Recognize ratios as multiplicative relationships between two quantities by examining a real world example

Big Ideas: Ratios are multiplicative relationships between two or more quantities that are related. Ratios describe a relationship that remains constant as total quantities are increased or decreased. Ratio relationships can be described as part-to-part or part-to-whole using the ratio language 'for every'. This lesson is a foundational introduction to the concept of ratios as a relationship between two or more related quantities. Students will build an understanding of the multiplicative relationship of ratios by determining the conditions in which various mixtures of red and white paint will yield the same shade of pink, and begin to describe part-to-part and part-to-total ratios using multiplicative language such as 'for every' and 'times as many'. The mathematical concepts in this lesson will build toward students' future work, including generating equivalent ratios to solve ratio problems (including percentages and unit rates); working with proportionality and scale factors; and expressing and graphing linear functions. Vocabulary: for every, times as many, part, total Special Materials: counters, tiles, or other manipulatives