In earlier grades, students have multiplied baseten numbers up to hundredths (either by multiplying two decimals to tenths or by multiplying a whole number and a decimal to hundredths). Here, students use what they know about fractions and place value to calculate products of decimals beyond the hundredths. They express each decimal as a product of a whole number and a fraction, and then they use the commutative and associative properties to compute the product. For example, they see that \((0.6)⋅(0.5)\) can be viewed as \(6⋅(0.1)⋅5⋅(0.1)\) and thus as \(\left(6 \cdot \frac{1}{10}\right) \cdot \left(5 \boldsymbol \cdot \frac {1}{10}\right)\). Multiplying the whole numbers and the fractions gives them \(30 \boldsymbol \cdot \frac{1}{100}\) and then 0.3.
Through repeated reasoning, students see how the number of decimal places in the factors can help them place the decimal point in the product (MP8).
Lesson overview
 5.1 Warmup: Multiplying by 10 (5 minutes)
 5.2 Activity: Fractionally Speaking: Powers of Ten (15 minutes)

5.3 Activity: Fractionally Speaking: Multiples of Powers of Ten (15 minutes)
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 5.4 Cooldown: Placing Decimal Points in Products (5 minutes)
Learning goals:
 Generalize (orally and in writing) that the number of decimal places in a product is related to the number of decimal places in the factors.
 Justify (orally) the product of two decimals, which each have only one nonzero digit, by multiplying equivalent fractions that have a power of ten in the denominator.
Learning goals (student facing):
 Let’s look at products that are decimals.
Learning targets (student facing):
 I can use place value and fractions to reason about multiplication of decimals.
Glossary:
 Access the complete Grade 6 glossary.
Standards

This lesson builds on the standards:CCSS.5.NBT.B.7MS.5.NBT.7MO.5.NBT.A.6MO.5.NBT.A.7MO.5.NBT.A.8 CCSS.5.NBT.A.2MS.5.NBT.2MO.5.NBT.A.4
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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