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Two rods that come together to create a rod is called complementary.

1. Take an orange rod and put a black rod side by side with it. What do you need to put end to end with the black to make it the length of the orange?

2. Which rod do you need to put with the dark green to make the length of the orange?

3. Find what you need to make the length of the orange if you start with:

Yellow rod        Blue rod         Red rod        Brown rod       Light green rod

4. Put a black rod and a light green end to end. Which rod is equivalent in length to this train?

5. Which rod do we need for the pink and dark green train? How about for the following trains:

*  blue and white?   *  red and brown?       *  dark green and pink?       * white and blue?

*  brown and red?    * red and black? *  white and brown?

6. Take any rod, then another smaller one. Find which rod must be put with the smaller one to make the length of the longer one.

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A staircase is when you stack one of every rod in a sequence.

1. Make a staircase of all the rods.

- Which rod is the biggest?

- Which is the smallest?

- Which comes before the biggest?

- Which comes before the smallest?

2. Look at the staircase. Which rods do we need if we want to make every step level with the orange rod?  Find them and put them in their place.

3. Take away the extra rods to return the original staircase. Can you tell what is needed for the blue? For the yellow? For the light green?

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Patterns is a train that is equivalent to a rod. A complete pattern is when you find all the possible trains for a rod.

1. Make a pattern for the yellow rod. (Find all the trains of all possible lengths.)

2. Make a complete pattern for the following rods:

* Light green

* Purple

* Dark green rod

3. Mystery rod: Which rods have the following trains in their patterns?

*  Red, white, red, white, red

*  Red, yellow, white

* Light green, red, white

* Light green, red, red, light green

*  White, light green, purple

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Trains are formed by putting rods end to end. The smallest train you can make has two rods.

1. Make as many trains as you can. Name the trains using the color names.

2. Make a train of two rods equivalent in length to the brown rod.

3. Make a train of two rods equivalent in length to the blue rod.

4. Can you make trains of more than two rods equivalent in length to the Orange rod? Black rod?