Sincerely, Your child s teacher

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1 Family Letter Content Overview Dear Family, In Unit 6 of Math Expressions, your child will apply the skills they have learned about operations with fractions, whole numbers, and decimals as they solve real world problems involving addition, subtraction, multiplication, and division. A situation equation shows the structure of the information in a problem. A solution equation shows the operation that can be used to solve a problem. Your child will review situation and solution equations for addition and subtraction, and for multiplication and division. These methods of representing problems are particularly helpful when problems involve larger numbers that students cannot add, subtract, multiply, or divide mentally. Your child will also solve multiplication and addition comparison problems and compare those types of problems, identifying how they are the same and how they are different. Addition Comparison Problem Terrell has 144 soccer trading cards. Manuel has 3 more cards than Terrell. How many cards does Manuel have? Multiplication Comparison Problem Elena has 74 stamps in her collection. Hassan has 3 times as many stamps. How many stamps does Hassan have? Students learn that in the addition problem, they are adding 3, and multiplying by 3 in the multiplication problem. Solving multistep problems is an important Grade 5 skill. Your child begins by solving one-step problems, then moves to two-step problems, and finally solves multistep problems which involve more than two steps. Your child will represent and use visual models and equations to find solutions for these problems. Sincerely, Your child s teacher This unit addresses the following standards from the Common Core State Standards for Mathematics with California Additions: 5.OA.1, 5.NBT.4, 5.NBT.5, 5.NBT.6, 5.NBT.7, 5.NF.1, 5.NF.2, 5.NF.3, 5.NF.4, 5.NF.4a, 5.NF.4b, 5.NF.5, 5.NF.5a, 5.NF.5b, 5.NF.6, 5.NF.7, 5.NF.7a, 5.NF.7b, 5.NF.7c, and all Mathematical Practices. UNIT 6 LESSON 1 Situation and Solution Equations for Addition and Subtraction 91

2 Carta a la familia Un vistazo general al contenido Estimada familia, En la Unidad 6 de Math Expressions, su niño aplicará las destrezas que ha aprendido acerca de operaciones con fracciones, y números enteros y decimales, para resolver problemas de la vida cotidiana que involucren suma, resta, multiplicación y división. Una ecuación de situación muestra la estructura de la información en un problema. Una ecuación de solución muestra la operación que se puede usar para resolver el problema. Su niño repasará ecuaciones de situación y de solución para suma y resta, y para multiplicación y división. Estos métodos de representar problemas son particularmente útiles cuando los problemas involucran números grandes que los estudiantes no pueden sumar, restar, multiplicar ni dividir mentalmente. Su niño también resolverá problemas de comparación con multiplicación y con suma, y comparará ese tipo de problemas, identificando sus diferencias y semejanzas. Problema de comparación con suma Terrell tiene 144 tarjetas coleccionables de fútbol. Manuel tiene 3 tarjetas más. Cuántas tarjetas tiene Manuel? Problema de comparación con multiplicación Elena tiene 74 estampillas en su colección. Hassan tiene el triple de estampillas. Cuántas estampillas tiene Hassan? Los estudiantes deben notar que en el problema con suma, suman 3 y en el problema con multiplicación multiplican por 3. Resolver problemas de varios pasos es una destreza importante del 5. grado. Su niño comenzará resolviendo problemas de un paso, luego de dos y finalmente resolverá problemas de varios pasos que tengan más de dos pasos. Usará modelos visuales y ecuaciones para representar y solucionar esos problemas. Atentamente, El maestro su niño Esta unidad se aplican los siguientes estándares auxiliares, contenidos en los Estándares estatales comunes de matemáticas con adiciones para California: 5.OA.1, 5.NBT.4, 5.NBT.5, 5.NBT.6, 5.NBT.7, 5.NF.1, 5.NF.2, 5.NF.3, 5.NF.4, 5.NF.4a, 5.NF.4b, 5.NF.5, 5.NF.5a, 5.NF.5b, 5.NF.6, 5.NF.7, 5.NF.7a, 5.NF.7b, 5.NF.7c, y todos los de prácticas matemáticas. 92 UNIT 6 LESSON 1 Situation and Solution Equations for Addition and Subtraction

3 1. The model represents the length of a whale (w) and the length of a porpoise (p). For numbers 1a 1d, select True or False for the statement. p w 1a. The whale is 5 times as long as the porpoise. True False 1b. The porpoise is 5 times as long as the whale. True False 1c. The whale is 1 as long as the porpoise. 5 True False 1d. The porpoise is 1 as long as the whale. 5 True False Write a word problem for the equation = = = 1 6 UNIT 6 TEST 93

4 5. Write a word problem for = Five students bought supplies. Two students each bought 2 pencils and an eraser. Three students each bought a pen and 3 pencils. Supply Cost pencil $0.15 eraser $0.59 pen $0.49 Select the equation that can be used to find the total cost (c) of the supplies. Mark all that apply. A c = B c = 2 ( ) + 3 ( ) C c = D c = 2 ( ) + 3 ( ) E c = F c = 2 ( ) + 3 ( ) 7. Students in the high school marching band are arranged in 17 equal rows. There are 85 students in the marching band. How many students are in each row? Write an equation and use it to solve the problem. Explain how you know your answer is reasonable. 94 UNIT 6 TEST

5 8. Penn volunteered a total of 72 hours over the last 12 weeks. He volunteered the same number of hours each week. How many hours did Penn volunteer in one week? Write an equation and use it to solve the problem. Explain how you know your answer is reasonable. 9. Henry has cups of flour. He uses 11 cups of the flour to 2 bake muffins. How much flour (f) does Henry have left? Complete the model to represent this problem. Write an equation. Then solve. Without solving the problem, choose the words that make the sentence true. 10. Fido eats 2 cups of kibble. Fifi eats 6 of what Fido eats. 5 more than Fifi eats less than the same as Fido. UNIT 6 TEST 95

6 11. Camille collects stickers. Her sticker book holds 5 stickers in each row. When a page is full, it holds 65 stickers. How many rows (r) of stickers are on a full page? Complete the model to represent this problem. r Write an equation. Then solve. 12. Julianne and Derek made signs for their school spirit week. Julianne made a sign that is feet long. Derek made a sign that is 5 as long 6 as Julianne s sign. How long is the sign Derek made? Complete the equation. = feet 13. Emilio made 65 potholders. Each potholder cost him $1.65 to make. If he sells each potholder for $2.12, how much profit will he make? $ 14. Without multiplying the numbers, classify the expression as less than 3.75 or greater than Write the letter of the expression in the appropriate box. A B C D E Less than 3.75 Greater than UNIT 6 TEST

7 15. Mr. and Mrs. Storey drove 3,200 miles during their vacation. Mr. Storey (y) drove 3 times as many miles as Mrs. Storey (x). Draw a model to represent the problem. How many miles did each person drive? 16. At an electronics store, a refrigerator costs 3 times as much as a DVD player. A dishwasher costs $125 more than a DVD player. Use the numbers to complete the sign. 0 2 Item Price DVD player $150 Refrigerator $ Dishwasher $ Mrs. Shin bought 12 refrigerators and 12 dishwashers for her apartment building. She received a discount of $90 on the entire purchase. Write an equation using parentheses to find the amount she owes. Then solve. UNIT 6 TEST 97

8 17. For numbers 17a 17e, choose Yes or No to indicate whether the comparison is additive. 17a. 250 times as long Yes No 17b. 123 more than Yes No 17c. $2.56 less than Yes No 17d. in 1 the time 2 Yes No 17e. 3.2 fewer seconds Yes No 18. Jerome scores 12 points in a basketball game. This is twice the number of points that Jaime scores. How many points did the rest of the team score? Solve the problem if possible. Identify extra information or information that is needed to solve the problem. 19. A car is 234 inches long. A model of the car is 1 times the 18 size of the actual car. Without solving the problem, select the answer that is the most reasonable length of the model of the car. A inches B 13 inches C D 216 inches 4,212 inches 20. A python (p) is 1.5 feet longer than a boa constrictor (b). Choose an expression from each column to create an equation that compares the lengths of the snakes. b p b 1.5p = b p b 1.5 p 98 UNIT 6 TEST