homework & practice 2 5

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Unit 1: Polynomial arithmetic

Unit 2: complex numbers, unit 3: polynomial factorization, unit 4: polynomial division, unit 5: polynomial graphs, unit 6: rational exponents and radicals, unit 7: exponential models, unit 8: logarithms, unit 9: transformations of functions, unit 10: equations, unit 11: trigonometry, unit 12: modeling.

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2.5: Homework

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• Julie Harland
• MiraCosta College
• Submit homework separately from this workbook and staple all pages together. (One staple for the entire submission of all the unit homework)
• Start a new module on the front side of a new page and write the module number on the top center of the page.
• Answers without supporting work will receive no credit.
• Some solutions are given in the solutions manual.
• You may work with classmates but do your own work.

Let U = {a, c, e, m n, r, u, v, w, x, z} with subsets A , B , C and D defined below: A = {m, n, r, u, x} B = { a, c , r, u, x} C = {e, v, w, x, z } D = {a, c, z} Using correct notation, find the following, show all work

Let U = {a, c, e, m n, r, u, v, w, x, z} with subsets A , B , C defined as follows:

Draw a Venn Diagram and place each element of the universe in the correct region

Use deMorgan's Laws to rewrite each of the following:

Use the distributive properties of sets to rewrite each of the following:

A survey was given to determine which of the three beverages (tea, milk and/or coffee) people drank each day. The results were as follows:

Take out your A–blocks and arrange them into subsets so that each subset only contains elements that have the same size and color.

Let A , B and C represent any sets. Answer True or False for the following statements. In order for a statement to be true, it must always be true. For each False statement, give an example of why it is False.

Draw a Venn diagram and shade in the region that represents the following

Identify the shaded area of each Venn diagram by set notation.

List all possible subsets for each set given.

Let A = {1, 2, 4}, B = {(a, c), 5} and C = {x}. Find the following:

Use your A–blocks to do this problem. Let X represent the set of large circles and Y represent the set of red circles. Using set notation and abbreviations, find the following:

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Poland's kids rejoice over new rules against homework. Teachers and parents aren't so sure

WARSAW, Poland — Ola Kozak is celebrating. The 11-year-old, who loves music and drawing, expects to have more free time for her hobbies after Poland’s government ordered strict limits on the amount of homework in the lower grades.

“I am happy,” said the fifth grader, who lives in a Warsaw suburb with her parents and younger siblings. The lilac-colored walls in her bedroom are covered in her art, and on her desk she keeps a framed picture she drew of Kurt Cobain.

“Most people in my class in the morning would copy the work off someone who had done the homework or would copy it from the internet. So it didn’t make sense,” she said.

The government of Prime Minister Donald Tusk enacted the ban against required homework this month amid a broad discussion about the need to modernize Poland’s education system, which critics say puts too much emphasis on rote learning and homework, and not enough on critical thinking and creativity.

Under the decree, teachers are no longer to give required homework to kids in the first to third grades. In grades four to eight, homework is now optional and doesn’t count towards a grade.

Not everyone likes the change – and even Ola’s parents are divided.

“If there is something that will make students enjoy school more, then it will probably be good both for the students and for the school,” said her father, Pawel Kozak.

His wife, Magda Kozak, was skeptical. “I am not pleased, because (homework) is a way to consolidate what was learned,” she said. “It helps stay on top of what the child has really learned and what’s going on at school.”

(Ola’s brother Julian, a third grader, says he sees both sides.)

Debates over the proper amount of homework are common around the globe. While some studies have shown little benefit to homework for young learners, other experts say it can help them learn how to develop study habits and academic concepts.

Poland’s educational system has undergone a number of controversial overhauls. Almost every new government has tried to make changes — something many teachers and parents say has left them confused and discouraged. For example, after communism was thrown off, middle schools were introduced. Then under the last government, the previous system was brought back. More controversy came in recent years when ultra-conservative views were pushed in new textbooks.

For years, teachers have been fleeing the system due to low wages and political pressure. The current government is trying to increase teacher salaries and has promised other changes that teachers approve of.

But Sławomir Broniarz, the head of the Polish Teachers’ Union, said that while he recognized the need to ease burdens on students, the new homework rules are another case of change imposed from above without adequate consultation with educators.

“In general, the teachers think that this happened too quickly, too hastily,” he said.

He argued that removing homework could widen the educational gaps between kids who have strong support at home and those from poorer families with less support and lower expectations. Instead, he urged wider changes to the entire curriculum.

The homework rules gained impetus in the runup to parliamentary elections last year, when a 14-year-old boy, Maciek Matuszewski, stood up at a campaign rally and told Tusk before a national audience that children “had no time to rest.” The boy said their rights were being violated with so much homework on weekends and so many tests on Mondays.

Tusk has since featured Matuszewski in social media videos and made him the face of the sudden change.

Education Minister Barbara Nowacka said she was prompted by research on children’s mental health. Of the various stresses children face, she said, “the one that could be removed fastest was the burden of homework.”

Pasi Sahlberg, a prominent Finnish educator and author, said the value of homework depends on what it is and how it is linked to overall learning. The need for homework can be “very individual and contextual.”

“We need to trust our teachers to decide what is good for each child,” Sahlberg said.

In South Korea, homework limits were set for elementary schools in 2017 amid concerns that kids were under too much pressure. However, teenagers in the education-obsessed country often cram long into the night and get tutoring to meet the requirements of demanding school and university admission tests.

In the U.S., teachers and parents decide for themselves how much homework to assign. Some elementary schools have done away with homework entirely to give children more time to play, participate in activities and spend time with families.

A guideline circulated by teachers unions in the U.S. recommends about 10 minutes of homework per grade. So, 10 minutes in first grade, 20 minutes in second grade and so on.

The COVID-19 pandemic and a crisis around youth mental health have complicated debates around homework. In the U.S., extended school closures in some places were accompanied by steep losses in learning , which were often addressed with tutoring and other interventions paid for with federal pandemic relief money. At the same time, increased attention to student wellbeing led some teachers to consider alternate approaches including reduced or optional homework.

It’s important for children to learn that mastering something “usually requires practice, a lot of practice,” said Sahlberg, in Finland. If reducing homework leads kids and parents to think school expectations for excellence will be lowered, “things will go wrong.”

AP writers Jan M. Olsen in Copenhagen, Denmark, Michael Melia in Hartford, Connecticut, and Hyung-jin Kim in Seoul, South Korea, contributed.