What Sort of Decimal Do You Have?

Lesson Content

• Lesson Plan Template:

  General Lesson Plan

• Learning Objectives: What should students know and be able to do as a result of this lesson?

  
  

  After completing the lesson students will be able to:

  • Make a list of three or numbers (written in word form, decimals, & fractions) in order from least to greatest.

  • Identify the necessity to compare decimals two at a time when ordering three or more decimals.

  • List three or more decimals with varying places in order from least to greatest.

  • Recognize the benefit to write one decimal beneath the other when ordering decimals.

  • Explain the method for ordering three or more decimals from least to greatest

• Prior Knowledge: What prior knowledge should students have for this lesson?

  
  

  Students will know and be able to use:

  • an understanding of place value (specifically tenths and hundredths).
  • represent fractions, with denominators of 10 and 100, in decimal notation.
  •   represent decimals, in tenths and hundredths, as fractions.
  • use appropriate and effective strategies for working with a partner.
  • understand the meaning of a numerator and a denominator.
  • read decimal notation to the hundredths place; fraction notation.
  • understand the idea that decimals and fractions are ways of expressing portions of a whole.

• Guiding Questions: What are the guiding questions for this lesson?

  
  

  1. How are fractions and decimals similar? (Possible answers should include they are naming the same value)

  2. How can we represent the same portion using fractions and decimals? (Possible answers should include the use of a model such as base ten blocks, area model or a line graph)

  3. Why can fractions be written as decimals to the hundredths place? (Possible answers should reflect the idea that fractions are based on 100 being the base denominator) Why can decimals be written as fractions? (Possible answers should indicate that decimals represent a part of a whole similar to a fraction)

  4. How can I determine whether a number is equivalent to, greater than, or less than another number? (Possible suggestion may include comparing numbers by lining up decimals and comparing; comparing fractions)

  5. How can knowing where ¼, ½ and ¾ are located on a number line help me find the appropriate location of other numbers on the number line? (Possible answers should suggest they are benchmarks to use as a guide)

  6. How can you show 0.5, 5/10, and one half are equal? What about 0.75, 75/100, and seventy-five hundredths; 1.50, 1 ½, and one and one half; 3.6, 3 6/10, and three and six tenths? (Possible answers may include converting fractions to decimals or use a model)

  7. What does the decimal point tell you about this number? (Possible answer should indicate that the decimal separates the whole parts from the parts less than one)

  8. Is this fraction >, =, or < 1? How about ½? How do you know? (Possible answers will vary but should relate the students understanding of place value)

  9. Explain how to create an equivalent fraction. (Possible answers should indicate that the student understands the fractions can be created by multiplying or dividing both the numerator and denominator by the same number)

  10. How are the numbers changing as you move to the left or right in your representation? Explain your thinking to me? (Possible answer indicate that number are 1o times larger moving to the left and 10 time smaller moving to the right of the decimal)

  11. What is the same about all of these numbers? Why is it the same? (Answers will vary but should indicate an understanding of equal amounts or unequal amounts)

• Teaching Phase: How will the teacher present the concept or skill to students?

  
  

  Prior Preparation:

  Time will be required to create and arrange the materials needed for this activity. This process should be completed several days prior to the planned lesson.

  • You will want a set for the teacher which will be used in the Closure Decimals_sort_game.docx
  •  Students groups will need their own set of cards to be created from Student_decimal_sort_cards.docx
  • As described in the Guiding Practice, these cards may be sorted into 2 groups.  One set of partners will organize one card group and another set of partners will sort the other card group. The two partner teams will then come together and organize the 2 groups of cards. (For further clarification, see the Guided Practice.)

  Vocabulary Review

  Using a predetermined technique or one of the suggested methods, the teacher will check student proficiency of the listed vocabulary necessary for this lesson.

  Vocabulary
  

  1. Whole number: The numbers {0, 1, 2, 3, ...} etc. without fractional or decimal part

  2. Decimal: A point or dot used to separate the whole number part from the fractional part of a number

  3. Fraction: Part of a whole

  4. Mixed number: a whole number and a fraction combined

  5. Word form: a way to write the number using words

  Discuss with students the vocabulary for the various examples. Students have been introduced and taught these definitions prior, but may need more practice reviewing the concepts. Select two students to assist. The first student will announce the vocabulary word. The second student will provide an example for the vocabulary word or call on another student to assist with the definitions. The teacher will monitor and provide details as needed. An alternative review would be for all students to use white boards with markers and provide an example for each vocabulary word the teacher reads. The teacher will make corrections as needed to clear up misconception regarding vocabulary words.

  Review of Concepts

  To begin the review process for the fraction, decimals, and word forms the teacher will start by explaining that each fraction has a corresponding decimal with the same value. The relationship should be made that decimals and fractions can be stated orally in the same way. In addition, fractions are read and written in a word form necessary in some tasks that people do during the day. If most students have shown proficiency, then this review can also be completed in a small group as remediation prior to lesson.

  Review of Equivalent Values:

  The teacher will provide students with the following representations on the board or on an overhead. Have the students read the numbers.

  3.25               3                                 Three and twenty-five hundredths

   

   

  Explain that this group of three represent the same numerical value and would be considered a set when sorted for this activity.

  You may need to provide further review in this sorting process with fraction/decimal/word form cards by organizing the equivalent fraction and decimal along with the word form. Encourage students to participate by explaining how they might arrange the equivalent fractions and decimals. Samples can be pulled from the teacher or student card sets to use for this review. Corrections will need to be made so that students are able to correctly sort the fractions, decimals and word sort cards into sets to complete the lesson.

   

  Formative Assessment is completed at this time. Provide students with the Fraction Assessment.  Allow 5 minutes to complete.  Review answers with students but do not allow corrections.   Collect Fraction Assessment as baseline on students.

   

  Look for students who correctly identify the listed fraction/decimal/word form using the corresponding equivalent parts of the set in their work. During observations of the review, be sure to display examples as needed for other students to inspect. You may also find students who incorrectly wrote proportions or may have not paid attention to units. As students share their work with the class, they compare answers, explain how they solved their problems, and connect solution strategies. They should be prepared to answer questions as they arise and defend their method. Students should be guided to make connects between the fractions and decimals through a leading question.

   

  Guiding Questions:

  1.) How are fractions and decimals similar?

  2.) How can we represent the same portion using fractions and decimals?

   

  Allow students the opportunity to express their understanding of the relationship between fractions and decimals. Guide the conversation to promote discussion that identifies the place value and the words associated with each place within the represented numbers.

   

  Next, direct the students to determine situations where the different numerical representations might be used in our daily lives. Comparing and contrasting the three methods of writing a value and discuss why they can be confusing. Collect area models for analysis when discussion is completed.

   

   

  Question: Why is it necessary to have three methods to write the identical value for the same thing?

  • Decimals: for money, timing of a race
  • Fractions: weighing items, measuring volume
  • Word form: checks, formal papers, writing very large and very small numbers

   

   

  At this point students with view the video on fractions and decimals located at

  http://safeshare.tv/w/IdlWgEMzLd

  Spend a few minutes answering any questions that students might have regarding the correlation between the two number forms.

• Guided Practice: What activities or exercises will the students complete with teacher guidance?

  
  

  Cooperative Learning Activity

  Card Sort for Value

  In this section students will be required to show they understand the connection between fraction, decimal, and the word form that represents the value by sorting cards to match the three numerical representations. Comparing and contrasting the three representations of a value can enhance their understanding of number relationships.

  The Student Fraction/Decimal/Word Form card sets are created with four sheets which can be divided into two groups consisting of Sheet #1 and #2 as one group and Sheet #3 and #4 as the second group. There are benchmark fraction/decimal groups embedded in these subgroups so that the students will have benchmarks to work with and assist them if they come together to assemble all cards as one long row.

  
  The teacher will group students into partnerships or small groups depending on student abilities, space, time and quantity of decimal/fraction sorting card sets created. Students will need an area of approximately 2 feet by 6 feet to sort the decimal/fraction cards. Students should be instructed that for each numerical value there are three cards which include a fraction, decimal, and a word form card. Their task is to match up all three and group them for each numerical value. They will work to complete matching all of the groups. Students should be instructed to inform the teacher when they have completed this portion of the task.

• Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?

  
  

  Cooperative Learning Activity

  Sort for Chronological Order

  Students work with a partner or small group under the guidance of the teacher to sort the decimal/fraction groups from the smallest to the largest value. When finished, the groups should form a line representing the Decimal/Fraction groups in numerical order. They will fasten their numbers sets together forming a line from the smallest to the largest values. This step can be altered by taking sets of Student Fraction/Decimal/Word Form card sets and dividing the sets so that two small groups work from one set. This will allow for a faster sorting process and then provide two groups to work together to organize the whole set once they successfully sort and organize their groups.

  
  If the Student Fraction/Decimal/Word Sort cards were split into two groups per set, pull the groups together after they have their half sorted and have the two groups work together to continue to organize the whole set from smallest to largest values. Be careful to partner up the correct groups if the sets are split for for the next activity.

  Organizing the Fraction/ Decimal groups allows students to provide justification to their response in how the sorted cards fit together. The finished number grouping will be represented on a row with each group taped together forming a small string of numbers.

  Students that have correctly lined up their fraction/decimal/word form cards will tape their cards in order. This will become part of their whole group review process.

  As a conclusion to the Fraction/decimal card sort cooperative activity, students will take their completed Fraction/Decimal Lineup and use it as their resource to complete a whole group discussion activity. The students will compare their group arrangements with teacher assistance.

  The following questions will assist students to guide them as they sort their sets.

  1. Is this fraction >, =, or < 1? How about ½? How do you know? (Possible answers will vary but should relate the students understanding of place value)

  2. How can knowing where ¼, ½ and ¾ are located on a number line help me find the appropriate location of other numbers on the number line? (Possible answers should suggest they are benchmarks to use as a guide)

  3. How can I determine whether a number is equivalent to, greater than, or less than another number? (Possible suggestion may include comparing numbers by lining up decimals and comparing; comparing fractions)

• Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?

  
  

  Prior to the lesson, the teacher should copy a set of teacher sorting cards, cut them out, and preferably laminate them and have magnetic strips placed on each card. This will allow for the cards to be placed onto a magnetic white board as the class reviews where each set of cards should be placed to arrangement them from smallest to largest. (The cards could also be taped onto a board or placed under an overhead projecting device.)

  After the groups have completed their card sorting and assembled the cards to form a row, have the groups come together as a whole group to discuss placement of the cards in the following manner.

  The teacher will start the review by placing one of the teacher cards on a magnetic board. The decimal values are suggested so that students will be able to line them up if they need to compare. At this time, the class will be asked if they have a number that is either larger of smaller than the number on the board. A benchmark value such as 0.50 might be used. Select a volunteer to read their number. The teacher will ask, "Explain how you know that your number is larger/smaller than the number on the board." The teacher will locate the identical decimal that the student mentions and place it according to the student.

  This process will continue as the class sorts through the teacher's set of cards. Have students sort through the teacher's cards, as time permits, noting that not all cards need to be used. Continue to question students as they volunteer with their numbers. Be sure to have them explain "How do you know that number is larger or smaller than another number on the board?"

  During this discussion, the teacher should ask the students for the key learning from this lesson. The following points should be made and students should record them in their math journals.

  • Both decimals and fractions are numbers that can represent the same value. This value may be parts of a whole.
  • The situation may determine which representation we use.

  Students will complete the _Summative_assessment.docx to show their understanding of the lesson.

• Summative Assessment

  
  

  Students will use the Summative_assessment.docx to sort a sample fraction/decimal/word form list in order from smallest to largest.

• Formative Assessment

  
  

  During the review section of the lesson, the teacher will start with the Formative_assessment.docx handout prior to presenting the video. This will serve as a benchmark of each student's abilities prior to instruction.

  The teacher will circulate and observe as the students are provided a short five minute time to write their responses.

  After the 5 minutes have ended, students will share their responses and explain how they solved each problem and the strategies applied. Allow students to offer alternative solutions by asking, "Did any one solve this in a different way?" "How is this method similar to the method you used?" Through leading questions, students should be guided to make connections between the fractions, decimals, and word form sections.

• Feedback to Students

  
  

  Students will receive feedback throughout the lesson. During the review section, students will be provided with opportunities to exhibit their decimal/fraction matching, receive peer support and offer explanations on their understanding of the fraction/decimal relationship. Questions will be posed to stimulate conversation and promote exchange of ideas among students. The following questions would be utilized during the review.

  1. How do your numbers and words match the fraction/decimal/word form? (Possible answers will include a model that students can use to correctly identify the corresponding value)
  2. Compare your responses to this one. What is the same? Different? Why?(Answers vary but will include the concept of similar or different amounts)

  As the lesson progresses, feedback will become more focused on the fraction/decimal correlations and student understanding related to comparisons among the numerical values of the given examples. Students will be encouraged in their correct responses and proper completion of the sorting task. As needed, students will be guided and redirected to consider changes needed in their decisions as they compare and order the fraction/decimal representations. The following questions would be useful to assist students in this process.

  1. How can I determine whether a number is equivalent to, greater than, or less than another number?
  2. How can knowing where ¼, ½ and ¾ are located on a number line help me find the appropriate location of other numbers on the number line?
  3. What does the decimal point tell you about this number?
  4. Is this fraction >, =, or < 1? How about ½? How do you know?
  5. Explain how to create an equivalent fraction.
  6. How are the numbers changing as you move to the left or right in your representation? Explain your thinking to me.
  7. What is the same about all of these numbers? Why is it the same?

  As the lesson moves into the modeling section, student feedback will shift to confirming or redirecting to assure that models represent the corresponding number involved. Students will be assisted in their thinking as they model through guided questions.

  1. What is the same about all of these numbers? How do you know it is the same?
  2. How does this model match the fraction/decimal/word form?
  3. Compare your model to this one. What is the same? Different? Why?