Guided Lessons

# Dividing Decimals By Powers of 10

Your students will be able to divide decimal numbers by powers of 10 and explain decimal placement patterns in the quotient.
Need extra help for EL students? Try the Divide by Powers of Ten pre-lesson.

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Need extra help for EL students? Try the Divide by Powers of Ten pre-lesson.
• Students will divide decimal numbers by powers of 10 and explain decimal placement patterns in the quotient.
The adjustment to the whole group lesson is a modification to differentiate for children who are English learners.
(5 minutes)
• 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.
(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.
(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.
(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.
• 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.

Enrichment:

• Have students add an extra digit of their choice on each dividend of the Powers of 10: Division worksheet.

Support:

• 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.
(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.