**Warmup**

**Activity #1**

**Use Double Number Line Diagrams to Compare Speeds.**

In this activity, you are going to explore time and distance, to find out how long it will take 2 riders to finish a race at various constant speeds, and different distances apart. You will also investigate how long it will take a rider to overtake another at various constant speeds, and different distances apart. The distance to cover in the race is 100 meters, and the maximum speed each rider can attain is 20 miles per hour. In the applet below that you are going to use for this activity, the purple slider controls Biker 1, and the brown slider controls Biker 2.

- Use the purple slider(meters) to set BIKER 1 to 0. Also use the brown slider(meters) to set the BIKER 2 to 0.
- Set their speeds to 5 MilesPerHour.
- Make sure the timer is set to 0.
- Then, click
**GO!**The timer should start recording. - Be vigilant to click
**Stop**when BIKERS hit 100 meters, or the timer will continue recording after they finish the race. - Record the time each BIKER took to finish the race. Rounded the time to the nearest second.
- Repeat the steps above at different speeds; (10, 15, 20, 25, 30 MilesPerHour)
- Now place BIKER 2 at different distances ahead of BIKER 1 and set choose different speeds. Be flexible..
- Record your data.
- Try to draw conclusions based on the data you collect. Explore!

Suppose that the two BIKERS competed for 10 seconds, each at a constant speed. BIKER 1 covered 40 meters and BIKER 2 covered 55 meters.

(1). Who was moving faster? Explain your reasoning.

(2). How far did each person move in 1 second? If you get stuck, consider drawing double number line diagrams to represent the situations.

(3). Use data from the activity to find how far BIKER 1 would travel in 10 seconds at 12 MPH.

**Activity #2**

**Compare Speed Using the Double Number Line.**

In this exercise, you are going to use a double line diagram to answer some questions.

Lin and Diego both ran for 10 seconds, each at a constant speed. Lin ran 40 meters and Diego ran 55 meters.

- Use the double number lines below to answer the questions that follow.

**(1)**. Who was moving faster? Explain your reasoning.

**(2).** How far did each person move in 1 second? If you get stuck, consider drawing double number line diagrams to represent the situations.

**(3). **Use your data from the previous activity to find how far *you *could travel in 10 seconds at your quicker speed.

**(4).** Han ran 100 meters in 20 seconds at a constant speed. Is this speed faster, slower, or the same as Lin’s? Diego’s? Yours?

**(5).** Lin and Diego want to run a race in which they will both finish when the timer reads exactly 30 seconds. Who should get a head start, and how long should the head start be?

**Activity #3**

**Complete a Double Number Line Diagram**.

In this exercise, you are going to complete double line diagrams. Read the story carefully and complete the diagrams.

(A). A scooter travels 30 feet in 2 seconds at a constant speed.

- Complete the double number line below to show the distance the scooter travels after 1, 3, 4, and 5 seconds.

(1). What is the speed of the scooter in feet per second?

(2). A skateboard travels 55 feet in 4 seconds. Is the skateboard going faster, slower, or the same speed as the scooter?

(B). A pet owner has 5 cats. Each cat has 2 ears and 4 paws.

- Complete the double number line to show the numbers of ears and paws for 1, 2, 3, 4, and 5 cats.

**(1)**. If there are 4 cats in the room, what is the ratio of paws to ears?

**(2).** If all 5 cats are in the room, how many more paws are there than ears?

**Challenge #1**

Han ran 10 meters in 2.7 seconds. Priya ran 10 meters in 2.4 seconds.

(1). Who ran faster? Explain how you know.

(2). At this rate, how long would it take each person to run 50 meters? Explain or show your reasoning.

**Challenge #2**

**A recipe for pasta dough says, “Use 150 grams of flour per large egg.”**

(1). How much flour is needed if 6 large eggs are used?

(2). How many eggs are needed if 450 grams of flour are used?

**Challenge #3**

**The grocery store is having a sale on frozen vegetables. 4 bags are being sold for $11.96. At this rate, what is the cost of:**

(1). 1 bag?

(2). 1 bag?

(3). If there are 3 cats in the room, what is the ratio of ears to paws?

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