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Order Up! Solving Expressions

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Lesson Plan

Order Up! Solving Expressions

Students will be able to solve numerical expressions involving all four operations using the order of operations (PEMDAS/GEMS).

Mastering the order of operations is like learning the rules of a game; it ensures everyone plays fairly and gets the same correct answer, laying a critical foundation for all future math!

Audience

5th Grade Students

Time

30 minutes

Approach

Direct instruction, guided practice, and independent application.

Materials

Whiteboard or projector, Order Up! Slide Deck, Order Up! Warm-Up, Order Up! Worksheet, Order Up! Answer Key, and Order Up! Cool-Down

Prep

Teacher Preparation

10 minutes

Step 1

Warm-Up: Operation Station

5 minutes

  • Distribute the Order Up! Warm-Up to students.
  • Instruct students to independently solve the basic operation problems.
  • Review answers as a class, highlighting any misconceptions about basic operations before introducing the order of operations.
  • Teacher Note: This warm-up activates prior knowledge of individual operations.

Step 2

Introduction: Why Order Matters!

5 minutes

  • Display the first slide of the Order Up! Slide Deck.
  • Ask students: "Imagine you have a recipe. Does the order you add ingredients matter? What if you bake the cake before mixing?" (Expected answer: Yes, order matters!)
  • Connect this to math: "Just like in recipes, the order we do things in math expressions matters. Today, we're learning the 'recipe' for solving math problems correctly every time: the order of operations!"

Step 3

Direct Instruction: GEMDAS Unpacked

10 minutes

  • Use the Order Up! Slide Deck to introduce GEMDAS.
  • Explain each step clearly: Groups, Exponents (mention these are often not in 5th grade, but good to know), Multiplication & Division (left to right), Addition & Subtraction (left to right).
  • Provide clear examples for each step using the slides.
  • Teacher Note: Emphasize 'left to right' for multiplication/division and addition/subtraction. Use the GEMDAS mnemonic device (Groups, Exponents, Multiplication/Division, Addition/Subtraction).

Step 4

Cool-Down: Exit Ticket

5 minutes

  • Distribute the Order Up! Cool-Down.
  • Students solve a simple expression using the order of operations independently.
  • Collect cool-downs to assess understanding and identify students who may need additional support.
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Slide Deck

Order Up! Why Math Needs a Recipe

Have you ever tried to bake a cake without following the recipe steps in order?

Math expressions are like recipes! We need a specific order to get the right answer.

Today, we'll learn the 'recipe' for solving math problems!

Welcome students and introduce the idea that order matters in math, just like in cooking or building.

Meet GEMDAS!

Groups ( ) or [ ]

Exponents (like 2^3 - we won't see many today, but good to know!)

Multiplication (x) and Division (÷) - from left to right

Addition (+) and Subtraction (-) - from left to right

Introduce the GEMDAS acronym. Explain that these are the 'rules' we follow. Emphasize GEMS as a clear way to remember the order: Groups, Exponents, Multiplication/Division, Subtraction/Addition.

Step 1: Groups Power!

Always solve anything inside Groups ( ) or [ ] first.

Think of them as a VIP section – they get special treatment!

Example: (5 + 3) x 2

First, solve 5 + 3 = 8

Then, 8 x 2 = 16

Explain Groups first. Emphasize that anything inside groups is a 'mini-problem' that must be solved before anything else.

Step 2: Multiply or Divide? (Left to Right!)

Next, tackle Multiplication (x) and Division (÷).

IMPORTANT: Do these operations as you see them from left to right in the problem.

Example: 12 ÷ 3 x 4

First, solve 12 ÷ 3 = 4

Then, 4 x 4 = 16

Introduce Multiplication and Division. Stress the 'left to right' rule. Give an example where division comes before multiplication.

Step 3: Add or Subtract? (Left to Right!)

Finally, handle **Addition (+) ** and Subtraction (-).

IMPORTANT: Just like with multiplication and division, do these operations as you see them from left to right.

Example: 10 - 2 + 5

First, solve 10 - 2 = 8

Then, 8 + 5 = 13

Introduce Addition and Subtraction. Again, stress the 'left to right' rule. Give an example where subtraction comes before addition.

Let's Practice Together!

Problem: 18 - (3 + 2) x 3

Step 1: Groups! (3 + 2) = 5

Now the problem is: 18 - 5 x 3

Step 2: Multiply/Divide! 5 x 3 = 15

Now the problem is: 18 - 15

Step 3: Add/Subtract! 18 - 15 = 3

Answer: 3

Provide a comprehensive example step-by-step. Go through each stage of GEMDAS clearly.

Another One! Teamwork!

Problem: 24 ÷ 4 + 2 x 5

Think: What comes first? Division or Multiplication? Remember: Left to Right!

Step 1: Multiply/Divide!
24 ÷ 4 = 6
Then, 2 x 5 = 10

Now the problem is: 6 + 10

Step 2: Add/Subtract!
6 + 10 = 16

Answer: 16

Another practice problem. Encourage students to try on their own, then reveal steps.

Your Turn! Worksheet Challenge!

Now it's time to show what you know!

Work through the problems on your Order Up! Worksheet.

Remember to use GEMDAS for every problem!

Ask questions if you get stuck, but try your best first!

Introduce the worksheet and explain that they will apply what they've learned independently. Remind them to use GEMDAS.

You did great! Wrap Up

We've learned that following the 'recipe' for math problems helps us get the right answers!

GEMDAS is your guide!

Next, we'll do a quick cool-down to see what you remember!

Briefly recap the importance of order of operations and prepare for the cool-down.

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Warm Up

Order Up! Warm-Up: Operation Station

Welcome to Operation Station! Before we learn about the 'recipe' for solving big math problems, let's make sure our basic operation skills are super sharp.

Solve each problem below. Show your work!

  1. 45 + 23 =


  2. 78 - 34 =


  3. 15 x 6 =


  4. 64 ÷ 8 =


  5. (10 + 5) - 7 =


Challenge Question!
6. (4 x 3) + (18 ÷ 2) =


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Worksheet

Order Up! Solving Expressions Practice

It's time to put your GEMDAS knowledge to the test! Remember to follow the order of operations carefully for each problem. Show your steps!

GEMDAS Reminder:

  1. Groups
  2. Exponents
  3. Multiplication or Division (from left to right)
  4. Addition or Subtraction (from left to right)

Instructions: Solve each numerical expression. Show all your steps clearly.

  1. 8 + 2 x 5 =





  2. (10 - 4) ÷ 2 =





  3. 20 ÷ 5 + 3 x 2 =





  4. 6 x (7 - 3) =





  5. 15 - 3 + 7 =





  6. (9 + 1) x (12 ÷ 4) =





  7. 30 ÷ 6 - 2 =





  8. 4 + 8 x 2 - 10 ÷ 5 =










Challenge Problem:

  1. 2 x (5 + 3) ÷ 4 + 7 =










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Answer Key

Order Up! Worksheet Answer Key

Here are the step-by-step solutions for the Order Up! Worksheet.

1. 8 + 2 x 5

  • Step 1: Multiplication. According to GEMDAS, multiplication comes before addition.
    2 x 5 = 10
  • Step 2: Addition. Now add the remaining numbers.
    8 + 10 = 18
  • Answer: 18

2. (10 - 4) ÷ 2

  • Step 1: Groups. Solve the operation inside the groups first.
    10 - 4 = 6
  • Step 2: Division. Now divide the result by 2.
    6 ÷ 2 = 3
  • Answer: 3

3. 20 ÷ 5 + 3 x 2

  • Step 1: Division. Work from left to right for multiplication and division.
    20 ÷ 5 = 4
  • Step 2: Multiplication. Next, perform the multiplication.
    3 x 2 = 6
  • Step 3: Addition. Finally, add the remaining numbers.
    4 + 6 = 10
  • Answer: 10

4. 6 x (7 - 3)

  • Step 1: Groups. Solve the operation inside the groups first.
    7 - 3 = 4
  • Step 2: Multiplication. Now multiply the result by 6.
    6 x 4 = 24
  • Answer: 24

5. 15 - 3 + 7

  • Step 1: Subtraction. For addition and subtraction, work from left to right.
    15 - 3 = 12
  • Step 2: Addition. Now add 7.
    12 + 7 = 19
  • Answer: 19

6. (9 + 1) x (12 ÷ 4)

  • Step 1: Groups (first set). Solve the operation in the first set of groups.
    9 + 1 = 10
  • Step 2: Groups (second set). Solve the operation in the second set of groups.
    12 ÷ 4 = 3
  • Step 3: Multiplication. Multiply the results from both groups.
    10 x 3 = 30
  • Answer: 30

7. 30 ÷ 6 - 2

  • Step 1: Division. Division comes before subtraction.
    30 ÷ 6 = 5
  • Step 2: Subtraction. Now subtract 2.
    5 - 2 = 3
  • Answer: 3

8. 4 + 8 x 2 - 10 ÷ 5

  • Step 1: Multiplication. Perform multiplication from left to right.
    8 x 2 = 16
  • Step 2: Division. Perform division from left to right.
    10 ÷ 5 = 2
  • Step 3: Addition. For addition and subtraction, work from left to right.
    4 + 16 = 20
  • Step 4: Subtraction. Complete the last operation.
    20 - 2 = 18
  • Answer: 18

9. 2 x (5 + 3) ÷ 4 + 7 (Challenge Problem)

  • Step 1: Groups. Solve the operation inside the groups.
    5 + 3 = 8
  • Step 2: Multiplication. Work from left to right for multiplication and division.
    2 x 8 = 16
  • Step 3: Division. Continue with division.
    16 ÷ 4 = 4
  • Step 4: Addition. Finally, perform the addition.
    4 + 7 = 11
  • Answer: 11
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Cool Down

Order Up! Cool-Down: Exit Ticket

Show what you know about the order of operations! Solve the problem below, showing all your steps.

Problem: 7 + (12 ÷ 3) - 5












Bonus Question: Why is it important to follow the order of operations when solving math problems?












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Order Up! Solving Expressions • Lenny Learning