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# Order of Operations with Fractions and Decimals

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Students will be able to solve math expressions involving fractions and decimals, using the order of operations.

(5 minutes)
• Ask students to review what they know about the order of operations and the acronym PEMDAS (P (parenthesis), E (exponents), M (multiply), D (divide), A (add), S (subtract), and record their knowledge on a piece of chart paper. Leave the chart paper visible for students to see throughout the lesson.
• Invite students to recap how to multiply fractions by whole numbers by solving 4 x 2/3. Draw a bar model to represent 2/3 and show how to multiply the fraction by the whole number.
(5 minutes)
• Distribute whiteboards and markers to each student.
• Show students the following problem on the board, and instruct them to try to solve it, remembering PEMDAS: 2 + 1/2 x 3 (Answer: 3 1/2).
• Tell students that today they will learn how to use PEMDAS to solve math problems involving fractions and decimals.
• Write '1/3 x 3 - 1' on the board, and model how you use PEMDAS to solve. Do the same for '1.2 - (0.3 + 0.4)'. Be sure to show each step of the process.
• Tell students that any operations inside parentheses must be done first, then exponents (indicate that there are none in this problem), followed by multiplication and division from left to right (whichever comes first), and finally addition and subtraction, also from left to right.
• Remind students that the order of operations allows us to calculate mathematical expressions in a consistent way, getting the same answer every time. Tell them that if we didn't have these rules, people would get different answers for the same problem.
• Inform students that the PEMDAS rules are the same for expressions with fractions and decimals.
(10 minutes)
• Write each of the following mathematical statements on a separate piece of of chart paper. (Note: These could be done in advance.) 1/2 x 4 - 2 + 10 50 ÷ 2 - 5 + (1/8 x 3) 2/3 x 1 + 6 - 4 ÷ 2 35 ÷ 7 - 0.5 x 2 ** (10 + 10) - 20 + 16 ÷ 4 + (0.25 x 4)
• Divide students into five groups, and assign one of the math problems to each group. Give each group a marker.
• Instruct students to solve the problem collaboratively, showing every step clearly before boxing their answer.
• Tell students to write at the bottom of the chart paper, one math problem which includes at least three operations (+, -, x, ÷) and a fraction or decimal. Make sure they do not attempt to solve the problem yet.
• Assist any groups that need help and double check the math expression each group writes to make sure it is valid.
• Each group will choose a representative to explain how they solved the problem.
(10 minutes)
• Instruct students to return to their seats, take out their math journals, and solve the five problems created by groups at the bottom of their chart papers. Remind them to show the steps involved and their math thinking in their journals.
• Have students compare their order of operations and answers to a table partner's work.

Support:

• Allow students to work on the independent practice with a supportive partner.
• Pull aside a small teacher-led group and guide them through the Order of Operations: First Things First worksheet.

Enrichment:

• Give students more difficult expressions with multiple operations to solve.
(5 minutes)
• Distribute an index card to each student, and have them solve the following problem, showing each step: (60 x 1/2) ÷ 3 + 16 - 2.5.
• Collect the index cards as an exit ticket to gauge students' understanding of the topic.
(5 minutes)
• Ask students to use the following sentence stem to reflect on their learning as they talk with a partner: ** The order of operations is important because _____.
• Invite a few students to share their conversations with the whole class.

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