Lesson 5
Decimal Points in Products
Lesson Narrative
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 \((0.6) \boldcdot (0.5)\) can be viewed as \(6 \boldcdot (0.1) \boldcdot 5 \boldcdot (0.1)\) and thus as \(\left(6 \boldcdot \frac{1}{10}\right) \boldcdot \left(5 \boldsymbol \boldcdot \frac {1}{10}\right)\). Multiplying the whole numbers and the fractions gives them \(30 \boldsymbol \boldcdot \frac{1}{100}\) 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).
Learning Goals
Teacher Facing
 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.
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.
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