Dennis McDonald, Math Support Teacher from Talbott Springs Elementary School, demonstrates several strategies for multiplying whole numbers with fractions for 3rd and 4th graders.
Transcript
(Dennis McDonald) Hi. I’m Dennis McDonald, Mathematics Support Teacher at Talbot Springs Elementary School. And this is Math in Minutes.
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Today we’re gonna look at strategies for multiplying whole numbers times fractions.
In third grade, students learn to multiply single-digit factors to find products, solving problems such as three times eight and six times nine.
In fourth grade, they learn how they can use similar strategies to multiply a whole number times a fraction, solving problems such as three times one-fourth and six times seven-eighths.
When students first begin multiplying whole numbers times fractions they begin working with unit fractions, or fractions that have one as the numerator.
Let’s take a look at one such problem and how a student might solve that problem. Let’s imagine that a dump truck carries one-fourth of a ton of dirt. We have three dump trucks. We want to know how much dirt is carried by all of the dump trucks? One-fourth is one truck. So three one-fourths, would represent three dump trucks. Each dump truck carries one-fourth of a ton of dirt. This makes three sets of one-fourth. Students know that they can add one-fourth, plus one-fourth, plus one-forth to make three-fourths. But they also know that three sets of one-fourth is the same as three times one-fourth. Since one-fourth, plus one-forth, plus one-fourth is three-fourths, three times one-fourth is also three-fourths. From there, students begin multiplying whole numbers times non-unit fractions.
Let’s take a look at a problem that uses a non-unit fraction.
Alyssa lives on a street that’s three-tenths of a mile long. Each morning she walks her dog along her street for three laps. How far does she travel each morning?
Three-tenths of a mile represents the distance of the street. We need three sets of three-tenths to represent the three laps that she makes on the street. Three-tenths, plus three-tenths, plus three-tenths… …makes nine-tenths of a mile. Three-tenths, plus three-tenths, plus three-tenths can also be represented as three sets of three-tenths, or three times three-tenths. Since three-tenths, plus three-tenths, plus three-tenths makes a sum of nine tenths, three times three-tenths gives us a product of nine-tenths.
Students also learn how to solve problems multiplying whole numbers times fractions with pictures. Let’s take a look at one such problem.
Darren is making batches of brownies. Each batch requires three-quarters of a cup of brown sugar. If he is making five batches, how much brown sugar will Darren need in all?
Students can draw a picture to represent this problem. This is the three-quarters of a cup needed for the first batch. Since there are five batches, we have five sets of three-fourths. Or, five times three-fourths. We have three, six, nine, twelve, fifteen fourths in total. Five times three-fourths equals fifteen-fourths.
This has been a look at the representations we use to understand multiplying whole numbers times fractions. See you next time on Math in Minutes.
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