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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 to the whole class and make any connections to previous shared information on the chart paper.
Guided Practice(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.
Independent working time(15 minutes)
- Distribute the Powers of 10: Division worksheet, and review the instructions.
- Explain that students will see the powers of 10 as whole numbers, find the quotient to the division problem and then describe any recognizable patterns of decimal movement.
- Tell students they can use calculators and review any previously shared information on the chart paper that enriches their understanding.
- Answer any clarifying questions about the assignment.
- Divide the students into pairs or small groups to complete the Powers of 10: Division worksheet.
- Circulate the room and guide students with leading questions as needed.
- Have students add an extra digit of their choice on each dividend of the Powers of 10: Division worksheet.
- Refer students to information on the chart paper to reference as they have questions.
- Use the ESL version of the worksheet as needed.
- 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 10, ____. 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.