EL Support Lesson
Talk About Your Strategy: Fractions of a Whole
Students will be able to use bar models and multiplication to find a fraction of a whole number.
Students will be able to explain the strategy used to solve a problem using peer interaction and sentence stems.
- Read aloud the content and language objective. Have students repeat or rephrase the student-facing version of the objectives to a table partner.
- Tell students that they will practise describing and explaining how they solved a problem involving multiplying a fraction by a whole number.
Explicit Instruction/Teacher modeling(8 minutes)
- Write a problem on the board and read it aloud: "Mary made 24 cupcakes. 1/3 are chocolate cupcakes and the rest are vanilla. How many chocolate cupcakes are there?"
- Tell students that we can solve this problem a variety of ways. One way is to use a bar model. Draw a bar model, and explain that we need to divide it into thirds so that we can figure out how many cupcakes is equal to a third of the 24. Show how you divide the bar into 3 equal sections and write 24 on top of the bar to show that the whole bar represents 24 cupcakes. Tell students that each section represents one third of the cupcakes. So we have to ask ourselves, what is a third of 24? Or in other words, what is 24 divided by 3? Tell students that the answer is 8. There are 8 chocolate cupcakes.
- Demonstrate that you can also solve this problem mentally with repeated addition by thinking of a number that you can add three times to get to 24. If students are comfortable with repeated addition and can decompose numbers, they can figure out that 8 + 8 + 8 = 24.
- Another way to solve this problem is by multiplying the numerator by the whole number to get 24/3. Then divide the new numerator by the denominator to get 8 as the answer.
- Repeat this process by modeling multiple strategies to solve another problem: "There are 36 pounds of rice in the food bank. Three-fourths of this was used to feed people in November. How many pounds of rice was used in November?"
- Be sure to use ample maths vocabulary to clearly describe the process of solving this problem in multiple ways.
- Display the paragraph frame of transition words such as "First, I... Then, I ... Finally, I..." for students to use throughout the lesson.
Guided practise(10 minutes)
- Distribute the Discussing Fractions of a Whole worksheet to students and display a teacher copy.
- Review the steps involved in the two strategies demonstrated at the top of the worksheet. Tell students that these are not the only ways to solve this type of problem. There are also other strategies such as repeated additions. Students are welcome to use any strategy that works well for them as long as they are able to accurately describe and explain their maths thinking.
- Model how to solve the first problem in the worksheet with the strategy of your choice. Write a description of the procedure in complete sentences and read it aloud to students.
- Instruct students to solve the second problem on the worksheet on their own. Place students into partnerships and have them verbally explain the steps they used to solve the problem. Each pair should listen to each other's strategies before writing down the steps they took in complete sentences.
- Provide the following questions for students to use as they share their description with their classmate.
- What strategy did you use to solve the problem?
- Why did you choose this strategy?
- What did you do when you got to this point?
- Why did you do that?
- Invite one or two pairs of students to model their sharing of the solution to the second problem in front of the class.
Group work time(12 minutes)
- Instruct students to independently complete the remaining problems (3–5) on the worksheet and write a description. Tell students to try different strategies with different problems so they are comfortable with a variety of ways to solve for a fraction of a whole.
- Once everyone has completed the worksheet, have students walk around the room with their worksheet and share one problem solution and description with a partner. They may choose any problem to share but each pair must share their work on the same problem.
- Use the Formative Assessment: Peer Explanations Checklist to listen in on students' discussions and note their progress.
- Tell students to use the clarifying questions provided in the previous section in their conversations with their peers. Inform students that they may need to return to their desk to revise or edit their descriptions of the solutions as they talk about their strategy with their partner. Tell students to modify their descriptions as needed. Continue this process until everyone has shared all the problems and made edits/revisions to their descriptions.
- Have a few students share their descriptions and mention the changes made throughout the process.
Additional EL adaptations
- 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.
- Provide students with a word bank to refer to when they complete the sentence stems/frames.
- Encourage students to explain the directions in their own words and/or write them down in their maths journals prior to group work.
- Have students share their answers aloud without referring to the sentence stems/frames for support.
- Encourage students to rephrase the directions and key learning points from the lesson.
- Show students the following problem and solution, and tell students to write a description of the steps taken to solve the problem using complete sentences:
- Problem: "Carla and her friends made 75 baby hats. They will donate 2/3 of the bracelets to a hospital. How many hats were donated?"
- Solution: a bar model with a total of 75, divided into 3 equal sections and the written answer of 50 hats.
- Have students orally describe the solution to a partner and invite a few students to share their descriptions with the whole class. (For example, "First, they drew a bar model with a total of 75. Then, they divided the bar model into thirds and divided 75 by 3 to get 25. Finally, they multiplied 25 by 2 since they need to figure out what two-thirds of 75 is and they got the answer 50.")
Review and closing(4 minutes)
- Ask students the following question: How helpful was it to share the explanation of your solution to your peers and receive feedback? Tell them to show their response on their fingers, with one finger indicating not very helpful and five fingers indicating extremely helpful.
- Invite a few students to share their reasoning using the following sentence stems:
- "I found it useful to share with my peers because..."
- "I found it not very helpful to share with my peers because..."