FIFTH GRADE Third Marking Period CCSS Extended Constructed

FIFTH GRADE Third Marking Period CCSS Extended Constructed Response Questions 2015 -2016 http: //prezi. com/yf 2 ram 2 nqthh/? utm_campaign=share&utm_mediu m=copy Elizabeth Public Schools

Intervention Block Framework Students work independently to solve extended constructed response question. Students work in groups to either discuss responses and compile 1 response or students work together to score each response based on the rubric. Students share responses or discussion points as a whole group.

Scoring Guide for Mathematics Extended Constructed Response Questions 3 -Point Response (Generic Rubric) The response shows complete understanding of the problem’s essential mathematical concepts. The student executes procedures completely and gives relevant responses to all parts of the task. The response contains few minor errors, if any. The response contains a clear, effective explanation detailing how the problem was solved so that the reader does not need to infer how and why decisions were made. 2 -Point Response The response shows nearly complete understanding of the problem’s essential mathematical concepts. The student executes nearly all procedures and gives relevant responses to most parts of the task. The response may have minor errors. The explanation detailing how the problem was solved may not be clear, causing the reader to make some inferences. 1 -Point Response The response shows limited understanding of the problem’s essential mathematical concepts. The response and procedures may be incomplete and/or may contain major errors. An incomplete explanation of how the problem was solved may contribute to questions as to how and why decisions were made. 0 -Point Response The response shows insufficient understanding of the problem’s essential mathematical concepts. The procedures, if any, contain major errors. There may be no explanation of the solution or the reader may not be able to understand the explanation. The reader may not be able to understand how and why decisions were made.

5. OA. 1 -Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

Ms. Johnson gives one-eighth of a pizza to each of her 24 students. Write a multiplication expression to represent the total number of pizzas Ms. Johnson gives to her students. How many pizzas does Ms. Johnson give to her students? Represent the number of pizzas given to Ms. Johnson’s class in a pictorial representation. 5. NF. 4 - Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

Ms. Webb is switching schools and needs to pack up her classroom. She has decided to rent a moving truck so that she can move her boxes in one trip. All of the trucks are 5 feet wide and 6 feet tall, but the trucks have different lengths. The choices of lengths are 10 feet, 14 feet, 17 feet, 20 feet, 24 feet, and 26 feet. Find the volume of each truck to determine how much it can hold. Ms. Webb stacked all of her boxes into a pile that is 12 feet wide, 7 feet long, and 3 feet high. Which truck should she rent? Ms. Bradley is also switching schools. She and Ms. Webb are thinking about renting a truck together. If Ms. Bradley’s stack of boxes is 9 feet wide, 11 feet long, and 4 feet high, which truck would the two teachers have to rent in order to hold all their boxes? 5. MD. 5 - Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

5. NF. 5 -Interpret multiplication as scaling (resizing) by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication and explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.

5. NF. 2 - Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators.

Dan is saving money to buy a bicycle. The bicycle costs $165. Dan earns $15 in allowance each week. If he saves his whole allowance, how many weeks will pass before Dan has enough money for this bicycle? Create a table to show long it will take and how much money Dan will have each week. Dan decides that he wants to spend a little bit of his allowance each week instead of saving it all. If he saves $10 a week, how long will it take him to save up for the bicycle? Add a column to your table showing this data. What if he only saves $5 a week? Add another column to your table showing how long it will take Dan to save enough for his bicycle. Use graph paper to draw a line graph displaying these three situations. Would having this graph help Dan make a decision about 5. OA. 3 - Analyze patterns and relationships 5. G. 1 & 5. G. 2 – Graph points on the coordinate plane to solve real-world and mathematical problems.

Choose one set of expressions. Set A Set B Set C Set D 1 + 2 + (3 + 4) 1 x 2 x (3 x 4) 1 + 2 x (3 + 4) (1 x 2) + 3 x 4 (1 + 2) + 3 + 4 (1 x 2) x 3 x 4 (1 + 2) x 3 + 4 1 x 2 + (3 x 4) 1 + (2 + 3) + 4 1 x (2 x 3) x 4 1 + (2 x 3) + 4 1 x (2 + 3) x 4 1 + 2 + 3 + 4 1 x 2 x 3 x 4 1 + 2 x 3 + 4 1 x 2 + 3 x 4 Find the value of each expression. What patterns do you notice? What impact does the position of the parentheses have on the value of the expressions? Find a partner who chose a different set than the one you chose. What did they notice about their expressions? Why do we use parentheses in mathematical expressions? When is it important to use parentheses? When are parentheses not necessary? 5. OA. 1 -Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

George had ½ of a gallon of milk left. He drank ¾ of what was left. • How much of a whole gallon did he drink? • How much of the gallon is left? Explain how you were able to solve this problem. 5. NF. 4 - Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

Bennett and Seth are having an argument about the formula for finding the volume of a rectangular prism. Bennett says that to find volume you have to know the length, height, and width of the figure. Seth says that you only need to know the base and height of the figure. Which student do you agree with? Why? Write an expression that shows each boy’s formula for finding volume. Draw a rectangular prism and label it with dimensions. How would Bennett find the volume of this prism? How would Seth find its volume? 5. MD. 5 - Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

5. NF. 5 -Interpret multiplication as scaling (resizing) by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication and explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.

5. NF. 2 - Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators.

Sarah has been able to save $20 before the summer has begun. She finds a job that will pay her $8 for each hour she works over summer break. If Sara saves all of her money, how much will she have after working 3 hours? hours 5 hours? hours 10 hours? hours Create a graph that shows the relationship between the hours Sara worked and the amount of money she has saved. What other information do you know from analyzing the graph? Write an equation you can use to find out how much Sara would have saved up after working 15 hours. 5. OA. 3 - Analyze patterns and relationships 5. G. 1 & 5. G. 2 – Graph points on the coordinate plane to solve real-world and mathematical problems.

Evaluate the following numerical expressions. You cannot use a calculator. a. 2 x 5 + 3 x 2 + 4 = _______ b. 2 x (5 + 3 x 2 + 4) = _______ c. 2 x 5 + 3 x (2 + 4) = _______ d. 2 x (5 + 3) x 2 + 4 = _______ e. (2 x 5) + (3 x 2) + 4 = _______ f. 2 x (5 + 3) x (2 + 4) = _______ Can the parentheses in any of these expressions be removed without changing the value of the expression? Which expressions would change? Explain your reasoning. 5. OA. 1 -Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

5. NF. 4 - Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

Matthew is building a treasure box with a total volume of 384 cubic inches. He wants the base of his treasure box to be 12 inches by 4 inches. What is the height of his treasure box? 5. MD. 5 - Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

5. NF. 5 -Interpret multiplication as scaling (resizing) by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication and explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.

5. NF. 2 - Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators.

Russell bought 3 movie tickets for a total of $21. Catherine bought 5 movie tickets for a total of $35. Create a table to show the pattern of the prices of movie tickets. How much is 1 ticket, 4 tickets? Graph ticket 2 tickets, and tickets the corresponding terms as ordered pairs on a coordinate plane. What pattern do you see? Explain why. 5. OA. 3 - Analyze patterns and relationships 5. G. 1 & 5. G. 2 – Graph points on the coordinate plane to solve real-world and mathematical problems.

Monique went to the store to buy groceries for her party. She bought 5 bananas for 50 cents each. She also bought 4 cartons of ice cream for $3. 00 each. At check-out, she was given 10 cents off the bananas. • Write an expression that represents the problem. • You may use models if you choose to do so. • Then solve the problem to determine how much Monique spent in all. Explain your reasoning. 5. OA. 1 -Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

5. NF. 4 - Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

The right rectangular prism represented below is partially filled with 1 -inch cubes with no gaps and no overlaps. What is the volume of the prism? Show two different volume formulas that can be used to find the volume, and explain how both formulas relate to counting the cubes in bottom layer and multiplying that value by the height of the prism. 5. MD. 5 - Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

5. NF. 5 -Interpret multiplication as scaling (resizing) by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication and explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.

5. NF. 2 - Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators.

Denise is working at the snack stand at a basketball game. Each frozen yogurt costs $3, and each sandwich costs frozen yogurt costs $3 $6. $6 Create a table to show the costs for buying 0, 1, 2, 3, 4, 5, or 6 frozen yogurts. Create another table to show the costs for the same number of sandwiches. Use your tables to create a line graph with the information. What patterns do you notice in your line graph? How do the costs of frozen yogurts compare to the costs of an equal number of sandwiches? 5. OA. 3 - Analyze patterns and relationships 5. G. 1 & 5. G. 2 – Graph points on the coordinate plane to solve real-world and mathematical problems.

Allison owns a bakery. She charges 50 cents per cookie and $3. 25 per pie. She buys 35 cookies and 15 pies for a holiday party. • Write an equation, using parentheses, to solve how much she spent. • Explain your reasoning 5. OA. 1 -Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

5. NF. 4 - Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

PNC Plaza is the tallest and largest skyscraper in Raleigh North Carolina. It is 538 feet high. Cassie’s Construction Company wants to build a skyscraper that is even taller. The spot they have to build the building on is 200 square feet. What are some possible dimensions for the base of the building? If they build the skyscraper to be 550 feet high, what will its volume be? 5. MD. 5 - Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

5. NF. 5 -Interpret multiplication as scaling (resizing) by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication and explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.

If Jeremy’s tomato plant grows at the same rate, how tall will the plant be on the next Monday? 5. NF. 2 - Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators.

5. OA. 3 - Analyze patterns and relationships 5. G. 1 & 5. G. 2 – Graph points on the coordinate plane to solve real-world and mathematical problems.

Jack is trying to figure out the following problem: [34 + 20 - (10 * 40) /4] List/show the steps needed to solve. Explain your reasoning. 5. OA. 1 -Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

5. NF. 4 - Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

This is a diagram of the Sears Tower (now called the Willis Tower) skyscraper in Chicago. The base of the tower is a 75 x 75 meter square. If each floor is 4 meters tall, what is the volume of the Sears Tower? 5. MD. 5 - Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

5. NF. 5 -Interpret multiplication as scaling (resizing) by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication and explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.

5. NF. 2 - Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators.

Draw a simple picture that can be formed with straight lines connecting points on a coordinate grid. Use at least 8 points but no more than 15 points. Record the ordered pairs you plotted in the order in which you connected them. Next, double each number of the original pair and plot the ordered number pairs on the same grid in a different color. Connect the points in the same order that you plot them. What do you notice happened to your picture? Think about what would happen if you only doubled one of the numbers in your ordered pairs. Write down what you think would happen. Double only one of the numbers in each of your ordered pairs and graph your points. Were you correct? Explain what happened 5. OA. 3 5. G. 1 & 5. G. 2 - Analyze patterns and relationships – Graph points on the coordinate plane to solve real-world and mathematical problems.

Analyze the following equation: 7 + 8 x 3 = 45 Where do the parentheses have to be placed for this equation to be true? Use the numbers 7, 8 and 3 in any order with any operation to get an answer of 59. Be sure to use parenthesis, brackets, or braces to make your answer true. Explain the steps you used to determine the correct answer. 5. OA. 1 -Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

5. NF. 4 - Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

A fifth grade class has a fish tank that is 26 inches long, 1 foot wide, and 16 inches deep. What volume of water can the tank hold in inches? 5. MD. 5 - Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

Mrs. Jones teaches in a room that is 60 feet wide and 40 feet long. Mr. Thomas teaches in a room that is half as wide, but has the same length. How do the dimensions and area of Mr. Thomas’ classroom compare to Mrs. Jones’ room? Draw a picture to prove your answer. 5. NF. 5 -Interpret multiplication as scaling (resizing) by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication and explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.

5. NF. 2 - Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators.

Farmer Brown has 12 animals in his barn. Some of them are cows, and the rest are chickens. Altogether, his animals have 40 legs. How many of them are cows, and how many are chickens? Use a table to explore the different possibilities. Using the table you created, graph a line. Did your graph help you solve the problem? If so, how? If not, how could you change your graph so it can help you understand the problem? 5. OA. 3 - Analyze patterns and relationships 5. G. 1 & 5. G. 2 – Graph points on the coordinate plane to solve real-world and mathematical problems.

5. OA. 1 -Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

5. NF. 4 - Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

Kylie and Trevor made the right rectangular prism model shown below with 1 -centimeter cubes. Kylie found the volume of the model by using a volume formula. Trevor found the volume of the model by multiplying the number of cubes in one layer by the number of layers, as shown to the right. What is the volume of the model? Use expressions, equations, and/or words to explain on the next page how the methods that Kylie and Trevor used should result in the same volume for the figure. 5. MD. 5 - Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

5. NF. 5 -Interpret multiplication as scaling (resizing) by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication and explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.

5. NF. 2 - Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators.

Joseph’s teacher said that beginning at age 2, children grow about 6 centimeters per year. Joseph is 125 centimeters tall and is 9 years old. In the table below, Joseph used his current age and height to calculate his possible height for each of the previous 3 years. Joseph’s Age and Height Joseph’s Age Joseph’s (years) Height Complete a line graph of Joseph’s estimated (centimeters) height from age 2 to age 13. How tall is 9 125 Joseph estimated to be at 13 years of age? 8 119 What is the difference in height from when he was 2 years old to 13 years old? 7 113 6 107 5. OA. 3 - Analyze patterns and relationships 5. G. 1 & 5. G. 2 – Graph points on the coordinate plane to solve real-world and mathematical problems.