Fractions at the Fair ASSESSMENT #LEMA10 Benchmark Grades: Can be adapted for second to fourth grades. Summary: Students demonstrate their knowledge of fractions by drawing a representation of the fractions, comparing fractions, and changing improper fractions to mixed numbers. Keywords: Working with fractions Writing equations Working with inequalities (< >) LEMA10 Page 1 Copyright 1999 Center for Performance Assessment All rights reserved 800-844-6599 Fractions at the Fair ASSESSMENT #LEMA10 Information for the Teacher Task Description This assessment allows the teacher to evaluate students’ ability to work with fractions. In Task 1, students demonstrate their understanding of fractions by drawing pictures of given fractions. Task 2 requires students to demonstrate their understanding of equal fractions. In Task 3, fractions with the same denominator are compared. Task 4 requires students to regroup improper fractions as mixed numbers. Required Materials Fraction kits are helpful if you permit the use of manipulatives during the assessment. Scoring key for the teacher Task 1: Students should represent 1/6 and 1/8. Task 2: Students should show that 1/2 equals 3/6 and 1/4 equals 2/8. Task 3: 4/5 > 2/5. Answers will vary on the third time he threw the ball. Task 4: 5/2 = 2 1/2 LEMA10 Page 2 Copyright 1999 Center for Performance Assessment All rights reserved 800-844-6599 Fractions at the Fair Math is everywhere! Have you ever been to a fair? It is a lot of fun and there are so many different things to do. In these pages, you will see how to find math even at a fair. LEMA10 Page 3 Copyright 1999 Center for Performance Assessment All rights reserved 800-844-6599 Task 1: How much to get in? Travis and Martin are two friends that are at the fair. Their moms gave them different amounts of money to spend. Travis has $6. Martin has $8. When they got to the fair, they found that it costs $1 to get in. In the boxes, draw pictures showing the part of $6 that Travis spent and the part of $8 that Martin spent to get in to the fair. Then write the parts as fractions. The fraction of the money Travis spent: _____________ The fraction of the money Martin spent: _____________ LEMA10 Page 4 Copyright 1999 Center for Performance Assessment All rights reserved 800-844-6599 Scoring Guide – Task 1 4 Advanced The criteria for a score of Proficient are successfully met. More advanced work is included. For example, the student compares the two fractions. Other examples include: _________________________________________________ 3 2 Proficient The student draws the parts correctly. The pictures show an understanding of fractions. A correct fraction is written for both boys. Basic One correct fraction and one correct picture are included. OR Both fractions and both pictures are accurate, but significant coaching is needed. More work is needed. 1 Below Basic The response does not include any correct fractions or pictures. The task should be repeated. LEMA10 Page 5 Copyright 1999 Center for Performance Assessment All rights reserved 800-844-6599 Scoring Guide – Task 1 I drew two pictures and wrote two fractions. My pictures and fractions are correct. I did not need help from the teacher. I think I did an extra great job because: I needed help drawing the pictures or writing the fractions. I will keep trying because I am almost there. I did not understand what to do. I will ask questions and try again. LEMA10 Page 6 Copyright 1999 Center for Performance Assessment All rights reserved 800-844-6599 Task 2: Food! Of course the first thing they want to do at the fair is eat. Travis decides to spend $2 on food. This means that so far Travis has spent $3. In other words, he has already spent one half, or three-sixth of his money. Draw a picture showing that these two fractions are equal. 1/2 3/6 Martin only spent $1 on food. So far he has spent $2 of his $8. Write two equivalent fractions showing how much Martin has spent and draw pictures to show how the fractions are equal. ______ LEMA10 Page 7 ______ Copyright 1999 Center for Performance Assessment All rights reserved 800-844-6599 Scoring Guide – Task 2 4 Advanced The criteria for a score of Proficient are successfully met. More advanced work is included. For example, the student compares the two sets of fractions. Other examples include: _________________________________________________ 3 2 Proficient Pictures are drawn to represent all the fractions. Equivalent fractions are written. All math is correct. No coaching is needed. Basic One fraction is written for Martin’s money, but the equivalent fraction could not be written. OR The pictures do not represent the equivalent fractions for Travis or Martin. Significant coaching is needed. More work is needed. 1 Below Basic It is unclear what the student completed. The task should be repeated. LEMA10 Page 8 Copyright 1999 Center for Performance Assessment All rights reserved 800-844-6599 Scoring Guide – Task 2 I drew pictures to show how the fractions are equal. I wrote the correct fractions. I didn’t need any help from the teacher. I think I did an extra great job because: _________________________________________________ I needed help seeing how the fractions are equal. It was hard to draw without help. I will keep trying because I am almost there. I did not understand what to do. I will ask questions and try again. LEMA10 Page 9 Copyright 1999 Center for Performance Assessment All rights reserved 800-844-6599 Task 3: Martin’s game Martin’s favorite game is throwing balls and knocking the bottles down. He is very good at the game. When he played the first time, he knocked 2/5 of the bottles down. When he played the second time, he knocked 4/5 of the bottles down. 1. Compare the first and second throws. Use greater than or less than. ______________________________________ 2. Now guess what fraction of the bottles he knocked down the third time. Write this number as a fraction. How did you get your guess? ______________________________________ 3. Compare the second and third throws. Use greater than or less than. ______________________________________ 4. Draw a picture comparing these three fractions on the back of your page. LEMA10 Page 10 Copyright 1999 Center for Performance Assessment All rights reserved 800-844-6599 Scoring Guide – Task 3 4 Advanced The criteria for a score of Proficient are successfully met. More advanced work is included. For example, the pictures show equivalent fractions (ten bottles instead of five bottles). Other examples include: _________________________________________________ 3 2 1 Proficient Two correct comparisons are written using greater than or less than. The pictures accurately compare the fractions. No coaching is needed. Basic The student demonstrates an understanding of greater than and less than, but is unable to show it with a comparison or with a picture. Significant coaching is needed. More practice with the symbols is needed. Below Basic The student shows no understanding of the concept of greater than and less than when discussing the fractions. The task should be repeated. LEMA10 Page 11 Copyright 1999 Center for Performance Assessment All rights reserved 800-844-6599 Scoring Guide – Task 3 I wrote comparisons without any help from my teacher. I compared the fractions. I did not need help from the teacher. I think I did an extra great job because: I needed help drawing or writing comparisons. I will keep trying because I am almost there. I did not understand what to do. I will ask questions and try again. LEMA10 Page 12 Copyright 1999 Center for Performance Assessment All rights reserved 800-844-6599 Task 4: The Ferris Wheel Travis and Martin meet three friends at the fair. They all want to ride on the Ferris wheel. A Ferris wheel seat can only hold two people. Write an improper fraction to show how many seats Travis, Martin, and their three friends will need. Show this number as a mixed number. Show all of your work. Work area: ___________ = ___________ Improper fraction Mixed number Draw a picture of the people on the Ferris wheel. LEMA10 Page 13 Copyright 1999 Center for Performance Assessment All rights reserved 800-844-6599 Scoring Guide – Task 4 4 Advanced The criteria for a score of Proficient are successfully met. More advanced work is included. For example, the drawing illustrates that the improper fraction equals the mixed number. Other examples include: _________________________________________________ 3 2 1 Proficient The correct improper fraction is written. The correct mixed number is written. The work is shown. A drawing is completed. No coaching is needed. Basic The student does not write the improper fraction and the mixed number, the work was not shown, or the picture was not drawn. Coaching is needed. More work is needed. Below Basic The student does not write the correct improper fraction or mixed number. The task should be repeated. LEMA10 Page 14 Copyright 1999 Center for Performance Assessment All rights reserved 800-844-6599 Scoring Guide – Task 4 I wrote an improper fraction and a mixed number. I showed all of my work. I didn’t need any help from the teacher. I think I did an extra great job because: I needed help changing the improper fraction to the mixed number. I will keep trying because I am almost there. I did not understand what to do. I will ask questions and try again. LEMA10 Page 15 Copyright 1999 Center for Performance Assessment All rights reserved 800-844-6599