Grade 5 Enduring Skill 1: Students will use strategies to develop understandings of volume. Demonstrators: 1. Understanding that a 1 unit by 1 unit by 1 unit cube is the standard unit for measuring volume. 2. Recognize volume as an attribute of 3D space. 3. Select appropriate tools, units, and strategies for solving problems that involve estimating and measuring volume. 4. Decompose more than 1 3-D shape. **Some questions will overlap with demonstrators Related Standards: 1. 5.MD.3a 2. 5.MD.3b 3. 5.MD.4 4. 5.MD.5 5. 5.MD.5c Assessment Items: 1. ES 1, Demonstrator 1, Standard 5.MD.3a Use the shapes below to answer the following question. How many of the unit cubes will fill the rectangular prism? 1. 60 unit cubes 2. 48 unit cubes 3. 24 unit cubes 4. 12 unit cubes
2. ES 1, Demonstrator 1, Standard 5.MD.3a The cube below measures 1 unit on each side. Which shows the volume of the cube? A. V= 1 unit + 1 unit - 1 unit B. V= 1 unit + 1 unit + 1 unit C. V= 1 unit x 1 unit + 1 unit D. V= 1 unit x 1 unit x 1 unit 3. ES 1, Demonstrator 1, Standard 5.MD.3a The cube shown is made from boxes that are each 1 cubic meter. What is the volume of the prism?
4. ES 1, Demonstrator 2, Standard 5.MD.3a Abigail fills a small box with equal-sized cubes. The volume of each is exactly 1 cubic centimeter. She can fit 42 cubes perfectly in the bottom of the box. She can stack 5 cubes on top of each other to reach the top of the box. 5. ES, Demonstrator 2, Standard 5.MD.3a Keiko piled some empty boxes in her mother s garage as shown. How many boxed are in the stack?
6. MD.4 Demonstrator 2-3 Marcelle estimated the volume of the two boxes below, using one of his books. His book has a volume of 48 cubic inches. Box 1 holds about 7 layers of books, and box 2 holds about 14 layers of books. Marcelle says that the volume of either box is about the same. Is Marcelle s estimate correct or incorrect? Explain your answer.
7. ES 1, Demonstrator 2-3, Standard 5.MD.5 One way to find the volume of the prism below would be to calculate the area of the base first and then multiply by the height. 8. ES1, Demonstrator 3,Standard 5.MD.5 John is making a chest that will have a volume of 1,200 cubic inches. The length is 20 inches and the width is 12 inches. How many inches tall will his chest be? A. 4 inches B. 5 inches C. 6 inches D. 7 inches
9. ES1, Demonstrators 2 & 3, 5.MD.5 What is the volume of the rectangular prism? 10. ES1, Demonstrator 3, Standard 5.MD.5 What is the volume of the rectangular prism.
11. ES 1, Demonstrator 3, Standard 5.MD.5 Calculate the volume of a container measuring 3 inches by 4 inches by 5 inches. 12. ES 1, Demonstrator 4, Standard, 5.MD.5c What is the volume of the figure shown?
13. ES1, Demonstrator 4, Standard 5.MD.5c What is the volume of the composite figure? 14. ES1, Demonstrator, Standard 5.MD.5c What is the volume of the composite figure below?
15. ES 1, Demonstrator 4, Standard 5.MD.5c Find the volume of the figure below. Show your work and explain. 16. ED 1, Demonstrator 4, Standard 5.MD.5c What is one possibility for the length, width, and height of a rectangular prism, if the volume of the prism is 36 cubic yards? Show your work.
17. ES 1, Demonstrator 4, Standard 5,MD.5c I want to construct a 2 level bird feeder to hang in a tree in my backyard. I want both levels to be rectangular prisms. The bottom level dimensions will be: length = 6 in; width = 10 in; and height = 4 in. The top level dimensions will be: length=3 in.; width = 5 in.; height = 2 in. a. What will be the volume of the bottom level of my bird feeder? Show or explain your answer. b. What will be the volume of the top level of my bird feeder? Show or explain your answer. c. I will need to know the volume of the completed bird feeder so I can buy enough seeds to fill both levels. What will be the volume of my bird feeder when it is completely built? Show or explain your answer.
Grade 5 Enduring Skill 2: Students will develop an understanding of decimal place value using the 8 mathematical practices Demonstrators: 1. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to it s right 2. Explain patterns in the placement of the decimal point 3. Read, write, and compare decimals to the thousandths 4. 4.Use place value understanding to round decimals up to the thousandths place **Some questions will overlap with demonstrators Related Standards: 1. 5.NBT.1 2. 5.NBT.2 3. 5.NBT.3 4. 5.NBT.4 Assessment Items: 1. ES 2, Demonstrator 1, Standard 5.NBT.1 In which number does the digit 6 have a value that is 10 times greater than its value in the number 15.265? (5.NBT.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right.) A. 15.256 B. 15.063 C. 15.526 D. 15.614
2. ES 2, Demonstrator 2, Standard 5.NBT.2 Victoria and Billy each multiplied 4.7 X 10 and 0.689 X 100. Victoria got 0.47 and 6.89 for her products. Billy got 47 and 68.9 for his products. Which student multiplied correctly? Explain your reasoning. (5.NBT.2 Explain patterns in the placement of the decimal point.) 3. ES 2, Demonstrator 3, Standard 5.NBT.3 Write a number that is greater than 4.508 but less than 4.512. Explain your reasoning related to place value. (5.NBT.3 Read, Write, and Compare decimals to thousandths.) 4. ES 2, Demonstrator 3, Standard 5.NBT.3 Which number sentence is true? (5.NBT.3 Read, Write, and Compare decimals to thousandths.) A. 4.047 > 4.157 B. 4.146 < 4.135 C. 4.224 > 4.265 D. 4.235 < 4.247
5. ES 2, Demonstrator 2, Standard 5.NBT.2 Mr. Farley filled the gas tank on his lawn mower with 4.2 gallons of gas. If he mowed his yard 10 times on the same tank of gas, how much gas did he use each time the lawn was mowed? (5.NBT.2 Explain patterns in the placement of the decimal point.) A. 0.042 gallons B. 0.42 gallons C. 42 gallons D. 420 gallons 6. ES 2, Demonstrator 4, Standard 5.NBT.4 The fastest runner in Saturday s race ran 6.24 meters. Round 6.24 to the nearest ones place and to the nearest tenths place. (5.NBT.4 Use place value understanding to round decimals)
7. ES 2, Demonstrator 4, Standard 5.NBT.4 The Math club bought 3 boxes of graph paper. Round the cost of each box to the nearest ten cents to estimate how the much the club spent on graph paper. (5.NBT.4; Use place value understanding to round decimals) MATH SUPPLIES Rulers Graph Paper Calculators Pencils $1.98 per bag $4.89 per box $2.15 each $0.59 each 8. ES 2, Demonstrator 1, Standard 5.NBT.1 A baker needs to buy some sugar to make cookies. The sugar costs $1.89 per pound. How much will the baker spend if he needs buy 10 pounds? What about 100 pounds? (5.NBT.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right.)
9. ES 2, Demonstrator 3, Standard 5.NBT.3 Determine the pattern to complete the hundredths decimal grid. (5.NBT.3 Read, Write, and Compare decimals to thousandths.) 0.3 3 0.24 0.45 10. ES 2, Demonstrator 4, Standard 5.NBT.4 Consider the benchmark numbers 0, 0.5, and 1. (5.NBT.4 Use place value understanding to round decimals) 0 0.5 1 Determine a decimal to the hundredths place between 0 and 1 that rounds to 0. Determine a decimal to the hundredths place between 0 and 1 that rounds to 0.5 Determine a decimal to the hundredths place between 0 and 1 that rounds to 1.
Grade 5 Enduring Skill 3: Students will develop an understanding of the operations of fractions using the 8 Mathematical Practices. Demonstrators : 1. Add and subtract fractions with unlike denominators by replacing with equivalent fractions, including mixed numbers. 2. Solve word problems involving addition and subtraction of fractions by using models or equations. Using benchmark fractions and number sense of fractions to estimate mentally (reasonableness). 3. Solve world problems involving the set of multiplication and division of unit fractions by whole numbers and whole numbers by unit fractions. 4. Use the meaning of fractions, multiplication and division to understand and explain why the procedures for multiplying and dividing fractions make sense. Related Standards: 1. 5.NF.1 2. 5.NF.2 3. 5.NF.3 4. 5.NF.4 5. 5.NF.5 6. 5.NF.6 7. 5.NF.7 Assessment Items: **Some demonstrators will overlap** 1. ES 3, Demonstrator 1, Standard 5NF1 Rodney has a board that is yard long. He cuts 1/5 yard off the board and uses the rest of the board to make a frame. How much of the board is used to make the frame?
2. ES 3, Demonstrator 3, Standard 5.NF.1 Joel made some muffins. He gave ¼ of the muffins to a neighbor. He took ⅜ of the muffins to school. What fraction of the muffins is left? A. 4/12 B. ⅜ C. 5/12 D. 8/8 3. ES 3, Demonstrator 1-2, Standard NF.2 Dena is biking down a 9/10 mile bike trail. She stops to greet a friend after biking ⅓ of a mile. How much farther does she need to travel? Draw a picture and write an equation to solve. 4. ES 3, Demonstrator 1-2, Standard 5.NF.2 Katie and her brother are both writing a report. Katie wrote ⅞ of her report and her brother wrote 3/7 of his report. What is the best estimate of how much more Katie wrote than her brother? A. 1/2 0 = ½ B. 1/2 1/2= 0 C. 1 1/2= ½ D. 1 0 = 1
5. ES 3, Demonstrator 3, Standard 5.NF.3 Mrs. Webster wants to divide the milk shown into servings that are ⅓ of a pint in size. How many servings are possible? (11-9) 6. ES 3, Demonstrator 3, Standard 5.NF.3
7. ES. 3, Demonstrator 3-4, Standard 5.NF.4 8. ES 3, Demonstrator 3-4, Standard 5.NF.6 In Wing A of a kennel, 5/8 of the 24 dogs are male. In Wing B, 4/5 of the 30 dogs are male. What is the total number of male dogs in the two wings of the kennel? Write an equation and solve. Draw models to represent Wing A and B. 9. ES 3, Demonstrator 3, Standard 5.NF.7 Julie bought 3 yards of cloth to make holiday napkins rings. If she needs ¾ yards to make each ring. How many rings can she make?
10. ES 3, Demonstrator 3, Standard 5.NF.7 One fourth of a box of cereal was shared equally among 3 people. How much cereal did each person get? Explain how you found your answer. 11. ES 3, Demonstrator 3, Standard 5.NF.4a Charlotte bought 16 songs. Three-fourths of the songs are pop songs. 12. ES 3, Demonstrator 4, Standard NF.5a Complete the statement with equal to, greater than, or less than.
13. ES 3, Demonstrator 3-4, Standard NF.4a Use the model to find the product. 14. ES 3, Demonstrator 3-4, Standard 5.NF.5b Rochelle saves ¼ of her allowance. If she decides to start to start saving ½ as much, which statement below is true? 15. ES 3, Demonstrator 3, Standard 5.NF.2
Grade 5 Enduring Skill 4: Students will develop an understanding of multi-digit whole number and decimal operations using the 8 Math Practices. Demonstrators : 1. Generate two numerical patterns using two given rules. 2. Convert among different - sized standard measurement units within a given measurement system. 3. Add,Subtract, Multiply and Divide decimals to hundredths. 4. Use parentheses, brackets, or braces in numerical expression, and evaluate expressions with these symbols. 5. Fluently multiply multi-digit whole numbers using the standard algorithm. 6. Find whole number quotients of whole numbers with up to four-digit dividends and two digit divisors. 7. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Related Standards: 1. 5.OA. 3 2. 5.MD.1 3. 5.NBT.7 4. 5.OA.1 5. 5.NBT.5 6. 5.NBT.6 7. 5.OA.2 Assessment Items: 1. ES 3, Demonstrator 4, Standard 5.OA.1) Consider the two expressions below. 2 x (10+5) 2 x 10 + 5 A) Are the equations equivalent? If not, find the value of each expression. B) Explain how the parentheses do or do not affect the value of the first expression.
2. ES 4, Demonstrator 7, Standard 5.OA.2 Which represents the following description: 18 fewer than 6 times 5 3. ES 4, Demonstrator 2, Standard 5.MD.1 The Statue of Liberty was a gift to the United States from the people of France. Some of the dimensions of the statue are shown here. Measurements of the Statue of Liberty Height from base of statue to the torch Length of hand Length of index finger Length of nose Thickness of right arm 151 ft. 1 in. 16 ft. 5 in. 8 ft 4 ft 6 in. 12 ft A. What is the height, from the base of the statue to the torch, in inches? B. what is the thickness of the statue s right arm in yards?
4. ES 4, Demonstrator 4, Standard(5.OA.1 Use parentheses, brackets, or braces in numerical expression, and evaluate expressions with these symbols.) Which of the following is equal to 2? A. 6 + (4 2) + 1 3 B. 6 + 4 (2 + 1) 3 C. (6 + 4) 2 1 3 D. (6 + 4 2) 1 3 5. ES 4, Demonstrator 5, Standard,.NBT.5
6. ES 4, Demonstrator 4, Standard 5.0A.1 Greg bought 3 packs of baseballs at $3.57 a pack. He had a coupon for $1.00 off the total cost. His dad paid half of the remaining cost. Evaluate the expression. [(3 x $3.57 ) - $1] 2 Use parentheses, brackets, or braces in numerical expression, and evaluate expressions with these symbols.) 7. ES 4, Demonstrator 5, Standard.NBT.5 Raul earns $24 per hour painting houses. If he works for 263 hours, how much will Raul earn in all? 8. ES 4, Demonstrator 3, Standard 5.NBT.7 Mrs. Smith is planning on taking her 27 students to the zoo. The cost of one student ticket is $15.27. How much will Mrs. Smith need to take all of her students to the zoo? A. $41.23 B. $412.29 C. $137.43 D. $411.29.Add,Subtract, Multiply and Divide decimals to hundredths)
9. ES 4, Demonstrator 6, Standard 5.NBT.6 10. ES 4, Demonstrator 6, Standard 5.NBT.6 A bakery sold croissants to local restaurants. The table shows how many croissants were sold to each restaurant. the croissants were sold 6 to a box.
11. ES 4, Demonstrator 3, Standard 5.NBT.7 Determine the equation being modeled below. Then solve. 12. ES 4, Demonstrator 6, Standard 5.NBT.6 13. ES 4, Demonstrator 5, Standard 5.NBT.6
14. ES 4, Demonstrator 4, Standard 5.OA.2 15. ES 4, Demonstrator 3, Standard 5.NBT.7 Mallory has been offered two different jobs. She can baby sit for 6 hours a week and get $8.50 an hour. Or she can work at the library for 14 hours a week and make $5.50 an hour. Which job will allow her to save the most money after 6 weeks? 16. ES 4, Demonstrator 4, Standard 5.NBT.7 Sol has to paint 365.7 square feet of wall space. He wants to paint 0.4 of the area light green. How many square feet does he want to paint light green?
17. ES 4, Demonstrator 1, Standard 5.OA.2 Wheel Graph The relationship between numbers of cars and numbers of wheels (W) is given by the expression W = 4 X C. This means the number of wheels is equal to 4 times the number of cars.
18. ES 4, Demonstrator 2, Standard 5.OA.2 Let s Graph Mrs. Pendle wrote the two patterns below on the board. 19. ES 4, Demonstrator 7, Standard 5.OA.2 Which represents the following description: