Unit 2:

Rational Numbers

In 7th grade, students learn to construct, solve and interpret proportions and two step equations using rational numbers in order to apply and represent these skills in real world situations including statistics, percent, geometry and probability. 

The Story of Math 7 - Unit 2: Rational Numbers (Up to 38 days)

The big ideas for this unit are learning four operations with rational numbers and using them to solve multistep problems and make conversions between rational numbers.  Depth can be added to this unit by exploring the supporting idea of complex numbers in this context.  Care must be taken to ensure a conceptual foundation for this instruction rather than jumping to rules to memorize.  In fact, students should build procedural fluency from conceptual understanding.  As soon as concepts are understood much of the practice to ensure procedural proficiency should be done in the context of solving multistep problems.  This way a review of order of operations is embedded and students are forced to think critically about which “rules' ' to apply.  Interleaved practice is important throughout all instruction in order to retain and apply information, but even more so here with integer rules.  “Here is the rule and practice it” with blocked practice is simply not effective, and it leads to the “Illusion of Mastery” rather than fluency (see the Interleaved Practice Guide).

Unit 2 Notes

Embedded review of fractions and decimals is done as students work with positive and negative values with visual models.  Different contexts, zero pairs, number lines and other integer models help students understand, retain, and create integer rules.  Students should also understand the meaning of "+" as "and" & the meaning of  "-" as "opposite" rather than only trying to memorize a set of rules they are not fluent in. See Hot Rocks & Cold Rocks for how to use context to learn/remember integer rules.

Vocabulary, Tools & Developmental Notes from SBAC

7.NS.A Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. (Target B)

7.EE.B Solve real-life and mathematical problems using numerical and algebraic expressions and equations.  (Target D)

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