Name: Date:. One of the shapes below is cut into fourths. Mark an X on the shape that is cut into fourths. Show or explain how you knew which shape to mark. 3. Lakeisha baked a pie and cut it into equal pieces as shown. Lakeisha ate 2 of the pie and her brother Chris ate 4 of the pie. a) Pieces Lakeisha ate: b) Pieces Chris ate: 2. Each of the grids below has the same figure drawn on it. On Grid A, draw lines to show how to divide the figure into fourths. On Grid B, show a different way to divide the figure into fourths. 4. Bryce drew this picture: Grid A Grid B Then he said, This shows that 4 2. is greater than What was his mistake? Draw a picture that shows why 2 is greater than 4. page
5. Choose True or False for the following equation: 4 > 2 4 < 2 4 = 2 2 > 4 2 < 4 7. For each item, choose Yes or No to indicate whether each number graphed on the number line represents one whole. a. Yes No b. Yes No c. Yes No d. Yes No 6. Mrs. Frances drew a picture on the board. Then she asked her students what fraction it represents. a) Emily said that the picture represents 2 6. Label the picture to show how Emily s answer can be correct. b) Raj said that the picture represents 2 3. Label the picture to show how Raj s answer can be correct. c) Alejandra said that the picture represents 2. Label the picture to show how Alejandra s answer can be correct. page 2
8. Rectangle F is divided into 4 equal areas as shown:. A zookeeper made this line plot to show the ages of all the monkeys at a zoo. Rectangle F a) What fraction is represented by the shaded area of Rectangle F? b) Rectangle G is divided into 4 equal areas, as shown: a) What fraction of the monkeys at this zoo are eight years old? b) What fraction of all the monkeys at this zoo are not 8 years old? Rectangle G What fraction is represented by the shaded area of Rectangle G? c) Is the shaded area of Rectangle F equal to the shaded area of Rectangle G? Explain your thinking. Use what you know about the area of Rectangle F and Rectangle G to explain your answer. 0. For items a. through c., select Yes or No to indicate whether each fraction can be placed in the box to make a true inequality. 3 4 > 3 4 a. 2 Yes No b. Yes No c. 2 Yes No page 3
. A Fractional Part Mrs. Washington asked her students what fractional part of these 2 circles is shaded. 2. Lena will use boards similar to the one shown below to build some shelves. a) Lena can use one entire board to make 4 shelves. Each shelf will be the same shape and size. She needs to make 4 shelves that are each the same shape and size. Draw straight lines on the board above to show where Lena could cut it to make the shelves. b) On the board below, draw straight lines to show another way Lena could cut the board to make 4 shelves that are each the same shape and size. Odessa thinks the answer is 2. Bob thinks the answer is 3 4. a) Who is correct Odessa, Bob, or both? b) Write how you would explain your answer to part a to Odessa and Bob. Draw your own pictures to go with your explanation. c) Lena can also make shelves that are the shape and size of the piece of board shown below. How many shelves of this shape and size could she make from the original board? d) Lena wants to use a new board of a different size. This board is shown below. What fraction of the original board is this new board? page 4
3. Tom, Nuno, and Paul each made a pizza. All the pizzas were the same size and shape. Tom cut his pizza into 2 equal pieces. Nuno cut his pizza into 3 equal pieces. Paul cut his pizza into 4 equal pieces. a) Which boy has the smallest size pieces of pizza? Show or explain how you got your answer. b) Each boy ate some of the pizza he made. Tom ate piece of his pizza. Nuno ate piece of his pizza. Paul ate 2 pieces of his pizza. Which boys ate the same amount of pizza? Show or explain how you got your answer. 5. Ms. Diaz works at a zoo. She created an exhibit with the animals listed in the table below. Animal Exhibit Type of Animal Number elephant 8 giraffe 2 rhino 4 a) What fraction of the animals are giraffes? Simplify your answer to lowest terms. Show or explain how you got your answer. Ms. Diaz plans to add more animals to the exhibit. She will add 2 more elephants. She will add more giraffes and rhinos so that the ratio of elephants to other animals is the same as before. b) What is the new total number of animals that will be in the exhibit? Show or explain how you got your answer. 4. Chet shaded part of the two large rectangles shown below. 6. Look at this number line. Key represents Step A Plot a point on the number line that represents the location of 2 6. Step B a) Write a fraction that represents the shaded part of the two large rectangles. b) Write a different number that is equivalent to the fraction you wrote in the previous part. Show or explain how you got your answer. c) Draw and shade a picture of rectangles that represents the number 2 3. Show or explain how you got your answer. Explain why the point you plotted is correct. Use what you know about number lines in your explanation. Use words, numbers, and/or symbols in your explanation. Benjamin says that if he divides the number line between 2 and 3 into two equal parts, the location of the point 2 6 will change. Explain why Benjamin is correct or incorrect. Use what you know about number lines in your explanation. Use words, numbers, and/or symbols in your explanation. page 5
7. Study the figure below. Draw lines on the figure to divide it into 4 equal parts. Draw an X on 4 of the figure. 8. The school Drama Club held a contest to select a design that can be used for the program cover and on posters for advertising its play. Brent s, Keisha s, and Miguel s cover designs were the three finalists. They were voted on by the entire Drama Club to determine the winning design. The designs are shown below. Brent received 4 5 Keisha received 3 Miguel received 2 5 of the votes. of the votes. of the votes. Use the voting information above to determine the first, second, and third place designs. Below, provide the work that shows how you arrived at your answers. page 6
. Mary, Ed, Rob, and Lilly are all reading the same book. Last week, 2. Look at the shapes in this chart. Mary read 2 of the book, Ed read 2 4 Rob read 3 of the book, of the book, and Lilly read 3 2 of the book. a) Pick two people from this list. Write a sentence that compares how much these two people read. Use the words more than, less than, or the same in your sentence. b) Pick two other people from the list. Write a sentence that compares how much these two people read. Use the words more than, less than, or the same in your sentence. a) If Shape H represents, what number does Shape R represent? b) If Shape Z represents 4 3, what number does Shape H represent? Show your work or explain how you know. c) If Shape R represents 6, what number does Shape Z represent? Show your work or explain how you know. 20. Look at this loaf of bread. 22. Dylan shaded part of this square gray to represent a fraction. Morgan ate 2 slices of bread. Trent ate slice of bread. a) What fraction of the loaf of bread did Morgan and Trent eat? b) What fraction of the loaf of bread is left over? Dylan explained that he shaded the square to represent the fraction 3 2, because he shaded 2 parts gray out of a total of 3 parts. a) What is the mistake in Dylan s explanation? b) What fraction of the square is shaded gray? page 7
23. Look at this number line. 25. Look at this number line. a) What fraction does point G represent on the number line? b) Write a different fraction that is equivalent to the fraction you wrote in the part above. a) What point on the number line shows the location of 4 5? b) What point on the number line shows the location of 5 8? 24. Blair and Carmen each made a pie. Each of these pies is cut into equal pieces. Blair s pie Carmen s pie Blair ate 2 pieces of her pie. a) Write a fraction to show the part of the pie Blair ate. Carmen ate 2 pieces of her pie. Blair said, Carmen and I ate the same amount of pie. b) Explain why Blair s statement is or is not correct. page 8
Problem-Attic format version 4.4.2 c 20 206 EducAide Software Licensed for use by Cherise Matechak Terms of Use at www.problem-attic.com 03/3/207. 2. 3. 4; 2 4. 5. 6. The second shape Response clearly shows two different ways to divide the figure into fourths. The two wholes have different areas, and are thus different sizes. In order to correctly compare these two fractions, we need to draw a picture of them with the same sized whole. The picture below correctly shows that 2 is greater than 4. False; True; False; True; False Emily s answer of 2 6 would mean that all six little boxes are the whole and two of these have been shaded: For Raj, there are 3 small boxes in the whole so the two shaded boxes represent two out of three or 2 3 : For Alejandra, each little box is one and so the whole is one little box as pictured below: 8.. 3 ; 2 3 4 ; 4 ; The areas are different. Rectangle F and Rectangle G are not the same whole. 0. Yes ( 3 4 2 = 3 3 = ) ; No ( 34 = 2 = 4 3 ) ( ; No 34 2 = 6). Both students are correct, 2 = 3 4 2. [drawing]; 6; 2 3 3. 4. 5. 6. 7. 8.. 20. 2. 22. 23. 2 3 Paul; Paul and Tom Mary and Ed read the same amount. Lilly read more than Rob. Ed read less than Lilly. three-eighths OR two-eighths and one-eighth; five-eighths One-third or equivalent; One and one-half or equivalent; One-fourth or equivalent 7. Yes; No; Yes; Yes 24. 25. 2 8 or equivalent value U; T