standard_description: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
- An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.
- An angle that turns through n one-degree angles is said to have an angle measure of n degrees.
problem_activity: Problem 1
Here are two algorithms for finding the value of 64 × 2.
|                                  Patrice’s method                                   |                                                                                                             Jerome’s method                                                                                                             |
|-------------------------------------------------------------------------------------|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| .. image:: https://d21royfkw9g4l6.cloudfront.net/uploads/2021/08/26/4-2-10-at1a.png | |https://d21royfkw9g4l6.cloudfront.net/uploads/2021/08/26/4-2-10-at1b.png|  |https://d21royfkw9g4l6.cloudfront.net/uploads/2021/08/26/4-2-10-at1b.png| image:: https://d21royfkw9g4l6.cloudfront.net/uploads/2021/08/26/4-2-10-at1b.png |
a.   How is Patrice’s method similar to and different from Jerome’s method?
b.   How do you think Jerome found the product 128?
Problem 2
Patrice solved the problem 813 × 7 using the partial products algorithm, as shown below:
[IMG]
Jerome solved in a different way from Patrice. Here is what he did:
|                      First, he found the partial product of 3 ones and 7, which is 21 ones, or 2 tens 1 one. He wrote the ones digit, 1, under the equal bar, and the 2 tens on the equal bar above the tens place in smaller handwriting.                      | Then, he found the partial product of 1 ten and 7, which was 7 tens. Because he had the 2 tens from the first partial product, he added those tens together and wrote 9 in the tens place in the product. Because he had accounted for the 2 tens from his first partial product, he crossed it off. |                                                  Finally, he found the partial product of 8 hundreds and 7, which was 56 tens. He wrote 56 in the hundreds and tens place in the product.                                                   |
|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| |https://d21royfkw9g4l6.cloudfront.net/uploads/2021/08/26/4-2-10-at2b_bGxguvo.png|  |https://d21royfkw9g4l6.cloudfront.net/uploads/2021/08/26/4-2-10-at2b_bGxguvo.png| image:: https://d21royfkw9g4l6.cloudfront.net/uploads/2021/08/26/4-2-10-at2b_bGxguvo.png |                               |https://d21royfkw9g4l6.cloudfront.net/uploads/2021/08/26/4-2-10-at2c.png|  |https://d21royfkw9g4l6.cloudfront.net/uploads/2021/08/26/4-2-10-at2c.png| image:: https://d21royfkw9g4l6.cloudfront.net/uploads/2021/08/26/4-2-10-at2c.png                                | |https://d21royfkw9g4l6.cloudfront.net/uploads/2021/08/26/4-2-10-at2d.png| * *  |https://d21royfkw9g4l6.cloudfront.net/uploads/2021/08/26/4-2-10-at2d.png| image:: https://d21royfkw9g4l6.cloudfront.net/uploads/2021/08/26/4-2-10-at2d.png |
a.   How is Patrice's method similar to and different from Jerome's method?
b.   What are the advantages and disadvantages of Patrice's method? Of Jerome's method?
Problem 3
Try using the standard algorithm to solve. If you get stuck, use an area model and/or the partial products algorithm to help. Then assess the reasonableness of your answer.
a.
$$54\times6$$
b.
$$9\times673$$
c.
$$1,605\times4$$


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