GRADE 7 MATH — TOPIC 2-2 Find Unit Rates with Ratios of Fractions SLIDE 1 — TITLE Topic 2-2: Find Unit Rates with Ratios of Fractions Essential Question: Why is it useful to write a ratio of fractions as a unit rate? Visual theme: Colorful, modern middle-school math presentation with fraction models, ratio tables, and real-world images of biking, cooking, and measuring. ⸻ SLIDE 2 — AIM & DO NOW Aim: How can we find unit rates with ratios of fractions and use them to solve multistep problems? Do Now — Review from Topic 2-1 1. A cyclist travels 120 miles in 3 hours. What is the unit rate in miles per hour? 2. Four notebooks cost $6. What is the cost per notebook? Directions: Solve both problems. Show your work and include units. Remember: To find a unit rate, divide the first quantity by the second quantity. ⸻ SLIDE 3 — HOW TO FIND UNIT RATES WITH RATIOS OF FRACTIONS Key Idea: A unit rate tells us how much of one quantity there is for 1 unit of another quantity. Method 1: Use an Equivalent-Ratios Table Example: A cyclist travels 7 miles in (\frac14) hour. Find the unit rate. Miles 7 28 Hours (\frac14) 1 Step 1: Ask, “What do I multiply (\frac14) by to get 1?” Step 2: Multiply both quantities by 4. [ 7\times4=28 ] [ \frac14\times4=1 ] Unit rate: 28 miles per hour. Method 2: Divide by the Second Quantity Example: A cyclist travels (\frac34) mile in (\frac12) hour. Find the unit rate. Step 1: Write the division expression. [ \frac34\div\frac12 ] Step 2: Keep, change, flip. Keep the first fraction, change division to multiplication, and flip the second fraction. [ \frac34\times\frac21 ] Step 3: Multiply and simplify. [ \frac{3\times2}{4\times1} =\frac64=\frac32=1\frac12 ] Answer: (1\frac12) miles per hour. Remember! * Divide the first quantity by the second quantity. * When dividing fractions, multiply by the reciprocal. * Simplify your answer. * Always include the correct units. ⸻ SLIDE 4 — LET’S PRACTICE TOGETHER: PROBLEM 1 Find the Unit Rate A machine uses (\frac56) yard of material in (\frac13) minute. How many yards of material does it use per minute? Step 1: Write the division expression. [ \frac56\div\frac13 ] Step 2: Multiply by the reciprocal. [ \frac56\times\frac31 ] Step 3: Multiply and simplify. [ \frac{15}{6}=\frac52=2\frac12 ] Answer: (2\frac12) yards per minute. Think About It: Why did we multiply by 3 instead of dividing by 3? ⸻ SLIDE 5 — LET’S PRACTICE TOGETHER: PROBLEM 2 Find and Interpret a Unit Rate A cyclist travels (\frac34) mile in (\frac12) hour. How far can the cyclist travel in 1 hour at the same speed? Work Together 1. Write a division expression. 2. Find the reciprocal of the second fraction. 3. Multiply and simplify. 4. Explain what the answer means. Show Your Work [ \frac34\div\frac12 ] [ =\frac34\times\frac21 ] [ =\frac64=\frac32 ] Answer: (1\frac12) miles per hour. The cyclist travels (1\frac12) miles in 1 hour at the same speed. ⸻ SLIDE 6 — LET’S PRACTICE TOG
GRADE 7 MATH — TOPIC 2-2 Find Unit Rates with Ratios of Fractions SLIDE 1 — TITLE Topic 2-2: Find Unit Rates with Ratios of Fractions Essential Question: Why is it useful to write a ratio of fractions as a unit rate? Visual theme: Colorful, modern middle-school math presentation with fraction models, ratio tables, and real-world images of biking, cooking, and measuring. ⸻ SLIDE 2 — AIM & DO NOW Aim: How can we find unit rates with ratios of fractions and use them to solve multistep problems? Do Now — Review from Topic 2-1 1. A cyclist travels 120 miles in 3 hours. What is the unit rate in miles per hour? 2. Four notebooks cost $6. What is the cost per notebook? Directions: Solve both problems. Show your work and include units. Remember: To find a unit rate, divide the first quantity by the second quantity. ⸻ SLIDE 3 — HOW TO FIND UNIT RATES WITH RATIOS OF FRACTIONS Key Idea: A unit rate tells us how much of one quantity there is for 1 unit of another quantity. Method 1: Use an Equivalent-Ratios Table Example: A cyclist travels 7 miles in (\frac14) hour. Find the unit rate. Miles 7 28 Hours (\frac14) 1 Step 1: Ask, “What do I multiply (\frac14) by to get 1?” Step 2: Multiply both quantities by 4. [ 7\times4=28 ] [ \frac14\times4=1 ] Unit rate: 28 miles per hour. Method 2: Divide by the Second Quantity Example: A cyclist travels (\frac34) mile in (\frac12) hour. Find the unit rate. Step 1: Write the division expression. [ \frac34\div\frac12 ] Step 2: Keep, change, flip. Keep the first fraction, change division to multiplication, and flip the second fraction. [ \frac34\times\frac21 ] Step 3: Multiply and simplify. [ \frac{3\times2}{4\times1} =\frac64=\frac32=1\frac12 ] Answer: (1\frac12) miles per hour. Remember! * Divide the first quantity by the second quantity. * When dividing fractions, multiply by the reciprocal. * Simplify your answer. * Always include the correct units. ⸻ SLIDE 4 — LET’S PRACTICE TOGETHER: PROBLEM 1 Find the Unit Rate A machine uses (\frac56) yard of material in (\frac13) minute. How many yards of material does it use per minute? Step 1: Write the division expression. [ \frac56\div\frac13 ] Step 2: Multiply by the reciprocal. [ \frac56\times\frac31 ] Step 3: Multiply and simplify. [ \frac{15}{6}=\frac52=2\frac12 ] Answer: (2\frac12) yards per minute. Think About It: Why did we multiply by 3 instead of dividing by 3? ⸻ SLIDE 5 — LET’S PRACTICE TOGETHER: PROBLEM 2 Find and Interpret a Unit Rate A cyclist travels (\frac34) mile in (\frac12) hour. How far can the cyclist travel in 1 hour at the same speed? Work Together 1. Write a division expression. 2. Find the reciprocal of the second fraction. 3. Multiply and simplify. 4. Explain what the answer means. Show Your Work [ \frac34\div\frac12 ] [ =\frac34\times\frac21 ] [ =\frac64=\frac32 ] Answer: (1\frac12) miles per hour. The cyclist travels (1\frac12) miles in 1 hour at the same speed. ⸻ SLIDE 6 — LET’S PRACTICE TOG
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This lesson plan focuses on understanding and applying ratios and unit rates. It begins with an introduction to the essential question and a review of whole-number unit rates through relatable examples like biking and cooking. Students will then learn to divide ratios of fractions by defining unit rates and using tables to scale fractions. Finally, they will apply their knowledge by solving problems related to material usage and interpreting cyclist speeds, ensuring they understand units and...