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EL Support Lesson
Adding Like Mixed Numbers
Students will be able to add like mixed numbers and improper fractions using the counting up strategy with number lines.
Students will be able to explain their mathematical thinking using grade-level vocabulary, visuals, and sentence stems.
- Pose this problem to students: "A cake recipe calls for 1 ⅓ cup of brown sugar and 1 ⅔ cup of white sugar. How much sugar does the recipe need?"
- Tell students to consider what the problem is asking, what mathematical operation they think the problem will require, and which strategies they may use to solve it. Have them turn to a partner and discuss the problem.
- Invite a few students to share their thinking and record their responses.
- Tell students that the two numbers in the word problem are called Mixed numbers. Show students the vocabulary card with this term, read aloud the definition and state a few examples. Ask students to share other instances when they have seen mixed numbers in the real world.
Explicit Instruction/Teacher modeling(8 minutes)
- Read aloud the student-friendly language objective for this lesson and have students repeat it.
- Distribute a copy of the glossary to students and display a teacher copy on the document camera. Read aloud each word, its definition and have students describe the images.
- Write "Sentence" in the empty column on the right of the glossary and model how to write a sentence using the word "mixed number" (e.g., 2 ¾ is a Mixed numberBecause it has an integer and a fraction.).
- Instruct students to write a sentence for the remaining vocabulary words. Place students into partnerships and have them share their sentences with each other. Invite a few students to share their sentence or their partner's sentence with the whole group.
- Tell students to glue the glossary into their maths journals for reference.
Guided practise(10 minutes)
- Display a copy of the Mixed Fraction Addition with Like Denominators #3 worksheet on the document camera. Read the directions aloud and go through each step of solving the first addition problem. Say, "I see that the visual model shows one whole and one eighth colored in green, which will be added to another whole fraction model and seven-eighths colored in. First, I will add the integers 1 and 1 which makes 2 wholes. Then, I will add the fractions ⅛ and ⅞ which mounts to the sum of 8⁄8. I know that 8/8 can also be written as 1 whole. This means that the sum of 1 ⅛ and 1 ⅞ is 3."
- Repeat this process of modeling with the second problem in the worksheet. You will need to shade or colour in the visual model according to the written mixed number. Emphasize the importance of shading the correct number of rectangles. Verbalize your thinking clearly as you set up and solve the problem. Tell students that it is often helpful to draw a separate visual model of the answer to check if it is correct. Show this process to students too.
- Distribute whiteboards and markers to students. Read aloud and display the following word problem and have students work on it with a partner by drawing a visual model and completing the sentence stems/frames on their whiteboard:
- There is 1 whole and ⅙ cheese pizzas left plus 2 wholes and 3⁄6Pepperoni pizzas left over after a party. How much total pizza was left over?
- "The problem is asking for the sum of ____And ____. First, I ____. Then, I ____. I know that the sum is ____Because ____."
- Tell students to work with an effective partner (a more advanced EL student or an EL who speaks the same home language) on this problem, and practise describing and explaining the process of solving it using the sentence frames provided. Explain that the sentence stems/frames are there to support them to be able to talk about their mathematical thinking using key year five maths vocabulary. Emphasize that eventually, students will not need the sentence frames and be able to discuss their solutions on their own.
- Review students' answers and have them share on the document camera the various strategies they used to find the sum.
Group work time(10 minutes)
- Lead students in an activity in which they will work in small groups to become experts on solving and describing one addition problem with like mixed numbers.
- Form small groups of four students. Assign each student a number (1–4).
- Distribute the same strip with one addition problem on it to all members of one group. Note: you will also need to use the problems from the Mixed Fraction Addition with Like Denominators #4 worksheet. Ensure that students still have their whiteboards and markers.
- Tell students that the whole group will shade in the visual models based on the addends in their problem and solve for the sum. Then, they must compare their answers to the other group members' work and write out a brief explanation of the process they took to solve it on the whiteboards. Note: students are encouraged to use the paragraph frame from the previous section.
- Call all number 1s from the groups to the front of the class to demonstrate and elaborate on how they solved each problem (each group should be presenting a different problem). The audience is encouraged to ask questions. Some questions to suggest and display are:
- How did you get that sum?
- What strategy did you use for ____?
- Is your answer reasonable? How do you know?
- Can you explain this part more specifically?
- Have the 2s, 3s, and 4s form respective groups (e.g., one group for the 2s, another for the 3s, etc.). Incorporate the 1s into these three groups and have them repeat the process of sharing each problem and solution process using the sentence stems/frames. Then, allow time for questions and answers from the group.
- Circulate the room and listen in on students' conversation. Encourage each student to share equally and to use key maths vocabulary from the lesson.
Additional EL adaptations
- Pair students with more advanced students or other ELs who speak the same home language (L1) for all partner activities.
- 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 vocabulary cards in English and students' home language (L1) if possible.
- Provide manipulatives such as fraction strips or linking cubes to help students solve the problems.
- Give students sentence stems for the assessment discussion such as: "I agree with how you..." and "I disagree with ____Because..."
- Have students write their explanation without relying on the sentence stems/frames.
- Encourage students to rephrase the directions and key learning points from the lesson.
- Tell students to create their own addition problems with mixed numbers to solve on their own.
- Hand out an index card to each student and post the following problem on the board: What is the sum of 3 ⅖ and 4 ⅕?
- Tell students to draw fraction models to help them solve the problem and write their solution on the index card.
- Have students switch their index card with a table partner. Give students a minute to analyze their partner's solution and then describe the steps and processes used to solve it with the original author of the problem. Students may agree, disagree, or clarify on any points of the discussion regarding the mathematical steps taken to solve the problem.
- Ask a few pairs of students to share their conversations with the whole class.
Review and closing(2 minutes)
- Tell students that today they learned an important skill related to fractions: adding like mixed numbers using visual models. However, the more important part of the lesson is that students are able to talk about how they go about solving these addition problems.
- Congratulate your students on their ability to verbalize their mathematical processes with their peers and teacher.