At a Glance...

B2.9 Multiply and divide decimal numbers by decimal numbers, in various contexts.

Activity 1: Looking for Patterns (Multiplication and Division of Decimal Numbers)

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Materials

• grid sheets (place value chart)
• calculator

Multiplying a decimal number by a decimal number

1. Have each student construct a place value chart like the one below.

Initial number: 5.6

Number	thousands	hundreds	tens	units	tenths	hundredths	thousandths
\(5.6\; \times \;100\)		5	6	0
\(5.6\; \times \;10\)
\(5.6\; \times \;1\)
\(5.6\; \times \;0.1\)
\(5.6\; \times \;0.01\)				0,	0	5	6

Divide the class into teams of two students. Each student will fill out the chart individually, and then analyze and compare it with their teammate. They note their observations and differences. Have the class review the chart with the students, noting their observations, comments and patterns.

Questions To Ask

• What do you notice about the number?
• Can you predict the result (without a calculator) of the following multiplication: 5.6 x 0.001? Why?

Initial number: 4.2

number	thousands	hundreds	tens	units	tenths	hundredths	thousandths
\(4.2\; \times \;200\)		8	4	0,
\(\ 4.2 \times 20\)
\(4.2\; \times \;2\)
\(4.2\; \times \;0.2\)
\(4.2\; \times \;0.02\)				0,	0	8	4

Questions To Ask

• What do you notice about the number?
• Can you predict the result (without a calculator) of the following multiplication : \(4.2\; \times \;0.002\)? Why?
2. Give some multiplications to be performed. The student must estimate the result and then do the work without using the calculator. The student compares their result with that of their teammate and checks the answers together using the calculator.
• \(3.0\; \times \;0.01\)
• \(5.6\; \times \;0.4\)
• \(1.8\; \times \;2.2\)

Division of a decimal number by a decimal number

1. Do the same procedure with division

Initial number: 5.6

number	thousands	hundreds	tens	units	tenths	hundredths	thousandths
\(5.6\; \div \;100\)				0,	0	5	6
\(5.6\; \div \;10\)
\(5.6\; \div \;1\)
\(5.6\; \div \;0.1\)
\(5.6\; \div \;0.01\)		5	6	0,

Initially, compare with the multiplication table,

Questions To Ask

• What do you notice about the number?
• Can you predict the result (without a calculator) of the following division: \(5.6\; \div \;0.001\)? Why?

Initial number: 4.2

number	thousands	hundreds	tens	units	tenths	hundredths	thousandths
\(4.2\; \div \;200\)				0,	0	2	1
\(4.2\; \div \;20\)
\(4.2\; \div \;2\)
\(4.2; \div \;0.2\)
\(4.2\; \div \;0.02\)		2	1	0,

Questions To Ask

• What do you notice about the number?
• Can you predict the result (without a calculator) of the following division: 4.2 ÷ 0.002? Why?
2. Give some divisions to be performed. The student must estimate and then do the work without using the calculator. They compare their result with that of their teammate and checks together the answers obtained with the calculator.
• \(5.0\; \div \;0.01\)
• \(5.6\; \div \;0.2\)
• \(8.4\; \div \;1.4\)

Activity 2: Rectangles (Multiplication and Division of Decimal Numbers)

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Materials

• grid paper
• whiteboard

Form teams of 4 students. Give them challenges to solve (2 examples below). Students should get used to using estimation to check if their answer is reasonable. Focus on strategies and understanding of operations.

Review the questions asked in each of the challenges.

Challenge 1

A rectangular lawn measures 10.5 metres by 9.2 metres. Clara subdivides her lawn in parts, as she wants to adjust the height of the mower to cut it according to the desired requirements.

• Estimate the total area, in square metres, of the lawn. Explain your strategy.
• Determine the exact area of the lawn in 2 different ways. Demonstrate and explain your strategies.

Challenge 2

For an agricultural fair, Chef Jacob has made a rectangular lasagna measuring 1.4 m by 1.2 m. He wants to serve pieces that are 7 cm by 6 cm.

• Estimate how many pieces the chef will serve. Explain your strategy.
• Explain or demonstrate how the chef will calculate the number of pieces he will be able to serve.