Math Connections: Ratios, Expressions & Geometry
Grade 7 Mathematics Common Core Standards Aligned 60-Minute Lesson
Warm-Up Challenge: Marble Ratios
If the ratio of red to blue marbles is 3:5 And there are 20 blue marbles How many red marbles are there? Work with a partner to solve!
Real-World Ratios & Proportions
Recipe scaling (cooking for more people) Map scales (1 inch = 10 miles) Model building (1:24 scale cars) Sports statistics (wins to losses) Art and design proportions
From Words to Expressions
Identify the unknown quantity (variable) Translate word relationships into math Example: 'Twice as many apples as oranges' If oranges = x, then apples = 2x Write equations to solve problems
Expression Puzzle Cards
Work in pairs with puzzle cards Read the word problem carefully Identify the variable and relationships Write the expression or equation Solve and explain your reasoning
Geometry: Breaking Down Complex Shapes
Composite shapes = simple shapes combined Identify rectangles, triangles, circles Calculate area of each simple shape Add areas together for total Use formulas: Rectangle = l×w, Triangle = ½×b×h
Shape Detective Challenge
Use your shape cutouts and graph paper Break the composite shape into simple parts Measure or count to find dimensions Calculate each area separately Find the total area and show your work
Bringing It All Together
How do ratios, expressions, and geometry connect? Can you think of a real-world situation that uses all three? Example: Scaling a building design What other connections can you make?