## Partitioning Shapes

#### Aligned To Common Core Standard:

**Grade 1 Operations** - 1.G.3

To understand the fractions, kids need to have a clear understanding of the shapes and how to partition them. This means breaking them into many parts. At this grade level we consider all of the new shapes that are created to be equal in size. The initial fraction lessons begin with partitioning shapes, which lays the foundation for the concept. It is best to start learning fractions with the most basic of shapes such as circles and rectangles. These worksheets help students learn to break circles and rectangles into equal and unequal sub-shapes. This is a good section to learn after you understand your basic geometric shapes and are comfortable with them.

- Halves and Quarters Step-by-step Lesson- Students learn the difference between halves and quarters. Great to start to work towards symmetry skills.
- Labeling Halves and Quarters Guided Lesson - We give you three sets of objects and we ask you what they are broken into. The focus is on determining quarters or halves.
- Broken Pieces Guided Lesson Explanation - Might have gone a bit overboard on the explanation front.
- Cut Me In Two Worksheet - We lay the groundwork to start understanding the concept of symmetry.
- Color One Half Worksheet - The alien outline is the best drawing I have made in years. You will split everything in two on this page.
- Equal Halves Worksheet - Determine equal halves of objects in minutes. Remember that the two pieces must be equal size.
- Cut Into Halves and Quarters - We give you a shape and ask you to get in touch with your inner Ninja.
- Matching Parts of Shapes - I love this sheet. It really helps kids master the skill. We take just a piece of the shape.

#### Guided Lessons

We split all types of things into halves and quarters here.

- Identify Shape Guided Lesson 1 - Just because there are two lines doesn't mean that you have quarters.
- Partitioning Circles Step-by-step Lesson 1 - Identify halves. One of the two equal parts of something is called a half. Now we see that figure A is divided into two equal parts. And figure B is divided into four equal parts.
- Partitioning Rectangles Lesson 2- The shape below has been broken into parts. Label the shape as being broken into quarters or halves.
- Partitioning Circles - Lesson 3- Again we count the number of equal parts. We have two equal parts in the figure. Two equal parts are halves.

#### Practice Worksheets

These lead us directly to symmetry which is a key skill at all levels of geometry.

- Partitioning Circles and Rectangles Worksheet 1 - Time to label them. Label the shapes below as being broken into quarters or halves.
- Color One Half Worksheet 2- Divide the objects into two equal halves by coloring one half.
- Cut In Two Worksheet 3- Draw a single line that cuts the object exactly in half. Each side should be a mirror of the other.
- Equal Halves Worksheet 4- Make equal halves of the image by drawing a line.

### What is Partitioning a Shape?

Partitioning means separating something into different sections. Partitioning can be done in two ways, which include equal and unequal parts. In equal partition, each of the partitioned sections is identical to the other partitioned sections. When you place these partitioned sections on each other, they will exactly lay down and match the sections below them. In most math problems, especially fractions, shapes will be considered to be portioned equally unless a direction tells you otherwise. When you partition a circle and a square in two halves, each partitioned half can be written as1/2. When you equally partition a circle in 4 parts, each section can be written as 1/4.

An unequal partition is where each partitioned section is of a different size; these sections, when placed on top of each other, will not match the sections below them. When the partitioned sections combine, they form a shape.

While we may just think of these as basic geometry problems, they have a great deal of application in the real world. Most basic construction projects are centered on this concept. Consider your home or apartment it is just a set area portioned into several different rooms. How big those partitions are, determines how large an area each room becomes. As we adavance further with our math skills understanding this concept will be important for working with base ten numbers and fractions. They are especially helpful for operations between fractions and whole numbers.