**Overview: **Students review the partial product multiplication strategy, then learn to multiply numbers that contain decimal places to the hundredths place. They learn how to determine where to place the decimal in the final answer. Students use playing cards to generate random digits and form problems with tenths and hundredths decimals, solve them, and solve a set of similar problems generated by peers.

**Subject:** Math: Arithmetic

**Related Concepts: **Multiplication, Decimal Multiplication, Place Value

**Essential Questions:** How can I multiply numbers that contain decimal points?

**Vocabulary:** multiplication, multiply, decimal, decimal point, tenths place, hundredths place, factor, product

## Lesson Procedure

**Introduction:**Review basic strategies for multiplying multi-digit numerals with the class, reminding them of the general procedure to do partial product method multiplication. Have several volunteers demonstrate the process on the classroom display. Provide volunteers with problems up to 3 digit by 3 digit multiplication.

**Direct Instruction:**Introduce the idea that decimal numbers can also be multiplied in the same fashion with an introductory video. Explain to students that multiplying decimals uses exactly the same process as multiplying whole numbers, then uses an extra step to place the decimal point correctly into the answer. Remind students that they DO NOT need to place decimals in their partial product numbers. Tell students that after multiplying and adding the partial products, they should count the number of places to the right of the decimal point in both of the factors that they just multiplied. This number should include BOTH factors. Tell them that then they start on the right-hand side of their answer and count the spots between numbers until their count matches the number of decimal places in both factors combined. Put the decimal point there.

**Guided Instruction:**Have students do quick practice with lots of supervision and opportunity to get questions answered as well as quick feedback on their process.

**Independent Practice:**

Separate students into workgroups of 2-4 members. Tell students that they will be creating worksheets for their classmates. Explain that they will use the playing cards to generate random numbers to include in each problem. They will need to make problems that have 4 digits in each number, and will make 10 problems. Give each group a deck of playing cards, paper, and pencil. Tell them to remove the face cards and the number 10 cards from the deck and shuffle the rest. Have them deal 8 cards from the modified deck (Aces stand for "1") and turn them face up. Each student in the group should use those 8 numbers to create three four-digit numbers. They should check to make sure each problem they create is unique within their group. They can choose where to place a decimal point into each factor for their personal problem, but must distribute the work evenly so there are numbers with tenths and hundredths.

Continue in the same manner to create 10 problems on each student's paper.

**Closure:**When the page of problems is complete, remind students to recopy each problem onto a separate page, and solve it to make an answer key.

**Assessment:**

- Have the students exchange papers with a classmate from a different group and solve the given problems after class as homework.
- Assess student work for accuracy in multiplication process, calculation, and placement of decimal point in the answer.

## Differentiation

Allow students who have not yet mastered multiplication facts to use a printed multiplication table up to 9 x 9.

Modify the exercises for special needs students by allowing calculator use but have them double check the placement of the decimal and be prepared to explain why the decimal has been placed where it is.

Provide advanced students with problems that require application of the skill.

Provide additional practice for students with lower experience or ability.

## Extension Ideas

Use the Decimal Practice Booklet to give students additional practice with all decimal skills.

Have students write their own word problems that require multiplying decimals and create an answer key by solving the problems they create.

## Attachments

Additional materials to guide your teaching:

- Multiplying Decimals
- Basic Math Multiplication of Decimals
- Worksheet: Multiplying Decimals
- Odd One Out: Number Sense Worksheet
- Real-Life Problems, Working with Decimals
- Decimals Practice Booklet
- Arithmetic and Pre-Algebra Resources
- Decimals Resources
- Multiplication and Division Resources
- Multiplying Decimals Resources