SOLVING SIMPLE EQUATIONS USING BAR MODELS (4th) FOURTH QUARTER GRADE 7 MATATAG TAGALOG MATH TUTORIAL

This lesson introduces solving equations using bar models, with the objective of finding unknowns in simple equations. An algebraic equation is defined as a mathematical statement showing two equal expressions, similar to a balance scale. Solving an equation means finding the value of the unknown variable that makes the equation true.

The bar model is a tool that helps visualize math problems using rectangles or bars. In an equation, the left side is represented by a bar on top, and the right side by a bar at the bottom, both having equal measure. These bars can be divided into parts and can represent either a whole or parts of an expression.

The equation x + 6 = 10 is represented with 'x' and '6' as parts of the top bar, and '10' as the whole bottom bar. By aligning the bars, it's shown that 'x' corresponds to '4', thus x = 4. Checking the solution (4 + 6 = 10) confirms its truth.

The expression 2x + 5 is shown as parts of the top bar and 9 as the whole bottom bar. The 9 is split into 5 and 4. Then, 2x is split into x and x, which corresponds to 4 being split into 2 and 2, revealing x = 2. The solution is verified: 2(2) + 5 = 9.

For subtraction, the whole is 'x', and 7 and 13 are its parts. When x is diminished by 7, the result is 13. By placing 7 and 13 together in the bottom bar, their sum (20) represents the value of x. The solution x = 20 is checked: 20 - 7 = 13.

In this equation, 3x is the whole, and 2 and 7 are its parts. The bottom bar shows 2 and 7, totaling 9. The top bar is divided into three equal 'x' parts. This means 'x' corresponds to 9 divided by 3, which is 3. The solution x = 3 is confirmed: 3(3) - 2 = 7.

The top bar represents 2x + 4 (as x, x, and 4), and the bottom bar represents x + 5 (as x and 5). By removing one 'x' from both top and bottom (as they are equal), the remaining equation is x + 4 = 5. Splitting 5 into 4 and 1 reveals that x = 1. Verification: 2(1) + 4 = 1 + 5, which simplifies to 6 = 6.

For 3x - 1 = 2x + 4, 3x is the whole. The parts are 1, 2x, and 4. The bottom bar is composed of these parts, and 2x and 1 + 4 (which is 5). The top bar is 3 'x's. By matching and cancelling, one 'x' from the top bar corresponds to the '5' remaining in the bottom bar. Thus, x = 5. Checking: 3(5) - 1 = 2(5) + 4, leading to 14 = 14.