Assessment Anchors

• M5.A.1: Demonstrate an understanding of numbers, ways of representing numbers, relationships among numbers, and number systems
• M5.D.1: Demonstrate an understanding of patterns, relations, and functions
• M5.D.2: Represent and/or analyze mathematical situations using numbers, symbols, words, tables, and/or graphs

Common Core Standards

• Operations and Algebraic Thinking: Write and interpret numerical expressions, Analyze patterns and relationships
• Number and Operations in Base Ten: Understand the place value system, Perform operations with multi-digit whole numbers and with decimals to hundredths.

 

21st Century Skills

Creativity, innovation, critical thinking, problem solving, communicating, collaborating, leadership, productivity, self-direction

Participation in this lesson supports the 'Compelling Why' of Student Achievement - the belief that every child can demonstrate academic proficiency in core academic disciplines, regardless of school, economic status, race, ethnicity, or ability. In this "hands-on" introductory unit, students will be reviewing place value and whole numbers, learning about decimal number values, ordering decimals, and creating decimal number patterns through addition/subtraction of tenths or hundredths. Students will have an opportunity to play the game 'Smaller to Larger' using Prentice Hall's Investigation series, which will give them the opportunity to explore the meaning and value of decimal numbers and compare decimal number values. At the conclusion of the unit students will make a connection to real-life math applications (sports) and create a baseball card that includes statistics (OBP, AVG, and SLG) in decimal form for a fictional athlete.

Math terminology:

• digit: any number from 0 to 9 (for base 10)
• place: the position of a digit in a number (its column) - for example, in the number 3,271, the 2 digit is in the hundreds place
• place value: the product of a digit multiplied by its place - for example, a 9 in the tens place would have a value of 90
• standard form: a number written in groups of three digits separated by commas and decimal to the right of the ones place - for example, 258
• expanded form: a number written as the sum of its place value parts - for example, 200 + 50 + 8
• word form: a number written as the words you would read to name its total value - for example, two hundred fifty eight
• equivalent: equal in value
• decimal number: any number with a whole value to the left of the decimal point and a partial value to the right of the decimal point - decimal numbers fall between two whole numbers on the number line
• tenths: the first decimal place value (one whole has been divided into 10 pieces)
• hundredths: the second decimal place value (one whole has been divided into 100 pieces)
• thousandths: the third decimal place value (one whole has been divided into 1,000 pieces)
• data table: a visual display of information using columns and rows
• pattern: an arrangement or sequence of data that can be repeated/replicated using a defined rule
• addition: the process of combining two or more values
• subtraction: the process of taking away one or more values
• sum: the end result/total in an addition problem
• difference: the end result/total in a subtraction problem

 

Baseball terminology: 

• on-base percentage (OBP): simply stated is a measure of how often a batter reaches base - it is calculated using a formula involving the number of hits, at bats, and other factors - all time best scores range from .482 to .424
• batting average (AVG): simply stated is the number of hits divided by the number of at bats - a batting average of .300 is excellent and .400 is nearly unachievable
• slugging percentage (SLG): simply stated is a popular measure of the power of a hitter - it is calculated as total bases divided by at bats - Babe Ruth's record (broken in 2001) was .847

In this introductory math unit, students will be reviewing place value and numeration.  The inclusion of decimal number values, in addition to whole number values they have previously learned, will extend the skill to the 5th grade level.  By the end of this unit, students should be able to:

• Identify and express decimal number values and whole number values in standard notation, expanded notation, and word form
• Place decimal number values on the number line
• Order decimal numbers and compare their value to other decimal numbers and whole numbers
• Illustrate that decimals and fractions are interrelated as "parts of a whole" using the hundredths grid
• Analyze a pattern and extend it (for both shapes and numbers)
• Create a new pattern and form an algebraic rule using addition or subtraction with decimal number values
• Explain how the rule works for the created pattern(s)
• Use a table to display data for the decimal patterns created

This beginning-year-unit will review numeration and place value.  Students will spend approximately (1) class period reviewing whole numbers and place value.  The following unit/lesson plan(s) will introduce decimal numbers in relation to place value and will require approximately 5-6 class periods (60 minutes each).  Additional time may be required outside of class to complete the final project (baseball card).

The lesson will utilize the following materials:

• Pencil, paper
• Computer
• Manipulatives and Game Pieces: decimal number cards, game mat
• 10x10 (hundredths) grid(s)
• Project supplies including: oak-tag, ruler, crayons/markers, glue, scissors
• Project Packet - directions and rubric/student checklist

 

W:	Students will know where they are headed as the daily agenda and learning objectives are shared.  Models and examples, along with final rubrics, will be shared, upfront, to provide guidance as to what ways they will be evaluated.
H:	Each instructional session will begin with a thought-provoking question with real life application.  These will be used to hook the students' interest.  The overall “hook” to the unit will be the focus on how math is used in sports, specifically, baseball.
E:	Students will have an opportunity to participate in a game, create their own final project, and see how math is used in sports and everyday activities.  Connections will also be made to money to help make their experiences more realistic.
R:	Students will reflect on what they learned as part of formative assessment #2 (ticket out the door) – they will be asked to reflect on what they’ve learned so far in the unit and/or topics that might still be confusing.
E:	Student understanding will be assessed informally throughout the unit as a part of the 3 formative assessments indicated.  Students will also be able to express what they’ve learned through the final project.  In addition to the project scoring rubric, students will be provided with a "Did I...?" checklist to help guide the creation of their baseball card.
T:	The lesson(s) will be tailored using a variety of instructional strategies and interventions including manipulatives and visual aids.  Since students are also creating their own final project, there will be a great opportunity for student choice and individualized support/enrichment in the completion of the activity.
O:	Student learning will be organized using explicit instruction and scaffolding.  Concepts will be introduced and modeled, there will be multiple opportunities for paired/small group work including the games, and then students will have an opportunity to practice individually (hundredths grid) before they will create a final, independent piece of work which will be assessed.

Instructional Strategy: Student Engagement

• In terms of social engagement, students will work in partners to solve the pattern problem(s) and students will play the game 'Smaller to Larger' in collaborative groups. These activities will only be successful if the students feel safe and supported by one another.
• Academically, students will be engaged through discussion and activity. Their understanding of the skill (place value, ordering, comparing) will be challenged through the use of decimal numbers.
• Students will be intellectually engaged by showing the connection between classroom skills (math, decimals) and real-world activities (sports). This should make the learning meaningful to them as the students see that the skills do have a practical application. Additionally, if baseball piques the interest level of the student, it may have an even greater positive effect.

Instructional Strategy: Empowering Learners

• Gradual Release: this will be demonstrated as I model on the overhead projector how to use the hundredths grid to identify decimal numbers and then give time to work with a partner/triad on a similar type of problem
• Explicit Instruction: after setting the tone and making clear the objectives, I will model to the students how to play the game 'Smaller to Larger'.  Students will then play the game with a partner and I will circle the room, monitoring student learning and completing formative assessments
• Scaffolding: student learning will be supported as the kids work throughout this unit.  Key vocabulary will be highlighted and used.  Additionally, students will be provided with a model of projects so that they can see a finished product. 

 Instructional Strategy: Learning Styles

• Auditory learners will focus on the speaking and listening components of learning.  In addition to discussion in groups, students will be communicating to play the game
• Visual learners will see and create patterns and visual representations of the data (baseball card)
• Tactual learners will utilize their hands-on skills to play the game
• Kinesthetic learners will benefit from creating the fictional athlete and baseball card and presenting their work

 

Depth of Knowledge Levels (Webb’s/Bloom’s)

• Knowledge: Students will identify the different place value units
• Comprehension: Students will illustrate the values of decimal numbers using the hundredths grid
• Application: Students will demonstrate how to order decimal numbers using decimal cards
• Analysis: Students will compare decimal values to determine which is larger and investigate the effects of changing numbers in the tenths and hundredths place
• Synthesis: Students will evaluate patterns to predict what comes next and then construct patterns of their own
• Creation: Students will decide what is an appropriate and sensible pattern for their player's AVG, SLG, and OBP and develop a unique baseball card illustrating this data

 

Instructional Plan/Lesson Sequence

Warm-Up

Throughout the unit, students will engage in a variety of tasks, including writing/responding to a prompt.  Anticipatory questions will include: Can you describe a situation in which you have seen or heard a very large number? (Day 1)  How much do you think a seed weighs?  A penny?  What do we need to use to measure very small numbers? (Day 2) What does it mean if I have $9.85?  How would I represent that decimal value? (Day3) Yesterday, we illustrated $9.85.  How does that number change if I add a penny to the total? What if I add a dime? (Day 4) How do we determine if a number (whole and decimal) is larger or smaller than another number in the same format? Can we compare decimal and non-decimal numbers? (Day 5) What are the next 3 shapes in this pattern?  How can decimal numbers be used to create a pattern? Can we create a "rule" that illustrates and explains the pattern? (Day 6)

Day 1

1. Students will use vocabulary squares (graphic organizer) to define and illustrate unit vocabulary (including: digit, place value, standard form, expanded form, word form). Vocab Squares.doc
2. Using whiteboards, students respond to a series of introductory/review questions posed by the teacher.  Students then turn and explain their answer/thinking to their partner (think pair share).
3. Provide each student with a place-value chart and discuss large numbers through the billions.  Begin exploring how to compare whole numbers by lining up place values and finding the larger number.
4. Students will express the numbers in standard notation, expanded notation, and word form.

Day 2

1. Provide students with a copy of the decimal place value chart. Decimal Place Value Chart.doc
2. Apply place value concepts to express different decimal number values using this tool.
3. Practice writing these numbers in standard, expanded, and word form - remind students to line-up decimals if you want to compare the values of numbers.
4. Begin illustrating several baseball scores for AVG, SLG, and OBP - displaying these statistics as decimal numbers in a data table.

Day 3-4

1. Students will use the provided hundredths grid to shade in the value 0.85. M12.pdf
2. Apply discrete decimal values (tenths and hundredths) to the total and students and have students illustrate how the grid changes.
3. Model the directions and game 'Smaller to Larger' and begin creating student manipulatives for game play (cutout cards, etc.).
4. Students play several rounds of the game demonstrating their ability to order decimal number values while teacher monitors for understanding (formative assessment).

Day 5-6

1. Students discuss the steps required to compare decimal numbers and how  (or if) it is possible to compare decimal and non-decimal numbers.
2. Using whiteboards, students complete a pattern by identifying the next three shapes in the sequence.  Students will then repeat this procedure for numerical values.
3. Using word form, students explain the rule that is being applied to create the pattern.
4. Students then create a new pattern and pair with a partner to see if he/she can determine the next values and explain the rule.
5. This process will be used to create the final project (baseball card), which will organize and display the decimal number data for AVG, SLG, and OBP. Decimal Project Example and Rubric.doc

 

ELL Overlay/IEP Student Needs

• Utilize assistive technology and computers to reinforce skills
• Provide opportunities to use manipulatives including online/virtual manipulatives to practice place value (included under materials & resources)
• Use visual aids and graphic organizers (place value chart, hundredths grid)
• Provide additional wait time and rephrasing of questions/directions
• Use vocabulary squares that promote the use of illustrations and examples in defining terminology

Gifted Students

• Have students calculate baseball statistics in lieu of creating fictional scores
• Have students express the patterns they create as an algebraic expression

Students will participate in a variety of formative and summative assessments throughout this unit.

Formative Assessment #1: At the conclusion of the lessons and activities designed to introduce/review vocabulary related to place value and decimal numbers, students will play the game 'Smaller to Larger' to demonstrate their understanding.  The observations of this activity will serve as one formative assessment.

• Students will use the hundredths (10x10) grid to display the value of decimal number data presented
• Teacher will monitor student work and ensure that the correct number of boxes are being colored in for each grid
• Students will demonstrate how adding or subtracting tenths & hundredths changes the boxes that are colored-in on the grid
• Students will explain how addition of tenths and hundredths makes the value larger and compare the values
• Using this knowledge and the materials provided, students will play 'Smaller to Larger'
• Teacher will move throughout the room making observations and checking for understanding

M12.pdf - Hundredths Grid
M18.pdf - Teacher Checklist for Student Assessment/Observations

M11.pdf - Decimal Cards (Set A)
M13.pdf - Decimal Cards (Set B)
M16.pdf - 'Smaller to Larger' activity

(Webb's DOK: Recall/Skill)

Formative Assessment #2: Students will complete a 'Ticket Out the Door' that includes two of the questions generated by the assessment creator (other questions included in the 5Q Assessment can be used throughout the unit).  This assessment will allow students to show decimal number values on a grid and order and compare three decimal numbers.  At the conclusion of the lesson the teacher will collect these tickets and check for student understanding before the next class period.  Students will also be asked to reflect on one thing they've learned and/or one thing they are still uncertain of/curious about.

5Q Assessment.doc

(Webb's DOK: Skill)

Formative Assessment #3: Students will be presented with a pattern (first with shapes, then numbers) and asked to identify the next 3 values in the sequence.  Students will complete the pattern on their whiteboards and display their answers for quick assessment.  After practicing this skill, students will then be asked to explain, in word form, how the pattern works.  Finally, students will be asked to create their own pattern and form a rule using no less than 7 values and explain to a partner what their pattern is.

(Webb's DOK: Strategic Thinking)

Summative Assessment:  Students will create a fictional baseball player and baseball stats card.  The final project will include a data table displaying 3 data sets (AVG, SLG, OBP) and a minimum of 5 values for each data set.  In addition to creating a decimal number pattern and rule, students will need to explain if the pattern is increasing or decreasing and how their patterns works.  Project directions and rubric will be added.  Prior to beginning the unit, students will also be shown an example of work completed by a previous student. Decimal Project Example and Rubric.doc

(Webb's DOK: Extended Thinking)

Several printable resources are included under assessments and materials. 

• Online Tool for Math Interventions - National Library of Virtual Manipulatives: http://enlvm.usu.edu/ma/nav/activity.jsp?sid=__shared&cid=emready@place_value&lid=3

 

• Baseball Players and Activities
• Vocabulary (Vocab Squares Handout/Vocabulary List)
• Test Your Knowledge (Pretest): http://kids.aol.com/quizzes/baseball-quiz/

Decimals, ordering decimal numbers, place value, patterns, algebraic thinking

Michael Quickel, 5th grade

June 23, 2011