Decimal Detectives Teacher Guide Decimal Detectives
Teacher Facilitation Guide
Grade 5 Math
Topic: Multiplying Decimals
Learning Objective
Students will be able to decompose multiples of ten to multiply decimals efficiently by breaking the multiplier into its factors (e.g., \( 30 = 3 \times 10 \)).
Materials Needed
Decimal Detectives Lesson Slides
Decomposition Detectives Student Worksheet
Vertical Math Sticky Notes (provided in materials)
Pencils and colored pens (red for decimal shifts)
Lesson Timeline
5 min Mental Math Sprint
5 min Video Viewing & Analysis
20 min Decomposition Detectives Activity
10 min Closure & Discussion
Teaching Protocol
1
Mental Math Sprint (Warm-up)
Display the sprint problems on the slides. The goal is to prime the strategy of multiplying by the digit first, then adding the zero. Example: "To find \( 4 \times 30 \), think \( 4 \times 3 = 12 \), then multiply by 10 to get 120."
2
Video Guided Inquiry
Video: "Multiplying Decimals by Tens"
Pause at 0:17
Ask: "Why did they change 30 to \( 3 \times 10 \)? How does this help us?"
Pause at 0:44
Ask: "When we multiply by 10, does the number get bigger or smaller? Which way should the decimal move?"
Pause at 1:19
Ask students to predict the final answer based on the intermediate result of 14.15.
3
Main Activity: Decomposition Detectives
Hand out the worksheets and sticky notes. Students must follow the "Detective Protocol":
Decompose the multiplier (e.g., \( 20 \rightarrow 2 \times 10 \)).Solve the first part on a "Sticky Note" using vertical multiplication.Shift the decimal point one place to the right to find the final product.
4
Closure: The Case of the Shifting Decimal
Discuss: "Why does the decimal move right at the end?" Encourage students to use place value language (e.g., "The digits are becoming 10 times larger, so they shift to a higher place value").
Key Vocabulary
Decomposition: Breaking a number (like 30) into smaller factors (like \( 3 \times 10 \)).Multiple of 10: A number that can be divided by 10 with no remainder (10, 20, 30, etc.).Decimal Shift: Moving the decimal point to change the place value of the digits.
Common Misconceptions
Shifting Left: Students may shift the decimal the wrong way. Remind them that multiplication by 10 makes the number larger.Forgetting the Shift: Students may stop after the vertical multiplication (Step 1). Emphasize the "Detective Checklist" on their worksheet.Zero Confusion: Students might think they just "add a zero" at the end, which fails when there are decimals (e.g., \( 5.1 \times 10 \) is not \( 5.10 \)). Decimal Detectives Slides Case #501
Decimal Detectives
The Case of the Decomposing Tens
Mental Math Sprint
Solve these cases as fast as you can! Use the "Zero Trick" :
"Multiply the non-zero digits first, then multiply by 10!"
\( 4 \times 10 = \text{?} \)
\( 7 \times 20 = \text{?} \)
\( 3 \times 30 = \text{?} \)
\( 6 \times 40 = \text{?} \)
Our Mission
Today, we will learn how to decompose multiples of ten to multiply decimals easily and accurately!
Evidence Review: Multiplying Decimals
Watch & Learn
Embedded media
Detective Briefing #1
Pause at 0:17
"Why did they change 30 to 3 × 10?"
Talk to your partner: How does this make the multiplication easier?
The Decomposition Protocol
1
Decompose
Break the multiplier into factors of 10.
\( \times 30 \rightarrow \times 3 \times 10 \)
2
Sticky Note Math
Multiply vertically using the single digit.
\( 16.7 \times 3 = 50.1 \)
3
Decimal Shift
Multiply by 10 by hopping the decimal one place RIGHT .
\( 50.1 \rightarrow 501 \)
Case Work
Open your folders and begin "Decomposition Detectives"
Instructions:
Complete the Mental Math Sprint on your worksheet.
Use the Yellow Sticky Notes for your vertical math.
Draw the Red Hop Arrow to shift the decimal.
CASE CLOSED!
Why does the decimal move to the RIGHT when we multiply by 10?
(Think about place value...)
Decomposition Detectives Worksheet Decomposition Detectives
Case File: Decimal Multiplication
Name:
Date:
Mental Math Sprint
1. \( 4 \times 10 = \)
2. \( 7 \times 20 = \)
3. \( 3 \times 30 = \)
4. \( 6 \times 40 = \)
Detective's Protocol:
1. Decompose the ten (e.g., \( 30 \rightarrow 3 \times 10 \))
2. Solve vertically on the sticky note
3. Shift the decimal point one place RIGHT
1
\( 4.5 \times 20 \)
Decomposed Equation:
Final Result:
Sticky Note Math
2
\( 12.3 \times 40 \)
Decomposed Equation:
Final Result:
Sticky Note Math
3
\( 2.81 \times 50 \)
Decomposed Equation:
Final Result:
Sticky Note Math
4
\( 15.6 \times 30 \)
Decomposed Equation:
Final Result:
Sticky Note Math
Detective Reflection:
When we multiply by 10 at the end, the value of the digits increases. How many places does the decimal shift, and in which direction?
Decomposition Detectives Answer Key Answer Key
Case File: Decimal Multiplication
Teacher Resource
Mental Math Sprint Answers
1. \( 4 \times 10 = \) 40
2. \( 7 \times 20 = \) 140
3. \( 3 \times 30 = \) 90
4. \( 6 \times 40 = \) 240
1
\( 4.5 \times 20 \)
Decomposed Equation:
\( 4.5 \times 2 \times 10 \)
Final Result:
90
Work:
\( 4.5 \times 2 = 9.0 \)
\( 9.0 \times 10 = 90 \)
2
\( 12.3 \times 40 \)
Decomposed Equation:
\( 12.3 \times 4 \times 10 \)
Final Result:
492
Work:
\( 12.3 \times 4 = 49.2 \)
\( 49.2 \times 10 = 492 \)
3
\( 2.81 \times 50 \)
Decomposed Equation:
\( 2.81 \times 5 \times 10 \)
Final Result:
140.5
Work:
\( 2.81 \times 5 = 14.05 \)
\( 14.05 \times 10 = 140.5 \)
4
\( 15.6 \times 30 \)
Decomposed Equation:
\( 15.6 \times 3 \times 10 \)
Final Result:
468
Work:
\( 15.6 \times 3 = 46.8 \)
\( 46.8 \times 10 = 468 \)
Sample Reflection Response:
"The decimal shifts one place to the right . This is because multiplying by 10 increases the place value of every digit by one power of ten, making the whole number 10 times larger."
Detective Sticky Notes Stationery Detective Scratchpads
Cut-out "Sticky Notes" for Vertical Math
Detective Evidence Note
Detective Evidence Note
Detective Evidence Note
Detective Evidence Note
✂️ Cut along the edges to create your detective scratchpad sticky notes ✂️
