Estimating rational numbers

Students round fractions and mixed numbers to their closest whole number by first changing the rational numbers into decimal numbers.

A lesson plan for grades 4–5 Mathematics

By Doreen Castelloe

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Learning outcomes

Students will:

• change a fraction or mixed number to a decimal number.
• round the decimal number to the nearest whole number.
• justify the answer.

Teacher planning

Time required for lesson

1 hours

Materials/resources

• paper
• pencil
• calculator
• Rounding Rational Numbers worksheet

Pre-activities

Students have been introduced to fractions, rounding, and decimals.

Activities

1. Read the directions on the worksheet “Rounding Rational Numbers.” Make certain students understand that 1/2 = 0.5
2. Use problem 1 as an example problem.
   • “What does the “/” in the fraction 1/4 mean? (Divided by)
   • “Using a calculator, punch in 1 (the numerator) and divide it by 4 (the denominator). What decimal do you get?” (0.25)
   • “Locate the digit in the tenths place. What is it?” (a 2)
   • “Does 2 require you to round up in the ones place or stay with the same number that is there?” (stay with the same number)
   • “What is that number?” (0)
   • “So would 0.25 round to 0 or to 1? (0)
   • “Since 0.25=1/4, would 1/4 round to 0 or to 1?” (0)
   • “Write 0 as your answer on the worksheet. The directions on the sheet also instruct you to justify your answer. What does justify mean?” (support your answer)
   • “How did we support our answer of 0?” (the 2 in the tenths place told us to round the ones place to 0)
   • “Let’s show our justification then by writing the following on our answer sheet beside the answer of 0: 1/4=0.25. Then underline the digit 2 in the tenths place to show that this number is the one we used to decide what to do to the 0 that sits in the ones place. Now write on your answer sheet: 2 tenths<5 tenths so you do not change the digit 0 in the ones place."
3. With the students, work through as many problems on the worksheet as you feel necessary for them to fully understand the process. I will probably do at least half the worksheet as a whole class activity before assigning problems 8-14 for students to do for independent practice.

Assessment

Check (for accuracy) the problems the students did for independent practice.

Supplemental information

Comments

If students are given plenty of practice doing the activity correctly as a whole class (problems 1-7), they should have a good understanding of how to finish the activity (problems 8-14) with both accuracy and understanding.