Lesson Title: 7.NS.2d Converting Fractions to Decimals
Date: _____________ Teacher(s): ____________________
Course: Common Core 7
Start/end times: _________________________
Lesson Standards/Objective(s): What mathematical skill(s) and understanding(s) will be developed? Which
Mathematical Practices do you expect students to engage in during the lesson?
7.NS.2d Convert a rational number to a decimal using long division; know that the decimal form of a rational
number terminates in 0s or eventually repeats.
MP1:
MP3:
MP5:
MP6:
MP7:
MP8:
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Lesson Launch Notes: Exactly how will you use the
first five minutes of the lesson?
Lesson Closure Notes: Exactly what summary activity,
questions, and discussion will close the lesson and
connect big ideas? List the questions. Provide a
foreshadowing of tomorrow.
Convert the following decimals to fractions:
Decimal
Fraction
0.5
0.25
0.8
0.125
Solutions:
Decimal
Fraction
0.5
5/10 = 1/2
0.25
25/100 = ¼
0.8
8/10 = 4/5
0.125
125/1000 = 5/40 = 1/8
Exit Ticket:
Convert each fraction to a decimal. Label as terminating
or repeating.
Terminating or
Fraction
Decimal
repeating




5
7
1
8
1
1
4
Solutions:
Fraction
5
7
1
8
1
1
4
Decimal
Terminating or
repeating
0.714285
repeating
0.125
terminating
1.25
terminating
Lesson Tasks, Problems, and Activities (attach resource sheets): What specific activities, investigations,
problems, questions, or tasks will students be working
on during the lesson? Be sure to indicate strategic
connections to appropriate mathematical practices.

1. Have four student pairs go to the board to enter one of the missing fraction values. Ask each pair to explain how
they obtained their answer (background knowledge, writing the decimal as a fraction using place value to
determine the denominator and then simplifying, etc.). Clarify, discuss or review the skill of changing a decimal
to a fraction using place value, as needed. (Look for evidence of MP6.)
2. Ask students “What is another way of representing a fraction in word form?” (¼ means the same as 1 divided by
HCPSS Secondary Mathematics Office (v2.1); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: 7.NS.2d Converting Fractions to Decimals
Course: Common Core 7
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
4 and ½ is the same as 1 divided by 2). Working in pairs, have the students divide up the un-simplified and
simplified fractions from the lesson launch (ex: one gets ½, 25/100, 8/10 and 1/8; the other gets 5/10, ¼, 2/5, and
125/1000). Using long division, have the students divide numerator by denominator to obtain a decimal. Have
students check their results. They should be the same as the equivalent decimal in the chart. (Look for evidence
of MP1 and MP6.)
3. In their notebooks, have students create a table (or continue the table from the lesson launch) with a column for
fractions and a column for decimals. There are 12 fraction cards that will be converted.
4. Provide each pair of students with an envelope of the Fraction Cards. Have students take turns choosing a card
from the envelope and using long division to convert to a decimal. The second student should enter the fraction
into the calculator using division to check the first partner’s work. Once the decimal value is found, students
should record the equivalent pair on the table in their notebook and on the back of the corresponding card.
Switch rolls and repeat, until all 12 fractions have been converted. Circulate to be sure students are taking turns
and that they are taking the division all the way to a terminating or repeating decimal. (Look for evidence of
MP6.)
5. Once students have completed and checked all conversions, have them sort the decimal values into groups.
Circulate and observe students thinking as they group the decimals. (Look for evidence of MP3 and MP7.)
6. Bring the class together. List on the board, all of the ways students sorted the decimal values, with the goal of
narrowing it to the two categories of terminating and repeating decimals. Be sure to discuss the third possibility
of divisors, non-terminating, non-repeating decimals (irrational numbers). Have students go back to the chart in
their notebook and label each fraction/decimal pair as repeating or terminating. (Look for evidence of MP3.)
7. Discuss as a class:
a. What one of two different things happened each time you converted a fraction to a decimal using division?
(the divisors are always terminating or repeating decimals)
b. Did you see any patterns with certain denominators?
(denominators of 11 generate a repeating decimal with multiples of 9 and the numerator to form the
repeating decimal pattern)
(Look for evidence of MP7 and MP8.)
8. Administer the exit ticket.
Evidence of Success: What exactly do I expect students to be able to do by the end of the lesson, and how will I
measure student success? That is, deliberate consideration of what performances will convince you (and any outside
observer) that your students have developed a deepened and conceptual understanding.
The students will be able to accurately convert fractions and mixed numbers to their decimal equivalents.
The students will be able to see that the division of the numerator by the denominator is complete when the decimal
terminates or ends in 0s or the decimal generates a repeating pattern.
The students will be able to classify the decimal form of the fraction as a terminating or a repeating decimal.
Success will be measured through class discussion (#7) and completion of the exit ticket without a calculator.
Notes and Nuances: Vocabulary, connections, anticipated misconceptions (and how they will be addressed), etc.
Vocabulary:
Dividend, divisor, terminating decimals, repeating decimals
Possible misconceptions:
 A decimal pattern that does not repeat is not a rational number (ex: 0.1010010001);
 If no repeating pattern is established then it is likely there is a calculation error;
 A 0 in the divisor does not always indicate an end to the division problem, there must be no “remainder.”
Resources: What materials or resources are essential
for students to successfully complete the lesson tasks or
Homework: Exactly what follow-up homework tasks,
problems, and/or exercises will be assigned upon the
HCPSS Secondary Mathematics Office (v2.1); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: 7.NS.2d Converting Fractions to Decimals
Course: Common Core 7
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
activities?
completion of the lesson?
Have students choose 3 fractions with the denominator of
One envelope per pair with the cut up Fraction Cards
9 and convert them to decimals using division. Write a
Calculators
description of any pattern that you observe. Choose a
fourth fraction with a denominator of 9 and “predict” this
Copies of exit ticket or slide/document to project
decimal equivalent using the pattern observed.
Lesson Reflections: How do you know that you were effective? What questions, connected to the lesson
standards/objectives and evidence of success, will you use to reflect on the effectiveness of this lesson?
Were students able to consistently recognize a fraction as a division problem?
Did students find success with finding divisors that were terminating or repeating and recognizing when the division
problem “ended?”
Did students see the decimal patterns in the ninths and elevenths?
Are there specific skills that need to be reinforced or revisited?
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this
product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.
HCPSS Secondary Mathematics Office (v2.1); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.