Multiply Decimals with Models
Students will be able to use models to multiply tenths.
- Show students a blank tenths model and a blank hundredths model. Ask students to share their background knowledge about the two models.
- Review decimal basics, if needed (i.e., place value, tenths place, hundredths place). Then, show students how to shade in the models to represent various decimals (e.g., 0.4, 0.12). Write each number in decimal and fraction form before shading in the model.
- Explain to students that today they will use models to multiply decimals in the tenths place.
Explicit Instruction/Teacher modeling(10 minutes)
- Write a multiplication problem on the board, like 0.3 x 0.5.
- Use a document camera to display one blank tenths model and shade in the first decimal (0.3) in blue.
- On a piece of clear plastic (e.g., transparency, sheet protector, or lamination scrap), trace a blank tenths model using permanent marker. Make sure the traced model is the exact same size as the first model you shaded. (Note: you may prepare the traced model before the lesson.)
- Shade in the decimal 0.5 on the clear plastic model using a wipeable yellow pen.
- Explicitly point out the value of each decimal on the two separate models and explain that you are going to use the two models to show students how to multiply 0.3 x 0.5.
- Layer the clear model on top of the first model so that one model is oriented vertically and the second model is oriented horizontally. (Note: when overlayed, the two models will combine to show hundredths.)
- Have students turn and talk to a neighbor about what they notice once the two models have been layered. Then, call on students to share their observations. Prompt students or provide insight if needed (e.g., the model is now showing hundredths instead of tenths, or some of the shaded regions overlap and other shaded parts do not).
- Direct students attention to the parts where the shaded sections overlap (this section should appear green). Explain that the parts that overlap represent the answer to the multiplication problem.
- Use the model to calculate the answer, 0.15 (i.e., count the hundredths). Point out that the product is smaller than the two factors. Remind students that when whole numbers are multiplied, the product is larger than the factors. But when decimals (or fractions) are multiplied, the product is smaller than the factors (e.g., when tenths are multiplied by tenths, the answer is a decimal in the hundredths place).
- Optional: make a connection to whole number multiplication (10 x 10 = 100).
Guided Practice(10 minutes)
- Display the worksheet Decimal Multiplication: Multiply Tenths with Models and review the example.
- Explain that, instead of shading in two tenths models, you can shade in tenths on a hundredths model to multiply two decimals. Remind students that when you multiply two decimals in the tenths place, the answer is in the hundredths place.
- Demonstrate how to solve the "Try it!" problem on the worksheet by shading in the hundredths model. (Note: use two colors, one for each decimal being multiplied. Shade one factor vertically and the other horizontally so that the overlapping part represents the answer.)
- Hand out the worksheet and instruct students to complete the first problem in the "Practice it!" section with a seat partner.
- Invite student volunteers to share their answers with the class, using a document camera to show their work.
Independent working time(10 minutes)
- Tell students to complete the remainder of the worksheet independently. Remind students to show their work for each problem.
- Invite students to share their completed work with the class using a document camera.
- Use the "Talk about it!" section at the bottom of the worksheet to discuss new understandings and "aha moments" as a class. Additionally, invite students to talk about strategies and observations with the class (e.g., it's faster to shade a whole section of tenths at once, instead of shading individual rows; the answers can be discovered using basic, whole number multiplication facts: 0.3 x 0.5 = 0.15 and 3 x 5 = 15).
- Correct any misconceptions that arise.
- Review decimal basics, like ordering and comparing place values. See optional resources.
- Strategically form partnerships during guided practice so that struggling students are paired with proficient students.
- Post key terms, definitions, and examples on a word wall or anchor chart for student reference.
- Write a multiplication problem on the board and ask students to visualize a model and solve it (without physically shading a model).
- Allow students to discover the standard algorithm using what they learned about models as a guide.
- Write four decimal multiplication problems in the tenths place on the board and number them one to four (e.g., "1. 0.6 x 0.9"). Then have students count off to four to identify which problem they will solve.
- Provide a single blank hundredths model to each student and tell students to shade the model to solve their assigned problem. Circulate to gauge understanding.
- Have students form homogenous groups (e.g., all "ones" together) to compare their work and make corrections if needed. Listen to group conversations to continue gathering information about student understanding.
- Have students form heterogeneous groups (e.g., one student with each number in a group) and have each student present their model to the group. Continue listening in to student conversations and note which students will need additional support.
Review and closing(5 minutes)
- Lead the class in a closing discussion:
- How do models help you make a picture in your mind?
- In what ways will the exercise of shading models help you multiply decimals in the future?
- When you multiply two numbers in the tenths place, why is the answer in the hundredths place? What would happen if you multiplied two decimals in the hundredths place?