

Draw a picture of theblocks to show

y2

+ 2xy+ 5x + 2y + 3

3

y2 + 2xy +5x +2y +3


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BUILDING MATH CONCEPTS

USING VISUAL MODELS

Evaluation of Algebraic Expressions

If x=5

If y=2

If x2=3

If y2=2

What is the value of y + 3 if y = 5?

y 3 35 + = 8


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Example

1. x = 2, the blocks shows ___________.

=

2x + 9

2. x = 1, the blocks shows ___________

3. x = 0, the blocks show ____________

2x 2x+ 9 + 9 = 13

= 13

2x + 9 = 11

2x + 9 = 9


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Negative Area

ADDING INTEGERS

Expression : 8 + (- 4 )

Simplest way 84 = 4

8

-4


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ADDING INTEGERS

Negative Area

To show 5 - 9, show 4 differently byadding zero

Negative Area

5 - 9 =5

Negative Area

-4


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ADDITION OF POLYNOMIAL

The blocks show (2x24x + 2) + (6x 5).

To find the sum, cancel blocks.

Negative Area2x2 + 2x -3

2x2 2x

-3


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Subtraction of Polynomials

Negative Area

(4y - 2) - (6y 5) (4y - 2) + (-6y + 5)

Subtract : (4y - 2) - (6y 5).

- 2y

3

= -2y + 3


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Multiplication ofPolynomials

Using 2 pieces of x2 and 10 pieces of x, arrange the blocks into a

rectangle.

2x2 + 8x


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Multiplication of Polynomials

x

x

x 1 1 1 1

2x

(x + 4)

Area :2x2 + 8

Length:

2xWidth:

x+4


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Area : 2x2 + 3x + 1

Length:

x+1Width:

2x +1

Arrange the blocks into a rectangle. Sketch the rectangle

and identify the area, length and width.

2x +1

x+1


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Show how to use blocks to represents the product.

1. x (5x+3)

5 x2 + 3x


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Multiplication of

Polynomials

Represent the product of 2x and x-3 using the blocks.

Using the blocks, x+3 is

illustrated as:

While, x-2 can be illustrated as:

Answer: 2x(x-3) = 2x2 -6x


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Show how to use algebra blocks to represent the product

Given:(x-1) (x+2)

Answer: x2 +x -2


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Division of Polynomials

Use the corner piece and tiles to solve division problems.

numeratorDenomin

ator

The blocks shows

15 or 15 divided be 5

5

Quotient

Therefore,

15 = 3

5


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These blocks shows x2 +3x

x

Consider the following algebra blocks

The rectangle formed gives the other

side length which is x+3.Hence, the complete division equation is

x2 + 3 = x + 3

x

X + 3


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Given: 2x2 + 7x +4

2x + 1

numerator

denomi

nator

remainder

Answer: 2x2 + 7x +4 = x + 3 remainder 1

2x + 1

X + 3 Remainder 1

Teaching Mathematics Strategies

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