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Mixed Operations with Decimals – Decimals in daily life – Money and measurements often use decimals – Review basic decimal operations – Add, subtract, multiply, and divide decimals – Evaluate decimal expressions – Follow the order of operations with decimals – Practice with real examples | This slide introduces students to the practical applications of decimals in everyday life, such as in currency and measurements. It also serves as a quick review of the basic operations involving decimals, which are addition, subtraction, multiplication, and division. The main focus of today’s lesson is on evaluating numerical expressions that include decimals, emphasizing the importance of following the order of operations (PEMDAS). Provide students with examples that are relevant and relatable, such as calculating the total cost of items or splitting a bill, to demonstrate these concepts in practice. Encourage students to solve problems step-by-step and to check their work carefully.

Understanding Decimals – Review of decimal places – Each place represents a power of 10 – Decimals as fractions – Decimals show parts of a whole, like fractions – Decimals in everyday life – Common in prices and lengths – Practice with money and measurements – Calculate change or measure ingredients | Begin with a quick review of decimal place values, emphasizing the importance of each position being a power of ten. Explain how decimals are another way to represent fractions, making the connection between the two concepts. Use relatable examples such as money (dollars and cents) and measurements (meters and centimeters) to show decimals in practical use. Encourage students to think of other examples where they encounter decimals. Conclude with practice problems involving money, such as calculating change, or measurements, like combining different lengths, to reinforce their understanding of decimals in real-world applications.

Decimals & Order of Operations – Review PEMDAS rules – PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction – Apply PEMDAS to whole numbers – Practice with examples like 3 * (4 + 2) – 5 – Extend PEMDAS to decimals – Same rules apply when using numbers like 3.5 * (4.1 + 2.2) – Solve decimal problems using PEMDAS – Example: Calculate 5.6 + 3.2 * (2.5 – 0.5) / 1.5 | Begin the lesson by recalling the order of operations, commonly remembered by the acronym PEMDAS. Provide practice problems that apply PEMDAS to whole numbers to ensure students are comfortable with the concept. Then, introduce how these same rules apply when working with decimal numbers. Emphasize that the order does not change when decimals are involved. Provide several examples and practice problems that include decimals in various places within the expressions. Encourage students to solve the problems step-by-step and to check their work with a partner. This slide aims to build a strong foundation in evaluating expressions with decimals, a key skill in algebra.

Adding and Subtracting Decimals – Align decimal points correctly – Place decimals in a column ensuring points line up – Example: Add 3.5 + 4.75 – 3.5 becomes 3.50, then add to get 8.25 – Example: Subtract 6.2 from 10.5 – Write 10.5 above 6.2, subtract to get 4.3 | When adding or subtracting decimals, it’s crucial for students to align the decimal points to ensure accuracy. Show them how to rewrite numbers so that all decimal points are in a vertical line. For the addition example, demonstrate how to add 3.5 and 4.75 by first converting 3.5 to 3.50 for easier alignment. For subtraction, illustrate the process by placing 10.5 above 6.2, emphasizing the importance of aligning the decimal points before subtracting. These examples will help students understand the concept of decimal place value in the context of addition and subtraction. Encourage students to practice with additional problems and to check their work by estimating the sums and differences.

Multiplying Decimals – How to place the decimal point – Count total decimal places in factors to place in product – Example: 2.3 x 0.4 – Multiply as whole numbers then place decimal for 2 places – Class participation problem – Solve 3.6 x 0.09 together and discuss | This slide focuses on teaching students how to multiply decimals and correctly place the decimal point in their answer. Start by explaining the rule for decimal placement: the number of decimal places in the product is the sum of the decimal places in the factors being multiplied. Use the example of multiplying 2.3 by 0.4 to illustrate this, showing that since there are three decimal places in total in the factors, the product must also have three decimal places. For the class participation, present the problem 3.6 x 0.09 and work through it as a class, ensuring to involve the students in each step of the process. This interactive approach helps reinforce the concept and allows for immediate feedback and correction of misunderstandings.

Dividing Decimals – Shift the decimal point – Move decimal in divisor to the right to make it a whole number, and do the same in the dividend. – Example: 5.6 ÷ 0.7 – 5.6 becomes 56 and 0.7 becomes 7. Now, 56 ÷ 7 equals 8. – Class practice: 12.5 ÷ 2.5 – Apply the same method: 12.5 becomes 125 and 2.5 becomes 25. What’s 125 ÷ 25? | This slide introduces the concept of dividing decimals by shifting the decimal point. Start by explaining the process of moving the decimal to the right in both the divisor and dividend until the divisor is a whole number. Use the example of 5.6 divided by 0.7 to illustrate this concept, showing step-by-step how to shift the decimal and perform the division. For the class practice, guide students to apply the same method with 12.5 divided by 2.5, and encourage them to solve it. Ensure to walk around the classroom to assist students who may need help and to check for understanding. Discuss the answers as a class to reinforce the concept.

Evaluating Expressions with Decimals – Combine operations with decimals – Example: 3.2 + 4.5 × 0.6 – First, multiply 4.5 by 0.6, then add 3.2 to the product – Follow guided practice steps – Use the order of operations: PEMDAS – Solve step-by-step problems – Practice with similar decimal problems | This slide introduces students to the concept of evaluating numerical expressions with decimals, emphasizing the importance of following the order of operations. Start by explaining how to combine different operations such as addition and multiplication when decimals are involved. Use the example on the slide to illustrate the process: first multiply 4.5 by 0.6 to get 2.7, then add the result to 3.2 to get the final answer of 5.9. Guide the students through a step-by-step solution to reinforce the concept. Provide additional practice problems for the students to solve, ensuring they apply the correct order of operations. Encourage students to work through the problems slowly and to check their work carefully.

Class Activity: Decimals Scavenger Hunt – Find decimal expressions in class – Work in pairs to solve expressions – Share solutions with the class – Explain how you got your answers – Discuss different solving methods – Talk about any strategies used | This interactive activity is designed to engage students with hands-on learning. Place decimal expressions around the classroom before the class starts. Students will work in pairs to find these expressions and solve them, encouraging collaboration. After solving, each pair will share their solutions and discuss the methods they used with the entire class. This will help students learn from each other and understand different approaches to evaluating decimal expressions. Possible expressions to use: adding, subtracting, multiplying, and dividing decimals. Ensure that the expressions vary in difficulty to cater to different skill levels within the class.

Wrapping Up: Decimals & Operations – Review of decimal expression evaluation – Remember the order of operations – PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction – Homework: Practice worksheet – Complete the worksheet to reinforce today’s lesson – Importance of practice – Consistent practice is key to mastering math skills | As we conclude today’s lesson, it’s crucial to emphasize the importance of the order of operations when evaluating decimal expressions. Remind students of the acronym PEMDAS as a tool to remember the sequence. For homework, students will receive a worksheet with a variety of decimal expressions to solve, ensuring they apply what they’ve learned. Encourage them to take their time and check their work for accuracy. This practice will help solidify their understanding and prepare them for more complex problems. During the next class, we can review any challenging problems from the homework and clarify any lingering questions.