# Applying Prior Strategies to Fraction Word Problems Involving Multiplication to the Whole

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## Objective

SWBAT solve word problems involving the multiplication of fractions by whole numbers.

#### Big Idea

Students explore using manipulatives, fractional models and word problem strategies from the past to solve word problems.

## Candy Factory: Reviewing Equivalent Fractions

10 minutes

Almost everyday when students come into the classroom for their math lesson, I have them work on an iPad app to spiral review or to strengthen fact knowledge. Today we opened up one of our favorite apps and began matching up candy bars with orders placed in the Candy Factory. My students LOVE this app. I love it because it is not only engaging, but is leveled and strengthens their conceptual understanding of equivalent fractions. I have noticed that, as we use this app, more students are recalling certain fraction equivalencies. This makes teaching them to simplify much easier. The visual that this app offers must be helping them retain.

## Tapping on Prior Knowledge to Solve Word Problems

15 minutes

Fraction Problems Word File

Because my students have had repetitive exposure to word problem strategies throughout the year, I thought it would be a good idea to tap onto their prior knowledge and review before delving  into word problems involving multiplication of fractions. The standard expects that 4th graders learn to solve one step word problems. Note: Multi- step word problems are reserved for just whole numbers in standard 4.OA.A.3, but this lesson does challenge them to solve a few two step problems. I think that this exposure will help them understand real life situations. When we go shopping and something is marked a third off, we figure the percentage and always subtract to find the price we pay for the item. A few problems in this lesson and on their homework involve this concept. However, only one step word problems will be assessed for mastery of the standard.

To start, we listed the strategies we have used. The teepee drawing on the list stands for a "Math Mountain". This strategy places the total at the top and then the two factors are listed at the bottom, helping to order an equation properly. The KWS stands for a dissecting g/o strategy we use that lists what we know, what we want to know and then, how to solve. ( You will see this on homework samples.)Fraction Word Problems Class Notes

We began dissecting the word problems together.  Right away, a student's hand shot up after I read the first problem. She said it looked like a division problem. I asked: Do you remember when we solved a problem long ago in our division unit about a person having 1/3 of 90 dollars saved for a bike?( Multiplicative Comparison 4.OA.A.2) She said that we divided ninety by three and got thirty dollars. "It's the same thing!" she exclaimed. We talked about the word "of" and why it means to multiply. I returned to a simpler example of 1/2 of 6 and drew six halves and repeated addition. I referred to prior knowledge that repeated addition is multiplication. Suddenly, this approach focused them and it all clicked in place.

When the two step problem arose, we talked about the importance of focusing on wording and visualizing the problem. Suddenly, someone asked about estimation problems. I drew an Estimation Sample and we talked about how rounding the fraction was not a logical idea, nor rounding the one digit factor.  This sample asked them to find the nearest whole number. When the problem was completed, they understood that a number line would be the fractional model of choice for supporting their reasoning. Discussion about how 2/5 is less than 1/2 was focused on by two students, who took charge of explaining why we chose the answer of 2. It was a teachable moment I latched onto and will include next year in the SB file.

We returned to solving our two step problem. We talked about shopping and real life situations involving coupons, discounts and noting that those words may turn up in our word problems now. We talked about the phrase, "after the discount", and "left" and how that indicates that subtraction from a total needed to happen.

## Assigning Independent Practice and Homework

15 minutes

I developed this homework sheet with a couple of two step real life situation problems. Everyone here shops at Kohl's Department Store. Everyone receives coupons in the mail for 10,20 or 30 percent off. We discussed how that would be the same as 1/10, 1/5, or 1/3 off of the price of our purchase. This discussion led into setting them up for independent practice as we strive to master the standard, and push ahead a little.

Homework is considered practice in my class and it is designed to be collaboratively done when working in class to develop the atmosphere that math is about striving to master a standard. So, I assigned the worksheet, and told them they could collaborate with one another. I told them I expected to see their work and proof of their understanding.

I worked with two students who struggle with word problems to get them started. After I saw they had set up their equations for the first problem, I roved around and noticed that everyone was dissecting the problem correctly, setting up the first equation and solving the first part. Students came to me asking if \$20 was correct. I asked them to go back to the question and see if they thought they had answered it. I listened as the discussions went on about the question. I stopped them all and reminded them that the question wanted to know how much was paid for the clothes?

Soon, they were solving it by subtracting \$20 from the \$60.

We closed the lesson after about 15 minutes of working collaboratively on two to three problems. I reminded them to look back at past notes as I had emailed today's class notes to each student for reference.

As always, I asked students to share "Aha!" moments. The student who had solved the first problem by listing 1/7 thirty-five times spoke first. He was so impressed about learning that he needed to learn to multiply numerators and denominators. See: One Seventh thirty-five times!

Another student was impressed that there can be two step problems. I learned "of" means to multiply was this student's declaration.Percentages are the same as fractions seemed to be something that our conversation brought to light for this student.