Ready-to-use resources for differentiated instruction

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1 Sample Packet 5th Grade Mathematics Sample Packet Differentiation Motivation Equity Ready-to-use resources for differentiated instruction

2 DOMAIN:CONCEPTS OBJECTIVES AND INSTRUCTIONAL TARGETS GRADE 5 MATHEMATICS Objective : Demonstrate an understanding of number concepts A Use place value to read, write, compare, and order whole numbers through the billions place. B Compare/order nonnegative rational numbers through the thousandths place value, excluding whole numbers C Determine relationships between/among fractions (denominators of,,, 5, 6, 8, 0, and ) D Recognize/compare fractions using patterns and pictorial models E Round decimals (to nearest tenth and hundredth place value F Factor whole numbers Objective : Demonstrate an understanding of mathematical relations, functions, other algebraic concepts A Use nonnegative rational number properties/inverse operations (whole numbers, fractions, decimals) B Determine missing elements in patterns C Use number line representations for whole numbers, fractions/decimals D Identify ordered pairs on coordinate plane Objective : Demonstrate an understanding of geometric properties/relationships A Recognize two dimensional figures B Recognize three dimensional figures C Identify translations, reflections, rotations, and their applications D Recognize similarity, congruence, symmetry E Lines and angles F Properties of triangles Objective : Demonstrate an understanding of measurement concepts using metric/customary units A Solve problems with metric/customary units B Convert within customary system C Convert within metric system D Determine area,perimeter, and volume (with/without grids) E Solve problems with area/volume with and without grids F Find perimeter/circumference

3 DOMAIN: CONCEPTS (cont d.) Objective 5: Demonstrate an understanding of probability/statistics A Determine possible outcomes in a given situation B Analyze data/interpret graphs C Use counting arrangements D Use fractions to describe the probability of an event E Find mean, median, and mode DOMAIN: OPERATIONS OBJECTIVES AND INSTRUCTIONAL TARGETS GRADE 5 MATHEMATICS Objective 6: Use operation of addition to solve problems A Add or more digit whole numbers with regrouping B Add using money with regrouping C Add decimals D Convert decimals to fractions E Review fractions F Addition of fractions G Understand equivalent fractions Objective 7: Use operation of subtraction to solve problems A Subtract whole numbers with regrouping B Subtraction of whole numbers and decimals/money C Subtraction of fractions Objective 8: Use operation of multiplication to solve problems A Multiply whole numbers digits or more B Multiplication of to digits by digit C Use of rounding/range in multiplication D Multiplication of money/decimals E Multiplication of fractions Objective 9: Use operation of division to solve problems A Divide whole numbers with and without remainders

4 DOMAIN: PROBLEM SOLVING OBJECTIVES AND INSTRUCTIONAL TARGETS GRADE 5 MATHEMATICS Objective 0: Estimate solutions to problem situation A Front-end digits using addition/subtraction B Rounding with addition/subtraction C Compatible numbers with addition/subtraction D Clustering Strategy E Range F Rounding/front-end digits with multiplication G Compatible numbers in division Objective : Determine solution strategies/analyze or solve problems. A Formulate strategies/solve problems using basic operations with whole numbers, fractions, and decimals B Determine strategies/solve problems using geometric concepts (perimeter, area, and circumference of rectangles, circles, and triangles) C Analyze/solve problems through the use of similarity, congruence, and symmetry/probability and statistics D Analyze/solve problems using probability and statistics concepts Objective : Solve problems using mathematical representation A Formulate an equation B Analyze/interpret charts and graphs and use the information derived to solve problems Objective : Evaluate reasonableness of solution to problems A Evaluate reasonableness B Making and testing predictions for reasonableness

5 Serves: 5th grade Appetizers OBJECTIVES 5 A and 5 D Ms. Pickins needed a representative from her homeroom for patrol guard. She had 6 volunteers. Matt, James, Tony, Clint, Julie, and Jennifer all wanted to help. She couldn t decide who to choose, so she put everyone s name in a box and drew her representative. What was the probability of a girl being picked for patrol? a. b. c. d OBJECTIVE A José and Joe decide to get a paper route during the summer. José will have 60 customers and Joe will have 75 customers. If the boys make less than 50 from each customer per week, how many days will it take José to make $5.00? a. 5 days b. 5 days c. 50 days 5 6 d. not enough information given OBJECTIVE B The Boy Scouts were selecting teams for the camp competition. The Arrowheads had the following numbers:,, 6, 0,?. By looking at the pattern, which of the following scouts would be an Arrowhead? a. Jacob, # b. Raymond, # c. Armando, #5 d. Levi, #0 6

6 Serves: 5th grade Appetizers II OBJECTIVES 5. A, 5. B, and 5.5 B 6 cm 6 cm OBJECTIVES 5. A, 5. B, and 5.5 B What is the area of this triangle? a. 6 cm b. 8 cm c. cm d. 6 cm e. answer not given OBJECTIVES 5. A, 5.5 B, and 5.6 A Mrs. Norbury made 8 cups of potato salad for the faculty While picnic. flying from One-fourth El Paso of to the Oklahoma salad was City, celery, Jan green and pepper, Kay each and had onion. a bag How of pretzels much celery, along green with their pepper, fruit juice. and onion Kay ate was in of the her salad? bag of pretzels. Jan ate more a. pretzels cups than Kay. Which fraction b. 0 of cups her bag of 8 8 pretzels could Jan have eaten? c. cups d. cups 6 e. answer not given 79

7 Grade 5 Main Dish Sample Objective: Lesson - Compare and Order Whole Numbers Final Test Journal Topics Reasonableness Problems

8 Grade 5 Main Dish - Objective NUMBER CONCEPTS Lesson - Compare and Order Whole Numbers Lesson - Compare and Order Decimals - Game Lesson - Fractions - Game Lesson - Recognize and Compare Fractions Lesson 5 - Rounding Decimals Lesson 6 - Factor Whole Numbers Final Test Journal Topics Reasonableness Problems

9 Lesson Definition: Understanding number concepts means to study and compare number relationships, patterns, sequences, and values. Statement of Importance: In order for students to better understand number concepts, they must first have a concrete understanding of the different terminology used to express numbers of the same value in different forms. It is a practical skill area that allows the students to be able to sequence or order numbers when not presented in the whole number form. Objective: At the close of the lesson, the student will know the practical value of understanding and comparing rational numbers. He/she will know that rational numbers can appear in different number forms yet can retain the same value. Brainstorm to think of the many ways we use numbers. $ x 6 6 Focus Activity:,,,,.. :00.5 <.8 add cup of sugar 5 ( T )

10 Lesson Definitions: Objective: Students will use place value to read, write, compare and order whole numbers through the billions place Expanded form - means to show the number value of each digit. Example : 55 = Example : 88 = Example :,58 = 0,000 +, If all of the numbers in expanded form were added up they would equal the first number of each example. Greater than is a term that means one thing is larger than another. In math the symbol > means greater than. Example : > is read twenty-three is greater than thirteen Example : 56 > 56 is read, two hundred fifty-six is greater than one hundred fifty-six Less than is a term that means one number of some thing is less than another. In math the symbol < means less than. Example : < is read thirteen is less than twenty-three. Example : 56 < 56 is read one hundred fifty-six is less than two hundred fifty-six Comparing and ordering numbers means to look at all of the groups of numbers first. In a group of numbers that must be ordered from greatest to least, determine the place value of the number that is farthest to the left in each group of numbers. Begin ordering the groups of numbers with the greatest value first. Example : 5, 75, Step : The place value farthest to the left is the tens place. Step : The three numbers in the tens place are a, 7, and. Step : Greatest to least would mean the 7 has the greatest value, the next and the has the least value. Step : Greatest to least is 75,, 5. Comparing and ordering numbers from least to greatest means to determine the place value of the number in the farthest to the left in each group of numbers. Begin ordering the groups of numbers with the least value first. Example : 75, 57, 56 Step : The place value farthest to the left is the hundreds place. Step : The three numbers in the hundreds place are, 5, 7 Step : Least to greatest would mean the has the least value, the 5 next, and the 7 with the greatest value. Step : Least to greatest is 56, 57, 75 ( T ) 6

11 Lesson Objective: Students will use place value to read, write, compare, and order whole numbers through the billions place Naming a number plus more - is another way of saying that a specific amount needs to be added to the original number. Example : 7,58, - Name,000 more means add,000 to 7,58,. 7,58, +,000 = 7,59, 7,58, and name,000 more = 7,59, Example : 58, - Name 0,000 more 58, + 0,000 = 558, Naming a number less a certain amount - is another way of saying that a specific amount needs to be subtracted from the original number. Example : 7,58, - Name,000 less means subtract,000 from 7,58,. 7,58, -,000 = 7,57, 7,58, and name,000 less = 7,57, Example : 58, - Name 0,000 less 58, - 0,000 = 58, PRACTICE Directions: On the first line write the original number plus more. On the second line write the original number using less. Name 00 more Name 00 less.,76. 5,06.,008,6,576,67 Name,000 more Name,000 less. 0, ,07 6.,68,00,79 6 ( T ) Name 0,000 more Name 0,000 less 7. 65, , ,5 7

12 Enrichment Objective: Students will be able to use place value to read, write, compare, and order whole numbers through the billions place Problem Directions: There are several different activities below that use number concepts. Follow the directions and see if you are able to solve the problems. Riddle # My thousands digit is. My ones digit is more than my thousands. My hundreds and ten digit are the same. They are three more than my ones digit. Number = Riddle # My thousands digit is. My hundreds digit is 5 more than my thousands digit. My ones digit is the sum of my thousands and hundreds digits. My tens digit is 9 x 0. Number = Riddle # My ones digit is x. My hundreds and thousands digit are the same. They are more than my ones digit. My tens digit is less than my thousands digit. Number = 6?? ( T ) 8

13 Practice # Problem # ( T ) Directions: Read each problem carefully. Decide which answer best completes the question. Show your work. Which digit is in the ten thousands place in this number? 7,5,96 a. 5 b. 6 c. 7 d. 9 Problem # Which of the following shows the correct expanded notation of the number 6,775? a b c d Problem # How much would the value of 8,506 be increased by replacing the with a? a. 00,000 b. 0,000 c.,000 d. 00 Problem # Which number below is equivalent to fourteen million, twenty-five thousand? a. 0,05,000 b.,05,000 c.,50 d.,5 Problem #5 Which underlined number is in the ten billions place? a. 8,5,09,670 b. 8,5,09,670 c. 8,5,09,670 d. 8,5,09,670 Problem #6 Which number below is equivalent to,908,? a. three thousand, nine hundred eight thousand, one hundred twenty-four b. three million, nine hundred eight thousand, one hundred twentyfour c. three million, nine and eight thousand, one hundred twentyfour d. thirty million, nine hundred eight thousand, one hundred twentyfour Problem #7 Which of the following shows the order of numbers from greatest to least? a.,08,97;,80,97;,0,756;,0,765 b.,80,97;,08,97;,0,765;,0,756 c.,0,765;,0,756;,80,97;,08,97 d.,0,765;,0,756;,08,97;,80,97 9

14 Application # Directions: Read each problem carefully. Decide which answer best completes the question. Show your work. Problem # Which of the following shows the correct expanded notation of 5,09,7? Problem #5 Which number is equivalent to 60,98,5,07? a. 5,000,000+,000,000+, b. 50,000,000+,000,000+00,000+9, c. 5,000, d Problem # Which number is equivalent to seventy two billion, nine hundred fifty-four million, two hundred twenty-seven thousand, three hundred thirty-three? a. 7,95,7,0 b. 7,90,07,00 c. 7,95,7, d. 7,900,50,7, Problem # How much would the value of 68,90,0 be increased by replacing the 8 with a 9? a.,000 b. 0,000 c. 00,000 d.,000,000 Problem # Which number is equivalent to one hundred ten billion, two hundred forty-one million, sixty-three thousand, one hundred eightyone? a. 00,0,06,8 b. 0,,06,08 c. 0,,06,8 d. 0,,60,8 a. sixty-ten billion, nine hundred eighteen, three hundred forty-five, and forty-seven b. sixty billion, nine hundred eighteen hundred million, three hundred forty five, forty-seven c. sixty billion, nine hundred eighteen million, three hundred forty-five thousand, forty-seven d. sixty ten billion, nine eighteen million, three forty-five thousand, forty-seven Problem #6 Which of the following is correct? a.,66,75 <,6,95 >,,95 b.,66,75 =,6,95 <,,59 c.,66,75 >,6,95 =,,59 d.,66,75 >,6,95 >,,59 Problem #7 The underlined number shows which place value?,70,897,0 a. hundred thousands place b. billions place c. thousands place d. millions place 0

15 Game Objective: Students will be able to read, write, compare, and order decimals through the thousandths place value Directions: Group size: Compare and Order Divide class into two teams Note: You may want to play this outside. It could get noisy! Materials: Sets of cards (page ) The teacher distributes a set of cards among students on each team. Both teams both receive the same set of cards. On a signal from the teacher, both teams must order their set of numbers from greatest to least or least to greatest. (The teacher will decide the order) The first team to line up its set of cards wins. Have the students make up new decimal cards to use. Variation: Play the game with fractions. Compare and order them!

16 Game Objective: Students will be able to read, write, compare, and order decimals through the thousandths place value Game Cards for Compare and Order A A A A B B B B C C C C D D D D E E E E

17 Game Materials: game board, answer sheet, and number cube. (The numbers on the die will represent fractions as follows: = ; = ; = ; 5 = ; 6 = ; and will = (If blank die are available, write the fractions on the blank sides). Directions: Objective: Students will be able to determine the relationships between and among equivalent fractions And the Answer Is? Before class: Make enough copies of the game board (page ) for each group. These should be copied on card stock and laminated. Group size: three students; one referee The person with the most letters in his/her first and last name goes first. Game play is counter clockwise. Player rolls the number cube. If a is rolled, the player must find the closest equivalent fraction to on the game board, and if correct, will move his/her game piece to that space. If there is a question about the accuracy of the player s answer, the referee will look on the answer sheet to verify the answer. Before the game is played, each group should write out equivalent fractions for possible rolls. Example: =,,, etc. 6 8 If there are no spaces with an equivalent fraction to match your roll, or if another player is occupying that space that you should move to, you lose a turn. If you roll times and you still cannot move, you must move your game piece back to start! If you roll the same fraction times in a row, you may move your game piece to the equivalent fraction closest to the finish space. Game Play: Each player has a token for game play. Players are to follow the arrows that designate the game path. When players get to the last column, they are to travel in a southwesterly direction in order to reach the bottom of the question mark. Players will follow the arrows home. Players must have the exact number to reach home.

18 Game Board Objective: Students will use problem solving skills in addition and subtraction Start Number Cube Pad Stop! Turn right and go up! To Home To Home HOME Home

19 Lesson Objective: Students will be able to recognize and compare fractions using patterns and pictorial models Initial Instruction: Recognize and Compare Fractions Teacher note: Although two fractions may appear to be different in appearance, they can represent the same value. Fractions can also be misleading by appearance in that larger numbers may not always be the greater in value. This is why it is so important for students to visualize fractional values as well as learn the strategies of computation. Relationships between fractions can be categorized three ways. They can be greater than (>), less than (<), or equal (=) to each other. Rule : A fraction is greater than another fraction if the denominators are the same and one of the numerators is larger than the other. Example: 5 > 8 8 Rule : A fraction is less than another if one of the numerators is smaller and the denominators are the same. Example: < 6 6 Rule : Fractions are equivalent or equal if they are of the same value when reduced. (See review on reducing.) Example: 8 = Rule : A fraction is less than another if the numerators are the same and the denominators aren t the same. The smaller denominator is the larger fraction. Example: > 5 > 5 Review on Reducing: The fraction 8 can be reduced by the common factor which divides into the numerator and the denominator 8 evenly. = So, the fraction reduces to ( T ) 5

20 Lesson 5 Checking for Understanding: Rounding Decimals Objective: Students will be able to round decimals to the nearest tenths and hundredths place value Ask: What is the sum of this problem when rounded to the nearest hundredth? Example # 6.9 Step : Round to the nearest +.07 hundredth and add a b c d. 7.0 Ask: What is the sum of this problem when rounded to the nearest hundredth? Example # Step : Round each number, then add a. 00. b c. 00 d Ask: What is the answer to this problem when rounded to the nearest hundredth? Example # 0. Step : Round each number to the nearest -.96 hundredth before subtracting a. 9.9 b. 8.9 c. 8. d

21 Cooperative Learning Objective: Students will review basic facts and rounding of whole numbers and decimals to the nearest hundredth, tenth, one, ten, or hundred Directions: Group size: Entire class I Have, Who Has? Materials: Set of playing cards for class (pages 69-7) Before class: Laminate set of game cards and cut them out Students must listen very carefully to each other, because they need to know when it is their turn to stand and read their card. The person who has the card with the star is first. That student will also be the last in the procedure. Directions: The first person stands and reads his/her card. The person who has the card that answers the firstquestion stands and reads his/her card. The person who has the answer to that question stands and reads his/her card. Directions: Play continues until all have read their cards and the first person answers the last person s question. Try this a second time. It will go much more quickly and smoothly! Then redistribute the cards so students have a different card to listen for and read. 68 7

22 Cooperative Learning Objective: Student will review basic facts and rounding of whole numbers and decimals to the nearest hundredth, tenth, one, ten, or hundred. Game Cards I have.8. Who has the number that shows.8 rounded to the nearest tenth? I have.5. Who has.5 rounded to the nearest tenth? I have.70. Who has.70 rounded to the nearest one? I have.. Who has. rounded to the nearest one? I have.. Who has. with 0.55 added to it? I have.0 Who has with 6.7 added to it? I have.0 Who has with 0.5 added to it? I have.85. Who has.85 minus.5? I have 9.7. Who has 9.7 rounded to the nearest hundredth? 8 69

23 Lesson 6 Objective: Students will be able to factor whole numbers Interactive Bulletin Board Activity Materials: Full page 00 s graph, page 78 Directions: Make a copy of the numbers from page 78. Cut the numbers apart and place them in the factor bag (a paper sack which has a tree drawn on the front). Put the numbers in the bag. Have students draw out a number. Tell them this is the number they will factor on their tree. After they are certain they have factored their number correctly they should place it on their tree. Color the tree making sure the factored number is clearly visible. Bulletin Board Directions: Cut out letters ( or 5 ) that say FACTOR TREE. Make a large tree with brown butcher paper - be sure to have lots of branches. Take the student s factored numbers and hang from the limbs. This makes a nice bulletin board to stimulate interest in 5th and 6th grade math. Teacher note: If making trees is not your strong suit, then take newspapers or brown butcher paper and make long, skinny rolls of varying lengths. Staple the rolls close together to make a trunk, using additional rolls of varying lengths to make the branches. 9 77

24 Lesson 6 Objective: Students will be able to factor whole numbers Interactive Bulletin Board Activity Numbers

25 Final Test Directions: Read each problem carefully. Decide which answer best completes the question. Show your work. Problem # Problem # Todd is manager at an electronics store. He is taking inventory and needs to list prices of cameras from least to greatest. Which shows the prices in the correct order? a. $.0, $.0, $., $.00 b. $.00, $.0, $., $.0 c. $.0, $., $.0, $.00 d. $.00, $.0, $., $.0 Problem # Bret works at a hardware store and is asked to arrange pieces of lumber from shortest to longest. What order should he choose? a. 7 ft, ft, 8 ft b. 7 ft, ft, 8 ft c. ft, ft, 8 ft d. 7 ft, ft, 8 ft Problem # Judy is a librarian at the public library and was arranging books from greatest to least according to the Dewey Decimal System. Which shows the book numbers in the correct order? a , 97.6, 98.59, 99. b. 99., 98.59, 97.6, c , 97.6, 99., d , 96.85, 97.6, 99. Problem #5 The average monthly income of Sally s mother is $,67.6. What is this amount rounded to the nearest dollar? a. $, b. $,68.00 c. $,67.60 d. $,67.00 Problem #6 In the past year there were.05 sunny days to every rainy day. What would this number be rounded to the nearest whole number? A large city received 5.96 inches of rainfall. What is the amount rounded to the nearest tenth of an inch? a. 5.0 in b. 5.9 in c. 5.9 in d. 6.0 in a..0 b..05 c.. d..5 8

26 Final Test Directions: Read each problem carefully. Decide which answer best completes the question. Show your work. Problem #7 Problem #0 Which expression shows 5 as a product of prime factors? a. x 5 b. x x 5 c. x 7 d. x 7 x Problem #8 What is the prime factorization of 9? a. x 8 b. x 9 c. 7 x 7 d. x x x Problem #9 What is the prime factorization of 05? a. 5 x b. 5 x 7 c. 5 x d. x 5 x 7 Kelly has a stamp collection. She has determined that 5% of the stamps are from the U.S. To find the number of stamps that are U.S., she must multiply the total number of stamps, 00, by - a. b. 5 c. d. Problem # Max spends 5 of his income on groceries a week. If he spends $0.00 a week on groceries, how much is his weekly income? a. $ b. $ c. $ d. $ Problem # The children at Matt s birthday party ate of the cake. If the cake was cut into ten 5 slices, how many slices are left? a. slices b. slices c. slices d. slice 85

27 Journal Writing August/September:. Take a poll of all fifth graders at school for the first time this year. Create a pictorial fraction that represents the new students compared to the old students.. Add up the total cost of school supplies purchased for this year and round it off to the nearest dollar. October:. Plan a Halloween party for your friends. Order the shopping list from cheapest to most expensive.. Keep track of the scores for the high school football team over a week period. Order the scores from highest to lowest. November:. Copy a favorite Thanksgiving Day recipe. Order the ingredients from smallest amount to the largest.. Chose one of Mom s favorite recipes for Thanksgiving dinner. Research and list the cost of each ingredient. List the ingredients in order from cheapest to most expensive. December:. Make a Christmas list of all the presents you plan to buy for people. Make a fractional representation of it.. Add up the costs of your gifts you purchased for your Christmas list. Figure the average cost of the gifts and the amount of cost difference from the most expensive to the least expensive. January:. Keep a record of the rainfall for the months of December, January, and February. Order these from the least amount to the greatest amount.. Check the newspaper daily and record states names that had snow. Make a class graph of the results. February:. Select 0 presidents. Order their ages from the oldest to the youngest when first elected.. Using a bag of candy hearts, make a graph showing the fraction part for each color of candy. 9 ( T )

28 Reasonableness - 5th Directions: Read each problem carefully. Decide which answer best completes the question. Show your work. Problem #6 Which of the following is a reasonable prime factorization of 8? Problem #9 The figures are shaded to show equivalent fractions. a. 9 x 9 b x 8 c. x 7 d. x x x Problem #7 Michelle owns a bakery. She determined that 5% of the donuts she made on Monday were glazed. If she baked 00 donuts, which of the following fractions is a reasonable equivalent? a. c. b. d. Problem #8 Constance uses of her daily income to restock the shelves of her store. If she spends $80 dollars a day, what is a reasonable total daily income for Constance? a. $0.00 b. $00.00 c. $0.00 d. $ Which of the following is a reasonable equivalent of? a. b. c. d. 6 Problem #0 The models are shaded to show two fractions. Which of the following answers is a reasonable representation of this model? 6 a. > b. < 8 c. = d. >