Lesson Plan: 5.NBT.A.3aForms of Place Values
(This lesson should be adapted, including instructional time, to meet the needs of your students.)
Background InformationContent/Grade Level / Number and Operations Base Ten / 5
Unit/Cluster / Read and write numbers to the thousandths
Essential Questions/Enduring Understandings Addressed in the Lesson / How does one place value compareto another place value?
What patterns can we identify in the place value of numbers?
How does the position of a number determine its value?
What is the purpose of the decimal place?
Place value has a direct relationship to the value of a number.
Decimals are parts of whole numbers.
Standards Addressed in This Lesson / 5.NBT.A.3aRead and write decimals to thousandths using base-ten numerals, number names, and expandedform.
It is critical that the Standards for Mathematical Practices are incorporated in ALL lesson activities throughout the unit as appropriate. It is not the expectation that all eight Mathematical Practices will be evident in every lesson. The Standards for Mathematical Practices make an excellent framework on which to plan your instruction. Look for the infusion of the Mathematical Practices throughout this unit.
Lesson Topic / Read and write decimals using base-ten numerals, number names and expanded form.
Relevance/Connections / 5.NBT.A.1Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and of what it represents in the place to its left.
5.NBT.A.2Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
Student Outcomes / Student will be able to name a number, write it as a base-ten numeral and write it in expanded form.
Prior Knowledge Needed to Support This Learning / 4. NBT.A.1Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.
4. NF.A.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
Method for determining student readiness for the lesson / This should be done the day before the lesson if at all possible.
- Hand each student a decimal card. (See Attachment #1)
- Students will use the two numbers they are given to illustrate them in 4 different ways. (See Attachment #2) Remind students that each grid equals one whole.
- After a few minutes ask students to find the other students that had their same numbers. Compare answers, discuss differences with each other. Then have students make a final copy with 4 answers that the group thinks are correct. Discuss these with the entire class—either tape them up or use document camera or any other means of sharing with the whole group.
- What do all of the groups have in common?
- Which number was larger in value? How do you know?
- Which group had the largest number? Which group had the smallest number? How can you prove that?
- How do you read your number in words? (Example 0.89 would be Eighty Nine Hundredths.)
- Name a number that is between your two numbers in value.
Learning Experience
Component / Details / Which Standards for Mathematical Practice(s) does this address? How is the Practice used to help students develop proficiency?
Warm Up / Each student will create a place value chart to fill in the number 617.23. UsePlace value Chart Attachment #3. Guide them to write the names of the places. (Hundreds, Tens, Ones, Tenths, Hundredths). Encourage students to come up with these place value names.
Talk about correct answers.
Motivation / Find 10 different places that decimals are used. (Search the Web with the class. Have students tell you where to search. Or have them do this in groups.)
Examples:
- Sports Statistics/standard size of tennis balls/height of nets, etc.
- Distance
- Banks/Money
- Stock Market
- Gasoline Stations
- Medicine/prescriptions/bone density
- Air Pressure in tires
- Teachers grading papers
Activity 1
UDL Components
- Multiple Means of Representation
- Multiple Means for Action and Expression
- Multiple Means for Engagement
Formative Assessment
Summary / Principle 1: Representation is present in the activity. Students will use prior knowledge for the place values of a number. Use of place value charts activates students’ knowledge through visual representation.
Principle II: Expressions is present in the activity. Students will discuss with their group members and neighbors, which promotes expression and communication.
Principle III: Engagement is present through this activity. Students will foster collaboration and community through communication with their classmates. This task allows for active participation, personal response, evaluations and reflections.
Directions:
- Each student will usethe place value chart from the warm-up to fill in the number 617.95.
- Teachers will then discuss the importance of the
- decimal and place value. (Refer to Motivation activity.) Teacher should guide students to make the connection that the greater the place value the greater the value of the number. Teacher should also guide students to make the connection that moving to the right one place is division by ten and moving to the left one place is multiplication by ten; moving to the right two places is division by 100 and moving to the left two places is multiplication by 100, etc.
- Then ask students to fill in the number 617.951 below the first number that they wrote in the Place Value Chart. Ask a student to show her answer to the class and explain why she wrote what she did.
- Is this number larger or smaller than the first number? Why? How would you write this using > or < symbols?
- What about 617.591? Is it larger or smaller than 617.951? Why? How would you write this using > or < symbols?
- Using word form, the teacher will write a number on the board, smartboard or document camera.Students, using standard form (make sure students understand this terminology), will write that number on their place value chart. Teacher should extend into the thousandths place value.
- ‘Student A’ creates a new number (written to the thousandths place) in standard form and then says their number to ‘Student B.’ ‘Student B’ should be able to create the same number using their place value chart. The goal is to make the connection between word form, standard form, place value and value. Activity should be repeated with ‘Student B’ giving ‘Student A’ an example.
- Take a few examples from the students and have them say their number and write them on the board.
- Teacher should stress the importance of the place value of each number. This will lead into expanded form. Using a student response, the teacher should model and explain expanded form.
- Using what we know about place value and the value, in what other ways might we represent 452.896
EXIT SLIP: teacher uses another number, up to the thousandths place value, on the board and students rewrite the number in standard form, word form and expanded form. Teacher collects exit slip. / Student will interpret and make meaning of the problem and begin to understand different forms and meaning of numbers when they are creating and filling in their place value chart.
(SMP #1)
Students will communicate with other classmates using appropriate mathematical language discussion of their numbers on the place value chart.
(SMP #6)
Students will develop a pattern with the numbers in expanded form, both decimal and fractional form.
(SMP #7)
Activity 2
UDL Components
- Multiple Means of Representation
- Multiple Means for Action and Expression
- Multiple Means for Engagement
Formative Assessment
Summary / Principle 1: Representation is present in the activity. Students will use prior knowledge for the place values of a number. Use of matching activity activates students’ knowledge through visual representation.
Principle II: Expressions is present in the activity. Students will interact with a peer while working the matching activity. This promotes expression and communication.
Principle III: Engagement is present through this matching activity. Students will foster collaboration and community through communication with their classmates. This task allows for active participation, personal response, evaluations and reflections.
- Teacher uses the previous activity’s exit slip as a warm-up. Teacher should review the correct and incorrect answers. Teacher should allow time for questions / answers.
- Using the strategy from the warm up, be sure to emphasize how to write the place values after the decimal.
- Teacher gives the students a new number to write in their place value chart. (Note – new number should be extended into the thousandths place value) Students then write the number in expanded form by multiplying by the place values, using the example above. Students compare their answer with their neighbor to ensure understanding. Students then create their own example to practice with their neighbor.
- Teacher takes students examples and has students write them on the board. The students will explain how they arrived at their answer. Teacher will then use this to lead class discussion. Repeat several times to ensure students’ understanding.
- Teacher will then begin ‘matching game’ with students. See example of ‘matching game’ below. (Attachment #4)‘Student A’ will be given a card with a number in word form, and will be asked to find ‘Student B’ who has the same number in standard form. Once the match is made, students will work together to write the number using expanded form. Teacher should circulate and offer assistance. The activity will be repeated several times, have the students switch cards throughout lesson.
(SMP #1)
Students begin to develop the relationship between place value and decimals when a connection is made between place value and the number being multiplied.
(SMP #2)
Students apply skills they already know about creating numbers by multiplying or dividing by the value of 10 and also reflect on whether the answer makes sense.
(SMP #4)
Students will communicate with other classmates using appropriate mathematical languages during the matching game.
(SMP #6)
Activity 3
UDL Components
- Multiple Means of Representation
- Multiple Means for Action and Expression
- Multiple Means for Engagement
Formative Assessment
Summary / Principle 1: Representation is present in the activity. Students will use prior knowledge for writing numbers in expanded form using decimals to write numbers in expanded for using fractions. The problems on the chart paper will trigger students’ interest through the visual representation as they walk around the room.
Principle II: Expressions is present in the activity. Students will interact with peers as they are actively involved in critiquing the problems on the chart paper. This promotes expression and communication.
Principle III: Engagement is present through the Gallery Walk. Students will foster collaboration and community through communication with their classmates. This task allows for active participation, personal response, evaluations and reflections.
- Teacher uses exit slip from activity 2 and discusses correct answers. Teacher then writes a new decimal with a value less than one on the board. (e.g 0.72 or 0.357) Teacher asks the students to represent the numberin as many ways possible. Teacher should not list the forms, but allow time for students to write out in word form, standard form, and expanded form. (Note – some students will think of fractional form) Teacher then collects answers and have random students write their answer on the board.
- Ask students to write their own example of a decimal less than one and repeat activity with their neighbor. While students are working, teacher writes 452.893 in expanded form using decimal on the board. Teacher then asks students, “Is there a way to write this number in expanded form using fractions?”
- Teacher will use the decimal form to make the connection between decimals and fractions. Teacher says/writes the decimal using tenths, hundredths, thousandths and asked if a student can write each place value as a fraction. Teacher should then give another example and have students repeat the same activity. (Note – all students should now use the fractional form)
Example:)
- Teacher then focuses on 0.89, and analyzes the place value of each number, states 8 is the tenths place which is and 9 is the hundredths place which is . Teacher then adds 5 to the end and then allows time for students to solve on own. Teacher remodels the expanded form as Teacher then posts another number on the board and has students complete on their own.
- Teacher posts five different numbers, (Attachment #5), up to the thousandths place value, written in different forms, around the room. Students work independently as they complete a gallery walk filling in all missing forms of the five posted numbers. When completed, students compare answers with their neighbor or group members at their seats.
- This time is allotted to work with students that are struggling with any of the previous three activities. Students that have mastered the concepts can work with one another repeating any of the activities done over the previous three activities.
(SMP #1)
Students will communicate with other classmates using appropriate mathematical languages during the gallery walk.
(SMP #6)
Students will develop a pattern with the numbers in expanded form, both decimal and fractional form.
( SMP #7)
Activity 4
UDL Components
- Multiple Means of Representation
- Multiple Means for Action and Expression
- Multiple Means for Engagement
Formative Assessment
Summary / Principle 1: Representation is present in the activity. Students will use their new found knowledge of place value, expansion and representation of numbers. The Quiz, Quiz Trade activity is a visual representation of the new concepts presented.
Principle II: Expressions is present in the activity. Students will interact with peers as they are actively involved in critiquing the problems with the Quiz,Quiz Trade activity. This promotes expression and communication.
Principle III: Engagement is present through the Quiz, Quiz Trade activity. Students will foster collaboration and community through communication with their classmates. This task allows for active participation, personal response, evaluations and reflections.
- The teacher will go over any questions or concerns that the students may have regarding the different forms. Students should be encouraged to ask questions to better assist them with the forms. Teacher should use examples of work to better enhance the students understandings.
- The teacher should then move into ‘Quiz, Quiz, Trade.’ See ‘Quiz, Quiz, Trade’ (Attachment #6).
- Each student will be given a card where one side is the question and the other side is the answer. Students line up facing each other and hold their question card to the student across from them (‘Student A’ can see the question, while ‘Student B’ can read the answer). ‘Student A’ answers the question, while ‘Student B’ can see the answer and help Student A, if needed.
- ‘Student B’ now reads his / her question and ‘Student A’ assist with the answer.
- “Student A” then trades cards with “Student B” and the entire line with “Student A” then moves one place to the right forming a new partner.The activity is repeated a few times trading cards and with different partners.
(SMP #1)
Students will express numerical answers with a degree of precision during Quiz, Quiz, Trade.
(SMP #6)
Students will look for shortcuts and see repeated calculations in expanded form as decimals and fractions. Students will see the overall process of the problem and attend to the details when completing the closure activity.
(SMP #8)
Closure / The teacher will give an assessment based on the previous four activities.
Teacher writes “Are these forms equivalent to 14.308?”
Explain your reasoning.
Answer: Students should recognize that in the fractional form 8 should be multiplied by .
Supporting Information
Interventions/Enrichments
- Students with Disabilities / Struggling Learners
- ELL
- Gifted and Talented
- Place value chart can be filled in for students
- Different types of forms already provided(expanded, word, fractional and standard)
- Use numbers with smaller values for examples
- Classmate assistance
- Manipulatives
- Small group instruction
- Use easier numbers to write in word form (e.g 8.02)
- Translation chart to be used for word form
- Classmate assistance
- Use of greater place values
- Extension on activities to develop deeper understanding by including numbers that contain zeroes
- Teacher Assistants (students become teachers)
- Student created activities(create problems in variety of forms)
Materials /
- Pencils
- Paper
- Index Cards (Exit Slips)
Technology / Document camera or Smartboard
Resources / Van de Walle, John, Teaching Student-Centered Mathematics, Grades 5-8, Volume 3, 2006.
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