Lesson Plan
Partial Products Power
Students will learn and practice the partial products method to multiply multi-digit numbers by breaking factors into place-value parts and summing the resulting products.
Understanding partial products strengthens students’ grasp of place value and multiplication structure, boosts calculation accuracy and efficiency, and lays the groundwork for advanced problem-solving and algebraic thinking.
Audience
5th Grade
Time
30 minutes
Approach
Demonstrate on board, practice collaboratively, then independently apply via worksheets and exit ticket.
Materials
- Chart Paper or Whiteboard, - Markers, - Partial Products Strategy Cards, - Worked Examples Worksheet, - Independent Practice Worksheet, and - Exit Ticket
Prep
Preparation
10 minutes
- Print copies of Worked Examples Worksheet, Independent Practice Worksheet, and Exit Ticket.
- Prepare Partial Products Strategy Cards: cut and organize for group distribution.
- Set up chart paper or whiteboard with column headers for place values (tens, ones) to model examples.
- Review answer keys and anticipate common student misconceptions.
Step 1
Warm-Up
5 minutes
- Pose a simple multiplication problem (e.g., 12 × 3) and ask students to solve mentally.
- Prompt students to share any strategies they used (e.g., doubling and adding).
- Introduce idea of breaking numbers into parts to simplify multiplication.
Step 2
Introduction to Partial Products
7 minutes
- Display a multi-digit problem (e.g., 23 × 15) on chart paper or whiteboard.
- Use Partial Products Strategy Cards to decompose each factor into tens and ones.
- Model each partial product (20 × 10, 20 × 5, 3 × 10, 3 × 5) and record on board.
- Sum the partial products to find the final answer, explaining each step.
Step 3
Guided Practice
8 minutes
- Distribute Worked Examples Worksheet.
- Students work in pairs to complete the first two problems using partial products.
- Circulate to support pairs, addressing errors and reinforcing place-value decomposition.
- Invite one pair to demonstrate their solution on the board.
Step 4
Independent Practice
7 minutes
- Hand out Independent Practice Worksheet.
- Students solve remaining problems individually using the partial products strategy.
- Teacher circulates to monitor understanding and provide individualized feedback.
Step 5
Cool-Down/Exit Ticket
3 minutes
- Give each student the Exit Ticket.
- Students complete a quick problem (e.g., 34 × 12) using partial products and submit before leaving.
- Review responses to gauge mastery and identify areas for reteaching.
Slide Deck
Partial Products Power
Objective:
• Learn the partial products method
• Strengthen understanding of place value and multiplication structure
Welcome everyone! Today we’re diving into a powerful strategy for multiplying multi-digit numbers. Introduce the lesson title and display the learning objective: “Students will learn and practice the partial products method to multiply multi-digit numbers by breaking factors into place-value parts and summing the resulting products.”
Warm-Up
Solve 12 × 3 in your head:
• What strategy did you use?
• How might breaking numbers into parts help us multiply larger numbers?
Kick things off with a quick mental warm-up. Prompt students to solve 12 × 3 mentally and share strategies. Transition: “Today we’ll build on those strategies by breaking numbers into parts.”
Introducing Partial Products
- Break each factor into place-value parts (tens and ones)
- Multiply each pair of parts (partial products)
- Add all partial products for the final answer
Introduce the concept of decomposing factors into tens and ones. Explain why this helps clarify the structure of multiplication and reduces errors.
Modeling: Decompose Factors
23 = 20 + 3
15 = 10 + 5
Set up grid:
| 10 | 5 |
---|----|----|
20 | | |
3 | | |
Model Step 1: Decompose 23 × 15. Write 23 = 20 + 3 and 15 = 10 + 5. Draw a four-box grid on the board for the partial products.
Modeling: Compute Partial Products
20 × 10 = 200
20 × 5 = 100
3 × 10 = 30
3 × 5 = 15
Model Step 2: Fill in each box with the product of its row and column headings. Talk through each calculation.
Modeling: Sum Partial Products
200 + 100 + 30 + 15 = 345
So, 23 × 15 = 345
Model Step 3: Add the partial products together to get the final answer. Emphasize lining up place values and adding carefully.
Guided Practice
• Work in pairs
• Complete first two problems on the Worked Examples Worksheet
• Use the grid to decompose and multiply
• Be ready to explain your steps
Transition to guided practice. Explain that students will now work in pairs on example problems using the same grid method. Circulate to support and correct misconceptions.
Independent Practice
• Solve remaining problems on the Independent Practice Worksheet
• Show all partial products in a grid
• Check your addition before submitting
Now students work independently. Encourage them to apply what they’ve learned and ask for help if needed. Walk around and provide feedback.
Exit Ticket
Complete 34 × 12 using the partial products method:
• Decompose 34 and 12
• Compute each partial product
• Sum your results and write your final answer
Turn in before you leave.
Explain the exit ticket procedure. This will show their individual mastery of partial products today.
Summary & Reflection
• Partial products clarify multiplication structure
• Helps prevent calculation errors
• Builds a strong foundation for algebraic concepts
Think of one time you might use this method outside of math class.
Wrap up the lesson by reinforcing the value of understanding place value in multiplication. Encourage students to use partial products as they encounter more complex problems.
Activity
Partial Products Strategy Cards
Print and cut these cards. Distribute one card per pair or small group. Students will use each card to:
- Decompose each factor into tens and ones.
- Set up a partial-products grid.
- Compute each partial product.
- Sum to find the final product.
Card A: 23 × 15
1. Decompose:
23 = __ + __
15 = __ + __
2. Set up Grid:
| Tens | Ones | |
|---|---|---|
| Tens | ||
| Ones |
Card B: 34 × 12
1. Decompose:
34 = __ + __
12 = __ + __
2. Set up Grid:
| Tens | Ones | |
|---|---|---|
| Tens | ||
| Ones |
Card C: 46 × 23
1. Decompose:
46 = __ + __
23 = __ + __
2. Set up Grid:
| Tens | Ones | |
|---|---|---|
| Tens | ||
| Ones |
Card D: 57 × 14
1. Decompose:
57 = __ + __
14 = __ + __
2. Set up Grid:
| Tens | Ones | |
|---|---|---|
| Tens | ||
| Ones |
Card E: 68 × 27
1. Decompose:
68 = __ + __
27 = __ + __
2. Set up Grid:
| Tens | Ones | |
|---|---|---|
| Tens | ||
| Ones |
Card F: 79 × 35
1. Decompose:
79 = __ + __
35 = __ + __
2. Set up Grid:
| Tens | Ones | |
|---|---|---|
| Tens | ||
| Ones |
Teacher Tip: Circulate as students work with their cards, prompt them to explain their decomposition and check each partial product before summing. Rotate cards so every group practices multiple problems.
Worksheet
Worked Examples Worksheet
Use the partial products method to work through these two example problems. Show all your work in the spaces provided.
Example 1: 23 × 15
- Decompose each factor into tens and ones:
23 = __ + __
15 = __ + __
- Draw and complete the partial-products grid:
| Tens | Ones | |
|---|---|---|
| Tens | ||
| Ones |
- Calculate each partial product:
20 × 10 = __
20 × 5 = __
3 × 10 = __
3 × 5 = __
- Add all partial products to find the final answer:
__ + __ + __ + __ = __
Example 2: 46 × 23
- Decompose each factor into tens and ones:
46 = __ + __
23 = __ + __
- Draw and complete the partial-products grid:
| Tens | Ones | |
|---|---|---|
| Tens | ||
| Ones |
- Calculate each partial product:
40 × 20 = __
40 × 3 = __
6 × 20 = __
6 × 3 = __
- Add all partial products to find the final answer:
__ + __ + __ + __ = __
Need extra help? Review the steps on the Partial Products Strategy Cards and model your grid accordingly.
Worksheet
Independent Practice Worksheet
Use the partial products method to solve each of the following problems. Show all your steps: decompose each factor, draw and complete a grid, compute each partial product, and sum for the final answer.
Problem 1: 34 × 12
- Decompose each factor:
34 = __ + __
12 = __ + __
2. Draw and complete the grid:
| Tens | Ones | |
|---|---|---|
| Tens | ||
| Ones |
- Calculate each partial product:
__ × __ = __
__ × __ = __
__ × __ = __
__ × __ = __
4. Add to find the final answer:
__ + __ + __ + __ = __
Problem 2: 57 × 14
- Decompose each factor:
57 = __ + __
14 = __ + __
2. Draw and complete the grid:
| Tens | Ones | |
|---|---|---|
| Tens | ||
| Ones |
- Calculate each partial product:
__ × __ = __
__ × __ = __
__ × __ = __
__ × __ = __
4. Add to find the final answer:
__ + __ + __ + __ = __
Problem 3: 68 × 27
- Decompose each factor:
68 = __ + __
27 = __ + __
2. Draw and complete the grid:
| Tens | Ones | |
|---|---|---|
| Tens | ||
| Ones |
- Calculate each partial product:
__ × __ = __
__ × __ = __
__ × __ = __
__ × __ = __
4. Add to find the final answer:
__ + __ + __ + __ = __
Problem 4: 79 × 35
- Decompose each factor:
79 = __ + __
35 = __ + __
2. Draw and complete the grid:
| Tens | Ones | |
|---|---|---|
| Tens | ||
| Ones |
- Calculate each partial product:
__ × __ = __
__ × __ = __
__ × __ = __
__ × __ = __
4. Add to find the final answer:
__ + __ + __ + __ = __
When you finish, check each partial product and ensure you’ve added accurately. Good luck!
Warm Up
Partial Products Warm-Up
Mental Multiplication (3 minutes)
- Solve each problem in your head. Write your answer on your whiteboard or paper.
- 12 × 3 = ___
- 14 × 6 = ___
- 15 × 4 = ___
- Turn and talk with your partner:
• Which strategies or steps did you use to multiply quickly?
• Did you break one factor into parts? If so, how? - Share out a couple of ideas with the whole class—be ready to explain your thinking.
Transition to Partial Products
• Today, we’ll build on these mental strategies by breaking multi-digit numbers into place-value parts and using partial products to solve larger multiplication problems.
Cool Down
Partial Products Exit Ticket
Use the partial products method to solve the following quick check. Show all your steps.
- Decompose each factor into tens and ones:
34 = __ + __
12 = __ + __ - Draw and complete the partial-products grid:
| Tens | Ones | |
|---|---|---|
| Tens | ||
| Ones |
- Calculate each partial product:
__ × __ = __
__ × __ = __
__ × __ = __
__ × __ = __
4. Add all partial products for your final answer:
__ + __ + __ + __ = __
Please turn this in before you leave. Good luck!