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Breaking Shapes Into Halves and Quarters

2.G.3
Answer Keys Here

Aligned To Common Core Standard:

Grade 2 Geometry - 2.G.3

What should you do when you are required to break a shape into equal parts? You will often be asked to divide a shape in half, sometimes in quarters, and further into to thirds.These worksheets demonstrate to students how to divide shapes (circles and rectangles) in half, quarters, and thirds. Partitions are an important concept in geometry that a kid begins to understand when studying shapes. Partitioning of shapes means to split a shape into different pieces. There are two types of partitioning, which include equal partition and unequal partition. Equal partitioning is a case where a shape is split into parts that are equal in size. Unequal partitioning is splitting a shape into unequal parts. Halves, quarters, and thirds are the basic types of equal partitioning. When circles and rectangles are split into two equal parts, we call it halving. Each of these two equal parts is called a half or semi-circle, and one half is represented as 1/2. When you partition these shapes into three equal parts, we call each of these parts as one-third of a shape which is represented by 1/3. Circles and rectangles can be split into four equal parts as well, and we call each of these parts as quarters or as one-fourth of the shape. it is represented by 1/4.

Shapes Into Halves and Quarters Worksheets And Lessons


  • Step-by-step Lesson- We teach you the difference between halves and quarters by using a square.
  • Guided Lesson - We first ask you how parts shapes are broken into. We move on to ask you how many of those shapes are shaded.
  • Guided Lesson Explanation - I find that numbering the parts helps a lot. You might want to get students into that habit.
  • Practice Worksheet - Determine the fraction of each shape that is shaded.
  • Matching Worksheet - Match the shaded shapes to their numeric or word based fraction.


Homework Sheets

We start by breaking all kinds of common shapes into pieces and parts.

  • Homework 1- Halves means that one of the two equal parts of something or 50% of one whole. Quarters means that one of four equal parts of something or 25% of one whole.
  • Homework 2- The shape below has been broken into parts. Label the shape as being broken into halves, thirds, or fourths.
  • Homework 3- What fraction of shape is filled? I like using short little labels here to help you.



Practice Worksheets

Now we start to ask students to identify the fraction that is right in front of them.

  • Practice 1- Label the drawings below as halves, thirds or fourths. Number all the partitioned pieces that you see.
  • Practice 2- What fraction of the shape which is filled? You will need to also separate those from the empty spaces that are present.
  • Practice 3- This is a very basic worksheet that is meant to give students some success.



Math Skill Quizzes

These are in the same exact form that have been present on countless State assessments.

  • Quiz 1- What fraction of the shape is filled?
  • Quiz 2- Label the drawings below as halves, thirds or fourths.
  • Quiz 3- Tell how many parts each shape is broken into. Label the parts equal or unequal.


How to Transition This to Understanding the Concept of Fractions

As students progress upwards and onwards with math understanding the nature of a fraction and their application in algebra becomes increasingly essential. Students often have a hard time comprehending what a numerator and denominator truly are. I feel this is because do not often see these as tangible in any form, they are just random bits of data. That is where an activity such as these worksheets and lesson can help teachers bridge that gap for their students.

When we start with this fundamental approach to visualizing fractions students inherently grasp a few things that they couldn't when it was just number. They concept of equality is demonstrated by even partitions across the shapes. This gives true meaning to the number of shaded portions (numerator) and the total number of parts (denominator) that there are. There are many other applications than simply recognizing a fractional structure. You can apply these concepts to the part-whole concept and ratios. Eventually you can use this when presenting the operation of division.

The next natural progression is to take these known fundamental fractions and match them to visuals. You can see this type of work in our visual fraction worksheet area. This brings all those elements of a fraction to life for students and in affect make them as concrete as basic integers for students. It also makes a great deal of sense to start your math operations with fractions in this form. Students can count the physical segments and see what would happen if you combined it. In class I often liken these fractional structure to battery slots, where a AA or AAA battery would normally go. Ever since their first toy was given to them, kids know what running around the house looking for extra batteries is all about, so I find this resonates with most kids.