Proportion Power Review GuideDATA ARCHITECT: REVIEW GUIDE Unit 3: Ratios, Proportions, & Percents REF: U3-REV-9 Student Name: Date: 01. Ratios & Proportions The Golden Rule To solve a proportion \(\frac{a}{b} = \frac{c}{d}\), use cross-multiplication: \(ad = bc\). Practice 1: Solve for \(x\): \(\frac{4}{7} = \frac{x}{21}\) Unit Rates A ratio where the denominator is 1. Divide the numerator by the denominator. Practice 2: If 5 pounds of apples cost $12.50, what is the unit price per pound? 02. Similar Figures Properties Corresponding angles are congruent (\(\cong\)) Corresponding sides are proportional Scale Factor \((k) = \frac{\text{New Side}}{\text{Original Side}}\) Practice 3: A 6-ft tall person casts a 4-ft shadow. At the same time, a tree casts a 10-ft shadow. How tall is the tree? 03. Percents & Change Percent of Change Formula \(\frac{\text{Amount of Change}}{\text{Original Amount}} \times 100 = \text{Percent Change}\) Practice 4: What is 15% of 80? Practice 5: A pair of shoes was $60 but is now on sale for $45. What is the percent decrease? TEST DAY STRATEGIES Check your units twice Sketch the similar figures Verify your cross-products
Proportion Power TestData Architect Assessment Unit 3: Ratios, Proportions, & Percents REF: U3-TEST-9 Student Name: Date: Score: SECTION 1: RATIOS & UNIT RATES 1. A box contains 12 red pens, 8 blue pens, and 4 black pens. What is the ratio of blue pens to the total number of pens in simplest form? A 1:3 B 1:2 C 2:3 D 1:4 2. A grocery store sells a 24-ounce jar of peanut butter for $4.80. What is the unit price per ounce? A $0.10 B $0.20 C $0.05 D $0.15 SECTION 2: SOLVING PROPORTIONS Solve each proportion for the missing variable. Show your work in the space provided. 3. \(\frac{x}{12} = \frac{15}{20}\) x = ________ 4. \(\frac{7}{y} = \frac{3}{12}\) y = ________ SECTION 3: SIMILAR FIGURES 5. A map uses a scale of 2 inches = 25 miles. If two cities are 7 inches apart on the map, what is the actual distance between them in miles? Answer: _________________ miles 6. Triangle ABC is similar to Triangle DEF. Side AB = 10, DE = 5, and BC = 14. What is the length of side EF? Answer: _________________ SECTION 4: PERCENTS & CHANGE 7. A laptop originally costs $1,200. It is on sale for 20% off. What is the sale price of the laptop? Answer: $ _________________ 8. The population of a town increased from 15,000 to 18,000. Calculate the percent of increase. Answer: _________________ % Bonus: Data Synthesis 9. A recipe requires 3 cups of flour to make 18 cookies. You want to make 45 cookies. How many cups of flour will you need? (Show your work as a proportion) Answer: _________________ cups
Proportion Power Answer KeyTeacher Key: Proportion Power Unit 3 Assessment Solutions REF: U3-KEY-9 Total Points: 20 Multiple Choice: 2 pts each Short Answer: 2 pts each Bonus: 2 pts Common Errors Watch for students using "new amount" as denominator in % change instead of "original amount". Section 1 Solutions 1 A (1:3) Work: Total = 12 + 8 + 4 = 24. Ratio = 8 / 24 = 1/3. 2 B ($0.20) Work: $4.80 / 24 ounces = $0.20 per ounce. Section 2 Solutions Problem 3 x = 9 Work: \(20x = 180 \rightarrow x = 180/20 = 9\) Problem 4 y = 28 Work: \(3y = 84 \rightarrow y = 84/3 = 28\) Section 3 Solutions Problem 5 87.5 miles Work: \(\frac{2}{25} = \frac{7}{x} \rightarrow 2x = 175 \rightarrow x = 87.5\) Problem 6 7 Work: \(\frac{10}{5} = \frac{14}{x} \rightarrow 10x = 70 \rightarrow x = 7\) Section 4 Solutions Problem 7 $960 Work: Discount = \(0.20 \times 1200 = 240\). Price = \(1200 - 240 = 960\). Problem 8 20% Increase Work: Change = \(18,000 - 15,000 = 3,000\). Percent = \(\frac{3,000}{15,000} \times 100 = 20\%\). Bonus Solution Problem 9 7.5 cups Work: \(\frac{3}{18} = \frac{x}{45} \rightarrow 18x = 135 \rightarrow x = 7.5\)
Proportion Power SlidesData Architect: Unit 3 Assessment Ratios • Proportions • Percents Review • Assessment • Reflection Mental Math Kickoff Ratio Flash 15 teachers for 450 students. What is the unit rate? Percent Snap 20% of $80. How much is the discount? Architect's Checklist Review Guide Ready Calculator Checked Growth Mindset ON Core Concepts Review Proportions Cross-multiply to solve for the unknown. Keep your units consistent! ad = bc Similarity Shapes are proportional. Set up a ratio of corresponding sides. Side A / Side B Percent Change Remember the ratio of difference over original amount. Change / Orig Assessment Protocols Zero Volume Respect the architectural studio focus. Show the Blueprint Work shown = credit earned. Pacing 45 minutes of construction time. Queries Raise a silent hand for assistance. Final Reflection 3 Concepts you feel confident about 2 Errors you'll look for next time 1 Question you still have Unit 3: Complete
Proportion Power Instructional GuideInstructional Guide: Proportion Power Unit 3 Assessment Strategy DURATION: 65 MIN Learning Objective Students will demonstrate mastery of solving problems involving ratios, proportions, similar figures, and percents (including percent of change) through a formal assessment and final reflection. Key Materials Unit 3 Test Review Guide Presentation Slides Instructional Arc 0-10m Review & Activation Display the Mental Math Kickoff slide. Have students use the first 5 minutes to complete the practice problems on their Review Guide. Briefly review the "Golden Rules" for proportions and percent change. Slides 1-3 10-55m Unit 3 Assessment Distribute the Proportion Power Test. Remind students of the "Testing Norms" (Slide 4). Students work independently. For students finishing early, suggest they double-check their cross-products and units. Slide 4 Main Event 55-65m Final Reflection Collect assessments. Use the Final Reflection slide (3-2-1 strategy) to have students journal or discuss their confidence levels and remaining questions. This data will inform the next unit's launch. Slide 5 DIFFERENTIATION Scaffolding Provide the Review Guide formula sheet for students with accommodations. Extension Challenge early finishers with the Bonus Architect problem (Question 9) for multi-step reasoning. TEACHER TIPS "Ensure students are sketching the similar figures in Section 3. Visualizing the scale helps them realize if an answer 'makes sense' (e.g., if the tree shadow is longer than the person shadow, the tree must be taller than the person)."
