options: Operations & Algebra: students learn to solve problems using algebraic thinking and operations such as addition, subtraction, multiplication, and division. They may learn to identify and explain arithmetic patterns, evaluate or manipulate numerical expressions, and reason with equations and inequalities.

Measurement & Data: students learn to work with data and measure attributes such as time, money, length, area, and volume. They may learn to compare measurements to operations and convert between different units of measure.

Statistics & Probability: students learn to analyze and produce data distributions, and build understanding of univariate and bivariate data. They learn to interpret data, make statistical inferences, justify conclusions, understand rules of probability, and use probability to make decisions.

Functions: students learn to define, use, and evaluate functions to model relationships between quantities.

Geometry: students learn to classify geometric figures by their properties, and understand and compare the relationships between them. Students develop and use formulas to compute lengths, areas, and volumes, and they use transformations to generate new shapes and compare existing ones. Geometry can be studied with and without coordinates.

Number & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.

Number Systems and Quantity: students learn to understand the complex number system and reason quantitatively.

Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.

Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.

Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.

Modeling: students learn to choose and use appropriate mathematics and statistics to analyze real-world empirical situations, improve decisions, and report on their conclusions and the reasoning behind them.
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.
$$1,605\times4$$


correct_option_index: 8