# ﻿Introducing Double Number Line Diagrams

Warmup

Activity #1

Introduce the Double Number Line Diagram by Mixing Paint.

A double number line diagram uses a pair of parallel number lines to represent equivalent ratios. The locations of the tick marks match on both number lines. The tick marks labeled 0 line up, but the other numbers are usually different.

In this activity, you are going to use the applet below to label a double number line diagram that will represent the paint mixture and equivalent amounts. Click on the icons below the applet to navigate through all the tools that are available to you. • On the double number line, label the tick marks to represent amounts of red and blue paint used to make batches of this shade of purple paint.
• To access any tool that you may need in the applet, click on icon. In order to deselect a tool, just click on another icon.

(1). How many batches are made with 12 cups of red paint?

(2). How many batches are made with 6 cups of blue paint?

Activity #2

Create Equivalent Ratios.

In this exercise, you are going to answer a few questions based on the following drink mixture: • Study the mixture and respond to the questions that follow.

(1). How can we tell that 4 : 1 and 12 : 3 are equivalent ratios?

(2). How are these representations the same? How are these representations different?

(3). How many teaspoons of drink mix should be used with 3 cups of water?

(4). How many cups of water should be used with 16 teaspoons of drink mix?

(5). What numbers should go in the empty boxes on the double number line diagram? What do these numbers mean?

Activity #3

Explore the Double Number Line.

In this activity, you are going to use the applet below to explore the double number line. The default ratio here is 2:5. Just follow the instructions below. • With the 2 boxes checked, verify that the corresponding numbers on the both scales are in the same ratio.​
• To see intermediate corresponding ratios, move the blue slider on both scales. ​
• To see intermediate corresponding ratios, move the blue slider on both scales. ​
• To change the ratio, enter a different number in Label1 and Label2, then press the ENTER key on your keyboard. Observe the new ratio display on the two scales. ​
• Again to see intermediate corresponding ratios, move the blue slider on both scales. ​
• Repeat steps 3 and 4 as you keep exploring..

Challenge #1

Challenge #2

Draw a parallelogram that is not a rectangle that has an area of 24 square units. Explain or show how you know the area is 24 square units.

Challenge #3

Recall that a perfect square is a number of objects that can be arranged into a square. For example, 9 is a perfect square because 9 objects can be arranged into 3 rows of 3. 16 is also a perfect square, because 16 objects can be arranged into 4 rows of 4. In contrast, 12 is not a perfect square because you can’t arrange 12 objects into a square.

(1). How many whole numbers starting with 1 and ending with 100 are perfect squares?

(2). What about whole numbers starting with 1 and ending with 1,000?