standard_description: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.
problem_activity: Problem 1
Here are two algorithms for finding the value of 64 × 2.
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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:
{"table": [{"_attributes": {"class": ["table", "table-bordered"], "style": "width: 100%;"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "vertical-align: top;"}, "_value": "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."}, {"_attributes": {"style": "vertical-align: top;"}, "_value": "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."}, {"_attributes": {"style": "vertical-align: top;"}, "_value": "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."}]}, {"td": [{"p": [{"_attributes": {"style": "text-align: center;"}, "img": [{"_attributes": {"src": "https://d21royfkw9g4l6.cloudfront.net/uploads/2021/08/26/4-2-10-at2b_bGxguvo.png", "style": "width: 75px; height: 95px;"}}]}]}, {"p": [{"_attributes": {"style": "text-align: center;"}, "img": [{"_attributes": {"src": "https://d21royfkw9g4l6.cloudfront.net/uploads/2021/08/26/4-2-10-at2c.png", "style": "width: 75px; height: 95px;"}}]}]}, {"_attributes": {"style": "vertical-align: bottom;"}, "p": [{"_attributes": {"style": "text-align: center;"}, "img": [{"_attributes": {"src": "https://d21royfkw9g4l6.cloudfront.net/uploads/2021/08/26/4-2-10-at2d.png", "style": "width: 75px; height: 95px;"}}], "em": [{}]}]}]}]}]}]}
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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