2.G.A.3 - About the Math, Learning Targets, and Increasing Rigor

Full Standard

Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

Measurement Topic

This standard is reported on the report card in these quarters as follows:

About the Math

 Skills and concepts below are learning goals for this standard.

• Partition a circle and rectangle into two, three, or four equal parts.
• Describe the equal shares with words (e.g., halves, thirds, fourths).
• Describe a whole by the number of equal parts (e.g., two halves make a whole).
• Explain and give examples to show that halves, thirds, and fourths of an identical whole need not be the same shape (e.g., half of a rectangle can be shown horizontally or vertically).

This standard is the first exposure to some fractional concepts. This experience should allow students to divide circles and rectangles into equal parts. It is not necessary to define these as fractions with a numerator and denominator. Instead the focus should be on the terms halves, thirds, and fourths. When we divide a circle into two, three, or four equal parts, they can be described by half, thirds, and fourths. Emphasize that it takes two halves, three thirds, and four fourths to make the circle or rectangle. Essential vocabulary for this standard includes: equal shares, whole, halves, thirds, and fourths Visit the online dictionary Links to an external site. for vocabulary support.

Progression of Standard within Grade 2

This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.

Progression of this Standard Across Grades

This progression is informed by the Achieve the Core Coherence Map Links to an external site.. Information is not the complete standard.

TASKS

These tasks can be used with small group or whole group instruction.

• Distribute a geoboard and geoboard paper to each student and group students into pairs. Have every student create a rectangle or square on the geoboard. Have students switch geoboards with their partner. Partition the rectangle or square into two equal shares. Use geoboard paper to record the original rectangle and how you partitioned the rectangle. Repeat this process a few more times. 
• Distribute a geoboard to each student. Have students create a rectangle and partition the shape into three equal pieces. Pose questions such as what part of the whole shape is each part? Did any students create the same original shape but partition the shape differently? Repeat and have the students partition the shape into two and four parts as well as three.
• Four friends are going to equally share a round pizza. Draw the pizza and show how you can share it. Is there a different way you could cut the round pizza to share it equally? How much of the pizza will each person receive? Now partition a rectangular pizza into fourths. Draw the pizza and show how you can share it. Is there a different way you could cut the round pizza to share it equally? How much of the pizza will each person receive?
• When the whole is the same size is one half always going to be larger than one third? Show me.
• If a shape is divided into four equal parts, what part of the whole shape is each part?
• It’s field day at our school! Four classes must share the rectangular play area equally. Show different ways to share the field and describe each area using the word fourth. What other shape could the play area be to be shared equally with these four classes? Enrichment: Now six classes must share the same area. Show different ways to share the field. Show how to share with eight classes.
• Jane went to two different birthday parties on the same day. At the first birthday party, the cake was a square and it was cut into fourths diagonally. At the second birthday party, the cake was the same sized square but it was cut into fourths horizontally. Jane says her piece of cake was bigger at the first party. Is she right? Use drawings to support your answer.
• How many different ways can you cut a rectangle into fourths? Show me. How many different ways can you cut a circle into fourths? Show me.
• Your family is going on a vacation. You need to leave your dog at the dog care center. The dog care center is an exact square. Three other dogs will be at the dog care center with your dog. Create a place for your dog to have an equal amount of space to eat, sleep, and play. What does it look like? Draw your kennel.

SLIDE-BASED TASKS 

  These links are HCPSS created instructional tasks. These tasks are provided in Google slides.  These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first (often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.

Additional Tasks

  These links provide instructional ideas connected to this standard. 

• Which Represents One-Half? Links to an external site. (Illustrative Math)
• Representing Half of a Rectangle ( Links to an external site.Illustrative Math)
• Fractions Folded Links to an external site. stop lesson after third bullet (Mathwire lesson plan) 
• Half and Half Links to an external site. (Inside Mathematics performance task)
• Sandwich Task Download Sandwich Task
  (Utah Core Academy Lesson)
• Banana Split Party Download Banana Split Party
  (Utah Core Academy lesson)
• Pie Task Download Pie Task
  (Utah Core Academy lesson)
• Rearranging Fractions Download Rearranging Fractions
  (Utah Core Academy lesson)
• Shape Pictures Download Shape Pictures
  (Utah Core Academy lesson)

Tasks From Print Resources

  These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them. 

Print Resources

Book Thumbnail	Book Title	Grade	Pages
	Teaching Student-Centered Mathematics	K-3	257 (Correct Shares, Activity 9.1)
	Hands-On Standards	1-2	60-61 (Recognizing Fractions) 62-63 (Identifying Simple Fractions)
	Roads to Reasoning	2	20-21 (What's "Fair?")
	SuperSource: Tangrams SuperSource: Snapcubes	K-2	50-53 (Same and Different) 62-65
	Math In Practice Teaching Second-Grade Math	2	Module 15

Centers

  These print resources can be used during independent or center time. These resources could also be used as lesson seeds.

• 2 Equal Parts Download 2 Equal Parts
  (HCPSS-adapted resource)
• Mr. Parker's Pies Download Mr. Parker's Pies
  (HCPSS-adapted resource)
• Halves, Thirds, Fourths Download Halves, Thirds, Fourths
  (HCPSS-adapted resource)
• Partitioning Geoboard Rectangles Download Partitioning Geoboard Rectangles
  (HCPSS-adapted resource)
• Partitioning Squares Download Partitioning Squares
  (HCPSS-adapted resource)

INDEPENDENT PRACTICE/HOMEWORK/ASSESSMENT

  These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.

• Partition Circles and Rectangles Links to an external site.
• Partition Squares into Halves, Thirds, and Fourths Links to an external site.
• Partition Circles into Halves, Thirds, and Fourths Links to an external site.
• Partition to Create Thirds and Fourths Links to an external site.
• Partition Rectangles into Halves in Different Ways Links to an external site.
• Describe Partitioned Shapes Based on the Number of Parts Links to an external site.
• Halves of the same whole do not need to be the same size Links to an external site.

Full Standard

Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

Measurement Topic

The standard is reported on the report card through these measurement topics. Expand the measurement topic for a description of what students who meet expectation are able to do.

2nd Grade Students Learning 2nd Grade Standards by Measurement Topic

1st Grade Students Learning 2nd Grade Standards by Measurement Topic

2G3 Anecdotal Data Collection Tool Links to an external site.

Visit the SBIR (Standards Based Instruction and Reporting) page in Course Essentials for more information and clarification. 

Rubric (for thinking and reasoning evidence)

Use this rubric for observation and constructed responses (tasks that require explanation, justification, and/or representation).

Rubric for Tasks (pdf) Links to an external site.

Exemplars for this standard (if available)

These samples are examples of what it might look like for a student who MEETS EXPECTATIONS, is MAKING PROGRESS, and/or is MAKING LIMITED/NO PROGRESS.