Prepared by:LETICIA L. LAYUGERL DELA VEGASitero Francisco Memorial National High SchoolMapulang Lupa National High SchoolBLOCK MODEL APPROACH IN SOLVING PROBLEMS

BUILDING MATH CONCEPTS USING VISUAL MODELSBelow are pictures of blocks that model the terms in Algebraic Expressions. Algebraic Expressions5x5xyx22xy

Example y22xy5x2y3

BUILDING MATH CONCEPTS USING VISUAL MODELSEvaluation of Algebraic ExpressionsIf x=5If y=2 If x2=3 If y2=2 What is the value of y + 3 if y = 5?+= 8

Example

x = 2, the blocks shows ___________.

=2x + 92. x = 1, the blocks shows ___________3. x = 0, the blocks show ____________2x2x= 132x + 9= 112x + 9= 9

ADDING INTEGERS

Expression : 8 + (- 4 ) Simplest way 8 4 = 48-4

ADDING INTEGERSTo show 5 - 9, show 4 differently by adding zero5 - 9 =5 -4

ADDITION OF POLYNOMIALThe blocks show (2x2 4x + 2) + (6x 5). To find the sum, cancel blocks.2x2 + 2x -3 2x22x-3

Subtraction of Polynomials(4y - 2) - (6y 5) (4y - 2) + (-6y + 5) Subtract : (4y - 2) - (6y 5). - 2y3= -2y + 3

Multiplication of PolynomialsUsing 2 pieces of x2 and 10 pieces of x, arrange the blocks into a rectangle.

2x2 + 8x

Multiplication of Polynomials2x (x + 4)Area :2x2 + 8Length: 2xWidth: x+4

Area : 2x2 + 3x + 1Length: x+1Width: 2x +1Arrange the blocks into a rectangle. Sketch the rectangle and identify the area, length and width.2x +1x+1

Show how to use blocks to represents the product. 1. x (5x+3)5 x2 + 3x

Multiplication of PolynomialsRepresent 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

Show how to use algebra blocks to represent the productGiven:(x-1) (x+2)Answer: x2 +x -2

Division of PolynomialsUse the corner piece and tiles to solve division problems.numeratorDenominatorThe blocks shows 15 or 15 divided be 5 5QuotientTherefore, 15 = 3 5

Consider the following algebra blocksThe rectangle formed gives the other side length which is x+3. Hence, the complete division equation is x2 + 3 = x + 3 xX + 3

Given: 2x2 + 7x +4 2x + 1numeratordenominatorremainderAnswer: 2x2 + 7x +4 = x + 3 remainder 1 2x + 1X + 3Remainder 1

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