Seventh Grade Tasks Weekly Enrichment Teacher Materials ...

Seventh Grade Problem Solving Tasks- Weekly Enrichment

Teacher Materials

Summer Dreamers

SOLVING MATH PROBLEMS KEY QUESTIONS WEEK 1

By the end of this lesson, students should be able to answer these key questions:

How do you generate equivalent rational numbers?

How do you compare rational numbers?

MATERIALS: Warm-Up: Who is Correct? Activity Master: Number Line ? assembled and posted on the wall

For each student: Fractions, Decimals, and Percents, Oh My! Race Car Stat Evaluate: Equivalent Rational Numbers

For each group of 2 students: Activity Master: Fractions, Decimals, and Percents ? cut apart, 1 set of cards per group

TEACHER TOOLS

ENGAGE: The Engage portion of the lesson is designed to access students' prior knowledge of percent models. This phase of the lesson is designed for groups of 2 students. (10 minutes)

1. Distribute "Who is Correct?" warm-up. 2. Prompt students to individually complete the warm-up "Who is

Correct?" 3. Upon completion of the warm-up, prompt students to share and justify

their solutions with a partner. 4. Actively monitor student work and ask facilitating questions when

appropriate.

Facilitating Questions:

What is the question asking you to do?

Answers may vary. Possible answer: Determine who is correct by determining the percent of the flag that is shaded.

What do you know?

Answers may vary. Possible answer: I know the answer given by each person, and I was given a picture of the flag.

What do you need to know?

Answers may vary. Possible answer: I need to know the percent of the flag that is shaded in order to determine who is correct.

What strategy could you use to determine who is correct?

Answers may vary. Possible answer: I could find the percent of the flag that is shaded then compare my answer to the answer of each person to determine who is correct.

How many squares make up the flag?

32

How many squares are shaded?

12

 How could you write a ratio that compares the number of shaded squares to the total number of squares on the flag?

Answers may vary. Possible answer: 3 to 8, 3:8, 3 out of 8, 3/8

What do you know about percents?

Answers may vary. Possible answer: I know that percents are how many out of a 100.

How could you use the ratio of the shaded squares to the total number of squares to help you determine what percent of the flag is shaded?

Answers may vary. Possible answer: I know the ratio of shaded squares to total squares is 3/8; therefore, I could use a factor of change to rewrite the ratio as a fraction with a denominator that is a power of 10, such as 1000.

What factor of change could you use to change 3/8 to thousandths?

Multiply by 125

What is 3/8 written as thousandths?

375/100

How could you rewrite 375/1000 as a percent?

Answers may vary. Possible answer: Multiply the numerator and the denominator by 1/10 in order to generate an equivalent fraction with a denominator of 100, 37.5/100. Then I could use the numerator as my percent, since percent means out of 100.

EXPLORE: The Explore portion of the lesson provides the student with an opportunity to be actively involved in investigating equivalent rational numbers. This phase of the lesson is designed for groups of 2 students. (25 minutes)

1. Distribute 1 set of Activity Master: Fractions, Decimals, and Percents to each group of students and Fractions, Decimals, and Percents, Oh My! to each student. (NOTE: Have Activity Master cards pre-cut for student use.)

2. Prompt students to complete Fractions, Decimals, and Percents, Oh My! 3. Actively monitor student work and ask facilitating questions when

appropriate.

Facilitating Questions:

What information is found on the cards?

Answers may vary. Possible answer: The cards contain rational numbers written in different forms.

Rewriting Fractions as Decimals

How could rewriting each fraction as hundredths help you write the decimal representation of the fraction?

Answers may vary. Possible answer: Decimals are just fractions that have denominators that are 10, 100, 1000, etc. (powers of 10). So if I rewrite the fraction as hundredths, I could write the decimal by using place value.

What factor of change could you use to rewrite this fraction as hundredths?

Answers may vary.

Rewriting Fractions as Percents

How could rewriting each fraction as hundredths help you write the percent representation of the fraction?

Answers may vary. Possible answer: Percents are just fractions that have denominators of 100. So if I rewrite the fraction as hundredths, I could write the percent by using the numerator.

What factor of change could you use to rewrite this fraction as hundredths?

Answers may vary.

x 125 .

62.5%

Rewriting Decimals as Percents

How could rewriting each decimal as a fraction help you write the decimal as a percent?

Answers may vary. Possible answer: Place value is based on powers of 10: 10, 100, 1000, etc. So if I rewrite the decimal as a fraction, I could apply a factor of change to the fractions to rewrite the fractions as hundredths then I could write the percent by using the numerator.

What factor of change could you use to rewrite this fraction as hundredths?

Answers may vary.

Rewriting Decimals as Fractions

How could place value help you write each decimal as a fraction in simplest form?

Answers may vary. Possible answer: Place value is based on powers of 10: 10, 100, 1000, etc. So I could rewrite the decimal as a fraction with a denominator of tenths, hundredths, or thousandths then simplify.

Rewriting Percents as Fractions

What procedures could be used to write a percent as a fraction in simplest form?

Answers may vary. Possible answer: Percents are just fractions that have denominators of 100. So if I rewrite the fraction as hundredths, then I could simplify.

Rewriting Percents as Decimals

How could rewriting a percent as a fraction help you write a percent as a decimal?

Answers may vary. Possible answer: Percents are just fractions that have denominators of 100. So if I rewrite the percent as a fraction, I could write the decimal by using place value.

Ordering from Least to Greatest

Which representation is the easiest to use to help you determine which rational number represents the largest amount? Why?

Answers may vary. Possible answer: To compare the rational numbers, I could use the fractions written as hundredths, the percent, or the decimal form to compare easily.

Which representation is the easiest to use to help you determine which rational number represents the smallest amount? Why?

Answers may vary. Possible answer: To compare the rational numbers, I could use the fractions written as hundredths, the percent, or the decimal form to compare easily.

Comparing 83.5%

How could you determine which of the numbers are equivalent to 83.5%?

Answers may vary. Possible answer: I could rewrite 83.5% as a fraction and as a decimal and compare my values with the values of the answer choices.

What process could you use to rewrite 83.5% as a fraction with a denominator of 100?

Answers may vary. Possible answer: Percents are just fractions that have denominators of 100. So I could rewrite 83.5% as a fraction where 83.5 is the numerator and 100 is the denominator.

What process could you use to rewrite 83.5% as a fraction with a denominator of 1000?

Answers may vary. Possible answer: I could rewrite 83.5% as a fraction where 83.5 is the numerator and 100 is the denominator then use a factor of change to rewrite the fraction as thousandths.

What factor of change could be used to convert 83.5/100 to thousandths?

10

What process could you use to rewrite 83.5% as a decimal?

Answers may vary. Possible answer: I could rewrite 83.5% as a fraction with a denominator of 1000 then write the decimal by using place value. 0.835

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