MATH. Applying the Standards. Grade

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1 CD Applying the Standards MATH Grade 4 Promotes deep understanding of math concepts Reinforces higher-order thinking through reflective math tasks Provides standard-specific math problems on each page Includes Common Core alignment chart and problem-solving rubric

2 Table of Contents Introduction Common Core Alignment Chart Problem-Solving Rubric Operations and Algebraic Thinking Number and Operations in Base Ten Number and Operations Fractions Measurement and Data Geometry Answer Key Introduction The purpose of this book is to engage students in applying the standards to real-world, higher-level thinking problems. Each Common Core mathematics standard is covered by one or more practice pages. Students will be expected to answer a few straightforward problems to prove basic understanding of the standard. Then, they are presented with a higher-level thinking problem. These problems are designed to require students to demonstrate their complete understanding and flexibility with the standard. Finally, a reflection question guides students to review their work on the previous problem. The reflection questions are designed to support the Standards for Mathematical Practice as students are asked to study their approaches, their successes, and their struggles. Use the included rubric to guide assessment of student responses and further plan any necessary remediation. Understanding and applying mathematical knowledge to realistic problems is an invaluable skill that will help students succeed in their school years and beyond. 2 Carson-Dellosa. CD Applying the Standards: Math

3 Rewrite each statement as a multiplication sentence. 1. three times larger than six 2. an eight-pound baby will quickly double in size 3. four times as many as nine 4. Grace collects unique buttons. Her grandmother gave her 3 buttons to start her collection. She quickly found enough buttons to triple her collection. Then, over the next year, her collection grew 8 times larger. If her collection continues to double each year after that, how many years will it be until she has over 300 buttons in her collection? Explain a different way to solve problem 4. Carson-Dellosa. CD Applying the Standards: Math 5

4 Solve. 1. Andre has 6 toy robots. Davis has 7 times as many toy robots as Andre. How many toy robots does Davis have? 2. Jan s savings account now has $64 in it. That is 8 times the amount she started with when she opened her account. How much money did Jan deposit when she first opened her account? 3. Scientists are tracking tree growth in a young forest. An oak tree measured 9 feet tall. A nearby maple tree measured 7 feet tall. When they measured the trees again 2 years later, the oak tree was 54 feet tall, and the maple tree was 49 feet tall. Which tree grew the fastest? Anna claims the oak tree grew faster because it is taller than the maple tree. Is her reasoning correct? Explain. 6 Carson-Dellosa. CD Applying the Standards: Math

5 Solve. 1. Kami has 28 shaped erasers. She gives 13 of them to her sister and shares the rest evenly between herself and 2 friends. How many erasers does Kami keep? 2. Derek scored twice as many goals in the final championship game as he had scored in the last 3 games of the season. If Derek scored 3 goals in each of the last 3 games of the season, how many goals did he score in the championship game? 3. A convention hall charges $45 per 6-person table and $57 per 8-person table for an event. If 329 people are expected to attend the event, what is the most cost-efficient combination of tables? Explain how you can use rounding to guess which table size is the least expensive for the number of attendees. Carson-Dellosa. CD Applying the Standards: Math 7

6 List all of the factor pairs for each number A carpenter is building a rectangular frame from a board that is 23 feet long. He wants to make a frame with sides that are whole numbers and the largest area possible. He wants to waste the least amount of wood. What will the dimensions of the frame be? Is it possible to make the frame without wasting any of the wood? Explain. 8 Carson-Dellosa. CD Applying the Standards: Math

7 List all multiples up to 100 for each number Miranda has a large collection of thimbles. She wants to display them in groups of 3 or 6. If she has 81 thimbles, how could her collection be arranged? Explain why knowledge of the multiples of 9 can help solve problem 5. Carson-Dellosa. CD Applying the Standards: Math 9

8 Tell whether each number is prime or composite Henry says that all even numbers are composite and all odd numbers are prime. Prove him right or wrong. How could you figure out if an odd number is prime or composite? 10 Carson-Dellosa. CD Applying the Standards: Math

9 Write the next three numbers in each pattern. 1. 4, 9, 14, 19,,, 2. 3, 12, 48, 192,,, 3. 11, 18, 15, 22, 19,,, 4. 2, 6, 8, 24, 26,,, 5. The distances in miles to the next four highway exits are shown on a sign. A rest stop is three exits past Fawn Lane. If the pattern continues, how far away is the rest stop? Deer Road 2 1/2 Buck Street 5 1/2 Doe Avenue 8 Fawn Lane 11 Describe the pattern of distances with fractions and without fractions. Carson-Dellosa. CD Applying the Standards: Math 11

10 Draw the next image for each pattern A mason is creating a square patio with two types of square stones: dark gray for the border and light gray for the center. The smallest patio he can make has 8 dark gray border stones and 1 light gray stone in the center. The next size patio has 4 light gray stones in the center and 12 dark gray border stones. The client wants a patio that is 5 stones by 5 stones in the center. How many dark gray stones will the mason need for the border? Write a rule for how the number of dark gray border stones change. Write a rule for how the number of light gray center stones change. Explain how the two rules are different. 12 Carson-Dellosa. CD Applying the Standards: Math

11 Answer Key Answers to some higher-level problems will vary but may include the answers provided. For all responses, accept all reasonable answers as long as students have proper evidence and support. Page = 18; = 16; = 36; 4. 3 years Page toy robots; 2. $8; 3. maple; The maple tree increased by 7 times, while the oak tree only increased by 6 times. Page erasers; goals; person tables and 3 6-person tables Page , 18; 2, 9; 3, 6; 2. 1, 55; 5, 11; 3. 1, 36; 2, 18; 3, 12; 4, 9; 6, 6; 4. 1, 63; 3, 21; 7, 9; 5. 5 feet 6 feet Page , 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100; 2. 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100; 3. 11, 22, 33, 44, 55, 66, 77, 88, 99; 4. 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99; 5. 9 groups of 3 and 9 groups of 6 Page composite; 2. prime; 3. composite; 4. prime; 5. 2 is an even number and a prime number; 15 is an odd number and a composite number Page , 29, 34; ; 3,072; 12,288; 3. 26, 23, 30; 4. 78, 80, 240; miles Page ; 2. ; 3. ; dark stones (length of light stone square 4 + 4) Page ; 2. 70; 3. 2; ; 5. bulk store for $50/1,000 Page ,805; 2. 15,238; 3. 9,170; ,054; ,203 Page >; 2. >; 3. <; 4. =; 5. 13,456; 65,431; 43,615 Page ; 2. 36,000; 3. 1,700,000; 4. 2,000; 5. no; = 1,800 Page ,713; ,031; 3. 5,911,473; ,965; 5. 1,486; She did not carry the tens and hundreds. She just wrote them beside the ones and tens in the answer. Page ; ; ; ; 5. (40 7) + (6 7) = = 322 Page ,600; 2. 2,331; 3. 3,300; 4. 53,616; sq. units Page ; ; 3. 2,500; 4. 4,800; 5. false; = 100 Page ; ; 3. 4,810; 4. 5,488; 5. (80 25) + (5 25) + 25 = 2,150 Page ; 2. 51; ; ; 5. 9 rows of 25 or 5 rows of 45 Page ; ; 3. 2,393; 4. 1,456; calories per meal Page r3; r6; r4; r6; days Page ,008 r2; r4; r1; r5; 5. James started putting the answer over the 1 instead of over the 7 (8 goes into 17 two times, not into 1 two times). Page = 2 8 ; = 3 6 ; = 1; = 6 8 ; 5. The circle could be divided into sixths. 3 6 = 1 2 Page ; ; 3. 12; ; 5. They are both correct. Page > 2 4 ; = 2 8 ; < 1 2 ; > 2 8 ; > Page <; 2. >; 3. =; 4. =; 5. yes; 1 3 > 1 4 Page ; ; 3. 10; ; ; Brian mistakenly added the denominators. Page = 1 4 ; = 1 6 ; 3. 20; or 1 2 ; or 3 4 Page ; ; ; ; ; Page ; or ; ; ; 1 5. She has 4 cups; Her mistake was adding the denominators so she did not recognize that the fractions make another whole cup. Page ; or ; ; or 2 3 ; or feet Page or 4 5 of a mile; inches; 3. The African animals got more than 1 2 of the available land. Page tank; pound; 3. 6 days Carson-Dellosa. CD Applying the Standards: Math 63

Reflect. Name. Rewrite each statement as a multiplication sentence. 1. three times larger than six. 2. an eight-pound baby will quickly double in size

Reflect. Name. Rewrite each statement as a multiplication sentence. 1. three times larger than six. 2. an eight-pound baby will quickly double in size Rewrite each statement as a multiplication sentence. 1. three times larger than six 2. an eight-pound baby will quickly double in size 3. four times as many as nine 4. Grace collects unique buttons. Her