Dividing Decimals By Powers of 10
Students will divide decimal numbers by powers of 10 and explain decimal placement patterns in the quotient.
- Show your students the following problem 37.5 ÷102
- Have your students brainstorm any details they understand about the expression and note their answers on a chart paper.
- Read the learning objective aloud to the class.
Explicit Instruction/Teacher Modeling(10 minutes)
- Review the concept of exponents as powers of ten, connecting them to thoughts that may have been previously shared on the chart paper.
- Demonstrate the procedure for calculating the power of 10 as a whole number equivalent. (For example 102 is (10 x 10), and (10 x 10) is equal to the whole number, 100.
- Note that a whole number like 100, has no exponents and no decimal.
- Using a calculator, model solving 37.5 ÷ 100 for your class.
- Share the answer, or quotient: 0.375.
- Note the movement of the decimal point in the quotient, (0.375) compared to the dividend (37.5)
- Point out that the decimal in the answer has moved two places to the left.
- Ask your students to turn and talk to a partner and describe any patterns they notice in the movement of the decimal and , 37.5 ÷ 102.
- Have your students share out their ideas, whole class and draw make any connections to previous shared information on the chart paper.
Guided Practice/Interactive Modeling(10 minutes)
- Show your students the following problem 37.5 ÷ 104 .
- Calculate 104 as a whole number equivalent: 104 is (10 x 10 x 10 x 10), which is equal to 10,000.
- Instruct your class to solve 37.5 ÷ 10,000 with a calculator.
- Tell them to note the movement of the decimal point in their quotient and observe the new position of the decimal from the dividend.
- You should observe that the decimal in the answer has moved four places to the left.
- Explain that today’s lesson requires that your students find the powers of ten as whole numbers, find the quotient to the division problem and describe any recognizable patterns of decimal movement. Calculators will be required. Note any previously shared information on the chart paper that enriches understanding.
- Answer any clarifying questions about the assignment.
- Divide the students into pairs or small groups for independent work time.
Independent Working Time(15 minutes)
- Distribute worksheets and calculators.
- Release your class to work in groups.
- Circulate the room and guide students with leading questions as needed.
- Refer students to information on the chart paper to reference as they have questions.
- Use ESL version worksheets as needed.
- Have students add an extra digit of their choice on each dividend of the Dividing By Powers of Ten worksheet.
- As you walk around the room performing check-ins, ask clarifying questions and gauge student awareness of the lesson objective and procedures.
- Collect and review practice sheets if desired.
Review and Closing(5 minutes)
- Have students check their answers with at least two other students and discuss answers that don’t match.
- Call the class to attention and ask if anyone wants to share missing parts of a scaffolded sentence frame similar to this one: I observed ____. My conclusion about today’s assignment is that when you divide a decimal number by a power of ten, ____. Post the sentence frame in a place where the whole class can see it.
- Collect student work and review at another time to make a note of any other academically evaluative criteria.