Multiplication with Partial Products
Students will be able to solve multiplication problems with a multi-digit factors using partial products as a strategy.
- Write ‘Partial Product’ on the board and ask students, "What does this mean?"
- Have students turn and talk to a partner to discuss its meaning. Remind students to think about similar words or math vocabulary they know.
- Underline product and ask, "In math, what is a product?" Answers should include "the answer to a multiplication problem."
- Underline part in the word partial, and prompt students, "If we know what the word part means, what might partial mean?" Answers might include that it's a piece of something; not the whole thing.
- Explain that partial products are parts of an answer to a multiplication problem.
- Tell students that today we are going to learn how to solve a multiplication problem by finding parts of the answer, or partial products.
Explicit Instruction/Teacher modeling(10 minutes)
- Write a problem on a piece of chart paper, like 34 x 15, in a stacked or horizontal format.
- With a red marker, circle the digit in the ones place in the bottom factor (5).
- Tell students that you are going to multiply the 5 by each place value of the top factor (34).
- Point to the ones place in the top factor and explain: 5 times 4 is 20. With the red marker, write 20 on the first line below the problem. In parenthesis to the right of the partial product, write (5 x 4).
- Point to the tens place in the top factor and explain: this 3 is in the tens place, so its value is 3 tens, or 30. Additionally, 5 times 30 is 150. With the red marker, write 150 below 20. In parenthesis to the right of the partial product, write (5 x 30).
- With a blue marker, circle the tens place in the bottom factor (1). Explain, this one is in the tens place, so its value is 10.
- Point to the ones place in the top factor and explain: 10 times 4 is 40. With the blue marker, write 40 below 150, making sure to align place values. In parenthesis to the right of the partial product, write (10 x 4).
- Point to the tens place in the top factor and explain: 10 times 30 is 300. With the blue marker, write 300 below 40. In parenthesis to the right of the partial product, write (10 x 30).
- Point out the four partial products and remind students that each number is a part of the total answer. Each partial product is the product of one place value times another.
- Using a black marker, add up the partial products and write the sum under the partial products (20 + 150 + 40 + 300 = 510).
- If students are familiar with the standard algorithm, explain that this strategy looks similar, but it does not involve regrouping or “carrying” the place values. Instead, each place value is multiplied individually and the partial products are added at the end.
- Keep the example problem posted throughout the lesson for student reference.
Guided Practice(15 minutes)
- Guide students through another example (i.e. 27 x 163).
- Hand out scratch paper, or instruct students to work in a math notebook.
- Write a problem on the board, like 12 x 48, and have students solve it with a partner. Go over the problem as a class.
- Write a problem on the board, like 9 x 218, and have students solve it independently. Go over the problem as a class.
Independent working time(15 minutes)
- Hand out the Multiplication Word Problems worksheet.
- Instruct students to cut out four problems of their choice.
- Have students glue each cutout problem into their math notebook and solve, showing their multiplication in parenthesis to the right of each partial product, as done in the example problems. (Note: Have students keep their extra problems to use for assessment).
- Circulate and offer support as needed.
- Provide additional examples before assigning independent work.
- For independent work, assign problems with one-digit times three-digit factors in place of the worksheet.
- Have students apply the partial products strategy to solve word problems (see resources).
- Hand out a small piece of scratch paper (or an index card) to each student.
- Have students cut out and glue a problem from their worksheet onto the scratch paper.
- Instruct students to solve using the partial products strategy.
- Collect student work as an exit ticket and check for understanding.
Review and closing(8 minutes)
- Compare this method of multiplication to other methods or strategies that students have learned (i.e. area model, arrays, standard algorithm). Solve one problem using two or more methods to provide an easy comparison.
- Ask students, "What similarities do you see between these methods?"
- Discuss as a class (i.e. the area model has the same partial products as the partial products method).