B2.3 Use mental math strategies to multiply and divide whole numbers and decimal numbers up to thousandths by powers of ten, and explain the strategies used.
Activity 1: Explain How You Did It (Transforming a Number Using Mental Math)
Materials
- 1 whiteboard for 2 students
- erasable felt-tip pens
- cards with an initial number with instructions
- a calculator if needed to check results
Divide the class group into pairs.
Distribute a whiteboard, 1 felt pen per dyad with an envelope with several cards.
One student takes a card and reads the instructions to their partner. The other student writes their answers on the whiteboard and explains the solution strategy used orally to the other student.
The student answering is not allowed to do any calculations or use the calculator. The person reading the instructions is responsible for validating the written answers.
Alternate the roles of the two students.
Sample cards:
- Write the following initial number on the whiteboard.
- Multiply the original number by 104… What do you get? Explain your strategy orally.
- Divide the original number by 102… What do you get? Explain your strategy orally.
- Divide the original number by 103 and multiply it by 103… What do you get? Explain your strategy orally.
- Write the following initial number on the whiteboard.
- Multiply the original number by 103… What do you get? Explain your strategy orally.
- Divide the original number by 102… What do you get? Explain your strategy orally.
- Divide the original number by 101 and then multiply by 102… What do you get? Explain your strategy orally.
Initial number: 321.4
Initial number: 4.59
Activity 2: Do You Have the Right Number?
Materials
- one whiteboard per student
- erasable felt-tip pen
On the board, write or project a number. The student is not allowed to use a calculator or a multiplication or division algorithm. They simply write their answer for each step.
Give one or more instructions to the student. Start with one calculation and gradually increase the number of instructions. When finished, ask the student to raise the whiteboard.
With a quick glance, analyze the students' answers. After each number, review the students' mental math strategies.
Examples
Number : 325
- Instruction: Multiply this number by 104
- What number do you get?
Number: 0.03
- Instructions: Divide this number by 102
Multiply this number by 105
- What number do you get?
Depending on student success, make the task more complex by increasing the number of instructions and using different representations of numbers (whole numbers, decimals, fractions and expressions containing exponents).
Number : 10,5
- Instructions: Divide this number by 102
Multiply this number by 103
Divide this number by 101
- What number do you get?