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Fraction Carpet Cover Up KEY Keisha is going to create several models to show customers how portions of room would look carpeted. For each given situation: 1. 2. 3. 4. 5. 6. 7. Give an estimate and how you determined your estimate. Use fraction squares to model the situation. The one whole square represents 1 room. Draw a diagram of the problem and label all parts correctly. Shade the area of the room that will be carpeted. Find a solution that states what fraction of the room will be carpeted. Justify your response. Review your estimate and solution. Write a number sentence to show the relationship between the numbers in the problem and the diagram. Problem 1 Two-thirds of the room is designated workspace. Four-fifths of the workspace will be carpeted. Estimate: The area of a rectangle may be calculated by doing length times width. The length and width are both close to 1, but less than 1, so the solution must be less than 1 square unit because 1 unit x 1 unit = 1 square unit. Two-thirds is the size of the group we begin with (portion of the room designated as workspace) which means we begin with less than 1 whole unit. We want less than one complete group of two-thirds (four fifths), which means we will carpet less than two thirds of the room. We will carpet a little less than twothirds because five-fifths would be all of the two thirds and since we will carpet four-fifths, (not quite a complete group of two thirds), the solution is somewhere between one-half and two-thirds. Diagram: 2 3 workspace 4 5 carpet Four-fifths of two-thirds is eight-fifteenths Number Sentence: 4 carpet 5 x 2 workspace 3 = 8 of the room is carpet 15 Review estimate and solution: The solution is between the estimate which was between 1 2 and . Write equivalent fractions for each estimate and the product to further compare 2 3 the fractions. Why Does This Work: 4x2 4 rows with 2 in each row number of equal size parts in double shaded region = = 5x3 5 rows with 3 in each row number of equal size parts in the whole square 2 4 = 0.8 and 0.67 5 3 0.8 x 0.67 is calculated by doing 67 x 8 = 536 Where do you place a decimal point for the product to be reasonable? 0.536 How does 0.536 relate to 8 ? 15 8 ÷ 15 = 0.533… which is reasonably close to 0.536. 1 2 2 3 0.533… is between 0.5 ( ) and 0.666… ( ) Fraction Carpet Cover Up KEY Keisha is going to create several models to show customers how portions of room would look carpeted. For each given situation: 1. 2. 3. 4. 5. 6. 7. Give an estimate and how you determined your estimate. Use fraction squares to model the situation. The one whole square represents 1 room. Draw a diagram of the problem and label all parts correctly. Shade the area of the room that will be carpeted. Find a solution that states what fraction of the room will be carpeted. Justify your response. Review your estimate and solution. Write a multiplication number sentence to show the relationship between the numbers in the problem and the diagram. Problem 2 One-half of the room is designated workspace. One-half of the workspace will be carpeted. Estimate: The area of a rectangle may be calculated by doing length times width. The length and width are both less than 1, so the solution must be less than 1 square unit because 1 unit x 1 unit = 1 square unit. Since half, of one-half is one-fourth, my estimate is one-fourth. Diagram: 1 workspace 2 1 2 carpet One-half of one-half is one-fourth Number Sentence: 1 carpet 2 x 1 workspace 2 = 1 of the room is carpet 4 Review estimate and solution: The solution and the estimate are the same. Why Does This Work: 1x1 1 row with 1 in each row number of equal size parts in double shaded region = = 2x2 2 rows with 2 in each row number of equal size parts in the whole square 1 1 = 0.5 and = 0.5 2 2 0.5 x 0.5 is calculated by doing 5 x 5 = 25 Where do you place a decimal point for the product to be reasonable? 0.25 How does 0.25 relate to 1 ? 4 1 ÷ 4 = 0.25 which is equivalent to 1 4 Fraction Carpet Cover Up KEY Keisha is going to create several models to show customers how portions of room would look carpeted. For each given situation: 1. 2. 3. 4. 5. 6. 7. Give an estimate and how you determined your estimate. Use fraction squares to model the situation. The one whole square represents 1 room. Draw a diagram of the problem and label all parts correctly. Shade the area of the room that will be carpeted. Find a solution that states what fraction of the room will be carpeted. Justify your response. Review your estimate and solution. Write a multiplication number sentence to show the relationship between the numbers in the problem and the diagram. Problem 3 Three-fourths of the room is designated workspace. One-third of the workspace will be carpeted. Estimate: The area of a rectangle may be calculated by doing length times width. The length and width are both less than 1, so the solution must be less than 1 square unit because 1 unit x 1 unit = 1 square unit. One-third of three-fourths is one-fourth, because there are three one-fourth pieces in three-fourths. My estimate is one-fourth. Diagram: 3 workspace 4 1 3 carpet One third of three-fourths is three twelfths 1 3 carpet x workspace = 3 4 simplify at this point so students may see the pattern. Number Sentence: 3 of the room is carpet. Do not 12 Review estimate and solution: The solution and the estimate are the same. By using the 3 3 1 GCF for 3 and 12 to simplify: , the equivalent fraction is . 12 3 4 Why Does This Work: 1x3 1 rows with 3 in each row number of equal size parts in double shaded region = = 3x4 3 rows with 4 in each row number of equal size parts in the whole square 1 3 0.33 and = 0.75 3 4 0.33 x 0.75 is calculated by doing 33 x 75 = 2475 Where do you place a decimal point for the product to be reasonable? 0.2475 How does 0.2475 relate to 3 ? 12 3 ÷ 12 = 0.25 which is reasonably close to 0.2475 0.25 is equivalent to 1 4 Fraction Carpet Cover Up KEY Keisha is going to create several models to show customers how portions of room would look carpeted. For each given situation: 1. 2. 3. 4. 5. 6. 7. Give an estimate and how you determined your estimate. Use fraction squares to model the situation. The one whole square represents 1 room. Draw a diagram of the problem and label all parts correctly. Shade the area of the room that will be carpeted. Find a solution that states what fraction of the room will be carpeted. Justify your response. Review your estimate and solution. Write a multiplication number sentence to show the relationship between the numbers in the problem and the diagram. Problem 4 Two-thirds of the room is designated workspace. One-half of the workspace will be carpeted. Estimate: The area of a rectangle may be calculated by doing length times width. The length and width are both less than 1, so the solution must be less than 1 square unit because 1 unit x 1 unit = 1 square unit. Since half of two-thirds is one-third (there are two one-thirds in two-thirds), my estimate is one-third. Diagram: 2 workspace 3 1 2 carpet One half of two thirds is two sixth 1 2 2 x = 2 3 6 (Note: do not simplify at this point so students may see the pattern.) Number Sentence: Review estimate and solution: The solution and the estimate are the same. By using the 2 2 1 GCF for 2 and 6 to simplify: , the equivalent fraction is . 6 2 3 Why Does This Work: 1x2 1 row with 2 in each row number of equal size parts in double shaded region = = 2x3 2 rows with 3 in each row number of equal size parts in the whole square 2 1 0.67 = 0.5 and 2 3 0.5 x 0.67 is calculated by doing 67 x 5 = 335 Where do you place a decimal point for the product to be reasonable? 0.335 How does 0.335 relate to 2 ? 6 2 ÷ 6 = 0.333… which is reasonably close to 0.335 0.333… is equivalent to 1 3