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Explaining Expressions

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This lesson can be used as a pre-lesson for the Solving Expressions in Word Problems lesson plan.

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This lesson can be used as a pre-lesson for the Solving Expressions in Word Problems lesson plan.

Students will be able to write and solve expressions with order of operations.

Language

Students will be able to create and explain expressions using drawings and peer supports.

(3 minutes)
• Write the expressions 3 x 6 and 3 x (3 + 3) on the board and ask students to turn and talk to their partners about what the expressions show. Give them whiteboards to draw pictures and show their ideas.
• Ask for volunteers to share their ideas and gather information about students' background knowledge based on their responses. Rephrase their explanations using key vocabulary terms (i.e., "decompose," "times," "parentheses," etc.).
• Have a student read the student-friendly language objective: "I can make and talk about expressions using drawings and peer supports."
(8 minutes)
• Show students how the expressions 3 x 6 and 3 x (3 + 3) are similar and different using a hundreds chart and drawings (e.g., array).
• Provide a context for each of the expressions and look for differences and similarities in the language. For example, for the expression 3 x 6, you could write on the board, "There are 3 boxes with 6 bottles of water in each box. How many bottles of water are there in all?"
• Write on the board 3 x (3 + 3) and the following word problem, "There are 3 boxes of water with 3 bottles that are full and 3 bottles that are empty in each box. How many bottles are there in all?". Have the story problem written together on the board and ask students to turn to their partners and come up with differences in both of the word problems (e.g., 3 empty and 3 full, bottles vs. water bottles, longer sentences, etc.).
• Choose volunteers to share their ideas aloud and model how to create the expression using the word problem. Tell students that there happen to be key words in these word problems (e.g., "each," "with," "in all") but that key words do not always appear in word problems.
• Model how to write an explanation on chart paper of the expression from the written story problems. For example, "I know there are 3 total boxes and each box has 6 bottles of water. That makes me think of an array, with three rows and six bottles in each row. I can even draw 3 boxes with six bottles in each box. But, I know 3 boxes times 6 bottles will give me the answer of 18 bottles total."
• Ask students to turn and talk to their partner about your explanation. Have them take turns retelling your explanation to each other. Then, ask for volunteers to tell you what you included in your explanation (e.g., number and what they represented, a visual to show the expression, a written word (times) that represents multiplication, etc.). Write their insight on the board as a sort of checklist for their own explanations for later in the lesson.
(8 minutes)
• Refer to the second expression from the Introduction section, 3 x (3 + 3), and the word problem written on the board. Have students brainstorm in partners how they would create an explanation for the word problem.
• Model an explanation on a different sheet of chart paper using drawings and transition words as you explain it. Remind students that they must focus on the expression inside the parentheses first.
• Have an advanced student retell your explanation and then have them share their explanation. Write the student's explanation on the chart paper, adjusting or asking for clarification as you listen and record their thoughts.
• Challenge an intermediate student to present their explanation for the expression (i.e., 3 x (3 + 3)) on the board given the word problem context. Rephrase the students' answers with some of the following sentence frames:
• "First, I ____. Then, I ____."
• "The visual that helps me understand the word problem is ____."
• "I know this problem involves ____ (operation) because ____."
• "I know I have the correct answer because ____."
• Monitor student explanations in peers and to the whole group throughout the whole lesson using the Formative Assessment: Peer Explanation Checklist to jot down noteworthy student phrases and keywords.
(10 minutes)
• Provide a new word problem for students to consider. For example, "Popcorn is for sale for \$2 a bag. The band earns \$1 for every bag sold. They sold 200 bags. How much money did they earn? (e.g., 200 x (\$2 â€“ \$1)).
• Allow them time to think about it on their own and then jot ideas or draw pictures on their whiteboards. Then, have them share their ideas about the expression with their partners ("I think the expression is ____ because ____. The band earned...").
• Use the notes you took from the Formative Assessment: Peer Explanation Checklist so that you choose students who can model correct language use. Ask them to model their explanations.
• Ask students to pay attention to the presenters because they will use the same problem to practice their explanations one more time. Remind them that you will take notes on their explanations and refer to the checklist on the board with ideas for good explanations.

Beginning

• Allow students to use their home language (L1) or their new language (L2) in all discussions. Provide bilingual reference materials to assist in their vocabulary word acquisition.
• Encourage them to use the vocabulary cards and terms in their conversations and writing. Allow them to draw pictures to support their understanding of the terms.
• Preteach the difference between an equation and an expression using simple calculations and ask them to create one sentence for each of the expressions.
• Pull aside a small, teacher-led group for all the partnership activities to guide them with correct vocabulary term usage and instruction during their explanations.

• Pair students with mixed ability groups so they can offer explanations and provide feedback to beginning ELs when appropriate.
• Have them model correct terms and phrases to use when they are explaining their answers.
• Ask them to provide sentence frames or stems for students to use in their explanations.
• Have them adjust student responses that need assistance. For example, have them ask their partner, "What do you think about adding/taking away ____?"
(6 minutes)
• Have students switch partners and share their explanations for the Independent section problem again with a partner.
• Walk around and take notes on a new copy of the Formative Assessment: Peer Explanation Checklist to serve as a formative assessment of their ability to to explain their thinking.
(5 minutes)
• Choose two examples of student explanations you wrote on the Formative Assessment: Peer Explanation Checklist and write them on the board. You can choose based on student growth or explanations that are exemplary.
• Pick a student to read them aloud and share what is good about the explanations (e.g., the explanation has specific numbers, it uses transition words, etc.).
• Have students share their partner's explanations and examples of phrases or ideas they recall that seemed clear and correct.

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