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The CROSSROADS Project Summer 2004 UNIT COVER PAGE Subject: Mathematics Grade Level (Circle): 4 Unit Title: Equivalent Fractions & Decimals Description: Equivalent Fractions and Decimals Math Standard: Number, Number Sense and Operations Standard Grade Level Indicator: Identify and generate equivalent forms of fractions and decimals. Duration: 5-7 days Creators (Design Team Members): Kathie Malone, Pam Warstler, Shelly Pilsitz Unit Test Template Unit Title: ____Crazy4Math Fractions & Decimals______ Grade Level : 4 Math Standard: _________NSO__________________ Indicator Number: ____1______ Teacher’s Name ________________________________ Building _________________________ District ________________________________________ Date of Testing ___________________ Skills & Concepts: Pre-Test Student’s Name ____________________________________ Total Score: _____/20 A. Multiple Choice (2 points each; 10 points total) Directions to the student: Show how you solve each problem in the box provided. Use words, pictures, or numbers. Then circle the LETTER of the correct answer. 1. Identify the shaded rectangle that represents the equivalent form of 6/8? How did you find your answer? a. b. c. d. 2. The following examples show fractions and decimals. Choose the example that is not equivalent. How did you find your answer? a. 1/4, 0.25 b. 3/10, 0.3 c. 1/4, 0.14 d. 3/4, 0.75 3. Which of the following examples is equivalent? How did you find your answer? a. 6/6, six tenths b. 2/3, one tenth c. one third, 0.13 d. 7/14, one half 4. Identify the equivalent pair. How did you find your answer? a. Five fifths is equal to five b. Five fifths is equal to ten c. Five fifths is equal to one d. Five fifths is equal to zero 5. Identify the equivalent decimal that represents the shaded area of this fraction bar. How did you find your answer? a. 0.5 b. 0.2 c. 0.1 d. 1.5 Objective Test Sub-Score: _____/10 B. Multiple-Step Problem Solving (3 points) Directions to the student: Find the answer to this question. Be sure to finish the WHOLE question. You may use words, pictures, or numbers. Be sure to show your work. In physical education class, Patty ran 7/8 of a mile. Sandy ran 3/8 of a mile. Pete ran 1/2 of a mile. Joe ran 1/4 of a mile. On the number line below, Patty’s and Sandy’s distances have already been plotted. Plot Pete’s and Joe’s distances on the same number line. 0 3/8 7/8 1 Sandy Patty Score: _____/3 C. Try It Another Way! (3 points) Directions to the student: Read the question below. An odometer on a bicycle measures miles in tenths. Sean bicycled ½ of a mile to school. Draw, write about, or use number sentences to show TWO DIFFERENT ways to represent how far Sean traveled in equivalent decimal form. Method #1 Method #2 Score: _____/3 D. Extended Response (4 points) Directions to the student: Use sentences to answer this question. Johnny cut his pizza in 10 pieces. He ate 2/5 of the pizza before he decided to share with his 7 friends. Does he have enough left to give each of his friends one piece of pizza? Explain why or why not. __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ Score: _____/4 Unit Pre-Test ANSWER KEY Multiple Choice (2 points each; 10 possible) 1. B 2. C 3. D 4. C 5. B Multi-Step Problem Solving (3 points each) Scoring Rubric: 3= All three correct: a. Pete’s distance plotted at 4/8, b. Joe’s distance plotted at 2/8, c. correct conversions 2= Two out of three correct from answers a., b., and c 1= One out of three correct from answers a., b., and c 0= Incorrectly plots both distances and shows no understanding of the concept. Try It Another Way! (3 points) Scoring Rubric: 3= Represents two ways to show the equivalent decimal form with appropriate explanations. 2= Represents two ways to show the equivalent decimal form with limited explanations. 1= Represents one way to show the equivalent decimal form with no explanation. 0= Represents no equivalent decimal or explanation. Extended Response (4 points) Scoring Rubric: 4= Include all four concepts: a. Answers no, b. Explains conversion 2/5 =4/10, c. Explains what’s left is6/10, d. Explains that 6 is not enough because 6 is less than 7. 3= Explains three out of the four concepts. 2= Explains two out of the four concepts. 1= Explains one out of the four concepts. 0= Shows no understanding. LESSON PLAN #1 Unit Title: Equivalent Fractions and Decimals Math Standard: Number, Number Sense, and Operations Math Indicator: Identify and generate equivalent forms of fractions and decimals. Objective: Each fourth grade mathematics student will demonstrate and explain that ten tenths is the same as one whole in both fraction and decimal form; e.g. 5/5=1.0, 6/6=1.0, 2/2=1.0, 10/10=1.0 Materials: pattern blocks, paper, pencil, inch graph paper strips (2 10 x 1 inch blue strips and 2 4 x1 inch yellow strips), scissors, worksheet (see attachment) Procedures: 1. Write the number 1 on the board. Ask: Is there any other way to represent the number 1? Explain to students that they will discover how to write the number 1 in fraction form in many different ways and in decimal form. Before they begin the activity, read through the directions on the worksheet and explain what they are expected to do. Review the assessment. 2. Pass out pattern blocks and worksheets. Using the pattern blocks, have each student do #1 and discuss their answers. Repeat with #2, #3, #4. 3. Have them compare their findings and discuss what discoveries that they made. Students should conclude that 1/1=1.0, 2/2=1.0, 3/3=1.0, 6/6 =1.0. So any number over itself equals 1.0. 4. Have students write their discoveries and conclusions from this activity in their own words on the space provided on their worksheet. 5. Pass out yellow and blue strips and scissors. 6. Using one of the yellow strips, have students complete #5 on the worksheet and discuss their answers. Using the other yellow strip, repeat the same process with #6. 7. Discuss discoveries and conclusions. Students should conclude that 4/4=1.0, 8/8=1.0 so any number over itself equals 1.0. They may also discover equivalent fractions such as 2/8=1/4, 6/8=3/4, etc. 8. Have students write their discoveries and conclusions from this activity in their own words on the space provided on the worksheet. 9. Using the blue strips have students complete #8 and #9 on the worksheet individually and discuss their answers, discoveries, and conclusions. 10. Have students write their discoveries and conclusions from this activity in their own words on the space provided on the worksheet. Product: Working Worksheet (see attachment) Assessment Criteria: On the working worksheet, students will show their conceptual knowledge of this concept through written words and sentences. Out of the three opportunities to explain this concept on the worksheet, students should show full understanding. Rubric: 3= Shows complete understanding 2= Shows some understanding 1= Shows little understanding 0= Shows no understanding Attachments (One Whole in Fraction and Decimal Form) One Whole in Fraction and Decimal Form Name ________________________________________________________ Directions: Use the pattern blocks to answer the following four questions. 1.Find one hexagon. How many hexagons is this? _____ Decimal form _____ What is your fraction?_____ 2.Create another hexagon using two different equal shapes. What is your fraction? _____ How many hexagons are there? _____ Decimal form _____ 3. Create another hexagon using three different equal shapes. What is your fraction? _____ How many hexagons are there? _____ Decimal form _____ 4. Create another hexagon using four different equal shapes. What is your fraction? _____ How many hexagons are there? _____ Decimal form _____ Write in your own words what you discovered or concluded from the above activities. 5. Fold and cut one of the yellow strips into 4 equal parts. What is the fraction for one part of the strip? _____ What is the fraction for two parts of the strip? _____ What is the fraction for three parts of the strip? _____ What is the fraction for four parts of the strip? _____ Which fraction is equal to one whole (1.0)? _____ 6. Using the other yellow strip, fold and cut the strip into 8 equal parts. What is the fraction for one part of the strip? _____ What is the fraction for four parts of the strip? _____ What is the fraction for eight parts of the strip? _____ Which one is equal to 1.0? _____ 7. Compare your two yellow strips and fractions for #5 and #6. What discoveries and conclusions have you come to? Do you see any relationships? Explain yourself in words and sentences. __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ 8. Using one of the blue strips, fold and cut the strip into 10 equal parts. What is the fraction for one part of the strip? _____ What is the fraction for three parts of the strip? _____ What is the fraction for ten parts of the strip? _____ Which one is equal to 1.0? _____ 9. Using the other blue strip, fold and cut this strip into 5 equal parts. What is the fraction for one part of the strip? _____ What is the fraction for two parts of the strip? _____ What is the fraction for three parts of the strip? _____ What is the fraction for five parts of the strip? _____ Which one is equal to one whole (1.0)? _____ 10. Compare your two yellow strips and fractions for #8 and #9. What discoveries and conclusions have you come to? Do you see any relationships? Explain yourself in words and sentences. __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ LESSON PLAN #2 Unit Title: Equivalent Fractions and Decimals Math Standard: Number, Number Sense, and Operations Math Indicator: Identify and generate equivalent forms of fractions and decimals. Objective: Each fourth grade mathematics student will identify equivalent fractions using concrete and pictorial models. Materials: Computers with internet access and printers, scrap paper and pencil Procedures: 1. Each student will access “Who Wants Pizza” A Fun Way to Learn about Fractions by typing in the URL: http://math.rice.edu/~lanius/fractions/index.html 2. Click on introduction. Students will read through the introduction. 3. At “Something for You to Do”, students will answer five questions by clicking on correct lettered circle. 4. Students click on “get score” 5. Students will answer final question in their head or by using scrap paper and click on answer to see if they are correct. 6. Have students print out pages 3 and 4. 7. Click on “To the Next Fun Activity” Who Wants Pizza? Practice 1 8. Students will click on squares to make the three fractions and click on “Submit” 9. Click on “To the Next Fun Activity” Who Wants Pizza? Part 2 10. Students will repeat the same process that they used in the above steps #2-9 11. Students read through Who Wants Pizza? Part 3 until “Something For You to Do” 12. Students answer the five questions by clicking on the correct lettered circle. Answer the next four in their head or by using scrap paper and click on answer for each question to check themselves. 13. Have students print out pages 3 and 4. 14. Click on file to close Product: Three print outs with # of correct answers on Part 1,2, and 3 Assessment Criteria: Rubric 5= All five answers are correct on each part (Part 1,2, and 3) 4= At least four answers are correct on each part 3= At least three answers are correct on each part 2= At least two answers are correct on each part 1= At least one answer is correct on each part 0= 0-1 answer is correct on each part Attachments (None) LESSON PLAN #3 Unit Title: Equivalent Fractions and Decimals Math Standard: Number, Number Sense, and Operations Math Indicator: Identify and generate equivalent forms of fractions and decimals. Objective: Each fourth grade mathematics student will identify and generate equivalent forms of fractions and decimals using physical, verbal, and symbolic representations. Materials: pizza circles (see attachment), pizza tables (see attachment), scissors, crayons, colored pencils, markers, pencils, one inch centimeter graph paper, rubric assessment Procedures: 1. Ask students what kind of toppings are their favorite on pizza. Make a tally chart on the board as they respond. Explain to students that they will be making eight different pizzas with a different topping on each. All their pizzas will be cut into a different number of equal pieces. They will be explaining on a chart through fractions, pictures, and/or decimal exchanges that could be made by gluing their pieces down and writing the equivalent fractions in fraction or decimal form to show equivalent fractions or decimals. 2. Review: Give student eight 16 x1 inch graph strips. Have them cut one strip into two equal parts. Label each part ½ and lay both on top of another full strip to discuss 2/2=1.0. Have them cut another strip into four equal parts. Label each part ¼ and lay all four parts on top of another full strip to show 4/4=1.0. Repeat these steps with the remaining four strips to show 1/8, 8/8=1.0 and1/16, 6/6=1.0. 3. Let them move their parts around to discover any other equivalent fractions and discuss their conclusions. As they share write their discoveries on the board. They should conclude 1/2=2/4=4/8=8/16 and/or 4/16=1/4=2/8. They may also discover that you multiply or divide to convert. 4. Give students a graph strip that is 10 x 1 inch. Have students cut up into 10 equal parts. Label each 1/10. Discuss how to write 0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0. Label decimals on the parts as well. 5. Give students another strip 10 x1 inch. Ask them how they could cut this into 5 equal parts. Cut it and label each 1/5. 6. Let them move their tenths and fifth parts around to discover any equivalent forms of fractions and/or decimals. Discuss their conclusions and write their discoveries on the board as they share. They should conclude that 1/2=5/10=0.5, 1/5=2/10=0.2, 4/10=2/5=0.4, 6/10=3/5=0.6, 8/10=4/5=0.8. 7. Pass out paper pizzas (circles) and equivalent pizza charts. 8. Directions for pizza activity: a. Draw a different topping on each pizza. b. Color each pizza with markers, crayons, or colored pencils. c. Cut out equal parts for each pizza (2,4,6,8,16,10, 12) d. Manipulate pieces of pizza to make equivalent fractions that will match the fraction or decimal on the chart. Write the equivalent fraction or decimal and include the equals sign in the picture, too. e. Share their answers with a partner. Peer checking. Revise any manipulations or written symbols. Glue pieces of pizza on chart to show equivalent fractions or decimals. f. Display charts on bulletin board for entire school. “Pizza Party” Product: Pizza Charts Assessment Criteria: 6= Have 6 correct equivalent fractions in picture form and fraction and/or decimal form. 5= Have 5 correct equivalent fractions in picture form and fraction and/or decimal form. 4= Have 4 correct equivalent fractions in picture form and fraction and/or decimal form. 3= Have 3 correct equivalent fractions in picture form and fraction and/or decimal form. 2= Have 2 correct equivalent fractions in picture form and fraction and/or decimal form. 1= Have 1 correct equivalent fraction in picture form and fraction and/or decimal form. 0= No correct equivalent fractions in picture form and fraction and/or decimal form. Attachments: See next two pages Pizza Conversions! Name _________________________ Directions: Convert each fraction to its decimal equivalent, or each decimal to its fractional equivalent. Draw a picture to show your thinking for each one. 2/6 = _____ 0.3 = _____ 12/16 = _____ 6/8 = _____ 1/2 = _____ (decimal form) 3/6 = _____ (decimal form) 0.5 = _____ Now YOU make one up! LESSON PLAN #4 Unit Title: Equivalent Fractions and Decimals Math Standard: Number, Number Sense and Operations Math Indicator: Identify and generate equivalent forms of fractions and decimals Objective: Each 4th grade mathematics student will use a 10x10 square and number line to show equivalent forms of familiar fractions and decimals . Materials: Decimal square paper (3 copies for each student) Construction paper Crayons/colored pencils Paper for group number lines Post-it notes Procedures: 1. Have students cut out 10 x 10 square and ten bar grids. With a 10x10 square have students fold the square in ½. Then shade in ½. Glue this shaded square on a piece of construction paper. Under the square write the fraction in familiar form, then as a base ten fraction, and finally as a decimal. (1/2, 50/100, 0.5) 2. Next explore fourths. (Repeat the process from # 1) Have the students show ¼ in 2 different ways (example shading in a 5x5 square and using strips). Repeat for ¾. 3. Let students explore with shaded diagrams that they made to discover equivalent fraction and decimal pairs. Discuss findings and record on chalkboard. 4. Next explore fifths using the 10 x 10 paper following the process in # 1. 5. Have students explore tenths using the ten bar grid by relating diagrams to the diagrams made in exploring fifths. ( example: 4/10 =2/5 =0.4) Extending the lesson using number lines to show equivalent fraction/decimal pairs. 6. Give each student a post-it with a fraction, number, or decimal on it. Students go to the board and without talking, put their post-its on the board from least to greatest in number line format. (1/2, 5/10, 50/100, 0.5, ¼, 25/100, 0.25, ¾, 75/100, 0.75, 1/5, 2/10, 20/100, 0.2, 2/5, 4/10, 40/100, 0.4, 3/5, 6/10, 60/100, 0.6, 4/5, 8/10, 80/100, 0.8, 5/5, 10/10, 100/100, 1.0 ) 7. Discuss this product (number line) noting relationships and making necessary revisions. 8. Discuss the number line concept to show equivalent fractions/decimals. 9. Explain the final product to students. Students will work in small groups to create original number lines that represent at least 5 plotted pairs of equivalent fractions/decimals. Product: Group generated number lines. Assessment Criteria: Rubric 5 = Five correctly plotted pairs of equivalent fractions/decimals 4 = Four correctly plotted pairs of equivalent fractions/decimals 3 = Three correctly plotted pairs of equivalent fractions/decimals 2 = Two correctly plotted pairs of equivalent fractions/decimals 1 = One correctly plotted pairs of equivalent fractions/decimals 0= 0 correctly plotted pairs of equivalent fractions/decimals Attachments none LESSON PLAN #5 Unit Title: Equivalent Fractions and Decimals Math Standard: Number, Number Sense and Operations Math Indicator: Identify and generate equivalent forms of fractions and decimals Objective: Each 4th grade mathematics student will: Use fractions and decimals to approximate what part of a chapter in one of their textbooks contains pictures. Materials: Textbooks (from any subject OTHER than math!) Grid transparency for each group (see attachments) Visa vie markers Calculators Textbook/pictures record sheet (see attachments) Procedures: Begin by asking students to predict what part of a chapter in their textbook contains pictures. Discuss this in equivalent decimals and fractions. Decide with the class what will be considered pictures (graphs, photos, etc.) Divide the class into small groups and give each group a set of materials. Assign the same chapter to all groups or vary the activity by assigning different chapters in the same book or use different books. Explain the worksheet to students to be sure they know what is expected of them. Tell students whether you expect one worksheet per group or one per each student. Be sure to explain to the students that the decimal and fraction data from each page must be in equivalent forms. Now might be a good time to review equivalent forms of fractions and decimals. Discuss with students appropriate ways to record data (ex charts). Allow student groups to determine how they are going to use the 100 grid to collect the data. Have groups experiment with the grid transparency and then bring the whole group back together to discuss their findings. (Example-lay the transparency on the page and color in with markers all the squares that cover the picture-count the colored squares.) Then instruct the students to use the grid to check each page in the chapter and record the data. Discuss with students how to add and find the mean. When groups have completed the worksheet, compare results as a class, and discuss. Product: Completed worksheet (one per group or one per each student-specify in directions) that shows data collected in equivalent decimal and fraction forms, explanation of how the grid sheet was used and explanation of results. Assessment Criteria: Rubric criteria: a) data collected in equivalent forms, b) reasonable explanation of how the group used the grid, c) mean in fraction and decimal form, d) reasonable explanation of results 4= all 4 a, b, c, d correct 3= 3 out of 4 correct 2= 2 out of 4 correct 1= 1 out of 4 correct 0= 0 correct Attachments 100 grid (copy as a transparency) Textbook/picture record sheet Textbook/picture Record Sheet 1. Make a prediction of how much of a chapter in your textbook contains pictures. Decimal___________________ Fraction_____________________ 2. Using your 100 grid transparency, determine what part of each page is pictures and record your data here. Be sure to use both fraction and decimal form. Create a chart to collect your data here. 3. Tell how you used the 100 grid transparency to decide what part of the chapter is pictures. _______________________________________________________________________________________ _______________________________________________________________________________________ _______________________________________________________________________________________ _______________________________________________________________________________________ _______________________________________________________________________________________ _______________________________________________________________________________________ _______________________________________________________________________________________ 4. Use your data to find the mean part of the chapter that is pictures. Show your work here. Be sure to show your answer as a decimal and a fraction. 5. Explain what your results show. _______________________________________________________________________________________ _______________________________________________________________________________________ _______________________________________________________________________________________ _______________________________________________________________________________________ _______________________________________________________________________________________ _______________________________________________________________________________________ 6. How do your results compare with your prediction? Explain. ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ RECOMMENDED UNIT RESOURCES Print Resources Activity Math: Using Manipulatives in the Classroom by Bloomer and Carlson Elementary Middle School Mathematics by John A. Van De Walle Internet Sites for Teacher Reference http://www.pbs.org/teachersource/mathline/lessonplans Internet Sites for STUDENT Use http://math .rice.edu/~lanius/fractions/index.html Additional Resources Unit Test Template Unit Title: ______________________________________________ Grade Level : 3 4 5 Math Standard: ___________________________ Indicator Number: __________ Teacher’s Name ________________________________ Building _________________________ District ________________________________________ Date of Testing ___________________ Skills & Concepts: Post-Test Student’s Name ____________________________________ Total Score: _____/20 A. Multiple Choice (2 points each; 10 points total) Directions to the student: Show how you solve each problem in the box provided. Use words, pictures, or numbers. Then circle the LETTER of the correct answer. 1. Identify the shaded shape that represents the equivalent form of 4/12? How did you find your answer? a. b. c. d. 2. Which of the following examples is NOT equivalent to 4/5? How did you find your answer? a. 0.8 b. c. d. 0.45 3. Which of the following examples is equivalent? How did you find your answer? a. six tenths, 0.6 b. three fourths, 0.34 c. two thirds, 0.33 d. five tenths, 0.5 4. Identify the example that represents one whole in fraction form? How did you find your answer? a. 100/100 b. 10/100 c. 1/100 d. 0/100 5. Identify the shaded parts of the rectangle that represents the equivalent form of 2/5. How did you find your answer? a. b. c. d. Objective Test Sub-Score: _____/10 B. Multiple-Step Problem Solving (3 points) Directions to the student: Find the answer to this question. Be sure to finish the WHOLE question. Be sure to show your work. Billy rode his skateboard 3/10 of a mile and Kyle rode his skateboard 4/5 of a mile. Plot each distance as a decimal on the number line. Label Billy’s distance with a “B” and Kyle’s distance with a “K.” 0 0.5 1 Score: _____/3 C. Try It Another Way! (3 points) Directions to the student: Read the question below. Miles can be measured in tenths. John had to run six tenths of a mile to reach his friend’s house. Draw, write about, or use number sentences to show two different ways to represent how far John ran in equivalent fraction form. Explain each answer in words. Method #1 Method #2 Score: _____/3 D. Extended Response (4 points) Directions to the student: Answer this question. Use sentences to explain your answer.0 What part of the entire picture is shaded? Write your answer in fraction and decimal form. Fraction Form ____________ Decimal Form ____________ Write an explanation of your answer. Explain how you got your answers using mathematical terms. _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ Score: _____/4 Unit Post-Test ANSWER KEY Multiple Choice (2 points each; 10 possible) 1. D 2. D 3. A 4. A 5. C Multi-Step Problem Solving (3 points each) Scoring Rubric: 3= Plotted both decimals correctly on the number line and showed work. 2= Plotted both decimals without showing work 1= Plotted one decimal without showing work. 0= Shows no correct answers Try It Another Way! (3 points) Scoring Rubric: 3= Represents two ways to show the equivalent fraction form with appropriate explanations. 2= Represents two ways to show the equivalent fraction form with limited explanations. 1= Represents one way to show the equivalent fraction form with no explanation. 0= Represents no equivalent fraction or explanation. Extended Response (4 points) Scoring Rubric: 4= Answers ½ and .5 and explains in detail what process they used to get their answer using mathematical terms. 3= Answers ½ and .5 with limited explanation. 2= Shows some understanding of equivalent fractions and decimals through answers or explanation. 1= Answers 1/2 with no explanation. 0= Answers incorrectly and has no appropriate explanation. The CROSSROADS Project Enhancing Mathematics Education, Grades 3-5 Stark County, Ohio UNIT TEST Composite Data Record Unit Title: ______________________________________________ Grade Level : 3 4 5 Math Standard: ___________________________ Indicator Number: __________ Teacher’s Name ________________________________ Building _________________________ District ________________________________________ Date of Pre-Testing ___________________ Date of Post-Testing ___________________ Number of Students Tested _____________ Number of Students Tested __________ POINTS AWARDED Pre-Test Class Average Post-Test Class Average Change (+/-) Part A (Multiple Choice) 10 points possible Part B (Multi-Step Problem Solving) 3 points possible Part C (Variant Methods) 3 points possible Part D (Extended Response) 4 points possible TOTAL Score 20 points possible Please write 1-3 paragraphs describing your experiences with this unit, what the test results suggest to you, and how you plan to use this information in your teaching practices. Attach this response along with the student test set described below to this page for submission. PAYMENT awarded with submission of: (1) this completed form, (2) paragraph(s) as described, and (3) ONE student’s pre- and post-test set. Please white-out the student’s last name to protect his/her identity. CROSSROADS Validation ________ Date __________

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4Th Grade Equivalent Fractions Worksheets document sample

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