Enhanced Instructional Transition Guide

Transcription

1 Enhanced Instructional Transition Guide Grade / Unit 0: Suggested Duration: days Unit 0: Fractions ( days) Possible Lesson 0 ( days) Possible Lesson 02 ( days) Possible Lesson 0 ( days) Possible Lesson 02 ( days) This lesson is one approach to teaching the State Standards associated with this unit. Districts are encouraged to customize this lesson by supplementing with district-approved resources, materials, and activities to best meet the needs of learners. The duration for this lesson is only a recommendation, and districts may modify the time frame to meet students needs. To better understand how your district is implementing CSCOPE lessons, please contact your child s teacher. (For your convenience, please find linked the TEA Commissioner s List of State Board of Education Approved Instructional Resources and Midcycle State Adopted Instructional Materials.) Lesson Synopsis: Students use manipulatives to model and generate equivalent fractions. Students generate and find equivalent fractions and fractions in simplest form. TEKS: The Texas Essential Knowledge and Skills (TEKS) listed below are the standards adopted by the State Board of Education, which are required by Texas law. Any standard that has a strike-through (e.g. sample phrase) indicates that portion of the standard is taught in a previous or subsequent unit. The TEKS are available on the Texas Education Agency website at Number, operation, and quantitative reasoning. The student uses fraction names and symbols (with denominators of 2 or less) to describe fractional parts of whole objects or sets of objects. The student is expected to:.2c Use fraction names and symbols to describe fractional parts of whole objects or sets of objects. Readiness Standard.2D Construct concrete models of equivalent fractions for fractional parts of whole objects. Underlying Processes and Mathematical Tools TEKS:.4 Underlying processes and mathematical tools. The student applies Grade mathematics to solve problems connected to everyday page of 0

2 Enhanced Instructional Transition Guide Grade / Unit 0: Suggested Duration: days experiences and activities in and outside of school. The student is expected to:.4a Identify the mathematics in everyday situations..4d Use tools such as real objects, manipulatives, and technology to solve problems.. Underlying processes and mathematical tools. The student communicates about Grade mathematics using informal language. The student is expected to:.a Explain and record observations using objects, words, pictures, numbers, and technology..b Relate informal language to mathematical language and symbols. Performance Indicator(s): page 2 of 0

3 Enhanced Instructional Transition Guide Grade / Unit 0: Suggested Duration: days Grade Unit0 PI02 Construct an equivalent representation of a whole or a set of objects in a given problem situation using concrete manipulatives. Describe the fractional parts of each representation using words, numbers, and symbols. Justify in writing how the equivalent fractions were determined. Sample Performance Indicator: Larry was creating a tile design for his new kitchen floor. Recreate Larry s Tile Design and construct Ron s Tile Design using concrete manipulatives so that the black tiles represent a fraction equivalent to Larry s black tiles and the white tiles represent a fraction equivalent to Larry s white tiles. Use the concrete models to write a statement of equivalence using words, numbers, and symbols for: () the number of white tiles in each tile design and (2) the number of black tiles in each tile design. Justify in writing how Larry s Tile Design was used to generate an equivalent fraction for the white tiles and an equivalent fraction for the black tiles in Ron s Tile Design. Standard(s):.2C,.2D,.4A,.4D,.A,.B ELPS ELPS.c.C, ELPS.c.H, ELPS.c.G Key Understanding(s): An equivalent fraction and/or an equivalent model can be generated from a given fraction, concrete object and/or pictorial model, and described using words, page of 0

4 Enhanced Instructional Transition Guide Grade / Unit 0: Suggested Duration: days numbers, and symbols. Fractional parts of a whole or sets of objects can be described using fraction names and symbols. Fractions can represent equal parts of a whole or sets of objects. The number of parts of the whole or set of objects defines the denominator, whereas, the number of specified parts of the whole or set of objects defines the numerator. Misconception(s): Some students may think the numerator and the denominator of a fraction share no relationship and confuse which number represents the numerator and which number represents the denominator. Remind students that the total number of equal parts should be the denominator, or bottom number, of the fraction. The numerator, or top number, of the fraction should be the number of parts under consideration. Some students may think when a fraction is written using a diagonal line, such as /, that the numerator and denominator have the same value. Only use a horizontal line to clearly separate the numerator from the denominator, such as. According to Galen (2004), this form of writing fractions is called case fraction form. Some students may think fraction bars, similar to the example below, means that one block is worth out of ; the next block is worth 2 out of, etc. This leads to confusion with the concept of fractions. Some students may think that the fraction with the larger digit has the greater value. Although this is true in some instances, students need to be exposed to problems where this is not true. Also, if students are using fraction strips, circles, or other fraction manipulatives, they will be able to compare fractions without making this common error. Vocabulary of Instruction: denominator equivalent fractions numerator page 4 of 0

5 Enhanced Instructional Transition Guide Grade / Unit 0: Suggested Duration: days Material List: cardstock ( sheets per teacher) concrete manipulatives (determined by the teacher) ( set per student) Fraction Circles ( set per student) (previously created in Unit 0 Lesson 0 Explore/Explain ) Labeled Fraction Strips ( per teacher) (previously created in Unit 0 Lesson 0 Explore/Explain ) math journal ( per student) paper (plain) ( sheet per student, sheet per teacher) pattern blocks (20 of each block) ( set per student) plastic zip bags (sandwich sized) ( per student, per teacher) scissors ( per teacher) Attachments: All attachments associated with this lesson are referenced in the body of the lesson. Due to considerations for grading or student assessment, attachments that are connected with Performance Indicators or serve as answer keys are available in the district site and are not accessible on the public website. Labeled Fraction Strips Sheet Table of Equivalent Fractions Recording Sheet KEY Table of Equivalent Fractions Recording Sheet Fraction Task Cards # # Fraction Task Recording Sheets KEY Fraction Task Recording Sheets Fraction Practice KEY Fraction Practice page of 0

6 Enhanced Instructional Transition Guide Grade / Unit 0: Suggested Duration: days GETTING READY FOR INSTRUCTION Teachers are encouraged to supplement and substitute resources, materials, and activities to meet the needs of learners. These lessons are one approach to teaching the TEKS/Specificity as well as addressing the Performance Indicators associated with each unit. District personnel may create original lessons using the Content Creator in the Tools Tab. All originally authored lessons can be saved in the My CSCOPE Tab within the My Content area. Suggested Day Suggested Instructional Procedures Notes for Teacher Topics: Equivalent fraction introduction Engage Students investigate equivalent fractions using fraction strips. Instructional Procedures: Spiraling Review MATERIALS Labeled Fraction Strips ( per teacher) (previously created in Unit 0 Lesson 0 Explore/Explain ) page of 0

7 Enhanced Instructional Transition Guide Grade / Unit 0: Suggested Duration: days Suggested Day Suggested Instructional Procedures. Display the following from Labeled Fraction Strips for the class to see: one-half strip; 2 onefourth strips; and 4 one-eighth strips. Notes for Teacher plastic zip bags (sandwich sized) ( per student, per teacher) scissors ( per teacher) math journal ( per student) Ask: How are these strips alike? (They are all the same size.) How are they different? (They are divided into different size parts.) 2. Display the word equivalent for the class to see. Explain to students that fractional parts that name the same amount are called equivalent fractional parts or equivalent fractions. Instruct students to record the vocabulary word, the definition, and a drawing to help them remember the term (e.g. pictures of the fraction strips used for the class discussion; etc.) in their math journal. Topics: ATTACHMENTS Equivalent fractions using fraction strips Teacher Resource: Labeled Fraction page 7 of 0

8 Enhanced Instructional Transition Guide Grade / Unit 0: Suggested Duration: days Suggested Day Explore/Explain Suggested Instructional Procedures Students investigate and find equivalent fractions using fraction strips. Instructional Procedures:. Distribute handout: Labeled Fraction Strips Sheet, a set of Labeled Fraction Strips, and handout: Table of Equivalent Fractions Recording Sheet to each student. Display Labeled Fraction Strips for the class to see. 2. Instruct students to shade in the first strip on handout: Labeled Fraction Strips Sheet. Using their set of Labeled Fraction Strips, instruct students to lay fraction strips on top of the shaded portion on handout: Labeled Fraction Strips Sheet until the portion is covered. Ask: Notes for Teacher Strips Sheet ( per teacher) Handout: Labeled Fraction Strips Sheet ( per student) Teacher Resource: Table of Equivalent Fractions Recording Sheet KEY ( per teacher) Handout: Table of Equivalent Fractions Recording Sheet ( per student) MATERIALS Labeled Fraction Strips ( set per student, set per teacher) (previously created) paper (plain) ( sheet per student, sheet per teacher) How many strips make up the same size as the strip? How do you know? (2) Answers may vary. It takes two strips to cover a strip; two strips covered the strip; State Resources etc. The digits in the fraction changed, but did the amount or value of the fraction change? Explain. (no) Answers may vary. The area the strips cover remains the same; it is always the half of the whole; etc. The TEA Module, TEKS Connections, Grade - has student lessons in Grade that address equivalent fractions. These lessons can be used to enhance student page 8 of 0

9 Enhanced Instructional Transition Guide Grade / Unit 0: Suggested Duration: days Suggested Day Suggested Instructional Procedures Could be another way to name? (yes) How could you describe and? (They are equivalent fractions because they cover the same amount of space.) Notes for Teacher understanding of equivalent fractions. MTC -: Equivalent Fractions Instruct students to use their Labeled Fraction Strips to find other fractions that are equivalent to. Ask: What other fractions are equivalent to? How do you know? (, etc.) Answers may vary. The strips cover the same area as ; etc. 4. Instruct students to use the handout: Table of Equivalent Fractions to record the fractions that are equivalent to. Monitor and assess students to check for understanding.. Display teacher resource: Labeled Fraction Strips Sheet for the class to see. Explain to students that you are going to demonstrate another way to determine which fractions are equivalent. Place a straightedge (sheet of paper) vertically on the page next to the fraction to find fractions that are equivalent to. page 9 of 0

10 Enhanced Instructional Transition Guide Grade / Unit 0: Suggested Duration: days Suggested Day Suggested Instructional Procedures Notes for Teacher. Distribute sheet of paper to each student to use as a straightedge. Instruct students to use this method to verify that they have found all of the fractions on the sheet that are equivalent to. Ask: How could you use the straightedge to find fractions equivalent to? (Line up the straightedge along the line and look for fractions that end at the same line.) When you look at fractions on the sheet this way, does it remind you of anything you have seen in mathematics before? Explain. (yes) Answers may vary. The bars line up like number lines; or it looks like what we used to compare fractions; etc. page 0 of 0

11 Enhanced Instructional Transition Guide Grade / Unit 0: Suggested Duration: days Suggested Day Suggested Instructional Procedures Notes for Teacher 7. Instruct students to find equivalent fractions for all the fractions listed on handout: Table of Equivalent Fractions. Encourage students to use their Labeled Fraction Strips, handout: Labeled Fraction Strip Sheet, and the straightedge to help them determine which fractions are equivalent. Monitor and assess students to check for understanding. 8. Facilitate a class discussion to debrief and discuss the equivalent fractions found. 2 Topics: Multiple representations of fractions Elaborate Students investigate, compare, order, and identify multiple representations of fractions including equivalents. Instructional Procedures:. Prior to instruction, create 2 sets of class resource: Fraction Task Cards # # by copying on cardstock, laminating, and cutting apart. If pattern blocks have not been organized into plastic zip bags in a previous lesson, place 20 of each block in a plastic zip bag for each student. 2. Place students into groups with 4 students per group. Distribute handout: Fraction Task Recording Sheets, Fraction Circles, Labeled Fraction Strips, and pattern blocks to each student.. Set up fraction stations in the classroom as follows: Groups # and #2: Provide class resource: Fraction Task Card # Spiraling Review ATTACHMENTS Class Resource: Fraction Task Cards # # (2 sets per class) Teacher Resource: Fraction Task Recording Sheets KEY ( per student) Handout: Fraction Task Recording Sheets ( per student) Teacher Resource: Fraction Practice KEY ( per teacher) Handout: Fraction Practice ( per student) MATERIALS cardstock ( sheets per teacher) Fraction Circles ( set per student) page of 0

12 Enhanced Instructional Transition Guide Grade / Unit 0: Suggested Duration: days Suggested Day Suggested Instructional Procedures Groups # and #4: Provide class resource: Fraction Task Card #2 Groups # and #: Provide class resource: Fraction Task Card # 4. Explain to students that they will begin working on the Fraction Task at their table. They will be allowed about 0 minutes to complete each task and record the results on the corresponding handout: Fraction Task Recording Sheets. Each student will be responsible for recording the task results on their own recording sheet, but they may work together as a group to complete the task.. Allow students about 0 minutes per task and then instruct students to rotate to the next station to complete the next task. Repeat the process until each group has completed fraction tasks. Monitor and assess student groups to check for understanding.. Facilitate a class discussion to debrief and discuss the task answers. 7. Distribute handout: Fraction Practice to each student to complete independently. Notes for Teacher (previously created in Unit 0 Lesson 0 Explore/Explain ) Labeled Fraction Strips ( set per student, set per teacher) (previously created) pattern blocks (20 of each block) ( set per student) TEACHER NOTE This activity is adapted from Texas Education Agency (2007), MTC Math TEKS Connections: Grades -, Grade Equivalent Fractions, p TEACHER NOTE If pattern block sets are not available, use the Pattern Block Template previously created in Unit 0 Lesson 0 Explore/Explain. State Resources TEXTEAMS: RETHINKING ELEMENTARY MATHEMATICS PART I Fraction Rectangles Task Card; Shake and Spill Task Card page 2 of 0

13 Enhanced Instructional Transition Guide Grade / Unit 0: Suggested Duration: days Suggested Day Suggested Instructional Procedures Notes for Teacher Evaluate MATERIALS Instructional Procedures:. Assess student understanding of related concepts and processes by using the Performance Indicator(s) aligned to this lesson. concrete manipulatives (determined by the teacher) ( set per student) Performance Indicator(s): Grade Unit0 PI02 Construct an equivalent representation of a whole or a set of objects in a given problem situation using concrete manipulatives. Describe the fractional parts of each representation using words, numbers, and symbols. Justify in writing how the equivalent fractions were determined. Sample Performance Indicator: Larry was creating a tile design for his new kitchen floor. Recreate Larry s Tile Design and construct Ron s Tile Design using concrete manipulatives so that the black tiles represent a fraction equivalent to Larry s black tiles and the white tiles represent a fraction equivalent to Larry s white tiles. page of 0

14 Enhanced Instructional Transition Guide Grade / Unit 0: Suggested Duration: days Suggested Day Suggested Instructional Procedures Notes for Teacher Use the concrete models to write a statement of equivalence using words, numbers, and symbols for: () the number of white tiles in each tile design and (2) the number of black tiles in each tile design. Justify in writing how Larry s Tile Design was used to generate an equivalent fraction for the white tiles and an equivalent fraction for the black tiles in Ron s Tile Design. Standard(s):.2C,.2D,.4A,.4D,.A,.B ELPS ELPS.c.C, ELPS.c.H, ELPS.c.G 04/2/20 page 4 of 0

15 Labeled Fraction Strips Sheet Grade Unit: 0 Lesson: 02 One Whole , TESCCC 09/7/2 page of

16 Table of Equivalent Fractions Recording Sheet KEY Use your fraction strips to find all equivalent fractions. Record them in the table. Fraction ,,,0, ,, 9 2 4,, , 8 2 8, Describe any patterns you see. Equivalent Fractions Grade Unit: 0 Lesson: 02 Answers may vary. In each row there are multiples of the numerators and the denominators of the given fraction for that row; etc. 202, TESCCC 09/7/2 page of

17 Table of Equivalent Fractions Recording Sheet Grade Unit: 0 Lesson: 02 Use your fraction strips to find all equivalent fractions. Record them in this table. Fraction Describe any patterns you see. Equivalent Fractions 202, TESCCC 09/7/2 page of

18 Fraction Task Card # Grade Unit: 0 Lesson: 02 Materials: Fraction Circles Problem: Randy s and Shondra s families each had same-sized pizzas to eat for dinner. Randy s family ate 0 of their pizza and Shondra s family ate of their pizza. Use fraction circles to compare how much pizza each family ate. Draw representations and label your models. Explain your thinking. Use words to describe your model. Use numbers and symbols to describe your model. 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% Adapted from Texas Education Agency (2007), MTC Math TEKS Connections: Grades -, Grade Equivalent Fractions, p , TESCCC 04/2/ Page of

19 Fraction Task Card #2 Grade Unit: 0 Lesson: 02 Materials: Fraction Strips Problem: Manny and Piper each had an insect collection. Manny had a beetle 4 of an inch long and Piper had a beetle of an inch long. Use fraction strips to compare the length of each beetle. Draw representations and label your models. Explain your thinking. Use words to describe your model. Use numbers and symbols to describe your model. One whole 2 2 Adapted from Texas Education Agency (2007), MTC Math TEKS Connections: Grades -, Grade Equivalent Fractions, p , TESCCC 04/2/ Page 2 of

20 Fraction Task Card # Grade Unit: 0 Lesson: 02 Materials: Pattern Blocks Problem: Cooper and Kelly each had a flower garden. Cooper planted roses in 2 of his garden. Kelly planted roses in 4 of her garden. Use pattern blocks to compare the fraction of each garden planted with roses. Draw representations and label your models. Explain your thinking. Use words to describe your model. Use numbers and symbols to describe your model. Adapted from Texas Education Agency (2007), MTC Math TEKS Connections: Grades -, Grade Equivalent Fractions, p , TESCCC 04/2/ Page of

21 Fraction Task Card # Recording Sheet KEY Grade Unit: 0 Lesson: 02 Draw representations of your models. Possible drawings: 0% 0% 0% 0% 0% 0% 0% 0% 0% 0%.7.7 %.7 % %.7.7% %.7% Randy s Family Shondra s Family Using words, describe your model. Explain your thinking. Answers may vary. Five-tenths is equal to three-sixths because the same amount on each pizza is shaded in both models. Answers may vary. Because the same-sized circles were used to represent each family s pizza, the models show that out of 0 equal parts is the same as out of equal parts. Using numbers and symbols, describe your model. 0 = Adapted from Texas Education Agency (2007), MTC Math TEKS Connections: Grades -, Grade Equivalent Fractions, p , TESCCC 04/2/ Page of

22 Fraction Task Card #2 Recording Sheet KEY Grade Unit: 0 Lesson: 02 Draw representations of your models. Possible drawing: One whole Manny s Beetle Piper s Beetle Using words, describe your model. Explain your thinking. Answers may vary. Four-fifths is less than five-sixths because the 4 strip is shorter than the strip OR Piper s Beetle is longer than Manny s Beetle because the model shows that is longer Answers may vary. Because the same-sized strips were used to represent each beetle, the models show that 4 out of equal parts is less than out of equal parts. than 4. Using numbers and symbols, describe your model. 4 Adapted from Texas Education Agency (2007), MTC Math TEKS Connections: Grades -, Grade Equivalent Fractions, p , TESCCC 04/2/ Page 2 of

23 Fraction Task Card # Recording Sheet KEY Grade Unit: 0 Lesson: 02 Draw representations of your models. Possible drawing: Kelly s Rose Garden Cooper s Rose Garden Using words, describe your model. Explain your thinking. Answers may vary. Four-sixths is equal to two-thirds because there is an equal amount of shading on both models. Answers may vary. Because the same-sized blocks were used to represent each garden, the models show that 4 out of equal parts is the same as 2 out of equal parts. Using numbers and symbols, describe your model. 4 = 2 Adapted from Texas Education Agency (2007), MTC Math TEKS Connections: Grades -, Grade Equivalent Fractions, p , TESCCC 04/2/ Page of

24 Fraction Task Card # Recording Sheet Grade Unit: 0 Lesson: 02 Draw representations of your models. Using words, describe your model. Explain your thinking. Using numbers and symbols, describe your model. Adapted from Texas Education Agency (2007), MTC Math TEKS Connections: Grades -, Grade Equivalent Fractions, p , TESCCC 04/2/ Page of

25 Fraction Task Card #2 Recording Sheet Grade Unit: 0 Lesson: 02 Draw representations of your models. Using words, describe your model. Explain your thinking. Using numbers and symbols, describe your model. Adapted from Texas Education Agency (2007), MTC Math TEKS Connections: Grades -, Grade Equivalent Fractions, p , TESCCC 04/2/ Page 2 of

26 Fraction Task Card # Recording Sheet Grade Unit: 0 Lesson: 02 Draw representations of your models. Using words, describe your model. Explain your thinking. Using numbers and symbols, describe your model. Adapted from Texas Education Agency (2007), MTC Math TEKS Connections: Grades -, Grade Equivalent Fractions, p , TESCCC 04/2/ Page of

27 Fraction Practice KEY Grade Unit: 0 Lesson: 02. Jerry placed six hats on the store shelf. Write the fraction that tells what part of the hats are cowboy hats. 2. Use 9 color tiles to build a square. Draw a pictorial model of your square. Draw an X in three of the squares. Write the fraction that tells the number of squares with an X compared to the entire square. 9 Write a fraction to show what parts of the square do not have an X. 9 x x x. John bought two candy bars and cut both into four pieces. How many pieces does he have? 8 pieces If he and his friend each ate three pieces, what fraction will describe the number of pieces left? 2 8 Draw a picture to explain your thinking. ate ate ate ate ate ate 202, TESCCC 04/2/ page of 2

28 Fraction Practice KEY 4. Circle the set of stars that shows more than 4 7 Grade Unit: 0 Lesson: 02 of the stars shaded? A. B. C. D.. John s father is painting the tiles of his patio black. Write the fraction that tells what part of the patio is painted , TESCCC 09/7/2 page 2 of 2

29 Fraction Practice Grade Unit: 0 Lesson: 02. Jerry placed six hats on the store shelf. Write the fraction that tells what part of the hats are cowboy hats. 2. Use 9 color tiles to build a square. Draw a pictorial model of your square. Draw an X in three of the squares. Write the fraction that tells the number of squares with an X compared to the entire square. Write a fraction to show what parts of the square do not have an X.. John bought two candy bars and cut both into four pieces. How many pieces does he have? If he and his friend each ate three pieces, what fraction will describe the number of pieces left? Draw a picture to explain your thinking. 202, TESCCC 04/2/ page of 2

30 Fraction Practice Grade Unit: 0 Lesson: Circle the set of stars that shows more than 4 7 of the stars shaded? A. B. C. D.. John s father is painting the tiles of his patio black. Write the fraction that tells what part of the patio is painted. 202, TESCCC 09/7/2 page 2 of 2