Develop a unit of learning at the end of which learners should be able to: reduce any angle in the first quadrant of a Cartesian plane to a difference of 90 and an acute angle.

I have tried it as follows:
1. write down any three acute angles.
2. draw the angles in a Cartesian plane
3. express the angle in terms of 90-A
4. use your expression to find three acute angles identified in 1 and reflect on your answer

Here's a modified version of your unit of learning:

1. Define the first quadrant of a Cartesian plane and explain that angles in this quadrant range from 0 to 90 degrees.
2. Introduce the concept of reducing an angle to a difference of 90 and an acute angle. Explain that this means finding the difference between the given angle and 90, resulting in an acute angle.
3. Provide examples of angles in the first quadrant and demonstrate how to reduce them to a difference of 90 and an acute angle using the formula: acute angle = 90 - given angle.
4. Guide learners through practicing this process with additional examples.
5. Present a set of exercises where learners are given different angles in the first quadrant and they need to reduce them to a difference of 90 and an acute angle.
6. Provide feedback and discuss the solutions to the exercises, highlighting any common mistakes or misconceptions.
7. Encourage learners to reflect on their understanding of the concept and ask them to explain the reasoning behind their answers.
8. Summarize the key points and highlight the importance of being able to reduce angles in the first quadrant to a difference of 90 and an acute angle in various applications.
9. Assess learners' understanding through a quiz or a practical task where they need to apply their knowledge to solve problems related to reducing angles in the first quadrant.
10. Provide additional resources or practice opportunities for learners who want to further improve their ability to reduce angles in the first quadrant.

To develop a unit of learning to achieve the goal of reducing any angle in the first quadrant of a Cartesian plane to a difference of 90 and an acute angle, you can follow the steps you have outlined. Here's a more detailed explanation of each step:

1. Start by selecting three acute angles. For example, you can choose 30 degrees, 45 degrees, and 60 degrees. These angles should all be in the first quadrant of the Cartesian plane.

2. Next, draw the angles on a Cartesian plane. Ensure that the initial side of the angle coincides with the positive x-axis.

3. Express each angle in terms of 90 - A, where A represents the given angle. This step involves subtracting the given angle from 90 degrees.

- For example, if the given angle is 30 degrees, you can express it as 90 - 30 = 60 degrees.

4. Once you have the expressions for each angle, use them to find the three acute angles you identified in step 1. Substitute the given angles into the expression and simplify.

- Continuing with the previous example, 90 - 30 = 60 degrees. Reflecting on this answer confirms that the difference between 90 degrees and 30 degrees is indeed 60 degrees, and it is an acute angle.

By following these steps and using different acute angles, learners can practice and understand how to reduce any angle in the first quadrant of a Cartesian plane to a difference of 90 degrees and an acute angle.