In this lesson students continue to study situations of fractional increase and decrease. They start to use decimal notation to express the situations. For example, they see that "one quarter less than \(x\)" can be expressed as \(\frac34 x\) or as \(0.75x\).
Lesson overview
 5.1 Warmup: Notice and Wonder: Fractions to Decimals (5 minutes)

5.2 Activity: Repeating Decimals (15 minutes)
 Includes "Are you Ready for More?" extension problem
 5.3 Activity: More and Less with Decimals (15 minutes)
 5.4 Optional Activity: Card Sort: More Representations (10 minutes)
 Lesson Synthesis
 5.5 Cooldown: Reading More (5 minutes)
Learning goals:
 Comprehend and use the term “repeating” (in spoken language) and the notation \(\overline{\phantom{“ “}}\) (in written language) to refer to a decimal expansion that keeps having the same number over and over forever.
 Coordinate fraction and decimal representations of situations involving adding or subtracting a fraction of the initial value.
 Use long division to generate a decimal representation of a fraction, and describe (in writing) the decimal that results.
Learning goals (student facing):
 Let's use decimals to describe increases and decreases.
Learning targets (student facing):
 I understand that “half as much again” and “multiply by 1.5” mean the same thing.
 I can use the distributive property to rewrite an equation like x+0.5x=1.5x.
 I can write fractions as decimals.
Required preparation
 Print and cut up slips from the Representations of Proportional Relationships Card Sort blackline master.
 Prepare 1 copy for every 2 students.
 These can be reused if you have more than one class.
 Consider making a few extra copies that are not cut up to serve as an answer key.
Glossary:
 long division  Long division is a way to show the steps for dividing numbers in decimal form. It finds the quotient one digit at a time, from left to right. For example, here is the long division for \(57 \div 4\).
 repeating decimal  A repeating decimal has digits that keep going in the same pattern over and over. The repeating digits are marked with a line above them. For example, the decimal representation for \(\frac13\)is \(0.\overline{3}\), which means 0.3333333 . . . The decimal representation for \(\frac{25}{22}\) is \(1.1\overline{36}\) which means 1.136363636 . . .
 Access the complete Grade 7 glossary.
Standards
 This lesson builds towards the standard:CCSS.7.RP.A.3MS.7.RP.3MO.7.RP.A.3
IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 20172019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/mathcurriculum/.
Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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