How Many Digits After?

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Tier 1

Lesson Plan

Decimal Multiplication Method

Students will accurately multiply decimals by counting the total number of decimal places in the factors to determine the correct placement of the decimal point in the product.

Understanding decimal placement is fundamental for real-world applications like calculating money, measurements, and scientific data, preventing common errors in everyday math.

Audience

6th Grade Students

Time

60 minutes

Approach

Direct instruction, guided practice, and independent application.

Materials

Whiteboard or projector, Markers or pens, Product Place Value Power, Decimal Point Placement Practice, Multiply and Conquer worksheet, and Multiplication Answer Guide

Prep

Teacher Preparation

15 minutes

Review the Decimal Multiplication Method lesson plan and all associated materials: Product Place Value Power, Decimal Point Placement Practice, Multiply and Conquer, and Multiplication Answer Guide.
Prepare the whiteboard or projector for displaying the slide deck.
Print copies of the Decimal Point Placement Practice activity and Multiply and Conquer worksheet.

Step 1

Introduction: The Decimal Dilemma (5 minutes)

5 minutes

Begin by asking students: "When you multiply numbers with decimals, how do you know where to put the decimal point in your answer?" Allow for a few student responses.
Introduce the lesson objective: "Today, we're going to become detectives of decimals, learning a foolproof way to place the decimal point correctly every time we multiply!"

Step 2

Direct Instruction: Product Place Value Power (20 minutes)

20 minutes

Present the Product Place Value Power slide deck.
Slide 1: Title Slide - Briefly reiterate the lesson's goal.
Slide 2: Review Whole Number Multiplication - Quickly go over a simple whole number multiplication problem (e.g., 12 x 3 = 36).
Slide 3: Introducing Decimals - Show an example like 1.2 x 3. Explain that we can think of 1.2 as 12 'tenths.'
Slide 4: The Core Rule: Count the Digits! - Introduce the main concept: count the total number of digits after the decimal point in all the numbers you are multiplying.
Slide 5: Example 1: 0.5 x 0.3 - Work through this example step-by-step, showing how 5 x 3 = 15, and since there's one decimal place in 0.5 and one in 0.3, the answer 0.15 has two decimal places.
Slide 6: Example 2: 1.2 x 0.04 - Guide students through this example. Emphasize that even if one number has many decimal places and another has none, all decimal places count.
Slide 7: Practice Together - Present a problem for students to try on their own, then review as a class.

Step 3

Guided Practice: Decimal Point Placement Practice (15 minutes)

15 minutes

Distribute the Decimal Point Placement Practice activity.
Explain the instructions: Students will solve several multiplication problems, focusing specifically on correctly placing the decimal point.
Circulate around the room, offering support and clarification. Encourage students to explain their reasoning for decimal placement.

Step 4

Independent Practice: Multiply and Conquer (15 minutes)

15 minutes

Distribute the Multiply and Conquer worksheet.
Instruct students to complete the worksheet independently. Remind them to apply the 'count the decimal places' rule they learned.
Collect the worksheets for assessment. The Multiplication Answer Guide can be used for grading later.

Step 5

Wrap-up: Quick Check (5 minutes)

5 minutes

Bring the class back together.
Ask students to quickly share one thing they learned about multiplying decimals today.
Pose a final quick check question: "If I multiply 2.15 by 3.2, how many digits will be after the decimal point in my answer? Why?" (Expected answer: 3 digits, because 2 + 1 = 3 decimal places in the factors.)

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Slide Deck

Product Place Value Power

Mastering Decimal Placement in Multiplication!

Greet students and introduce the exciting journey into mastering decimal multiplication. Ask them if they've ever wondered how to know where to put the decimal in the answer.

Quick Review: Whole Numbers

What is 12 x 3?

(Think: How many groups of 3 are there if you have 12 groups?)

Before diving into decimals, let's refresh our memory on simple whole number multiplication. Ask students to solve this problem mentally or on a scratch piece of paper.

Stepping into Decimals

What about 1.2 x 3?

First, multiply 12 x 3 = 36.

But where does the decimal go?

Now, let's introduce a decimal. Explain that 1.2 is like having 12 'tenths.' We multiply the numbers as if they were whole numbers first.

The Golden Rule: Count the Digits!

To place the decimal point in the product (your answer):

Multiply the numbers as if they were whole numbers.
Count the total number of digits after the decimal point in all the factors.
Place the decimal point in your product so it has the same total number of decimal places.

This is the golden rule! Emphasize that students need to count all the decimal places in all the numbers being multiplied. This total tells them how many decimal places will be in the final answer.

Example 1: Let's Try!

Problem: 0.5 x 0.3

Multiply: 5 x 3 = 15
Count decimal places:
- 0.5 has 1 decimal place.
- 0.3 has 1 decimal place.
- Total: 2 decimal places.
Place decimal: Count 2 places from the right in 15.
- Your answer is 0.15.

Walk through this example slowly. Show 0.5 (1 decimal place) and 0.3 (1 decimal place). Total of 2 decimal places. So 15 becomes 0.15.

Example 2: A Bit Trickier!

Problem: 1.2 x 0.04

Multiply: 12 x 4 = 48
Count decimal places:
- 1.2 has 1 decimal place.
- 0.04 has 2 decimal places.
- Total: 3 decimal places.
Place decimal: Count 3 places from the right in 48. You might need to add a zero!
- Your answer is 0.048.

Guide students through this one. Point out that 1.2 has one decimal place and 0.04 has two. A common mistake is to only count one from the 1.2. Make sure they add them up.

Your Turn! Practice Together

Problem: 2.1 x 0.6

First, multiply the whole numbers: ______ x ______ = ______
Next, count the total decimal places: ______ + ______ = ______
Finally, place the decimal in your product: __________

Have students try this on their own, perhaps with a partner, before revealing the answer. Encourage them to explain their decimal placement.

Your Turn! Answer Revealed

Problem: 2.1 x 0.6

First, multiply the whole numbers: 21 x 6 = 126
Next, count the total decimal places: 1 + 1 = 2
Finally, place the decimal in your product: 1.26

Reveal the answer and explain the steps again, reinforcing the concept.

You've Got the Power!

By counting the digits after the decimal point, you now have the power to correctly place the decimal in any multiplication problem!

Keep practicing, and you'll be a decimal detective in no time!

Encourage students to think about why this method works and how it connects to fractions. Remind them they'll practice more in the activity.

Activity

Decimal Point Placement Practice

Instructions: For each problem below, first multiply the numbers as if they were whole numbers. Then, count the total number of digits after the decimal point in the original factors. Finally, place the decimal point in your product to make the answer correct.

Example:
0.4 x 0.2

Multiply 4 x 2 = 8
Count decimal places: 0.4 (1) + 0.2 (1) = 2 decimal places total.
Place decimal: 0.08

0.7 x 0.3
- Multiply whole numbers:
- Total decimal places:
- Product:
1.5 x 2
- Multiply whole numbers:
- Total decimal places:
- Product:
0.06 x 0.4
- Multiply whole numbers:
- Total decimal places:
- Product:
2.3 x 1.1
- Multiply whole numbers:
- Total decimal places:
- Product:
0.01 x 0.05
- Multiply whole numbers:
- Total decimal places:
- Product:
3.14 x 0.2
- Multiply whole numbers:
- Total decimal places:
- Product:

Worksheet

Multiply and Conquer

Instructions: Solve each multiplication problem below. Remember to count the total number of decimal places in the factors to correctly place the decimal point in your product. Show your work!

0.9 x 0.6
2.5 x 3
0.12 x 0.5
4.7 x 0.2
1.03 x 0.04
7 x 0.8
0.25 x 1.2
5.0 x 0.11
0.003 x 9
10.5 x 0.05

Answer Key

Multiplication Answer Guide

Here are the answers and step-by-step reasoning for the "Multiply and Conquer" worksheet.

0.9 x 0.6
- Thought Process:
  - Multiply the whole numbers: 9 x 6 = 54
  - Count decimal places: 0.9 has 1 decimal place. 0.6 has 1 decimal place. Total = 1 + 1 = 2 decimal places.
  - Place the decimal point: Starting from the right of 54, move 2 places to the left. This gives 0.54.
- Answer: 0.54
2.5 x 3
- Thought Process:
  - Multiply the whole numbers: 25 x 3 = 75
  - Count decimal places: 2.5 has 1 decimal place. 3 has 0 decimal places. Total = 1 + 0 = 1 decimal place.
  - Place the decimal point: Starting from the right of 75, move 1 place to the left. This gives 7.5.
- Answer: 7.5
0.12 x 0.5
- Thought Process:
  - Multiply the whole numbers: 12 x 5 = 60
  - Count decimal places: 0.12 has 2 decimal places. 0.5 has 1 decimal place. Total = 2 + 1 = 3 decimal places.
  - Place the decimal point: Starting from the right of 60, move 3 places to the left. We need to add a zero: 0.060, which simplifies to 0.06.
- Answer: 0.06
4.7 x 0.2
- Thought Process:
  - Multiply the whole numbers: 47 x 2 = 94
  - Count decimal places: 4.7 has 1 decimal place. 0.2 has 1 decimal place. Total = 1 + 1 = 2 decimal places.
  - Place the decimal point: Starting from the right of 94, move 2 places to the left. This gives 0.94.
- Answer: 0.94
1.03 x 0.04
- Thought Process:
  - Multiply the whole numbers: 103 x 4 = 412
  - Count decimal places: 1.03 has 2 decimal places. 0.04 has 2 decimal places. Total = 2 + 2 = 4 decimal places.
  - Place the decimal point: Starting from the right of 412, move 4 places to the left. We need to add a zero: 0.0412.
- Answer: 0.0412
7 x 0.8
- Thought Process:
  - Multiply the whole numbers: 7 x 8 = 56
  - Count decimal places: 7 has 0 decimal places. 0.8 has 1 decimal place. Total = 0 + 1 = 1 decimal place.
  - Place the decimal point: Starting from the right of 56, move 1 place to the left. This gives 5.6.
- Answer: 5.6
0.25 x 1.2
- Thought Process:
  - Multiply the whole numbers: 25 x 12 = 300
  - Count decimal places: 0.25 has 2 decimal places. 1.2 has 1 decimal place. Total = 2 + 1 = 3 decimal places.
  - Place the decimal point: Starting from the right of 300, move 3 places to the left. This gives 0.300, which simplifies to 0.3.
- Answer: 0.3
5.0 x 0.11
- Thought Process:
  - Multiply the whole numbers: 50 x 11 = 550
  - Count decimal places: 5.0 has 1 decimal place. 0.11 has 2 decimal places. Total = 1 + 2 = 3 decimal places.
  - Place the decimal point: Starting from the right of 550, move 3 places to the left. This gives 0.550, which simplifies to 0.55.
- Answer: 0.55
0.003 x 9
- Thought Process:
  - Multiply the whole numbers: 3 x 9 = 27
  - Count decimal places: 0.003 has 3 decimal places. 9 has 0 decimal places. Total = 3 + 0 = 3 decimal places.
  - Place the decimal point: Starting from the right of 27, move 3 places to the left. We need to add a zero: 0.027.
- Answer: 0.027
10.5 x 0.05
- Thought Process:
  - Multiply the whole numbers: 105 x 5 = 525
  - Count decimal places: 10.5 has 1 decimal place. 0.05 has 2 decimal places. Total = 1 + 2 = 3 decimal places.
  - Place the decimal point: Starting from the right of 525, move 3 places to the left. This gives 0.525.
- Answer: 0.525