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Word Problems: Multiplying Fractions by Whole Numbers

This lesson can be used as a pre-lesson for the Multiplication Models: Fractions and Whole Numbers lesson plan.
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This lesson can be used as a pre-lesson for the Multiplication Models: Fractions and Whole Numbers lesson plan.

Students will be able to multiply a fraction by a whole number.

Language

Students will be able to create story problems for math expressions with key math vocabulary using peer support.

(2 minutes)
• Present students with a word problem: "I love to bake and I need to make two cakes for my friend's birthday party. A recipe calls for 3/4 cup of sugar and I want to double the recipe. How many cups of sugar do I need?"
• Give students a minute of thinking time before they verbally share with a partner how they would solve this problem (some students may add 3/4 + 3/4, while others might think of multiplying the whole number 2 by 3/4).
• Invite students to share their solutions with the whole class and record their responses on the board.
• Validate students' answers and explain that today they will practice creating word problems to go with math equations that involve multiplying a whole number and a fraction.
(6 minutes)
• Read aloud the student-friendly content and language objectives for the lesson, and have students restate them to a peer.
• Show the vocabulary cards on the document camera, one at a time, inviting students to participate by reading the word and its definition aloud. Connect the vocabulary words to the problem presented in the introduction. (For example, say, "In the sample problem, the whole number was 2 and the fraction was 3/4. The numerator was 3 and the denominator was 4. We had to multiply the whole number and the fraction.")
• Tell students to conduct a quick self-assessment of their knowledge of each word by showing a thumbs up if they confidently know the meaning of the word, a thumbs to the side if they have somewhat of an idea of its meaning, and a thumbs down if they are not familiar with the word at all. Repeat this process for each tiered vocabulary words.
• Distribute a Glossary to students and have them work with a partner to label the last column "Example," and have students write an example of the word in this column (e.g., for the word "denominator," they would write a fraction or draw a fraction model, and label the denominator).
• Instruct students to glue the completed Glossary in their math journal for future reference.
(12 minutes)
• Display and read aloud the expression 4 x 2/3. Tell students that when you multiply a fraction by a whole number, you can just multiply the numerator by the whole number and leave the denominator the same.
• Think aloud as you reread the expression and begin to solve it. Draw a model (pie or bar model) of 2/3 four times to show a visual that matches the problem. Say, "I multiply 4 by 2 to get 8 and I leave the denominator as it is. The answer is 8/3."
• Tell students that the word problems they create today should have the following elements: a whole number, a fraction, a question, and a situation that is realistic and makes sense.
• Brainstorm with students ideas about what measurements or quantities would make sense for the fractions in the problems. Ask for students' ideas. The list could include:
• cooking/recipe measurements such as cups, pounds, gallons, kilograms
• length or distance measurements such as feet, inches, centimeters, meters, miles
• fractions of a pie/pizza
• Remind students that they should have fun with the task of writing story problems and that they are welcome to get inspiration from topics that interest them such as sports or food. As long as the story problem or situation makes sense, it is valid.
• Model out loud as you think of possible story problems or situations you could craft to match the problem you solved earlier. Say, "I would like to write a problem about cookies because I love to bake and eat cookies. So, I could say that I need to make 4 batches of cookies. Each recipe uses 2/3 cup of sugar. There are the two numbers needed in my story problem. Now, I just have to ask the question. How many cups of sugar will I need to make 4 batches of cookies?" Emphasize the importance of punctuation and using complete sentences to craft the story problem.
• Show students another expression, this time with the fraction written before the whole number: 5/8 x 6.
• Explain that it does not matter if the fraction or the whole number is written first because when we multiply, the order does not matter. The product, or answer to a multiplication problem, is the same no matter which factor comes before.
• Repeat the process of solving the problem. This time ask for students' to contribute their ideas of how to solve it (e.g., by drawing a model or solving using the algorithmâ€”multiply the numerator by the whole number and leave the denominator the same). Invite students to remind you of the steps needed to solve the expression.
• Explain to students the process of simplifying the improper fraction. In this case, the answer will be 30/8 which can be simplified by dividing the numerator and denominator by 2 to get the answer 15/4. Then, elicit students' ideas of a story to go with it, this time using a different type of situation such as a length/distance measurement. Ask prompting questions to guide them such as: Where in the world might you see a fraction like 5/8? In what situation might you need to multiple 5/8 by 6?
• Decide as a whole group on a situation that would work. Write it down and have students read it to themselves. Then, have students discuss with a partner additional ideas they have to revise the problem and make it clearer or better using the sentence stems/frames as a guide:
• "I think we could make the sentence better by changing it to say ____."
• "How about we add ____ to the problem story so that ____?"
• "What if we say ____?"
• Invite students to share their ideas before you revise the story problem to the point where the whole class agrees that it is an ideal situation to represent the math expression.
(10 minutes)
• Tell students they will now practice creating a story problem with a partner before writing two stories independently.
• Place students into partnerships and distribute a copy of the Crafting Word Problems: Fractions Multiplied by Whole Numbers worksheet to students. Display a teacher copy on the document camera.
• Read the directions aloud and review the sample problem. Inform students that the situations they create might be very different from one another and that there is not just one correct situation to match an expression.
• Assign students to work on the first problem in collaboration with their partner. Specify that it is acceptable for the pair of students to write the same story problem as long as they both helped create it.
• Invite a few pairs of students to share their story problem and solution once completed. Have the students who are listening to the story problems contribute ideas for edits or revisions using the same sentence stems/frames from the previous section.
• Instruct students to complete the last two problems on the worksheet on their own. Circulate to offer assistance as needed.

Beginning

• Allow students to explain the process of solving the problems in their home language before rephrasing, using sentence stems/frames, in English.
• Have students work in a smaller, teacher-led group during group work.
• Create and display a word/phrase bank with helpful terms from the lesson for students to refer to, with images if applicable.
• Group students intentionally based on academic and language needs.

• Have students share their answers aloud without referring to the sentence stems/frames for support.
• Allow learners to utilize glossaries and dictionaries for unfamiliar words.
• Have learners repeat instructions and key vocabulary for the class.
(4 minutes)
• Display and read aloud the equation: 4/5 x 6 = 24/5 on a piece of chart paper. Distribute an index card to each student and have them write their name on it.
• Give students some time to think of a situation to match the equation. Then tell the students to verbally share the situation with their table partner before writing it down on their index card
• Instruct students to come up to the chart paper and tape their index card.
• Read aloud a few example situations and point out how varied the situations can be for the same mathematical expression.
(4 minutes)
• Lead students in a reflective activity to close the lesson. Ask them to think of a peer they would like to compliment who worked extra hard or who was particularly helpful during this lesson.
• Display the following sentence stems for students to use as they compliment their classmates. Model a few examples for students.
• "I would like to compliment ____ for ____."
• "During the lesson, I noticed how____ did an excellent job at ____."
• Have each student share one peer compliment.

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