Math Lab Activity

– Dot Paper Fraction

You’re going to visually explore fractional parts and equivalent fractions using dot paper.

Objective:

This activity will help us better understand fractions and how they relate to each other. you’ll work through examples together and then you’ll have a chance to solve problems on your own.

Materials Needed:

• Dot diagram sheet 
• Photocopy of the ‘4 by 4 Dot Paper Diagrams’ 
• Pencil

Exploring Fractions on a 3 by 4 Rectangle:

Imagine we have a rectangle that measures 3 units in width and 4 units in height. This rectangle will be our canvas for understanding fractions visually. Let’s see how we can represent different fractions on this diagram by shading in a portion of the rectangle.

This visual representation helps us see how fractions are parts of a whole. By shading in certain areas of the rectangle, we can understand fractions like 1/2, 1/3, 2/3, 1/4, and 3/4 better. Remember, fractions are a way of expressing how many parts of a whole we have, and this dot paper method can make it easier to grasp.

• Fractional Parts on Dot Paper:
  1. Watch as I explain how to represent fractions on dot paper. Remember, each dot represents a part of a whole.
  2. Follow along on your ‘4 by 4 Dot Paper Diagrams’ page and draw the fractions as I show them on the overhead projector.

Equivalent Fractions

Understanding Equivalency: Sometimes, fractions might look different, but they can still represent the same amount. Let’s talk about the idea of equivalent fractions. Imagine you have a rectangle divided into six equal parts and two of those parts are shaded. That’s 2 out of 6 parts, which can be written as 2/6.

Exploring Equivalency: But did you know that 2/6 is the same as 1/3? Let’s see how. If you take your 2/6 shaded rectangle and divide each of those parts into two equal parts, you end up with a total of twelve parts. Now, shade in four of those parts. You’ll see that 4 out of 12 parts are shaded, which can be written as 4/12.

Equivalent Fractions: Now, look at the shaded parts for both 2/6 and 4/12. They’re the same! Both represent the same amount – one-third (1/3) of the whole shape. So, 2/6 is equal to 1/3, and 4/12 is also equal to 1/3.

Equivalent Fractions on Dot Paper:
1. Now, let’s explore equivalent fractions using dot paper.
2. Watch carefully as I show how to represent equivalent fractions on dot paper.
3. Try drawing the equivalent fractions on your ‘4 by 4 Dot Paper Diagrams’ page on your own.

• Exploration: Take your ‘4 by 4 Dot Paper Diagrams’ page and draw a rectangle. Shade in 2 out of 6 parts to represent 2/6. Then, divide each part into two and shade in 4 out of the 12 smaller parts. You’ll see that both shaded portions are the same and represent 1/3.

• Discovering Equivalency: Now, try to discover other pairs of fractions that are equivalent, just like 2/6 and 1/3. Divide and shade on the dot paper to see if you can find more examples of fractions that are equal to each other.

Exploring Fractions with Shaded Polygons on Dot Paper:

In this part of the activity, we will learn how to determine fractional parts of polygons that are shaded on dot paper. Follow these steps to understand the process better:

Step 1: Outline the Polygon and Shade a Portion
– Begin by drawing any polygon on the dot diagram. It could be a triangle, square, or any other shape you like.
– Shade a specific portion of the polygon. This shaded part represents the fraction we want to find out.

Step 2: Dividing the Polygon into Equal Sections
– Look at the shaded region and use it as a guideline to divide the entire polygon into equal sections. These sections should be drawn horizontally or vertically, connecting the dots.
– Count the total number of these equal sections. We’ll use this count as the denominator of the fraction.

Step 3: Counting the Shaded Sections
– Count the number of sections that are shaded within the polygon.
– This count will be the numerator of the fraction.

Step 4: Finding the Fraction
– The fraction that represents the shaded portion of the polygon is determined by the number of shaded sections (numerator) over the total number of equal sections (denominator).
– Write the fraction in the form numerator/denominator.

Step 5: Simplifying (Reducing) the Fraction
– In some cases, the fraction might be simplified or reduced to its simplest form. This means finding a common factor for both the numerator and denominator and dividing them by it.

Example:
Let’s say you’ve drawn a square on the dot paper and shaded 2 out of the 4 equal sections. Here’s how you would find the fraction:

– Denominator (total sections): 4
– Numerator (shaded sections): 2

So, the fraction representing the shaded portion is 2/4. But we can simplify it by dividing both the numerator and denominator by 2: 2 ÷ 2 / 4 ÷ 2 = 1/2.

Remember, the key is to count and use the equal sections you’ve drawn as a guide to find the fraction that represents the shaded part of the polygon. If you have any questions or if things seem tricky, don’t worry! Feel free to ask for help, and remember that practice will make this process easier and more intuitive.

Dot Paper Fraction Problems Handout:
1. You’ve seen how to work with fractions on dot paper through our examples. Now it’s your turn!
2. I’ll hand out the ‘Dot Paper Fraction Problems’ handout. Work with a partner to solve the problems using the dot paper diagrams and the techniques we’ve learned.
3. Remember the rule: Your polygons must have straight sides formed by connecting two dots with a line segment.

Remember, this activity is about exploring and understanding fractions visually, so have fun, and don’t hesitate to ask questions if you need help. Enjoy the exploration!

Ignite Your Mathematical Mind:

• If you’re feeling confident, you can take your understanding further by using additional copies of the ‘4 by 4 Dot Paper Diagrams’ page.
• Create your own problems involving fractions and equivalent fractions. Solve them on the dot paper.
• Feel free to challenge yourself by exploring different shapes and more complex fractions.