Fractions and Decimals

At the completion of this unit, the students will be able to:

1. Identify and show fractional parts of regions and sets.
2. Use division to divide objects into equal parts that are fractions of a whole and represent the numbers on a number line.
3. Express fractions greater than 1 as mixed numbers or improper fractions.
4. Identify fractions that are equivalent to a given fraction using computational procedures.
5. Determine which two fractions are greater or less in order to compare and order fractions and mixed numbers.
6. Determine common and greatest common factors of numbers.
7. Identify and find simplest forms of fractions.
8. Represent decimals (tenths,hundredths, and thousandths) as fractions, and fractions with denominators of 10, 100, and 1000 as decimals.
9. Label a point on a number line using a fraction and a decimal, and write a fraction and a decimal for a point on a number line.
10. Explain how to estimate fractional amounts of objects.
11. Use models and computational procedures to add and subtract fractions with like denominators.
12. Determine common and least common multiples of numbers.
13. Use models and computational procedures to add and subtract fractions with unlike denominators.
14. Use models and computational procedures to add and subtract mixed numbers.
15. Use try, check, and revise in order to solve problems.

Yes

Students will be assessed:

1. Using the 9-1 Meanings of Fractions Quick Check and Practice  worksheets to show the student can identify and show fractional parts of regions and sets.
2. Using the 9-2 Fractions and Division Quick Check and Practice  worksheets to show the is able to use division to divide objects into equal parts that are fractions of a whole and represent them on a number line.
3. Using the 9-3 Mixed Numbers and Improper Fractions Quick Check and Practice worksheets to show that the student can express fractions greater than one as mixed numbers or improper fractions.
4. Using the 9-4 Equivalent Fractions Quick Check and Practice worksheets to show the student can identify and find fractions that are equivalent to a given fraction using  computational procedures.
5. Using the 9-5 Comparing and Ordering Fractions and Mixed Numbers Quick Check and Practice worksheets to show the student is able to determine which of two fractions are greater or less in order to compare and order fractions and mixed numbers.
6. Using the 9-6 Common Factors and Greatest Common Factor Quick Check and Practice worksheets to show the student can determine common and greatest common factors of numbers.
7. Using the 9-7 Fractions in Simplest Form Quick Check and Practice worksheets to show that the student can identify and find the simplest forms of fractions.
8. Using the 9-8 Tenths and Hundredths and 9-9 Thousandths Quick Check and Practice worksheets to show that the student is able to represent decimals (tenths, hundredths, and thousandths) as fractions, and fractions with denominators of 10, 100, and 1000 as decimals.
9. Using the 9-10 Fractions and Decimals on the Number Line Quick Check and Practice worksheets to show that the student can label a point on a number line using a fraction and a decimal, and write a fraction or decimal for a point on a number line.
10. Using the 9-11 Problem Solving: Writing to Explain Quick Check and Practice worksheets to show that the student is able to explain how to estimate fractional amounts of objects.
11. Using the 10-1 Adding and Subtracting Fractions with like Denominators Quick Check and Practice worksheets to show that the student is able to use models and computational procedures to add and subtract fractions with like denominators.
12. Using the 10-2 Common Multiples and Least Common Multiples Quick Check and Practice worksheets to show that the student can determine common and least common multiples of numbers.
13. Using the 10-3 Adding Fractions with Unlike Denominators and 10-4 Subtracting Fractions with Unlike Denominators Quick Check and Practice worksheets to show that the student can use models and computational procedures to add and subtract fractions with unlike denominators.
14. Using the 10-5 Adding Mixed Numbers and 10-6 Subtracting Mixed Numbers Quick Check and Practice worksheets to show that the student is able to use models and computational procedures to add and subtract mixed numbers.
15. Using the 10-7 Problem Solving: Try, Check, and Revise Quick Check and Practice worksheets to show that the student is able to use try, check, and revise in order to solve problems.
16. After completing practice on objectives 1-10, using the Topic 9 Fractions and Decimals Multiple Choice Exam and Topic 9 Fractions and Decimals Free-Response Exam to show students can:
    
    
    • Identify and show fractional parts of regions and sets. (Question 1) (Questions 1, 2)
    • Use division to divide objects into equal parts that are fractions of a whole and represent them on a number line. (Question 3) (Questions 3-6)
    • Express fractions greater than one as mixed numbers or improper fractions.. (Question 8) (Questions 7-10)
    • Identify and find fractions that are equivalent to a given fraction using  computational procedures. (Question 14) (Questions 11-14)
    • Determine which of two fractions are greater or less in order to compare and order fractions and mixed numbers. (Questions 4, 7) (Questions 15-17)
    • Determine common and greatest common factors of numbers. (Question 12) (Questions 18-20)
    • Identify and find the simplest forms of fractions. (Questions 2, 11) (Questions 21-22)
    • Represent decimals (tenths, hundredths, and thousandths) as fractions, and fractions with denominators of 10, 100, and 1000 as decimals. (Questions 5, 9, 13) (Questions 23-30)
    • Label a point on a number line using a fraction and a decimal, and write a fraction and a decimal for a point on a number line. (Question 10) (Questions 31-33)
    • Explain how to estimate fractional amounts of objects. (Question 6) (Question 34, 35)
17. After completing practice on objectives 11-15, using the Topic 10 Adding and Subtracting Fractions and Mixed Numbers Multiple Choice Exam and Topic 10 Adding and Subtracting Fractions and Mixed Numbers Free-Response Exam to show students can:

• Use models and computational procedures to add and subtract fractions with like denominators. (Questions 1, 7, 14) (Questions 1-2, 7-8, 15, 17)
• Determine common and least common multiples of numbers (Questions 4, 6) (Questions 13-14, 19)
• Use models and computational procedures to add and subtract fractions with unlike denominators.(Questions 5, 11, 8, 10) (Questions 3, 9)
• Use models and computational procedures to add and subtract mixed numbers.(Questions 3, 12, 2, 13) (Questions 4-6, 16, 21, 10-12)
• Use try, check, and revise in order to solve problems(Question 9) (Questions 18, 20)

80%

During whole group instruction, students will:

1. Take notes from the SMART Board, follow along as the teacher works example problems, working out the problems on their slates, and then work guided practice questions on Identifying and showing fractional parts of regions and sets.
2. Take notes from the SMART Board, follow along as the teacher works example problems, working out the problems on their slates, and then work guided practice questions on using division to divide objects into equal parts that are fractions of a whole and represent the numbers on a number line. Students will work in pairs to write fractions for how much each person would get if they shared 5 oranges among 6 people and 3 sandwiches among 5 people.  The will draw models and record their fractions and the related division on a sheet of paper.
3. Take notes from the SMART Board, follow along as the teacher works example problems, working out the problems on their slates, and then work guided practice on expressing fractions greater than 1 as mixed numbers or improper fractions.
4. Take notes from the SMART Board, follow along as the teacher works example problems, working out the problems on their slates, and then work guided practice questions on identifying fractions that are equivalent to a given fraction using computational procedures. The students will use the Interactive Recording Sheet 21 to look for patterns and recognize that some fractions have the same value.
5. Take notes from the SMART Board, follow along as the teacher works example problems, working out the problems on their slates, and then work guided practice questions on determining which two fractions are greater or less in order to compare and order fractions and mixed numbers. Students will work in groups to solve the following problem. Harold has ribbons with the following widths: 2/3 cm, 5/6 cm, and 7/10 cm. He needs to tie a package with the thinnest ribbon.  Which ribbon should he use?
6. Take notes from the SMART Board, follow along as the teacher works example problems, working out the problems on their slates, participate in discussion, and then work guided practice questions on determining common and greatest common factors of numbers.
7. Take notes from the SMART Board, follow along as the teacher works example problems, working out the problems on their slates, participate in discussion, and then work guided practice questions on identifying and finding the simplest form of fractions. Students will work in pairs, using Interactive Recording Sheet 23, to record fractions of an area model and then write those fractions in simplest form.
8. Take notes from the SMART Board, follow along as the teacher works example problems, working out the problems on their slates, participate in discussion, and then work guided practice questions on representing decimals (tenths, hundredths, and thousandths) as fractions, and fractions with denominators of 10, 100, and 1000 as decimals. The students will use place value charts and fraction model strips to model answers to questions posed by the teacher.
9. Take notes from the SMART Board, follow along as the teacher works example problems, working out the problems on their slates, participate in discussion, and then work guided practice questions on labeling a point on a number line using a fraction and a decimal, and write a fraction and a decimal for a point on a number line.
10. Take notes from the SMART Board, follow along as the teacher works example problems, working out the problems on their slates, participate in discussion, and then work guided practice questions on explaining how to estimate fractional amounts of objects.
11. Take notes from the SMART Board, follow along as the teacher works example problems, working out the problems on their slates, participate in discussion, and then work guided practice questions on using models and computational procedures to add and subtract fraction with like denominators. Students will use fraction strips to model the sum and difference for given problems.
12. Take notes from the SMART Board, follow along as the teacher works example problems, working out the problems on their slates, participate in discussion, and then work guided practice questions on determining common and least common multiples of numbers.
13. Take notes from the SMART Board, follow along as the teacher works example problems, working out the problems on their slates, participate in discussion, and then work guided practice questions on using models and computational procedures to add and subtract fractions with unlike denominators.
14. Take notes from the SMART Board, follow along as the teacher works example problems, working out the problems on their slates, participate in discussion, and then work guided practice questions on using models and computation procedures to add and subtract mixed numbers.
15. Take notes from the SMART Board, follow along as the teacher works example problems, working out the problems on their slates, participate in discussion, and then work guided practice questions on using try, check, and revise in order to solve problems. Students will work in pairs to try, check, revise and solve given problems in the student edition pages 270-271.

During independent work time, students will complete the:

1. 9-1 Meanings of Fractions Quick Check and Practice worksheet.
2. 9-2 Fractions and Division Quick Check and Practice worksheet.
3. 9-3 Mixed Numbers and Improper Fractions Quick Check and Practice worksheet.
4. 9-4 Equivalent Fractions Quick Check and Practice worksheet.
5. 9-5 Comparing and Ordering Fractions and Mixed Numbers Quick Check and Practice worksheet.
6. 9-6 Common and Greatest Common Factor Quick Check and Practice worksheet.
7. 9-7 Fractions in Simplest Form Quick Check and Practice worksheet.
8. 9-8 and 9-9 Tenths, Hundredths, and Thousandths Quick Check and Practice worksheet.
9. 9-10 Fractions and Decimals on the Number Line Quick Check and Practice worksheet.
10. 9-11 Problem Solving: Writing to Explain Quick Check and Practice worksheet.
11. 10-1 Adding and Subtracting Fractions with Like Denominators Quick Check and Practice worksheet.
12. 10-2 Common and Least Common Multiple Quick Check and Practice worksheet.
13. 10-3 and 10-4 Adding and Subtracting Fractions with Unlike Denominators Quick Check and Practice worksheet.
14. 10-5  and 10-6 Adding and Subtracting Mixed Numbers Quick Check and Practice worksheet.
15. 10-7 Problem Solving: Try, Check, and Revise Quick Check and Practice worksheet.

For extra practice and review, the students will complete each topic skill quiz.  They will log onto their laptop computers and go to the QuizShow icon on their desktop.  Then they will complete the quiz for the skill(s) as directed by the teacher.

During whole group instruction, the teacher will:

1. Display the Visual Learning Animations CD-ROM on the SMART Board, use prepared lesson materials to discuss, model examples and provide guided practice problems, providing assistance and feedback as needed on identifying and showing fractional parts of regions and sets.
2. Display the Visual Learning Animations CD-ROM on the SMART Board, use prepared lesson materials to discuss, model examples and provide guided practice problems, providing assistance and feedback as needed on using division to dived objects into equal parts that are fractions and represent on a number line.
3. Display the Visual Learning Animations CD-ROM on the SMART Board, use prepared lesson materials to discuss, model examples and provide guided practice problems, providing assistance and feedback as needed on expressing fraction greater than 1 as mixed numbers or improper fractions.
4. Display the Visual Learning Animations CD-ROM on the SMART Board, use prepared lesson materials to discuss, model examples and provide guided practice problems, providing assistance and feedback as needed on identifying fractions that are equivalent to a given fraction.
5. Display the Visual Learning Animations CD-ROM on the SMART Board, use prepared lesson materials to discuss, model examples and provide guided practice problems, providing assistance and feedback as needed on comparing and ordering fractions and mixed numbers.
6. Display the Visual Learning Animations CD-ROM on the SMART Board, use prepared lesson materials to discuss, model examples and provide guided practice problems, providing assistance and feedback as needed on determining common and greatest common factors of numbers.
7. Display the Visual Learning Animations CD-ROM on the SMART Board, use prepared lesson materials to discuss, model examples and provide guided practice problems, providing assistance and feedback as needed on identifying and finding the simplest for of given fractions.
8. Display the Visual Learning Animations CD-ROM on the SMART Board, use prepared lesson materials to discuss, model examples and provide guided practice problems, providing assistance and feedback as needed on representing decimals and fractions (tenths, hundredths, and thousandths) as fractions and decimals on a number line.
9. Display the Visual Learning Animations CD-ROM on the SMART Board, use prepared lesson materials to discuss, model examples and provide guided practice problems, providing assistance and feedback as needed on labeling a point on a number line using a fraction and a decimal, and writing a fraction and a decimal on a number line.
10. Display the Visual Learning Animations CD-ROM on the SMART Board, use prepared lesson materials to discuss, model examples and provide guided practice problems, providing assistance and feedback as needed on explaining how to estimate fractional amounts of objects.
11. Display the Visual Learning Animations CD-ROM on the SMART Board, use prepared lesson materials to discuss, model examples and provide guided practice problems, providing assistance and feedback as needed on using models and computational procedures to add and subtract fractions with like denominators. The teacher will also pose this problem to the students: Mel ran 1/6 mile on a road leading from his cabin to a trail.  Then he ran 4/6 mile on the trail to a lake.  How far did Mel run from the cabin to the lake?  The teacher will assist the students as they work the problem out on their slates.  Then, they class will have discussion about the steps taken to solve the problem.
12. Display the Visual Learning Animations CD-ROM on the SMART Board, use prepared lesson materials to discuss, model examples and provide guided practice problems, providing assistance and feedback as needed on determining common and least common multiples of numbers.
13. Display the Visual Learning Animations CD-ROM on the SMART Board, use prepared lesson materials to discuss, model examples and provide guided practice problems, providing assistance and feedback as needed on using models and computational procedures to add and subtract fractions with unlike denominators. The teacher will also demonstrate how to use fraction strips to help formulate a method for adding and subtracting fractions.
14. Display the Visual Learning Animations CD-ROM on the SMART Board, use prepared lesson materials to discuss, model examples and provide guided practice problems, providing assistance and feedback as needed on using models and computational procedures to add and subtract mixed numbers. The teacher may also direct the students to eTools at www.pearsonsuccessnet.com.
15. Display the Visual Learning Animations CD-ROM on the SMART Board, use prepared lesson materials to discuss, model examples and provide guided practice problems, providing assistance and feedback as needed on using try, check, and revise in order to solve problems.

While students are completing independent practice problems, the teacher will observe and assist students that are having difficulties.

EnVision Math Series with Teaching Components and Manipulatives
Student Laptop Computers
SmartBoard
Student Slates and Markers
www.pearsonsuccessnet.com

Use reteaching and intervention materials for each objective if needed.

Math Centers and provided enrichment activities may be used.

Teacher-student meetings
Peer tutoring
Modified assignments if required