1. First Marking Period CCSS Extended Constructed Response Questions 2015-2016 http://prezi.com/ymlcyz18b0gm/?utm_campaign=share& utm_medium=copy http://prezi.com/ymlcyz18b0gm/?utm_campaign=share& utm_medium=copy Fifth Grade Elizabeth Public Schools

2. ›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. Intervention Block Framework

4. Scoring Guide for Mathematics Extended Constructed Response Questions (Generic Rubric) 3-Point Response 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. 5.NBT.1 - Recognize that in a multi-digit number, a digit in the 1s place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left Kipton has a digital scale. He puts a marshmallow on the scale and it reads 7.2 grams. How much would you expect 10 marshmallows to weigh? Justify your response. Kipton takes the marshmallows off the scale. He then puts on 10 jellybeans and the scale reads 12.0 grams. How much would you expect 1 jellybean to weigh? Explain why you are correct. Kipton then takes off the jellybeans and puts on 10 brand-new pink erasers. The scale reads, 312.4 grams. How much would you expect 1,000 pink erasers to weigh? Why? How would you explain solving these problems to a friend?

6. Annual rainfall total for cities in New Jersey are listed below. Elizabeth 0.86 meters Union 0.836 meters Newark1.5 meters Linden1.368 meters Imagine Linden’s rainfall is the same every year. How much rain would fall in 100 years? Write an equation using an exponent that would express the 100-year total rainfall. Explain how the digits have shifted position and why. 5.NBT.2 - Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

7. Eric is playing a video game. At a certain point in the game, he has 31,500 points. Then the following events happen, in order: 1. He earns 2,450 additional points. 2. He loses 3,310 points. 3. The game ends, and his score doubles. Write an expression for the number of points Eric has at the end of the game. Do not evaluate the expression. The expression should keep track of what happens in each step listed above. Eric's sister Leila plays the same game. When she is finished playing, her score is given by the expression 3(24,500+3,610)−6,780. Describe a sequence of events that might have led to Leila earning this score. 5.OA.2 - Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.

8.  Mr. Brown is a traveling salesman. He has driven from Pittsburgh, Pennsylvania to Washington D.C. and back 116 times over the past two years. The distance between Pittsburgh and Washington is 242 miles. how many total miles has he driven in these trips. Don't forget each trip is a "round trip." Show your work using the standard algorithm. 5.NBT.5- Multiply multi-digit whole numbers using the standard algorithm

9.  Clinton bought five packs of baseball cards. Each pack of cards was priced at $1.19. If Clinton paid with a ten dollar bill, how much change should he have received? If there are 5 cards in each pack, how much would each card cost? 5.NBT.7- Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

10. 5.G.3- Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. An attribute is a feature or characteristic of a certain thing. A parallelogram can be a rectangle. Use what you know about parallelogram and rectangle attributes to explain when this is true in all situations. Use a chart, table, or any other type of organizer to begin your writing. Then, prepare your explanation in paragraph form.

11. 5.NBT.1 - Recognize that in a multi-digit number, a digit in the 1s place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left Jossie drew the picture below to represent: 0.24 She said, “The little squares represent tenths and the rectangles represent hundredths, which makes sense because ten little squares makes one rectangle, and ten times ten is one hundred.” Part A: Is there any mistakes with Jossie’s reasoning? Part B: Name three numbers that Jossie’s could represent, in each case, what does a little square represent? What does a rectangle represent?

12. The table below gives you the approximate distance of 3 planets from the sun. How far is each planet from the sun in million kilometers? Susan said, “Venus is more than twice as far from the sun as Mercury is.” Tyrone said, “Mercury is more than twice as far from the sun as Earth is.” Are Susan and Tyrone correct? If yes, use numbers, words or pictures to prove they are correct. If no, rewrite the statements so they are correct. What is the benefit of using powers of ten to represent numbers? MercuryVenusEarth 5.7 x 10 7 km1.08 x 10 8 km1.5 x 10 8 km 5.NBT.2 - Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

13. Write an expression that records the calculations described below, but do not evaluate: Add 2 and 4 and multiply the sum by 3. Next, add 5 to that product and then double the result. Explain your reasoning. 5.OA.2 - Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.

14.  Kelly's Sports Cards sold 1,785 deluxe packs of football cards in 2012. If each deluxe pack of football cards contains 142 cards, how many total cards did Kelly's Sports Cards sell in 2012? Show your work using the standard algorithm. 5.NBT.5- Multiply multi-digit whole numbers using the standard algorithm

15.  Will gained 8.89 pounds between his 2nd and 3rd birthdays. At age 3, he weighed 36.19 pounds. How much did he weigh in pounds on his second birthday? If Will gains exactly 8.89 pounds each year, how much will he weigh at age 10? 5.NBT.7- Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

16. 5.G.3- Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. Study the picture above. Answer the following questions. Justify your answers with detailed explanations. 1. Why is the trapezoid inside the quadrilateral but outside the parallelogram? 2. Why is there a rhombus and a rectangle inside the parallelogram? 3. Why are there two squares, one inside the rhombus and one inside the rectangle? 4. Do you agree with the placement of the trapezoid? Redraw this diagram to show the actual relationship of the trapezoid to the parallelograms.

17. 5.NBT.1 - Recognize that in a multi-digit number, a digit in the 1s place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left Netta drew the picture above on graph paper. She said, “In my picture, a big square represents 1. Since ten rectangles make a big square, a rectangle represents 0.1. Since 100 little squares make a big square, a little square represents 0.01. So this picture represents 2.43.” Is Netta correct? Explain. Manny said, “I drew the same picture. But in my picture, a little square represents 1. So this picture represents 2.43.” Is Manny correct? Explain. Name some other number that this picture could represent. For each of these numbers, what does a little square represent? What does a rectangle represent? What does a big square represent? Explain.

18. Using pictures, numbers, or words explain the pattern you can use to find the product when multiplying a whole number by 10, 100, 1000 or by any other power of 10. Will this pattern be the same when multiplying a decimal by a power of 10? Explain with examples. 5.NBT.2 - Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

19. Leo and Silvia are looking at the following problem: How does the product of 60 × 225 compare to the product of 30 × 225? Silvia says she can compare these products without multiplying the numbers out. Explain how she might do this. Draw pictures to illustrate your explanation. 5.OA.2 - Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.

20.  The First National Airlines company flies 648 times per year. Each airplane carries 99 passengers. How many total passengers fly on First National Airlines each year? Show your work using the standard algorithm. 5.NBT.5- Multiply multi-digit whole numbers using the standard algorithm

21.  After 3 weeks of work, Baily received $21.36 in allowance money. How much did he earn per week? If Baily earned that same amount per week for 8.5 weeks, how much would he earn? 5.NBT.7- Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

22. 5.NBT.1 - Recognize that in a multi-digit number, a digit in the 1s place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left A computer made by Company XYZ processes information in nanoseconds. A nanosecond is one billionth of a second. Write this number as a decimal. If a new computer was created that was 100 times faster than the computer made by Company XYZ, how fast would it process information? If a new computer was created that was 1,000 times slower than the computer made by Company XYZ, how fast would it process information? Explain your reasoning.

23. 7.77 Draw a place value chart to model the number 7.77 A.Use words, numbers, and your model to explain why each of the digits has a different value. Be sure to use “ten times as much” and “one tenth of” in your explanation. B.Multiply 7.77 x 10 4. Explain the shift of the digits, the change in the value of each digit, and the number of zeroes in the product. C.Divide the product from (b) by 10 2. Explain the shift of the digits and how the value of each digit changed. 5.NBT.2 - Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

24. Draw a picture that represents 4×(9+2). How many times bigger is the value of 4×(9+2) than 9+2 ? Explain your reasoning. 5.OA.2 - Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.

25.  Briley's fast food chain orders a lot of French fries to serve its customers. In April, the food chain order 395 bags of potatoes. Each bag of potatoes contains 56 potatoes. How many total potatoes did the chain order? Show your work using the standard algorithm. 5.NBT.5- Multiply multi-digit whole numbers using the standard algorithm

26.  How much more does Niko earn than Miley in one week? If Taylor and Miley both work for 2 weeks, how much more will Taylor earn? How much money will Pinky earn in a month? About how long will Miley have to work to earn the same amount? NameEducation LevelWeekly Income MiloHigh School Dropout$440.50 NikoHigh School Graduate$650.35 Taylor2 Year College Graduate$771.25 Pinky4 Year College Graduate$1,099.20 5.NBT.7- Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

27. 5.G.3- Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. A Venn Diagram is a type of graphic organizer that helps display the similarities and differences of different things. An example is shown below. Create a list of the different attributes of a trapezoid and parallelogram. You should have two lists, one for each polygon. Then, use the Venn Diagram to display the similarities and differences of a trapezoid and a parallelogram. Your Venn Diagram should have a minimum of 5 attributes in each category (A Different, Similar, and B Different). Prepare to compare and discuss with your classmates.

28. 5.NBT.1 - Recognize that in a multi-digit number, a digit in the 1s place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left Why does the number 13,543 have a different value than 13,453? Justify your reasoning. 286,489 is an odd number. How many times greater is the 8 in the ten thousands place than the 8 in the tens place? There are two 3’s in the number 2,033,541. Jessica says that the 3 on the left is 10 times the value of the 3 on the right. Esperanza says the 3 on the right is 1/10 the value of the 3 on the left. Who is correct? Explain your thinking.

29. The place value of the 5 in 0.5 is how many times the place value of the 5 in 50 ? Explain your answer in words. Be sure to use “times as much” in your explanation. 5.NBT.2 - Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

30. Explain your reasoning. Museum Rate Plans Plan A: Pay $ 3.00 per person to visit the Museum. Plan B: Monthly membership is $8.00 for each person, but you can go as many times as you like during the month. Plan C: A family membership for a month is $17.00. Everyone in your family can go as often as they like for a month. You and your sister want to go see the dinosaur exhibit three times this month. Which plan should you buy to save money? Explain your reasoning. 5.OA.2 - Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.

31.  During the spring and summer concert months, the state fairgrounds has a capacity of 872 people. Each night there was a concert, the fairgrounds was at full capacity. If there were 109 nights in which there was a concert, how many total people were at the concerts during the spring and summer months? Show your work using the standard algorithm. 5.NBT.5- Multiply multi-digit whole numbers using the standard algorithm

32.  5.NBT.7- Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Mary can type 24.55 words per minute on the typewriter. Rachel can type 4.77 words faster. How many words per minute can Rachel type? How many words can Mary type in 1 hour? If Rachel wanted to improve her typing speed to 50.25 words per minute, how many more words would she need to type per minute?

33. 5.NBT.1 - Recognize that in a multi-digit number, a digit in the 1s place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left Pizza Shack earned $2,304 in revenue for the month of March. Pizza Galore, a competitor, earned revenue for the month of March also. If Pizza Galore earned 100 times more than the Pizza Shack, how much did Pizza Galore earn? Explain your thinking. In April, Pizza Shack recorded 1/10 of the revenue it recorded in March, how much revenue did it record in April? In May, Pizza Shack recorded revenue that was 100 times greater than what it earned in March. How much revenue did the Pizza Shack record in May? Explain your reasoning.

34. How many times do you need to divide 45.695 by ten to get 0.0045695? Explain the steps in solving this question. 5.NBT.2 - Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

35. First expression: Add the first two numbers together then divide the sum by the third number. Second expression: Subtract the second from the first number and then multiply the difference by the third. 5.OA.2 - Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. A perfect trio involves only three different whole numbers written as the following two different expressions but resulting in the same solution. If your two expressions are equal, the TRIO is Perfect! -Can you find three whole numbers that are perfect trios? -If not, how can you show that there are not any perfect trios? Is there a way to prove there are no perfect trios? Explain using examples. -Is there more than one perfect trio? If so, how many? List the trio(s) you found. How do you know if you found them all? Describe any special characteristics of perfect trios. How can you go about finding them? Explain completely.

36.  A deluxe box of Sour Scratch Kids contains 248 packages. Each package contains 45 individual Sour Scratch Kids. How many total Sour Scratch Kids come in a deluxe box? Show your work using the standard algorithm. 5.NBT.5- Multiply multi-digit whole numbers using the standard algorithm

37.  5.NBT.7- Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Kayla's mom bought bananas and avocados at the super market. Bananas and avocados are priced per pound. The bananas weighed 2.93 pounds, and the avocados weighed 2.33 pounds. How much did the bananas and avocados weigh in total pounds? If Kayla’s mom paid with a $20 dollar bill, how much change would she receive?

38. 5.NBT.1 - Recognize that in a multi-digit number, a digit in the 1s place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left Shelly had the answer 25.67 showing on her calculator after dividing a number by ten. What was the original number? Explain how you know? Compare the value of the 7 from the original number to the value of 7 in her answer? What is the relationship between the two 7’s? Explain.

39.  Gage's Family Amusement park uses a lot of ice during the summer months to keep refreshments cool. Every day, it uses 1,750 bags of ice. If each bag of ice contains 362 ice cubes, how many total ice cubes are used every day at the amusement park? Show your work using the standard algorithm. 5.NBT.5- Multiply multi-digit whole numbers using the standard algorithm

40. 5.NBT.1 - Recognize that in a multi-digit number, a digit in the 1s place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left What is happening to the number 23? Explain the pattern that you see. What do you think would happen if you multiplied your number by 1,000,000? Pick a decimal number to multiply. What is happening to your decimal? Explain the pattern that you see. What do you think would happen if you multiplied your number by 1,000,000?

41.  Bernie's General Store sells a lot of juice bottles. It ordered 287 cases of orange juice in 2012. If each case contains 144 bottles, how many total bottles of orange juice did it buy? Show your work using the standard algorithm. 5.NBT.5- Multiply multi-digit whole numbers using the standard algorithm

42. 5.OA.2 - Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. As explained in Harry Potter and the Sorcerer’s Stone, "The four houses are called Gryffindor, Hufflepuff, Ravenclaw, and Slytherin. Each house has its own noble history and each has produced outstanding witches and wizards. While you are at Hogwarts, your triumphs will earn your house points, while any rule breaking will lose house points. At the end of the year, the house with the most points is awarded the House Cup, a great honor. I hope each of you will be a credit to whichever house becomes yours." Slide 1 of 3

43. Slide 2 of 3 5.OA.2 - Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. A house at Hogwarts is given 10 points when a student knows the answer to an important question in class. A house at Hogwarts is given 5 points when students show they have learned a magic spell. At the end of one week, Harry wants to know how many points Gryffindor has earned. He sees they have earned 40 points for answering questions correctly. Write an equation that represents the number of points the Gryffindor students earned for answering questions correctly.

44. 5.OA.2 - Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Slide 3 of 3 Professor McGonagall kept track of the number of points Gryffindor students received for correct answers and knowing magic spells during one week. She wrote these two expressions on the board to show the total points: (10 x 2) + (7 x 5) 10(2) + 7(5) How are these expressions the same? How are they different? Will the answer for these equations be the same or different? How do you know? Professor McGonagall wrote an equation to show the total number of points Gryffindor earned during one week. (10 × 3) + (5 × 4) = 50 If students earned 10 points for answering difficult questions correctly and 5 points for using a magic spell correctly, use words to explain the equation above.

45. Slide 1 of 4 5.OA.2 - Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Students at Hogwarts typically earn 15 points for tackling a boggart and 20 points for identifying potions. Complete the chart as shown in the example:

46. 5.OA.2 - Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Slide 2 of 4 Students at Hogwarts typically earn 5 points for using a magic spell correctly and 10 points for correctly answering a difficult question. Complete the chart as shown in the example:

47. 5.OA.2 - Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Slide 3 of 4 This time you are going to find out how many points the houses at Hogwarts lost! To find the total number of points lost, you will need to write an expression with the given value to find the total number of points each house lost. Students at Hogwarts typically lose 10 points for being late to class and students lose 20 points for being out of bed at midnight. Complete the chart as shown in the example:

48. 5.OA.2 - Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Slide 4 of 4 Write an expression below for the number of points each house earned and lost according to the previous charts.