1. GPB Fourth Grade Session Resource Packet
GPB Fourth Grade Session Resource Packet
You will need the following materials while participating in the session:
Fourth Grade Handouts (included in this packet)
Color tiles, pattern blocks, grid paper, paper
Note-taking materials
Session Format:
Why CCGPS?
How to read the standards
Fourth Grade Overview
What’s New in Fourth Grade
Six Lenses
Focus Activity- Pattern Block Fractions-
http://illuminations.nctm.org/LessonDetail.aspx?ID=U113
Coherence Activity- Fourth Grade Handout 1- Pattern Block Angles
Fluency Activity- Clear the Board- http://www.mathsolutions.com/documents/0-941355-75-
6_L.pdf
Deep Understanding Activity- The Factor Game-
http://www.mathsolutions.com/documents/978-1-935099-02-4_NL36_L1.pdf
Application - Mathematizing Fourth Grade- Intro to Multiplication of Fractions-
http://www.mathsolutions.com/documents/0-941355-64-0_L.pdf
Balanced Approach Activity- Fourth Grade Handout 3- Ms. Guy’s Puppy Problem
Suggestions and Resources
Six Lenses-
Focus
Coherence
Fluency
Deep Understanding
Applications
Balanced Approach
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
Feb 16, 2012 Page 1 of 16
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2. GPB Fourth Grade Session Resource Packet
K-5 Overview
Kindergarten
• Know number names and the count sequence.
• Count to tell the number of objects.
• Compare numbers.
• Understand addition as putting together and adding to, and understand subtraction as taking
apart and taking from.
• Work with numbers 11–19 to gain foundations for place value.
• Describe and compare measurable attributes.
• Classify objects and count the number of objects in categories.
• Identify and describe shapes.
• Analyze, compare, create, and compose shapes.
1st Grade
• Represent and solve problems involving addition and subtraction.
• Understand and apply properties of operations and the relationship between addition and
subtraction.
• Add and subtract within 20.
• Work with addition and subtraction equations.
• Extend the counting sequence.
• Understand place value.
• Use place value understanding and properties of operations to add and subtract.
• Measure lengths indirectly and by iterating length units.
• Tell and write time.
• Represent and interpret data.
• Reason with shapes and their attributes.
2nd Grade
• Represent and solve problems involving addition and subtraction.
• Add and subtract within 20.
• Work with equal groups of objects to gain foundations for multiplication.
• Understand place value.
• Use place value understanding and properties of operations to add and subtract.
• Measure and estimate lengths in standard units.
• Relate addition and subtraction to length.
• Work with time and money.
• Represent and interpret data.
• Reason with shapes and their attributes.
3rd Grade
• Represent and solve problems involving multiplication and division.
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Dr. John D. Barge, State School Superintendent
Feb 16, 2012 Page 2 of 16
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3. GPB Fourth Grade Session Resource Packet
• Understand properties of multiplication and the relationship between multiplication and
division.
• Multiply and divide within 100.
• Solve problems involving the four operations, and identify and explain patterns in arithmetic.
• Use place value understanding and properties of operations to perform multi-digit arithmetic.
• Develop understanding of fractions as numbers.
• Solve problems involving measurement and estimation of intervals of time, liquid volumes, and
masses of objects.
• Represent and interpret data.
• Geometric measurement: understand concepts of area and relate area to multiplication and to
addition.
• Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish
between linear and area measures.
• Reason with shapes and their attributes.
4th Grade
• Use the four operations with whole numbers to solve problems.
• Gain familiarity with factors and multiples.
• Generate and analyze patterns.
• Generalize place value understanding for multi-digit whole numbers.
• Use place value understanding and properties of operations to perform multi-digit arithmetic.
• Extend understanding of fraction equivalence and ordering.
• Build fractions from unit fractions by applying and extending previous understandings of
operations on whole numbers.
• Understand decimal notation for fractions, and compare decimal fractions.
• Solve problems involving measurement and conversion of measurements from a larger unit to a
smaller unit.
• Represent and interpret data.
• Geometric measurement: understand concepts of angle and measure angles.
• Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
5th Grade
• Write and interpret numerical expressions.
• Analyze patterns and relationships.
• Understand the place value system.
• Perform operations with multi-digit whole numbers and with decimals to hundredths.
• Use equivalent fractions as a strategy to add and subtract fractions.
• Apply and extend previous understandings of multiplication and division to multiply and divide
fractions.
• Convert like measurement units within a given measurement system.
• Represent and interpret data.
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
Feb 16, 2012 Page 3 of 16
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4. GPB Fourth Grade Session Resource Packet
• Geometric measurement: understand concepts of volume and relate volume to multiplication
and to addition.
• Graph points on the coordinate plane to solve real-world and mathematical problems.
• Classify two-dimensional figures into categories based on their properties.
Resources:
Teaching Guides/CCGPS: https://www.georgiastandards.org/Pages/default.aspx
https://portal.doe.k12.ga.us/Login.aspx
Rekenrek: http://www.mathlearningcenter.org/media/Rekenrek_0308.pdf
Open Number Line:
http://www.uwosh.edu/coehs/mindsongmath/concepts/documents/Empty_Number_Line.pdf
Math Solutions Free Resources: http://www.mathsolutions.com/index.cfm?page=wp9&crid=122
VandeWalle, “Teaching Student-Centered Mathematics, 3-5” (Sent to every GA elementary school,
Fall 2011)
Unit 1 Fourth Grade Webinar, 3:15, May 9, 2012
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Dr. John D. Barge, State School Superintendent
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5. GPB Fourth Grade Session Resource Packet
Take out the pattern block pieces and put circle on overhead.
By looking at the common geometric shapes of pattern blocks students can
explore angles and their combinations, as well as lay some foundations for
further study in geometry and the use of circle graphs.
Angles are formed by two rays that intersect at a point called the vertex.
The unit of measurement for angles was created by the Babylonians, and is
formed by dividing a circle into 360 equal parts.
By placing pattern blocks around the center of the circle so that their
corners (vertices) touch the center, students can determine the measure of
the various angles formed by the corners of the different shapes. For
example, with squares...
...and triangles.
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Dr. John D. Barge, State School Superintendent
Feb 16, 2012 Page 5 of 16
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6. GPB Fourth Grade Session Resource Packet
How many degrees are in the corners shown around the centers of these
circles?
Can you use known angles to determine unknown angles?
Give groups pattern blocks, paper plates and chart paper to show their
work and share with class. Explain how you solved the angle problem!
(This is in the back of Cloak for a Dreamer)
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Dr. John D. Barge, State School Superintendent
Feb 16, 2012 Page 6 of 16
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7. GPB Fourth Grade Session Resource Packet
Miss Guy's Puppy Problem (Handout 4)
Miss Guy has a very energetic puppy. The puppy loves to
play outdoors, so Miss Guy decided to build a pen to allow
her pet to be outside while she is at school. She just
happens to have 50 feet of fencing in her basement that
she can use for the pen.
What are some of the ways she can set up the pen that
uses all the fencing?
What are the dimensions of the rectangular pen with the
most space available for the puppy to play?
Write a letter to Miss Guy explaining her choices and
which pen you would recommend she build. Be sure to
show how you made your decisions and include a
mathematical representation to support your solution.
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
Feb 16, 2012 Page 7 of 16
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8. GPB Fourth Grade Session Resource Packet
Grade Levels 3 - 5
Miss Guy's Puppy Problem
Miss Guy has a very energetic puppy. The puppy loves to play outdoors, so Miss Guy decided to build a
pen to allow her pet to be outside while she is at school. She just happens to have 50 feet of fencing in
her basement that she can use for the pen.
What are some of the ways she can set up the pen that uses all the fencing?
What are the dimensions of the rectangular pen with the most space available for the puppy to play?
Write a letter to Miss Guy explaining her choices and which pen you would recommend she build.
Be sure to show how you made your decisions and include a mathematical representation to
support your solution.
Context
This task was given to students after a unit on measurement. Two of the major concepts addressed
in this unit were those of area and perimeter. The two fourth grade classes were given a menu of
problems to choose from. This was the most popular problem, perhaps because Miss Guy actually
has a new puppy.
What This Task Accomplishes
This problem directly addresses the concepts of area and perimeter and is a good assessment of student
mastery and understanding of these concepts. There is the opportunity for students to discover the
relationship between area and perimeter. This task also provides students with a real-world application of
the skills they have been developing in class.
What the Student Will Do
Students were given a choice to work independently or in groups. Most students began by sketching
rectangles and figuring dimensions that would total 50 feet. Few students were able to discover the size
for a square pen, 12 1/2 feet per side, but many were able to find the 12 x 13 foot pen. Calculators were
used to compute the areas of the pens. A group of students used the side of the house as one side of
the pen, which resulted in an alternative solution to the problem, with a larger area.
Time Required for Task
Two 45-minute periods
Miss Guy's Puppy Problem
Copyright ©, 2003. Exemplars. All rights reserved.
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
Feb 16, 2012 Page 8 of 16
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9. GPB Fourth Grade Session Resource Packet
Interdisciplinary Links
Students could research the recommended pen sizes for dogs, horses, sheep or any other animal and
compare the fencing types. It might be interesting to discuss grazing requirements of farm animals and
plans for rotating pastures with area farmers.
Teaching Tips
Most students needed to make a lot of sketches of rectangles. Having a puppy they knew about starring
in the problem helped motivate students to find the largest possible area.
Suggested Materials
Graph paper
Calculators
Rulers
Tiles
Possible Solutions
The pen with the most area is 12 1/2 feet x 12 1/2 feet. 12 feet x 13 feet is the largest pen possible
when using whole numbers. If the student uses the side of the house as one side of the pen, answers
will vary.
Benchmark Descriptors
Novice
A solution that shows an incomplete understanding or inability to solve the problem. A solution that does not use 50 feet of
fencing or address the areas of potential pens. Reasoning is lacking or inaccurate. It is not clear what the student did to solve the
task.
Apprentice
A solution that attempts to address the area of the pens using 50 feet of fencing, but is incomplete or incorrect in the final result. A
solution which shows some understanding of the problem, but has a weak or random explanation or strategy. The student lacks
communication about what was done to solve the task.
Practitioner
A solution that shows understanding of the perimeter and area aspects of the problem. A solution in which the student is able to
apply fundamentals of multiplication and addition to calculate the area and perimeter of the pens. The student finds the largest
possible pen either in whole numbers or using fractions and supports the answer. The student is able to communicate with some
clarity what was done to solve the problem and why.
Expert
A solution that shows understanding of the perimeter and area aspects of the problem. A solution in which the student is able to
apply fundamentals of multiplication and addition to calculate the area and perimeter of the pens. The student finds the largest
possible pen either in whole numbers or using fractions and supports the answer. The student is able to communicate with some
clarity what was done to solve the problem and why.
Miss Guy's Puppy Problem
Copyright ©, 2003. Exemplars. All rights reserved.
Georgia Department of Education
Dr. John D. Barge, State School Superintendent
Feb 16, 2012 Page 9 of 16
All Rights Reserved

10. GPB Fourth Grade Session Resource Packet
Novice
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Dr. John D. Barge, State School Superintendent
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11. GPB Fourth Grade Session Resource Packet
Novice
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Dr. John D. Barge, State School Superintendent
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12. GPB Fourth Grade Session Resource Packet
Apprentice
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Dr. John D. Barge, State School Superintendent
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13. GPB Fourth Grade Session Resource Packet
Apprentice
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Dr. John D. Barge, State School Superintendent
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14. GPB Fourth Grade Session Resource Packet
Apprentice
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Dr. John D. Barge, State School Superintendent
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15. GPB Fourth Grade Session Resource Packet
Practitioner
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Dr. John D. Barge, State School Superintendent
Feb 16, 2012 Page 15 of 16
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16. GPB Fourth Grade Session Resource Packet
Expert
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Dr. John D. Barge, State School Superintendent
Feb 16, 2012 Page 16 of 16
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