Common Core State Standards

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1 Common Core State Standards Common Core State Standards 7.NS.2 7.NS.2d 7.EE.3 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $ If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Mathematical Practices 1, 3, and 4 are aspects of mathematical thinking that are emphasized in every lesson. Students are given opportunities to be persistent in their problem solving, to express their reasoning, and apply mathematics to realworld situations. Exercises 18, 20, and 21 focus on Mathematical Practice 1 Make sense of problems and persevere in solving them. Exercises 19 focuses on Mathematical Practice 7 Look for and make use of structure. Exercise 22 focuses on Mathematical Practice 3 Construct viable arguments and critique the reasoning of others. Exercise 23 focuses on Mathematical Practice 4 Model with mathematics. Exercise 35 focuses on Mathematical Practice 6 Attend to precision. Printed by: Nicole Sladich Page 1 of 14 Printed on 11/04/ :13 PM

2 1 Launch the Lesson Focus narrowing the scope Objective Write fractions as terminating or repeating decimals and write decimals as fractions. 7.NS.2, 7.NS.2d, 7.EE.3 Coherence Previous Students used models to describe relationships between rational numbers. connecting within and across grades Now Students write rational numbers as decimals and fractions. Next Students compare and order rational numbers by writing them in the same form. Rigor pursuing concepts, fluency, and applications See the Levels of Complexity chart in the Practice and Apply section. Lesson Vocabulary repeating decimal bar notation terminating decimal As students enter the classroom, have them complete the Common Core Quick Check to review and assess the skills presented in the previous lesson. Engage Explore Explain Elaborate Evaluate Ideas for Use You may wish to launch the lesson using a whole group, small group, think-pair-share activity, or independent activity. Pairs Discussion Have students work in pairs to create and match (face-up) fraction and decimal cards that have equivalent values. 1, 5 Alternate Strategy Have students work in pairs to create a fractiondecimal equivalence chart with denominators 2 10 to detect a pattern for terminating and repeating decimals 1, 8 Resources Common Core Quick Check: Terminating and Repeating Decimals Printed by: Nicole Sladich Page 2 of 14 Printed on 11/04/ :13 PM

3 2 Teach the Concept Focus: Mathematical Background When the denominator of a fraction is a factor or a multiple of 10, the fraction can be written as a decimal by using mental math and place value. For classroom presentation, use the Step-by-Step Examples to demonstrate the examples from the Student Edition. Engage Explore Explain Elaborate Evaluate Ask the scaffolded questions for each example to differentiate instruction. 1. Write fractions as decimals. What is in word form? seventy-four hundredths Is the denominator a power of 10? Explain. yes; 100 = 10 2 How many decimal places will have to the right of the decimal point? 2 If was written in simplest form, could you still write it as the same decimal? yes; = 0.74 Need Another Example? Write as a decimal Write fractions as decimals. Is 20 a power of 10? Explain. no; 20 is a multiple of 10 How can you write as a decimal? Write an equivalent fraction with a denominator that is a power of 10. What is another way to write as a decimal? Sample answer: Divide the numerator by the denominator. Printed by: Nicole Sladich Page 3 of 14 Printed on 11/04/ :13 PM

4 How do you know that your answer is correct? Sample answer: Simplify the fraction to yield. Need Another Example? Write as a decimal Write mixed numbers as decimals. What place value will 5 represent in the decimal? ones How can you think of a mixed number as a sum? A mixed number is the sum of the whole number part and the fraction part. Describe another way you could write as a decimal. Sample answer: Write it as an improper fraction. Then divide the numerator by the denominator. Need Another Example? Write as a decimal Write fractions as decimals using division. Which number will be the dividend? the numerator, 3 Why do we annex zeros after 3? 12 is greater than 3 What type of decimal is 0.375? terminating Why did the division stop? The remainder was zero. Write the fractions,,,,, and, as decimals. Then describe the pattern , 0.25, 0.5, 0.625, 0.75, 0.875; Sample answer: Each decimal increases by for every numerator increase of 1, when the denominator is 8. Need Another Example? Write as a decimal Write fractions as decimals using division. Printed by: Nicole Sladich Page 4 of 14 Printed on 11/04/ :13 PM

5 Is the decimal negative or positive? negative Can we divide without the negative sign? yes; Then place the negative sign in the answer. What type of decimal is 0.025? terminating Why did the division stop? The remainder was zero. Is there another method to use? Yes, write an equivalent fraction with the denominator as a power of 10 (103). Need Another Example? Write as a decimal Write a fraction as a repeating decimal. Why will the division never end? The digit 7 repeats, so there will always be a remainder. How can you indicate that a decimal repeats? use bar notation over the repeating number(s) Describe another method to use. Sample answer: When the denominator of a fraction is 9, the resulting decimal repeats the digit of the numerator. Need Another Example? Write as a decimal. 7. Write a decimal as a fraction. What decimal represents the amount of goldfish? 0.15 Express this decimal in word form. fifteen hundredths How can you write fifteen hundredths as a fraction in simplest form? Place the numerator 15 over the denominator 100 and then divide both by their GCF, 5. What percentage of fish in the aquarium are Molly fish? Explain. 0.2 = or 20% What type of fish is the most common in the tank? Explain. Angelfish; 0.40 is the greatest value in the chart. Need Another Example? Jorge read that the part of his favorite cereal that was whole grain wheat is Determine what fraction of his cereal is whole grain wheat. Write in simplest form. Use the animation Terminating Decimals with Example 7. Printed by: Nicole Sladich Page 5 of 14 Printed on 11/04/ :13 PM

6 1. 2. Alternate Teaching Strategy If students do not understand changing mixed numbers to decimals, Then use one of these reteach options: Quick Review Math Handbook, pp Have students change the mixed number to an improper fraction and then divide the numerator by the denominator. Formative Assessment Use these exercises to assess students' understanding of the concepts in this lesson. below. If some of your students are not ready for assignments, use the differentiated activities Roundrobin Have students go around in a circle verbally generating common fraction-decimal equivalents. 1, 7 Trade-a-Problem Have students write their own real-world problem that requires writing a fraction-decimal equivalent. Have them trade with a partner to solve each other s problem. Have them verbally discuss and resolve any differences. 1, 4, 7 Tips for New Teachers Mental Math Encourage students to use mental math whenever possible when writing fractions as decimals. Have them first ask themselves whether the denominator of a fraction is a factor of 10 (or of 100 or 1,000). If it is, by what number can they multiply the denominator to get a power of ten? Once they multiply the numerator and denominator by that number, they will have an equivalent fraction that can be written as a decimal by using place value. Resources Virtual Manipulatives Terminating Decimals Fractions as Decimals Fractions as Decimals Mixed Numbers as Decimals Write a Fraction as a Decimal Using Division Write a Fraction as a Decimal Using Division Write a Fraction as a Repeating Decimal Real-World Example: Write a Decimal as a Fraction Use Mental Math: Fractions as Decimals Use Division: Fractions as Decimals Use Division: Fractions as Decimals Write a Repeating Decimal Write Fractions as Repeating Decimals Write Fractions as Repeating Decimals Real-World Example: Write a Decimal as a Fraction etoolkit Hot Topic 2-5: Naming and Ordering Decimals Printed by: Nicole Sladich Page 6 of 14 Printed on 11/04/ :13 PM

7 3 Practice & Apply Engage Explore Explain Elaborate Evaluate Independent Practice and Extra Practice The Independent Practice pages are meant to be used as the homework assignment. The Extra Practice page can be used for additional reinforcement or as a second-day assignment. Levels of Complexity The levels of the exercises progress from 1 to 3, with Level 1 indicating the lowest level of complexity. Suggested Assignments You can use the table below that includes exercises of all complexity levels to select appropriate exercises for your students' needs. Differentiated Homework Options Approaching Level 1 17, 19, 22, 23, 36, 37 On Level 1 17 odd, 18, 19, 22, 23, 36, 37 Beyond Level 18 23, 36, 37 practice. can provide additional remediation support with personalized instruction and Create Your Own Homework Online esolutionsmanual can be used to create worksheets for the suggested assignments above, or to create your own worksheets for differentiated homework or review. The following worksheets are also available for additional homework practice: The Skills Practice editable worksheet provides students with additional practice in the skills taught in this lesson. The Homework Practice editable worksheet helps students practice skills in this lesson and use those skills to solve problems. The Problem-Solving Practice editable worksheet helps students become better problem solvers by providing frequent opportunities to solve real-world problems. The Extra Practice worksheet provides additional practice for the skills taught in this lesson. The Step-by-Step Solutions provide a worked out solution for selected exercises from the Independent Practice in the Student Edition. Printed by: Nicole Sladich Page 7 of 14 Printed on 11/04/ :13 PM

8 Common Error Students may have trouble with bar placement on repeating digits. Have students circle the repeating digits in the quotient and only place the bar over the circled digits. Resources Step by Step Solutions: Terminating and Repeating Decimals Skills Practice: Terminating and Repeating Decimals Skills Practice Answers: Terminating and Repeating Decimals Homework Practice: Terminating and Repeating Decimals Homework Practice Answers: Terminating and Repeating Decimals Problem-Solving Practice: Terminating and Repeating Decimals Problem-Solving Practice Answers: Terminating and Repeating Decimals Extra Practice: Terminating and Repeating Decimals Extra Practice Answers, Chapter 4 Homework Practice: Terminating and Repeating Decimals Problem-Solving Practice: Terminating and Repeating Decimals Skills Practice: Terminating and Repeating Decimals Extra Practice: Terminating and Repeating Decimals esolutions, Glencoe Math Course 2 Printed by: Nicole Sladich Page 8 of 14 Printed on 11/04/ :13 PM

9 Additional Activities for Differentiated Instruction Differentiated Instruction activities for Approaching Level, On Level, and Beyond Level Learners can also be found at point-of-use in the Launch the Lesson and Teach the Concept sections. The following are additional activities that can be used with this lesson. Option 1: Visual/Spatial Learners It may be helpful to use a common fraction such as when showing students how to write a fraction as a decimal using division. Using a fraction whose decimal equivalent they already know will allow students to feel confident with the division steps and to make connections. The Reteach Worksheet provides additional examples and practice for students who may have difficulty in grasping the math concepts in this lesson. Option 2: Kinesthetic Learners Materials: index cards Prepare enough index cards for the class so that half of the students will receive a card with a fraction written on it and half the class will receive a card with a decimal (terminating or repeating) equivalent for one of the fractions written on it. Have students move around the room to find the matching form of their number. Option 3: Interpersonal Learners Separate the class into groups of two to three students. Have students choose between using mental math, paper and pencil, or a calculator for each exercise in the Got It? section. As they complete each exercise, have them discuss whether or not their method was the most efficient or appropriate. Encourage them to use mental math whenever possible. For example, in Exercise 1, mental math is appropriate because the denominator, 5, is a factor of 10. Since 5 2 = 10, multiply the numerator by 2 as well. Since 2 2 = 4, the fraction is equivalent to 4 tenths, or 0.4. In Exercise 7, either paper and pencil or a calculator are appropriate since the denominator, 9, is not a factor of 100. Option 4: Logical Learners Have students find the decimal equivalents of. Have them predict the decimal equivalents for. Have students explain their predictions. Then based on those predictions, have students predict the decimal equivalent of. Ask: Printed by: Nicole Sladich Page 9 of 14 Printed on 11/04/ :13 PM

10 If any number divided by itself equals 1, why does seem to be equal to? As the digit 9 of repeats infinitely, gets closer to 1. The Enrich Worksheet provides students with valuable opportunities for extending this lesson. Resources Reteach: Terminating and Repeating Decimals Reteach Answers: Terminating and Repeating Decimals Enrich: Writing Repeating Decimals as Fractions Enrich Answers: Writing Repeating Decimals as Fractions Reteach: Terminating and Repeating Decimals Enrich: Writing Repeating Decimals as Fractions Printed by: Nicole Sladich Page 10 of 14 Printed on 11/04/ :13 PM

11 Additional Activities for English Learners Differentiated Instruction activities for English Learners can also be found at point-of-use in the Launch the Lesson and Teach the Concept sections. The following are additional activities that can be used with this lesson. Option 1: Use Chapter 4, from the Interactive Guide for English Learners. Option 2: Logical Learners Materials: index cards Make index cards with different representations of division problems. Have students identify the dividend and the divisor in each of the different representations. Word Wall Printable English/Spanish Word Wall cards are available for the following vocabulary words in this lesson: bar notation repeating decimal terminating decimal Resources Word Wall Cards Interactive Guide for English Learners, Student Edition, Course 2, Lesson 4-1: Terminating and Repeating Decimals Interactive Guide for English Learners, Teacher Edition, Course 2, Lesson 4-1: Terminating and Repeating Decimals Interactive Guide for English Learners, Course 2, Teacher Edition Interactive Guide for English Learners, Course 2, Student Edition Visual Kinesthetic Vocabulary, Course 2, Student Edition Visual Kinesthetic Vocabulary, Course 2, Teacher Edition Printed by: Nicole Sladich Page 11 of 14 Printed on 11/04/ :13 PM

12 Assessment Formative Assessment Use this activity as a closing formative assessment before dismissing students from your class. Tell students that the next lesson will be about comparing and ordering rational numbers. Have them write how they think what they learned in this lesson will connect with the next lesson. Give them the following writing prompts. In this lesson, I learned In this lesson, I learned What I learned in this lesson will help me in the next lesson because See students' work. The online Self-Check Quiz for this lesson allows students to review concepts from each lesson. Exercises 36 and 37 prepare students for more rigorous thinking needed when taking the CCSS assessment. 36. This test item requires students to explain and apply mathematical concepts and solve problems with precision, while making use of structure. Depth of Knowledge CCSS Content Standard Mathematical Practices Online Experience DOK1 7.NS.2d, 7.EE.3 MP1, MP6, MP7 Students select and drag the correct answers to the table. Scoring Rubric 2 points Students correctly identify each decimal equivalent. 1 point Students correctly identify 2-3 decimal equivalents. 37. This test item requires students to explain and apply mathematical concepts and solve problems with precision, while making use of structure. Depth of Knowledge CCSS Content Standard Mathematical Practices Online Experience DOK1 7.EE.3 MP1, MP6 Students will be required to click on the bubbles to select all answers that are correct. Scoring Rubric 1 point Students correctly answer the question. Printed by: Nicole Sladich Page 12 of 14 Printed on 11/04/ :13 PM

13 Quick Check Are students continuing to struggle with terminating and repeating decimals? If Yes Reteach Worksheet If No Differentiated Instruction Option 1 Skills Practice Worksheet Differentiated Instruction Options 2 and 3 Enrich Worksheet Differentiated Instruction Option 4 Resources Self-Check Quiz: Terminating and Repeating Decimals Printed by: Nicole Sladich Page 13 of 14 Printed on 11/04/ :13 PM

14 Printed by: Nicole Sladich Page 14 of 14 Printed on 11/04/ :13 PM

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