Grade 5
Classroom Challenge
A Formative Assessment Lesson
Place Value
Baseball Statistics
Teacher Guide
Grade 5 Lesson: Baseball Statistics
Introduction
This Classroom Challenge has been modeled after the secondary level lessons created by the Mathematics
Assessment Project, University of Nottingham and UC Berkeley. In their booklet, A Brief Guide for teachers
and administrators April 2013, they state “A Classroom Challenge (CC) is a classroom-ready lesson that
supports formative assessment. The CC helps teachers assess and improve students’ understanding of
mathematical concepts and skills and their ability to use the ‘mathematical practices’ described in the
Common Core State Standards.”
This formative assessment lesson “first allows students to demonstrate their prior understandings and
abilities in employing the mathematical practices, and then involves students in resolving their own
difficulties and misconceptions through structured discussion. This results in more secure long-term
learning, reducing the need for re-teaching that otherwise takes so much classroom time.”
Instructional Prerequisites (These are met after approximately 2/3 of the unit has been taught.)
• Students are able to compare two decimals to hundredths.
• Students are able to use place value understanding to round whole numbers.
Common Core State Standards for Mathematics
5.NBT.3b
5.NBT.4
Compare two decimals to thousandths based on meanings of the digits in each place, using
>, =, < symbols to record the results of comparisons.
Use place value understanding to round decimals to any place.
Standards for Mathematical Practices for this lesson:
MP1:
Make sense of problems and persevere in solving them.
MP3:
Construct viable arguments and critique the reasoning of others.
MP4:
Model with mathematics.
MP6:
Attend to precision
Materials required
• Each individual student will need a copy of the task “Baseball Statistics.”
• Each small group of students will need an additional blank copy of the task printed and a piece of
poster paper, on which they will compile the group responses.
• Each individual student will need a copy of the Math Performance Task Reflection.
• Manipulatives should be available such as graph paper and number lines.
Time Needed
• The suggested lesson will take approximately 3 math sessions. Exact timings will depend on your
class.
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Suggested Lesson Outline for Baseball Statistics – Grade 5
Objective:
Students will be able to compare, round, and order decimals and show their positions on a
number line.
Introduction: (Vocabulary reference support, approximately 10 minutes)
• Refer to Unit Word Wall or create a class Circle Map for “Decimal and Rounding Vocabulary” that
should be displayed during task. Say, “Today you will use what you’ve learned about place value to
compare and round decimals.”
Independent Task: (No teacher assistance, approximately 20 minutes)
• Give each student a copy of the “Baseball Statistics” task. Say, “Read through the questions and try
to answer them as carefully as you can. Show how you work out each answer. Don’t worry if you
cannot understand or complete everything. In the next lesson you will do further work on this task.”
Do not score them; collect and read students’ responses to make notes about their current levels of
understanding and their different solution strategies.
Collaborative Small-Group Work: (approximately 10 minutes)
• Organize students into groups of three to four. Give out a large piece of paper for making a poster
of their solutions and a copy of the task for reference. Say,
“I want you to work in groups now. Your task is to produce a product/document that reflects your
groups’ discussion during consensus using math vocabulary/language. In your groups, work on one
problem at a time. Take turns to explain your method for solving the problem. (Students may use
whiteboards to explain their thinking.) Listen carefully to each other. If you have more than one way of
solving the problem, decide as a group which method you prefer. Write your solution on the poster.
Before you move on to the next problem, make sure every person in your group understands and can
explain the group’s method.”
• The teacher walks the room and uses “Suggested Prompts for Common Issues During Group
Discussion” to support student problem solving. (You can cut out the table included to use for
reference as you walk the room.) Ask questions that help students clarify their thinking. If the whole
class is struggling on the same issue, write relevant questions on the board and hold an interim
discussion. Note different student approaches to the task so you can use this information to focus a
whole class discussion towards the end of the lesson. Teacher might also note the group dynamics
such as the flow of conversation between members.
Whole Class Discussion: (approximately 10 minutes)
• Select students with unique, correct, or incorrect solutions to present their work to the class. Ask
students to compare the different solution methods. Say, “Which approach did you like best? Why?”
As necessary, teacher gives further explanations on how students can use precise
language/vocabulary to explain their mathematical reasoning.
Looking at Sample Student Responses (approximately 40 minutes, Day 2)
• See the attached document for discussion question samples.
Closure: (approximately 10 minutes, Day 2)
• Ask students to read through their original responses to the task and then fill out the “Math
Performance Task Reflection”. Teacher and/or student(s) models an advanced proficient Task
Reflection.
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Name ________________________
Date _______________
Baseball Statistics
Many baseball statistics are expressed in decimals. The chart shows some of the statistics for the players
on the Dodgers.
Batting Average:
Andre Ethier
.292
James Loney
.288
Jamey Carroll
.290
Dodgers 2011 Statistics
On Base Percentage:
Juan Uribe
.264
Rafael Furcal
.272
Clayton Kershaw
.267
Slugging Percentage:
Aaron Miles
.346
Juan Rivera
.406
A.J. Ellis
.376
Juan Castro
.286
1. Which of the players listed has the highest Batting Average?
______________________________
How does the meaning of the digits in each place help you find the highest batting average?
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
2. Use the number line. Mark and label the three On Base Percentages in the chart above.
0.26
0.27
0.28
Explain which of the three players has the highest On Base Percentages. Use place value to justify
your reasoning.
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
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3. Look at the four numbers in the Slugging Percentage chart. Find two of these numbers that are the
same when they are rounded to the nearest tenth.
Batting Average:
Andre Ethier
.292
James Loney
.288
Jamey Carroll
.290
Dodgers 2011 Statistics
On Base Percentage:
Juan Uribe
.264
Rafael Furcal
.272
Clayton Kershaw
.267
Slugging Percentage:
Aaron Miles
.346
Juan Rivera
.406
A.J. Ellis
.376
Juan Castro
.286
Explain why these two numbers are the same when rounded to the nearest tenth.
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
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Solutions
Performance Task: Students compare order and round decimals.
Question #1
Students compare decimals to find the player with the highest batting percentage.
Correct answer: Andre Ethier
Possible explanation: The tenths are the same for all three players. Andre and Jamey have the same
number of hundredths, but Andre has a greater number of thousandths.
Question #2
Students order three decimals using a number line and find the player with the highest on base
percentage.
Correct answer: Rafael has the highest On Base Percentage
.264
0.26
.267
.272
0.27
0.28
Question #3
Students round decimals to the nearest tenth and explain why two decimals are the same after
rounding
Possible correct answers: .346 and .286
Possible explanation: .346 rounds down to .3 and .286 rounds up to .3.
406 and .376
Possible explanation: .406 rounds down to .4 and .376 rounds up to.4.
Suggested Prompts for Common Issues During Group Discussion
Common Issues:
Suggested Questions and Prompts
Group has difficulty getting started
□ What do you know?
□ What do you need to find out?
□ Reread the problem and underline key
information.
Group makes an incorrect interpretation of the
□ How can you explain this problem in your
constraints
own words?
□ What directions do you have to follow?
Group presents work poorly
□ Would someone unfamiliar with your
type of solution easily understand your
work?
□ Have you explained how you arrived at
your answer?
Group produces a correct solution.
□ Can you now use a different method?
(Group needs an extension task.)
Which method do you prefer? Why?
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Rules for Math Talk
 Every student must listen respectfully
to what others say.
 Every student must speak so that
others can hear what is said.
 Every student will participate by
speaking out at some point.
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Looking at Sample Student Responses
Purpose: The purpose of this activity is to give students additional opportunities to explain
mathematical reasoning with oral and written language.
Standard for Mathematical Practice:
Construct viable arguments and critique the reasoning of others
Materials Required:
• See the following three pages of sample responses.
• Copy the “Possible Discussion Questions” found below onto chart paper or onto the class
whiteboard to be displayed and used when discussing student work samples.
Input:
The teacher will “think out loud” as she/he critiques the sample student response. For
example, the teacher might say, “____ organized the work by drawing a picture and
writing an equation. I’m not sure what the student meant when….I think the work might
be better if….”
Structured Guided Practice:
The teacher leads students through a discussion of a different page of sample student
responses using active participation strategies such as “tell your neighbor what you like
about the student response.”
Small Group Discussion:
Students discuss or write a written response to one of the sample student responses that
has not been previously discussed.
Possible Discussion Questions
• What approach was used?
• How has the student organized the work?
• What mistakes have been made?
• What isn’t clear?
• What questions do you want to ask this student?
• In what ways might the work be improved?
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Sample Response to Discuss: Joselyn (Teacher Model)
Baseball Statistics
Many baseball statistics are expressed in decimals. The chart shows some of the statistics for the
players on the Dodgers.
Batting Average:
Andre Ethier
.292
James Loney
.288
Jamey Carroll
.290
Dodgers 2011 Statistics
On Base Percentage:
Juan Uribe
.264
Rafael Furcal
.272
Clayton Kershaw
.267
Slugging Percentage:
Aaron Miles
.346
Juan Rivera
.406
A.J. Ellis
.376
Juan Castro
.286
1. Which of the players listed has the highest Batting Average?
\
How does the meaning of the digits in each place help you find the highest batting average?
Suggested Discussion Questions
What approach was used?
What questions do you want to ask this student?
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Sample Response to Discuss: Hannah (Structured Guided Practice)
2. Use the number line. Mark and label the three On Base Percentages in the chart above. Then
write which of the three players has the highest On Base Percentages. Use place value to
explain your reasoning.
\
What approach was used?
Suggested Discussion Questions
What mistakes have been made?
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Group Name __________________________________
Date ____________
Sample Response to Discuss: Max
What approach was used?
Suggested Discussion Questions
What mistakes have been made?
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Sample Comments that might be made about student work for teacher reference:
Which of the players listed has the highest Batting Average?
How does the meaning of the digits in each place help you find the highest batting average?
Jocelyn
Jocelyn used the approach of lining up the decimal points and the digits in each number. Her mistake
was that she said, “Finally, I went to the thousands, and that’s how I received 392”. She should have
said “thousandths” and “.392”. Discuss difference between thousandths and thousands and the
difference between whole numbers (greater than 1) and decimals
(less than 1).
Use the number line. Mark and label the three On Base Percentages in the chart above. Then write
which of the three players has the highest On Base Percentages. Use place value to explain your
reasoning.
Hannah
Hannah labeled the number line correctly. She explained her reasoning using place value vocabulary
but she said, “He has a 2 in the oneths place”. I would want to ask her what she means by “oneths”. I
think she meant to write “tenths” but it isn’t clear.
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Look at the four numbers in the Slugging Percentage chart. Find two of these numbers that are the
same when they are rounded to the nearest tenth. Explain how you know.
Max
Max set up his work in an organized way and labeled the place value of the digits. He underlined the
digit in the tenths place in .406 and rounded it to .400. However, his rounding is incorrect on the three
other decimals. He needs to explain what strategy or procedure he follows when rounding decimals.
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Math Performance Task Reflection
Mathematician’s Name _____________________________
Title of Activity ________________________________________________________________
Look at your original solution. Make improvements to your work.
Explain what you changed in the work.
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
Why did you make the change?
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
Bonus: If you have time, show a different way to solve this problem on the back of the page.
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