GPB Third Grade Session Resource Packet€¦ · GPB Third Grade Session Resource Packet Georgia Department of Education Dr. John D. Barge, State School Superintendent ... Coherence

GPB Third Grade Session Resource Packet

Georgia Department of Education

Dr. John D. Barge, State School Superintendent

Feb 28, 2012 Page 1 of 24

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You will need the following materials while participating in the session:

Third Grade Handouts (included in this packet)

Connecting cubes, color tiles, 2 color counters (or 2 colors of cubes), tracing paper or patty paper, 2

paper clips

Note-taking materials

Session Format:

Why CCGPS?

How to read the standards

Third Grade Overview

What’s New/Different in Third Grade

Six Lenses

Focus Activity- True or False?

Coherence Activity- Third Grade Handout 1- My Monkey

Fluency Activity- Third Grade Handout 2- Multiplication Four Across

Deep Understanding Activity- Third Grade Handout 3- Score It!

Application - Mathematizing Third Grade

Balanced Approach Activity- Third Grade Handout 4- Ms. Guy’s Puppy Problem

Suggestions and Resources

Six Lenses-

Focus

Coherence

Fluency

Deep Understanding

Applications

Balanced Approach




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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.






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3rd Grade

• Represent and solve problems involving multiplication and division.

• 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.


• 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.


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.


• 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.




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• Convert like measurement units within a given measurement system.


• 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

Dot Cards and Ten Frames:

http://www.edplus.canterbury.ac.nz/literacy_numeracy/maths/numdocuments/dot_card_and_ten

_frame_package2005.pdf

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 lessons-

http://www.mathsolutions.com/index.cfm?page=wp9&crid=56

Video clips-


Exemplars.com:

Free tasks-

http://www.exemplars.com/education-materials/math-k-12

NZMaths:

Numeracy resources-

http://nzmaths.co.nz/numeracy-projects

VandeWalle texts, “Teaching Student-Centered Mathematics K-3” and “Teaching Student-Centered

Mathematics 3-5” sent to each elementary school in Fall 2011. (1 copy of each, per school)

https://www.georgiastandards.org/Pages/default.aspx

https://portal.doe.k12.ga.us/Login.aspx

http://www.edplus.canterbury.ac.nz/literacy_numeracy/maths/numdocuments/dot_card_and_ten_frame_package2005.pdf

http://www.edplus.canterbury.ac.nz/literacy_numeracy/maths/numdocuments/dot_card_and_ten_frame_package2005.pdf

http://www.mathlearningcenter.org/media/Rekenrek_0308.pdf

http://www.uwosh.edu/coehs/mindsongmath/concepts/documents/Empty_Number_Line.pdf



http://www.exemplars.com/education-materials/math-k-12

http://nzmaths.co.nz/numeracy-projects




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(Handout 1)

My Monkey

I shared a bag of grapes with my monkey. I ended up with

17 more grapes than my monkey and my monkey had 29.

How many grapes were in the bag to begin with?

Use a number line to find and explain the answer.




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Multiplication Four Across (Handout 2)

Materials: Two paper clips and several two color counters.

Number of Players: 2

Directions: The first player takes the two paper clips and places them on the row of digits appearing below the grid, either on two different digits or on the same digit (being able to put them on the same digit allows for multiplying a digit by itself). He or she multiplies the two numbers together, produces a product, and places a two-color counter over that product on the game board. The second player moves ONE of the paper clips to a different digit, produces a product and places a two-color counter over that product on the game board. Play alternates in this way, each player moving only one marker at a time to a different digit, until one player has captured four squares in a row (horizontally, vertically, or diagonally).

1 2 3 4 5 6

7 8 9 10 12 14

15 16 18 20 21 24

25 27 28 30 32 35

36 40 42 45 48 49

54 56 63 64 72 81

1 2 3 4 5 6 7 8 9




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(Handout 3)

PRACTICE TASK: SCORE IT!

(Adapted from NC Math and from http://nrich.maths.org/191)

STANDARDS ADDRESSED

MCC3.G.1 Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may

share attributes (e.g., having four sides), and that the shared attributes can define a larger category

(e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and

draw examples of quadrilaterals that do not belong to any of these subcategories.

STANDARDS FOR MATHEMATICAL PRACTICES

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

BACKGROUND KNOWLEDGE

Students often struggle with finding shapes if the shape looks different than what is typical seen. In this

activity, students are encouraged to find the triangles, quadrilaterals, pentagons, and hexagons seen in

two different figures. This will help to continue to build student’s spatial sense and geometric

reasoning. It takes many experiences with shapes to be able to move develop these skills with students.

ESSENTIAL QUESTIONS

How might finding shapes within other shapes help me in life?

Can you provide an example of a non-regular pentagon or hexagon?

Do quadrilaterals have to look like rectangles? How do you know?

MATERIALS

Printed copies of the Student Sheet OR Use technology to Display Student Sheet

Math Journal or paper to keep track of number of shapes and total score

http://nrich.maths.org/191




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GROUPING

Individual or Partner

TASK DIRECTIONS

Students will find all of the shapes in Figure A (triangles, quadrilaterals, pentagons, and hexagons) and

Figure B (rectangles that include the special case: square.) Some students might be able to solve this by

simply tracing over the shape with their pencils. Others might need to draw the shapes on paper. For

the struggling student, you may want to get tracing paper or lightweight paper to have students trace of

the lines to find all of the shapes.

FORMATIVE ASSESSMENT QUESTIONS/PROMPTS

How could you make sure you find all of the shapes within other shapes?

How do you think this type of task helps you for the future?

Do you struggle with finding shapes that were not regularly shaped?

DIFFERENTIATION

Extension Allow students to create another type of figure like either A or B. Once they know how many

shapes are in their large shape, allow other students to solve for the answer.

Intervention Suggestions: Tracing paper or lightweight paper to trace the lines; colored pencils and have

student change colors for each type of shape; allow student to have their own Copier Paper that has

either Figure multiple times (to cut out or trace over)




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Student Sheet

Direction: Use Figure A and find all of the triangles, quadrilaterals, pentagons and hexagons. Once you

believe you have found all of the shapes, give the appropriate amount of points to each shape found.

Total your score to see if you get the correct score!

Score This Figure:

2 points for Triangles

3 points for Quadrilaterals

4 points for Pentagons

5 points for hexagons

Figure A

Directions: Use Figure B and find all of the rectangles. Remember what you have learned about

rectangles and squares. Do you see any shapes that are similar to each other?

Figure B




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Copier Sheet: Print to give each student their own copy of the design.




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Copier Sheet: Print to give each student their own copy of the design.




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Teacher Answer Key for Figure A:

Figure A:

There are 5 triangles, 3 quadrilaterals, 3 pentagons, 2 hexagons for a total of 41 points.

Triangles:

Quadrilaterals:




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Pentagons:

Hexagons:

Teacher Answer Key for Figure B:

14 solutions




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1

2

3

4

5

6

7

8

9

10

11

12

13

14




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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.




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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


Copyright ©, 2003. Exemplars. All rights reserved.




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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.


Copyright ©, 2003. Exemplars. All rights reserved.




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Novice




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Novice




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Apprentice




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Apprentice




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Apprentice




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Practitioner




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Expert

Documents

GPB Third Grade Session Resource Packet€¦ · GPB Third Grade Session Resource Packet Georgia Department of Education Dr. John D. Barge, State School Superintendent ... Coherence