Notes & FAQs

The team agreed that students need to have instruction in equations before proportions as students use the cross product property and solving equations to solve both percent application problems and proportion problems.  Now that students have had instruction on rational number operations and solving equations with rational coefficients, students are ready to access the concepts regarding percents and proportions with rationals.

The team agreed to begin the unit with multi-step ratio and percent problems because the use of equations as a solution pathway is an extension of the work done in the previous unit. Students then continue that work when solving proportions and build on their prior knowledge of ratios from 6th grade to recognize and represent proportional relationships in all the various forms.

After close examination of the standards, 2013 Math framework, and the evidence required this is a topic that is covered in math 6 and could be reviewed in 7th grade, but it is not a standard.  This topic might be a great prerequisite skill to practice throughout the beginning of the unit.

See slides 82-92.

The team suggests teaching all forms simultaneously as a way to ensure students are understanding the relationship between tables, graphs, equations, diagrams, and verbal descriptions.

Students dealt with equivalent ratios in sixth grade with whole number numerators and denominators.  This is now formalized in seventh grade into proportions.  Ratios in seventh grade include a ratio of one fraction to another (complex fractions).  While you might connect back to sixth grade equivalent ratios with whole numbers, instruction should move quickly to ratios of fractional relationships.

See slides 71-81 to see how finding common denominators to divide makes sense visually, and complex fractions can actually make the division easier instead of harder in this context.

 After instruction on 7.RP.2, instruction on 7.G.1 involving scale factor and drawings can be seen as an extension of constructing and solving proportions as students determine and use scale factors.  Scale drawings can also be used to set a context for instruction of 7.RP.2

When looking at the item specifications for the targets in the allowable tools calculators are included.  In Target E, however, it does state that it varies by task so students should be able to work through this unit with and without a calculator.  Teachers should precisely examine and consider what the objective of the lesson is prior to determining whether or not a calculator can be used.  For example - In 7.RP.3, if the objective is to compute simple interest then students should be able to use calculators.  In 7.RP.2, if the objective is to label graph and graph through (0,0) then a calculator does not seem appropriate.