UB Waldorf School, Inc. Module 1: Algebra Lesson 1: Linear Equation (PDF)

**Module 1: Algebra** **Week 1, September 23, 2024** **Lesson 1: Linear Equation** **8:00 am -- 10:00 am** **I. SBWAT** - Review concepts discussed last meeting. - **Solve linear Equations Involving More than one operation, fractions, ratios and proportion.** - Portray active partic...

**Module 1: Algebra** **Week 1, September 23, 2024** **Lesson 1: Linear Equation** **8:00 am -- 10:00 am** **I. SBWAT** - Review concepts discussed last meeting. - **Solve linear Equations Involving More than one operation, fractions, ratios and proportion.** - Portray active participation in class. **II. CIRCLE TIME** - Verse +-----------------------------------+-----------------------------------+ | **Lubos Kong Minamasdan ang | Lubos kong minamasdan ang | | Mundo** | kaluluwa | | | | | Lubos kong minamasdan ang mundo | Na nananahan sa aking kalooban | | | | | Kung saan ang araw ay | Ang espirito ng Diyos ay | | nagliliwanag | nabubuhay at kumikilos | | | | | Kung saan ang mga bituin ay | Sa liwanag ng araw at kaluluwa | | nagniningning | | | | Sa kaitaasan ng mundo sa labas | | Kung saan ang nahihimlay ang mga | | | bato | Sa kaibuturan ng aking kalooban | | | | | Ang mga halaman, sila ay | Espirito ng Diyos sa iyo | | nabubuhay at lumalago | | | | Ako ay bumabaling at humihiling | | Ang mga hayop, sila ay nakadarama | | | at nabubuhay | Na ang lakas, ganda at galing | | | | | At ang tao, sa espirito ay | Sa pag -- aaral at sa paggawa | | nagbibigay | | | | Sa akin ay mabuhay at managana. | | Ng tahanan sa kanyang kaluluwa | | +-----------------------------------+-----------------------------------+ - Poem (Mathematics Poem) - Movement Activity Bothmer Movement - Tongue Twister Exercise **III. LESSON PROPER** **Recall** 1\. Let us go back to your Math previous blocks, what are the concepts that you have discussed? **Discussion** 1\. The teacher will discuss the lesson about **Solving linear Equations Involving More than one operation, fractions, ratios and proportion.** 2\. The students will share their thoughts regarding the lesson. **IV. WRITTEN/HANDS-ON ACTIVITY** (45 mins.) 1. In the Main Lesson book, write down the important information from the discussion. **Step 1: Simplify each side of the equation separately.** - Distribute any multiplication over parenthesis. - Combine like terms where possible. - Simplify fraction or ratios. **Step 2: Clear fractions by finding a common denominator.** - Multiply every term in the equation by the least common denominator (LCD) to eliminate fractions. **Step 3: Isolate the variable on one side of the equation.** - Use addition or subtraction to move constant terms to the opposite side. - Use multiplication or division to isolate the variables **Step 4: Solve for the variable.** - Once the variable is isolated, simplify the equation to find its value. **Step 5:** Check your solution by substituting it back into the original equation. **Example Problems and Solutions** **Example 1: Linear Equation with Fractions** Solve: [\$\\frac{2x}{3} - \\frac{5}{4} = \\frac{7}{6}\$]{.math.inline} **Solution:** 1. Find the least common denominator (LCD) for 3,4, and 6, which is 12 2. Multiply every term by 12 to clear the factions: \ [\$\$12 \\times \\frac{2x}{3} - 12 \\times \\frac{5}{4} = 12 \\times \\frac{7}{6}\$\$]{.math.display}\ *\ * [8*x* − 15 = 14]{.math.inline} 3. Isolate the variable by adding 15 to both sides. 4. Divide by 8 to solve for x: [\$x = \\frac{29}{8}\$]{.math.inline} **Example 2: Solving a Proportion** Solve: [\$\\frac{x + 2}{3} = \\frac{4x}{9}\$]{.math.inline} **Solution:** 1. Cross-multiply to eliminate the fractions: \ [9(*x*+2) = 3(4*x*)]{.math.display}\ 2. Distribute: 9x + 18 = 12x 3. Subtract 9x from both sides to isolate: 9x -- 9x + 18 = 12x -- 9x 18 = 3x 4. Divide by 3 to solve for x: [\$\\frac{18}{3} = \\frac{3x}{3}\$]{.math.inline} **Example 3: Linear Equation with Ratios:** Solve: [\$\\frac{2 \\times \\ + \\ 5}{3} = \\frac{x\\ - \\ 4}{2}\$]{.math.inline} **Solution:** 1. Cross-multiply 2(2x + 5) = 3(x -- 4) 2. Distribute 4x + 10 = 3x -- 12 3. Subtract 3x from both sides: 4. Subtract 10 from both sides: x + 10 -- 10 = - 10 -- 12 x = -22 **Example 4: Equation Involving a Fraction and Variable** **Solve:** [\$\\frac{3x + 1}{5} - \\frac{x}{2} = 2\$]{.math.inline} **Solution:** 1. **Find the least common denominator (LCD), which is 10.** 2. **Multiply every term by 10:** \ [\$\$10 \\times \\frac{3x + 1}{5} - 10 \\times \\frac{x}{2} = 10 \\times 2\$\$]{.math.display}\ \ [2(3*x*+1) − 5*x* = 20]{.math.display}\ 3. **Distribute:** [6*x* + 2 − 5*x* = 20]{.math.inline} 4. **Combine like terms:** [*x* + 2 = 20]{.math.inline} 4. **Subtract 2 from both sides: x = 18** **Activity: Solve the following. Show your solution.** 1. [\$\\frac{3x - 2}{5} = \\frac{6}{7}\$]{.math.inline} 2. [\$\\frac{x + 3}{2x - 5} = \\frac{3}{4}\$]{.math.inline} 3. [\$2\\left( x - 3 \\right) + \\frac{4x}{5} = \\frac{8}{5} + 2x\$]{.math.inline} 4. [\$\\frac{2x}{3} + \\frac{4}{5} = \\frac{7x}{15}\$]{.math.inline} 5. The proportion of students who passed a test to those who failed is [\$\\frac{4x}{5} = \\frac{8}{10}\$]{.math.inline}. How many students passed if the total number of students is 30? 6. [\$\\frac{x}{2} + \\frac{3}{4} = \\frac{5x - 1}{8}\$]{.math.inline} 7. [5(*x*−4)=3+2(*x*+7)]{.math.inline} 8. A recipe calls for a ratio of flour to sugar of [\$\\frac{3}{4}\$]{.math.inline}. If you have 8 cups of sugar, how many cups of flour are needed? **V. INTRODUCTION FOR TOMORROWS LESSON** **VI. CLOSING VERSE** **To Finish What I Start** **Light be in my thought,** **Love be in my heart,** **Strength be in my will** **To finish what I start.** **VI. ASSIGNMENT**