This problem pertains to Cuisenaire Rods:
1-white
2-red
3-green
4-purple
5-yellow
6-dark green
7-black
8-brown
9-blue
10-orange
Question:
(a) If an all-brown train is equal in length to an all-orange train, what can be said about the number of brown rods compared to the number of orange rods?
(b) If a number can be represented by an all-red train, and an all-black train, it has at least eight factors. Name these factors.
(c) What is the smallest number of red rods for which an all-red train is equal in length to an all-blue train?
wow, haven't seen Cuisenaire Rods since the early 60's
Don't tell me they are still using these.
To solve these problems using Cuisenaire rods, you need to understand the relationships between the different colors and the corresponding numbers represented by them. Here are the explanations for each question:
(a) If an all-brown train is equal in length to an all-orange train, we need to find the number of brown rods compared to the number of orange rods. Here's how you can figure it out:
- Look at the list of Cuisenaire rods colors and numbers given.
- Find the lengths of all-brown and all-orange trains in terms of the number of rods. Here, since all the rods have different numbers, you can count the rods directly.
- Based on the list, all-brown train refers to 8 brown rods, and all-orange train refers to 10 orange rods.
- Since the two trains are equal in length, it means that the number of brown rods is equal to the number of orange rods. So, we can say that there are 8 brown rods compared to 10 orange rods.
(b) If a number can be represented by an all-red train and an all-black train, it has at least eight factors. To identify these factors, follow these steps:
- Look at the list of Cuisenaire rods colors and numbers.
- The all-red train refers to 2 red rods, and the all-black train refers to 7 black rods.
- To determine the factors, multiply the number represented by the all-red train (2) with the number represented by the all-black train (7). This gives us 2 * 7 = 14.
- Now, think of all possible factors of 14. Factors are the numbers that divide evenly into another number. In this case, the factors of 14 are 1, 2, 7, and 14.
- Hence, a number represented by an all-red train and an all-black train has at least eight factors, which are 1, 2, 7, 14, -1, -2, -7, -14.
(c) To find the smallest number of red rods for which an all-red train is equal in length to an all-blue train, we need to compare the lengths of these two trains. Here's how you do it:
- Refer to the list of Cuisenaire rods colors and numbers.
- The all-red train refers to 2 red rods, and we need to find the smallest number of red rods for which an all-red train is equal in length to an all-blue train.
- Observe the list again, and we can see that an all-blue train refers to 9 blue rods.
- Since we want the two trains to be equal in length, the number of red rods must also be equal to the number of blue rods.
- Therefore, the smallest number of red rods required is 9.