7th Grade Ratios and Proportional Relationships
Dive into the world of ratios and proportional relationships in 7th grade math with detailed explanations on ratios, proportions, unit rates, and solving multi-step problems. Explore the Big Ideas, Progressions, and Standards associated with this essential mathematical concept. Enhance your understanding of how ratios are used to measure and compare different quantities and how proportional relationships can be represented and analyzed in various contexts.
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7thGrade Ratios and Proportional Relationships John Barker & Jennifer Thomas Nevada Math Project March 2015
Big Ideas Ratio A ratio is used to measure two different things in two different units. Ex. How far a car drives with how long it takes to get to the destination. Ex. Cost of different bags of jellybeans in dollars per pound. Proportional Relationships Examining relationships between two equal ratios. Ex. Painting a room and need to mix 3 colors together to create a new color. Constructing Proportions Writing and solving proportions with unknown variables.
Progressions Seventh grade ratio and proportions is a continuation of the sixth grade standards. Students need to remember from sixth grade that: Ratios and Proportions involve multiplication, not addition. Move from using only fractions to using ratios and proportions to describe the relationship between amounts. Students will use ratios in algebra, geometry, and calculus in high school. Use ratios in cases that involve pairs of rational number entries, and compute associated unit rates. Identify these unit rates in representations of proportional relationships. Work with equations in two variables to represent and analyze proportional relationships. Solve multi-step ratio and percent problems, such as problems involving percent increase and decrease. Progressions Document - https://commoncoretools.files.wordpress.com/2012/02/ccss_progressio n_rp_67_2011_11_12_corrected.pdf
Standards 7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. 1 2 3
7.RP.2 Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional relationship e.g. by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c. Represent proportional relationships by equations d. Explain what a point (x,y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0,0) and (1,r) where r is the unit rate.
7.RP.3 Use proportional relationships to solve multistep and percent problems. 1 2
Percent of Total Problem: Marjorie baked 1000 cupcakes. She sold 87% of her cupcakes. How many cupcakes did she sell? Try using a model method to solve your problem instead of just the algorithm!
Percent of Total Solution o Using the model method you will break your model into ten equal sections (because it has to equal 100%). From there you will break one section of the model into tenths (to break down the model even further to find the 7% of the 87%). o You will then count the number of 100 s that are represented by 80% (this would be 8). Multiply 8 x 100 = 800. o Then to find the 7% left over you need to take the box you broke into tenths (by dividing 100 by 10 = 10). You then take 7 of the tenths and multiply by their value which is 10. This gives you 7 x 10 = 70. o Final step is to add the two answers together 800+70 = 870 cupcakes, or 87% of her total amount of 1000 cupcakes.
Resources Illustrative Mathematics - https://www.illustrativemathematics.org/content-standards/RP/7/A Learnzillion - https://learnzillion.com/search?utf8=%E2%9C%93&query=Ratios%20 and%20proportions&page=1&models%5B%5D=LessonSet Math Snacks http://mathsnacks.com/index.html Math Playground - http://www.mathplayground.com/thinkingblocks.html Khan Academy - https://www.khanacademy.org/math/cc- seventh-grade-math/cc-7th-ratio-proportion Pasco School District - http://www.psd1.org/cms/lib4/WA01001055/Centricity/Domain/30/ Common%20Core%20Page/Math%20Repacking%20Docs/7th%20M ath%20Ratio%20Proportion%20Teacher%20Checklist2.pdf
