Dividing Decimals: Estimation
Students will be able to round a decimal to a whole number to estimate a quotient.
- Show a video to review the concept of rounding (see related media).
- Write a decimal, like 5.63, on the board and ask students to round it to the tenths place. Then ask students to round it to the nearest whole number (e.g., "Show me a thumbs-up if we should round up or a thumbs-down if we should round down.").
- Tell students, "Today we are going to learn how to use rounding to estimate quotients when we are dividing decimals."
Explicit Instruction/Teacher modeling(10 minutes)
- Write a division problem with decimals on the board (e.g., 11.7 ÷ 4).
- Divide the two whole numbers and explain that since 12 ÷ 4=3, then 11.7 ÷ 4 must be close to 3 (i.e., 11.7 ÷ 4 = 2.94).
- Explain: when we solve the division problem, we are finding the exact answer, or quotient. An estimate is something close to the correct answer, but it is not exact.
- Ask your students, "When might it be helpful to estimate an answer instead of finding an exact answer?" Take student responses.
- Discuss: estimating helps us get close to the answer easily and quickly. Since an estimate is close to the actual quotient, it can also help us check our work. We can estimate an answer to see if our actual answer is close to our estimate. That tells us whether our answer is logical.
- Revisit the problem on the board and ask students to round the decimal to the nearest whole number.
- Divide the two whole numbers and explain that since 12 ÷ 4 = 3, then 11.7 ÷ 4 must be close to 3 (i.e., 11.7 ÷ 4 ≈ 3).
- Compare the estimate to the actual quotient.
Guided Practice(10 minutes)
- Write a second problem on the board (e.g., 39.5 ÷ 5). Have students work with a partner to estimate the quotient. Invite a pair of students to show and/or explain their process.
- Write another problem on the board (e.g., 48.3 ÷ 8) and instruct students to estimate the quotient independently. Then, review as a class.
Independent working time(20 minutes)
- Hand out the Estimation Station game pieces and have students play the game with a partner.
- Circulate the room as students play and provide support as needed.
- When students are finished, collect the Game Tracking Sheet as one piece of assessment.
- Provide extra rounding practice with the digit that determines the rounding underlined (i.e., underline the digit 6 when asking students to round 15.62 to the nearest whole number).
- Provide additional division practice (see optional materials).
- Have students write or solve a word problem with a context that would lend itself to estimation.
- Provide challenge problems that require increased depth of knowledge and a solid understanding of place value (i.e., "round 0.631 to the nearest whole number" or "round 4.57291 to the thousandths place").
- Before collecting the Estimation Station game pieces, instruct students to choose a card at random.
- Hand out an index card or small piece of scratch paper and have students write the problem they chose. Then instruct them to round and estimate. Collect their work as an exit card and check for understanding.
Review and closing(5 minutes)
- Ask students, "What are the benefits of estimating? When would someone use this skill in the real world? When would estimating not be appropriate?"
- Discuss as a class.