Model Place Value Relationships Instructional Time: 1 day

Transcripción

1 Lesson 1.1 Model Place Value Relationships CC.4.NBT.1 Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. Model the 10-to-1 relationship among placevalue positions in the base-ten number system. Cómo puedes describir el valor de un dígito? base-ten blocks Animated Math Models itools Base-Ten blocks 0 min. activity is for students to describe the value of a digit using the relationship among place value positions in the base-ten number system. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction. place value to develop sound mathematical practices by asking these questions. Por qué son buenos los bloques de base diez para representar los valores posicionales? Qué conclusiones puedes sacar de los modelos de valor posicional? Cómo cambiarías tu modelo si se te pidiera que mostraras ; 0; 00;,000 y 0,000? once they understand these place value Exercises 9, 1, 13 or Cómo puedes describir el valor de un dígito? Es diez veces el valor del dígito a la derecha. How does a digit in the ten thousands place compare to a digit in the thousands place? Chapter 1 7 New York City Implementation Guide NYC37

2 Lesson 1. Read and Write Numbers Note: The instructional time for this lesson can also be days. Use the extra time to complete Unlock the Problem on page 1 as a class. CC.4.NBT. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using., 5, and, symbols to record the results of comparisons. Read and write whole numbers in standard form, word form, and expanded form. Cómo puedes leer y escribir números hasta las centenas de millar? HMH Mega Math Real World Video, Ch. 1 itools: Base-Ten Blocks 0 min. activity is for students to express the value of whole numbers in different forms. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction. whole numbers to develop sound mathematical practices by asking these questions. En qué situaciones sería mejor usar la forma en palabras o la forma desarrollada en lugar de la forma normal? Representan los números el mismo valor cuando se escriben en formas diferentes? Cómo sabes qué dígito tiene el mayor valor en un número? Qué palabra del vocabulario matemático describe cada conjunto de tres dígitos? once they understand these whole number Exercises 1 15, 18 Cómo puedes leer y escribir números hasta las centenas de millar? Puedo usar dígitos para leer y escribir la forma normal, nombres de palabras para escribir la forma en palabras o el valor total de cada dígito como sumandos para leer y escribir la forma desarrollada. Is 70 thousand written in standard form or word form? Explain. 8 Chapter 1 NYC38 New York City Implementation Guide

3 Lesson 1.3 Compare and Order Numbers CC.4.NBT. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using., 5, and, symbols to record the results of comparisons. Compare and order whole numbers based on the values of the digits in each number. Cómo puedes comparar y ordenar números? HMH Mega Math itools: Base-Ten Blocks Animated Math Models 0 min. activity is for students to compare and order whole numbers by using a place-value chart and the number line. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction. whole numbers to develop sound mathematical practices by asking these questions. Qué plantea el problema? Qué hiciste primero? Por qué? Qué haces si los dos dígitos más a la izquierda son los mismos? Qué haces si los dos números que estás comparando tienen diferentes números de dígitos? once they understand these comparison The exercises below require higher order Exercises or 0 3 Cómo puedes comparar y ordenar números? Para comparar y ordenar números, comienzo con los dígitos con el mayor valor posicional y comparo los que están en la misma posición. Suppose the leftmost digits of two numbers are 8 and 3. Can you tell which number is greater? Explain. Chapter 1 9 New York City Implementation Guide NYC39

4 Lesson 1.4 Round Numbers CC.4.NBT.3 Use place value understanding to round multi-digit whole numbers to any place. Round a whole number to any place. Cómo puedes redondear números? Animated Math Models HMH Mega Math Funcionará siempre el uso del método de la recta numérica? Cómo lo sabes? Cómo sabes que la respuesta es razonable? Qué otro modelo podrías usar para resolver el problema? Qué estrategia podría facilitar el problema? 0 min. activity is for students to round a whole number to any place using the number line and place value. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction. rounding whole numbers to develop sound mathematical practices by asking these questions. once they understand these rounding Exercises 10, 11, 1 Cómo puedes redondear números? Puedo usar una recta numérica o el valor posicional para determinar si debo redondear a un número mayor o uno menor. Jessie says to round 763,400 to the nearest ten thousand, he will round to 770,000. Is he right? Explain. 30 Chapter 1 NYC40 New York City Implementation Guide

5 Lesson 1.5 Investigate Rename Numbers CC.4.NBT.1 Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. Also CC.4.NBT. Rename whole numbers by regrouping. Cómo puedes convertir un número natural? base-ten blocks itools: Base-Ten Blocks 0 min. Investigate Activity to Build Conceptual Understanding activity is for students to use regrouping to rename numbers. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction. whole numbers and regrouping to develop sound mathematical practices by asking these questions. Por qué son buenos los bloques de base diez para representar números? Qué conclusiones puedes sacar de tu modelo con bloques de base diez? Cómo cambiaría tu modelo si se te pidiera que mostraras,00 de dos formas? Share and Show Approximately 0 min. once they understand these whole number Exercises 7 10 Cómo puedes convertir un número natural? Puedo hacer dibujos rápidos de bloques de base diez o una tabla de valor posicional para ayudarme a convertir números. Explain how you can rename 5,400 as hundreds. Include a quick picture or a place-value chart in your explanation. Chapter 1 31 New York City Implementation Guide NYC41

6 Lesson 1.6 Add Whole Numbers CC.4.NBT.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm. Also CC.4.NBT.3, CC.4.OA.3 Add whole numbers and determine whether solutions to addition problems are reasonable. Cómo puedes sumar números naturales? HMH Mega Math itools: Base-Ten Blocks 0 min. activity is for students to add whole numbers and use estimation to tell whether an answer is reasonable. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction. whole number addition to develop sound mathematical practices by asking these questions. Has resuelto algún problema parecido a este? Qué hiciste primero? Por qué? Funcionará siempre ese método? Cómo lo sabes? once they understand these addition and estimation concepts. Select exercises based on Exercises or Cómo puedes sumar números naturales? Puedo alinear los dígitos según su valor posicional y luego sumar de derecha a izquierda, reagrupando cuando sea necesario para calcular la suma. Have students write a story problem that can be solved by finding the sum of 506,11 and 44,809. Then have them solve the problem. 3 Chapter 1 NYC4 New York City Implementation Guide

7 Lesson 1.7 Subtract Whole Numbers CC.4.NBT.1 Fluently add and subtract multi-digit whole numbers using the standard algorithm. Also CC.4.NBT.3, CC.4.OA.3 Subtract whole numbers and determine whether solutions to subtraction problems are reasonable. Cómo puedes restar números naturales? HMH Mega Math itools: Base-Ten Blocks Animated Math Models 0 min. activity is for students to estimate and subtract whole numbers, then use addition to check the answer. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction. whole number subtraction to develop sound mathematical practices by asking these questions. Has resuelto algún problema parecido a este? Qué haces primero? Por qué? Funcionará siempre ese método? Cómo lo sabes? once they understand these subtraction The exercises below require higher order Exercises 1 14 or Cómo puedes restar números naturales? Puedo alinear los dígitos según su valor posicional y luego restar de derecha a izquierda, reagrupando cuando sea necesario para calcular la diferencia. Have students write a story problem that can be solved by finding the difference of 43,906 and 61,87. Then have them solve the problem. Chapter 1 33 New York City Implementation Guide NYC43

8 Lesson 1.8 Problem Solving Comparison Problems with Addition and Subtraction CC.4.NBT.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm. Use the strategy draw a diagram to solve comparison problems with addition and subtraction. Cómo puedes resolver problemas de comparación con suma y resta con la estrategia de dibujar un diagrama? 0 min. for this lesson, in which conceptual activity is for students to organize information to solve addition and subtraction comparison problems. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction. comparison to develop sound mathematical practices by asking these questions. Qué operación elegiste para representar la situación? Por qué representa la situación esa operación? Cómo sabes que la respuesta es razonable? once they understand these addition and subtraction concepts. Select exercises based on Exercises 5, 6, 7 Cómo puedes resolver problemas de comparación con suma y resta con la estrategia de dibujar un diagrama? Cuando tengo un problema de comparación de suma y resta para resolver, puedo dibujar un modelo de barras para representar la situación. Write a comparison problem you can solve using addition or subtraction. Draw a bar model to represent the situation. Describe how the information in the bar model is related to the problem. 34 Chapter 1 NYC44 New York City Implementation Guide

9 Lesson.1 Algebra Multiplication Comparisons CC.4.OA.1 Interpret a multiplication equation as comparison, e.g., interpret as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. Relate multiplication equations and comparison statements. Cómo puedes representar comparaciones de multiplicación? itools: Counters 0 min. activity is for students to use models to compare quantities. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction. multiplication to develop sound mathematical practices by asking these questions. Por qué es bueno un modelo de barras para representar este problema? Qué conclusiones puedes sacar de tu modelo? Qué operación usaste para representar la situación? Por qué representa la situación esa operación? once they understand these multiplication Exercises 8, 10, 11 Cómo puedes representar comparaciones de multiplicación? Puedo usar un modelo de barras para representar las dos cantidades que se están comparando. Por ejemplo, significa que 16 es veces 8. El modelo muestra una sola casilla con un 8 adentro al lado de dos casillas con un 8 adentro. Chapter 37 New York City Implementation Guide NYC45

10 Lesson. Algebra Comparisons Problems CC.4.OA. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. Solve problems involving multiplicative comparison and additive comparison. Cómo te ayuda un modelo a resolver un problema de comparación? HMH Mega Math itools Counters 0 min. activity is for students to use models to solve comparison problems that are multiplicative and additive. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction. addition and multiplication to develop sound mathematical practices by asking these questions. Por qué es un modelo de barras un buen modelo para este problema? Qué conclusiones puedes sacar de tu modelo? Cómo cambiarías tu modelo si el perro de Evan pesara diez veces más? Cómo cambiarías tu modelo si el perro de Evan pesara tres veces más? once they understand these comparison Exercises 4, 5, 7 or 8 10 Cómo te ayuda un modelo a resolver un problema de comparación? Un modelo de barras te ayuda a visualizar las cantidades que se comparan y te ayuda a decidir si tienes que multiplicar o restar para resolver. Write a problem involving how much more than and solve it. Explain how drawing a diagram helped you solve the problem. 38 Chapter NYC46 New York City Implementation Guide

11 Lesson.3 Multiply Tens, Hundreds, and Thousands CC.4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Also CC.4.NBT.1 Multiply tens, hundreds, and thousands by whole numbers through 10. Cómo te ayuda la comprensión del valor posicional a multiplicar decenas, centenas y millares? Animated Math Models itools: Base-Ten Blocks itools: Number Charts itools: Number Lines 0 min. activity is for students to use models to multiply tens, hundreds, and thousands by whole numbers. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction. multiplication to develop sound mathematical practices by asking these questions. Qué operación usaste para representar la situación? Por qué representa la situación esa operación? Por qué es el dibujo rápido un buen modelo para este problema? Cómo cambiarías tu modelo si hubiesen 6 vagones en el tren? Qué estrategia podrías usar para facilitar los cálculos? once they understand these multiplication Exercises 15, 16, 17 Cómo te ayuda la comprensión del valor posicional a multiplicar decenas, centenas y millares? Explain how finding is similar to finding 7 3,000. Then find each product. Chapter 39 New York City Implementation Guide NYC47

12 Lesson.4 Estimate Products CC.4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Also CC.4.NBT.3 Estimate products by rounding and determine if exact answers to multiplication problems are reasonable. Cómo puedes estimar productos mediante el redondeo y determinar si son razonables las respuestas exactas? Animated Math Models itools: Number Lines 0 min. activity is for students to estimate products by rounding and tell whether exact answers to multiplication problems are reasonable. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction. estimation and multiplication to develop sound mathematical practices by asking these questions. Qué operación elegiste? Por qué? Cómo puedes usar un problema más simple como ayuda para calcular la respuesta? Cómo sabes que la respuesta es razonable? Cuál es otra forma de resolver el problema? Problem Solving Approximately 10 min. once they understand these estimation and multiplication concepts. Select exercises based on students depth of understanding. The exercises below require higher order thinking skills and critical reasoning, making them especially rich. Exercises 5, 6, 7 Cómo puedes estimar productos mediante el redondeo y determinar si son razonables las respuestas exactas? Una manera es redondear el factor mayor al lugar mayor más cercano y luego multiplicar mentalmente. Describe a real-life multiplication situation for which an estimate makes sense. 40 Chapter NYC48 New York City Implementation Guide

13 Lesson.5 Investigate Multiply Using the Distributive Property CC.4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Use the Distributive Property to multiply a -digit number by a 1-digit number. Cómo puedes aplicar la propiedad distributiva para multiplicar un número de dígitos por uno de 1 dígito? grid paper color pencils base-ten blocks Animated Math Models itools: Base-Ten Blocks 0 min. Investigate Activity to Build Conceptual Understanding activity is for students to use the Distributive Property to break apart numbers and make them easier to multiply. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction. the Distributive Property to develop sound mathematical practices by asking these questions. Por qué es un rectángulo un buen modelo para este problema? Qué conclusiones puedes sacar de tu modelo? Cómo cambiaría tu modelo si multiplicaras 13 x 6? Por qué puedes aplicar la propiedad distributiva para resolver este problema? Problem Solving Approximately 10 min. once they understand these multiplication The exercise below requires higher order making it especially rich. Exercise 19 Cómo puedes aplicar la propiedad distributiva para multiplicar un número de dígitos por uno de 1 dígito? La propiedad distributiva me permite separar el número mayor como la suma de dos números más pequeños. Luego puedo multiplicar cada uno de los números menores por el factor de 1 dígito, usando operaciones básicas que conozco. Después sumo estos productos parciales para calcular el producto total. Chapter 41 New York City Implementation Guide NYC49

14 Lesson.6 Multiply Using Expanded Form CC.4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Use expanded form to multiply a multidigit number by a 1-digit number. Cómo puedes multiplicar un número de varios dígitos por uno de 1 dígito usando la forma desarrollada? itools: Base-Ten Blocks 0 min. activity is for students to use expanded form and the Distributive Property to multiply whole numbers. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction. multiplication and the Distributive Property to develop sound mathematical practices by asking these questions. Por qué es un rectángulo un buen modelo para este problema? Cómo cambiaría tu modelo si hubiese un dígito en el lugar de los millares? Qué conclusiones puedes sacar de tu modelo? Cómo sabes que la respuesta es razonable? once they understand these multiplication Exercises 9 11 or 1 14 Cómo puedes multiplicar un número de varios dígitos por uno de 1 dígito usando la forma desarrollada? Puedo escribir el número mayor en forma desarrollada. Luego puedo aplicar la propiedad distributiva para multiplicar cada sumando por el número de 1 dígito y sumar los productos parciales para calcular el producto. Explain how you can find using expanded form. 4 Chapter NYC50 New York City Implementation Guide

15 Lesson.7 Multiply Using Partial Products CC.4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Use place value and partial products to multiply a multidigit number by a 1-digit number. Cómo puedes multiplicar por un número de 1 dígito usando el valor posicional y los productos parciales? itools: Base-Ten Blocks 0 min. activity is for students to develop strategies to multiply a multidigit number by a 1-digit number. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction. multiplication to develop sound mathematical practices by asking these questions. Qué hiciste primero? Por qué? Has resuelto un problema parecido a este? Cómo puedes usar un problema más simple como ayuda para resolver este? Cuál es una situación que se podría representar por esta ecuación? once they understand these multiplication Exercises or 19 1 Cómo puedes multiplicar por un número de 1 dígito usando el valor posicional y los productos parciales? Puedo descomponer el número mayor en millares, centenas, decenas y unidades. Luego, puedo multiplicar cada parte por el otro factor. Por último, puedo sumar los productos parciales. Explain how you can find using two different methods. Chapter 43 New York City Implementation Guide NYC51

16 Lesson.8 Multiply Using Mental Math CC.4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Use mental math properties to multiply a multidigit number by a 1-digit number. Cómo puedes multiplicar números mentalmente con la ayuda de las propiedades? Animated Math Models itools: Measurement 0 min. activity is for students to develop mental math strategies to multiply a multidigit number by a 1-digit number. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction. multiplication to develop sound mathematical practices by asking these questions. Qué hiciste primero? Por qué? Has resuelto un problema parecido a este? Descríbelo. Qué propiedades aplicaste para resolver el problema? Funcionará siempre ese método? once they understand these multiplication Exercises or Cómo puedes multiplicar números mentalmente con la ayuda de las propiedades? Puedo descomponer un número en números que sean fáciles de multiplicar mentalmente. Show how to multiply using friendly numbers and then using properties and mental math. Write about which method you like better and why. 44 Chapter NYC5 New York City Implementation Guide

17 Lesson.9 Problem Solving Multistep Multiplication Problems CC.4.OA.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental math computation and estimation strategies including rounding. Also CC.4.NBT.5 Use the draw a diagram strategy to solve multistep problems. Cuándo puedes resolver un problema de multiplicación de varios pasos con la estrategia de dibujar un diagrama? 0 min. activity is for students to organize information to solve multistep problems. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction. multiplication to develop sound mathematical practices by asking these questions. once they understand these multiplication Exercises 5, 7, 8 Cuándo puedes resolver un problema de multiplicación de varios pasos con la estrategia de dibujar un diagrama? Un diagrama me ayuda a organizar la información del problema. Me ayuda a visualizar cómo se relaciona la información del problema. Write a word problem that can be solved using multiplication of two-digit numbers. Solve your word problem and explain the solution. Chapter 45 New York City Implementation Guide NYC53

18 Lesson.10 Multiply -Digit Numbers with Regrouping CC.4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Use regrouping to multiply a -digit number by a 1-digit number. Cómo puedes usar la reagrupación para multiplicar un número de dígitos por uno de 1 dígito? Animated Math Models HMH Mega Math Real World Video, Ch. itools: Base-Ten Blocks 0 min. activity is for students to develop methods to estimate products and multiply a -digit number by a 1-digit number. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction. multiplication to develop sound mathematical practices by asking these questions. Por qué son los bloques de base diez un buen modelo? Qué hiciste primero? Por qué? Funcionará siempre ese método? Cómo sabes que la respuesta es razonable? once they understand these estimation and multiplication concepts. Select exercises based on Exercises 18, 0, 1 or 5 Cómo puedes usar la reagrupación para multiplicar un número de dígitos por uno de 1 dígito? Necesito pensar en los productos en términos de los valores de los dígitos. Por ejemplo, para calcular 3 3 5, primero multiplico las unidades para obtener Pienso en 15 como 1 decena y 5 unidades. Luego multiplico las decenas para obtener 3 3 decenas 5 6 decenas. Sumo las decenas reagrupadas para obtener Chapter NYC54 New York City Implementation Guide

19 Lesson.11 Multiply 3-Digit and 4-Digit Numbers with Regrouping CC.4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Use regrouping to multiply a multidigit number by a 1-digit number. Cómo puedes usar la reagrupación para multiplicar? HMH Mega Math itools: Base-Ten Blocks Animated Math Models 0 min. activity is for students to estimate products and use regrouping to multiply and solve multistep problems. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction. multiplication to develop sound mathematical practices by asking these questions. Qué hiciste primero? Por qué? Funcionará siempre ese método? Qué propiedades aplicaste para calcular la respuesta? Cómo sabes que la respuesta es razonable? once they understand these estimation and multiplication concepts. Select exercises based on Exercises or Cómo puedes usar la reagrupación para multiplicar? Comienzo por la derecha. Primero multiplico las unidades, luego las decenas, después las centenas y por último los millares. Reagrupo cuando el producto en cualquier lugar es 10 o más. Anoto el número reagrupado en la columna encima del siguiente número mayor. Explain how finding can help you find 4 3 5,384. Then find both products. Chapter 47 New York City Implementation Guide NYC55

20 Lesson.1 Algebra Solve Multistep Problems Using Equations CC.4.OA.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental math computation and estimation strategies including rounding. Represent and solve multistep problems using equations. Cómo puedes usar ecuaciones para representar y resolver problemas de varios pasos? HMH Mega Math 0 min. activity is for students to use equations to represent and solve multistep problems. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction. multiplication to develop sound mathematical practices by asking these questions. Qué operación elegiste para representar la situación? Por qué representa la situación esa operación? Qué podrías usar como ayuda para resolver el problema? Cómo sabes que la respuesta es razonable? once they understand these algebra and multiplication concepts. Select exercises based on Exercises 7 9 or 11 Cómo puedes usar ecuaciones para representar y resolver problemas de varios pasos? Puedo hacer modelos con la información dada. Luego puedo usar los modelos para escribir y resolver las ecuaciones necesarias para resolver el problema. Write a word problem that could be solved by writing and solving a multistep equation. Then solve your problem. 48 Chapter NYC56 New York City Implementation Guide

21 Lesson 3.1 Multiply by Tens CC.4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Also CC.4.NBT.1 Use place value and multiplication properties to multiply by tens. Qué estrategias puedes usar para multiplicar por decenas? Animated Math Models HMH Mega Math itools: Number Lines itools: Base-Ten Blocks 0 min. activity is for students to use different strategies to multiply by tens. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction. multiplication properties to develop sound mathematical practices by asking these questions. Has resuelto algún problema parecido a este? Descríbelo. Qué operación usaste para representar la situación? Por qué? Qué propiedades aplicaste para calcular la respuesta? once they understand these multiplication Exercises or 17 0 Qué estrategias puedes usar para multiplicar por decenas? Puedo usar el valor posicional, la propiedad asociativa, una recta numérica y el cálculo mental. Write the steps for how to use a number line to multiply a -digit number by 0. Give an example. Chapter 3 51 New York City Implementation Guide NYC57

22 Lesson 3. Estimate Products CC.4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Also CC.4.NBT.3 Estimate products by rounding or by using compatible numbers. Qué estrategias puedes usar para hacer una estimación de los productos? itools: Number Lines itools: Base-Ten Blocks Animated Math Models 0 min. activity is for students to use different strategies to estimate products. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction. estimation and multiplication to develop sound mathematical practices by asking these questions. Has resuelto algún problema parecido a este? Describe las semejanzas. Qué operación usaste para representar la situación? Por qué representa la situación esa operación? Cómo sabes que la respuesta es razonable? once they understand these estimation The exercises below require higher order Exercises 19 or 3 6 Qué estrategias puedes usar para hacer una estimación de los productos? Puedo redondear cada factor al valor posicional mayor o usar números compatibles. 5 Chapter 3 NYC58 New York City Implementation Guide

23 Lesson 3.3 Investigate Area Models and Partial Products CC.4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Use area models and partial products to multiply -digit numbers. Cómo puedes multiplicar números de dígitos con modelos de área y productos parciales? color pencils itools: Number Charts itools: Base-Ten Blocks 0 min. Investigate Activity to Build Conceptual Understanding activity is for students to use models to multiply -digit numbers. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction. multiplication to develop sound mathematical practices by asking these questions. Por qué es un rectángulo un buen modelo para este problema? Qué conclusiones puedes sacar de tu modelo? Cómo puedes usar un problema más simple como ayuda para hallar la respuesta? Qué propiedades aplicaste para calcular la respuesta? Problem Solving Approximately 10 min. once they understand these multiplication The exercise below requires higher order making it especially rich. Exercise 9 Cómo puedes multiplicar números de dígitos con modelos de área y productos parciales? Puedo dibujar un modelo de área para hallar los productos parciales y luego sumarlos para calcular la respuesta final. Describe how to model -digit by -digit multiplication using an area model. Chapter 3 53 New York City Implementation Guide NYC59

24 Lesson 3.4 Multiply Using Partial Products CC.4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Use place value and partial products to multiply -digit numbers. Cómo puedes multiplicar números de dígitos mediante el valor posicional y los productos parciales? Centimeter Grid Paper itools: Base-Ten Blocks 0 min. activity is for students to use different strategies to multiply -digit numbers. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction. multiplication to develop sound mathematical practices by asking these questions. Por qué es un rectángulo un buen modelo para este problema? Qué conclusiones puedes sacar de tu modelo? Qué propiedades aplicaste para calcular la respuesta? Cómo sabes que la respuesta es razonable? once they understand these multiplication Exercises 18 1 or 5 Cómo puedes multiplicar números de dígitos mediante el valor posicional y los productos parciales? Puedo descomponer los números en decenas y unidades y multiplicar para hallar productos parciales y luego sumarlos. Explain why it works to break apart a number by place values to multiply. 54 Chapter 3 NYC60 New York City Implementation Guide

25 Lesson 3.5 Multiply with Regrouping CC.4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Use regrouping to multiply -digit numbers. Cómo puedes usar la reagrupación para multiplicar números de dígitos? Animated Math Models HMH Mega Math itools: Base-Ten Blocks itools: Number Charts 0 min. activity is for students to multiply -digit numbers using place value and regrouping. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction. multiplication to develop sound mathematical practices by asking these questions. Qué operación usaste para representar la situación? Por qué? Qué propiedades aplicaste? Funcionará siempre el método que usaste? once they understand these multiplication Exercises 15, 18, 19 Cómo puedes usar la reagrupación para multiplicar números de dígitos? Puedo multiplicar las unidades. Luego puedo volver a escribir el producto como unidades y decenas reagrupadas. Después puedo multiplicar las decenas y sumar las decenas reagrupadas al producto. Chapter 3 55 New York City Implementation Guide NYC61

26 Lesson 3.6 Choose a Multiplication Method Note: The instructional time for this lesson can also be days. Use the extra time for the class to use both methods to solve On Your Own exercises. Have students discuss how the methods are related and why they both yield accurate results. Ask students to explain the efficiency and ease of each method. CC.4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Choose a method to multiply -digit numbers. Cómo puedes calcular y anotar los productos de números de dígitos? Animated Math Models HMH Mega Math itools: Base-Ten Blocks itools: Number Charts 0 min. for this lesson, in which conceptual development is key. The goal of this activity is for students to use different methods to multiply -digit numbers. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction. multiplication to develop sound mathematical practices by asking these questions. Qué operación usaste para representar la situación? Por qué? Qué modelo podrías usar como ayuda para resolver el problema? Qué propiedades aplicaste para calcular la respuesta? once they understand these multiplication methods. Select exercises based on Exercises 14, 18, 19 Cómo puedes calcular y anotar los productos de números de dígitos? Puedo usar productos parciales o la reagrupación. How is multiplication using partial products different from multiplication using regrouping? How are they similar? 56 Chapter 3 NYC6 New York City Implementation Guide

27 Lesson 3.7 Problem Solving Multiply -Digit Numbers CC.4.OA.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental math computation and estimation strategies including rounding. Also CC.4.NBT.5 Use the strategy draw a diagram to solve multistep multiplication problems. Cómo puedes resolver problemas de multiplicación de varios pasos con la estrategia de dibujar un diagrama? HMH Mega Math Real World Video, Ch. 3 itools: Base-Ten Blocks 0 min. activity is for students to organize information to solve multistep multiplication problems. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction. multiplication to develop sound mathematical practices by asking these questions. Qué hiciste primero? Por qué? Qué operación usaste? Por qué es un modelo de barras un buen modelo para este problema? Cómo apoya tu trabajo el diagrama? once they understand these multiplication Exercises 5, 6, 7 Cómo puedes resolver problemas de multiplicación de varios pasos con la estrategia de dibujar un diagrama? Puedo usar una operación para calcular los números que necesito. Luego dibujo un modelo de barras para mostrar cómo se comparan los dos números entre sí. Después uso el modelo de barras para ayudar a escribir una ecuación que calcule cuánto mayor es una cantidad que la otra. Chapter 3 57 New York City Implementation Guide NYC63

28 Lesson 4.1 Estimate Quotients Using Multiples CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Use multiples to estimate quotients. Cómo puedes usar múltiplos para estimar cocientes? itools: Number Charts 0 min. activity is for students to estimate quotients using multiples. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction. division to develop sound mathematical practices by asking these questions. Qué pide el problema planteado? Has resuelto algún problema parecido a este? Describe las semejanzas. Por qué es hacer una lista un buen modelo para este problema? Qué conclusiones puedes sacar de tu modelo? once they understand these estimation and division concepts. Select exercises based on The exercises below require higher order Exercises 16 1 or 5 Cómo puedes usar múltiplos para estimar cocientes? Puedo hacer una lista de múltiplos del divisor hasta encontrar dos múltiplos entre los cuales está el dividendo. Los números positivos que usé para hallar los múltiplos son los cocientes de la estimación. El múltiplo más cercano al dividendo producirá la mejor estimación. Si la lista de múltiplos es muy larga, puedo más bien multiplicar el divisor por múltiplos de diez. 60 Chapter 4 NYC64 New York City Implementation Guide

29 Lesson 4. Investigate Remainders CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Use models to divide whole numbers that do not divide evenly. Cómo puedes usar modelos para dividir números naturales que no se dividen en partes iguales? counters Animated Math Models HMH Mega Math itools: Counters 0 min. Investigate Activity to Build Conceptual Understanding activity is for students to divide whole numbers that do not divide evenly. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction. division to develop sound mathematical practices by asking these questions. Qué operación usaste para representar la situación? Por qué? Por qué es hacer un dibujo rápido un buen modelo para este problema? Qué conclusiones puedes sacar de tu modelo? Cómo cambiarías tu modelo si hubiesen 4 jugadores? Problem Solving Approximately 10 min. once they understand these division The exercise below requires higher order making it especially rich. Exercise 18 Cómo puedes usar modelos para dividir números naturales que no se dividen en partes iguales? Puedo dividir el número total de fichas en grupos iguales colocando el mismo número de fichas en cada grupo hasta que la cantidad de fichas que quedan por dividir sea menor que el divisor. El residuo es el número de fichas que sobran. Describe a real-life situation where you would have a remainder. Chapter 4 61 New York City Implementation Guide NYC65

30 Lesson 4.3 Interpret the Remainder CC.4.OA.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental math computation and estimation strategies including rounding. Also CC.4.NBT.6 Use remainders to solve the division problem. Cómo puedes usar residuos para resolver problemas de división? HMH Mega Math itools: Counters 0 min. activity is for students to interpret remainders in division problems in different ways. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction. division to develop sound mathematical practices by asking these questions. Qué operación representa la situación? Por qué? Cuál es otra manera de resolver el problema planteado? Cómo sabes que tiene sentido tu respuesta? once they understand these division Exercises 4 6 or 7 10 Cómo puedes usar residuos para resolver problemas de división? Uso residuos de distintas formas según la situación. Puedo escribir el residuo en forma de fracción, como la de una unidad de medición. Puedo usar un residuo como respuesta cuando la pregunta es cuántos o cuántas quedan. Puedo sumarle 1 al cociente en situaciones cuando sólo tienen sentido cocientes de números naturales y hay que justificar la cantidad que sobra. O, no tengo que incluir el residuo en absoluto cuando la situación sólo pide el cociente de un número natural. Write word problems that represent each way you can use a remainder in a division problem. Include solutions. 6 Chapter 4 NYC66 New York City Implementation Guide

31 Lesson 4.4 Divide Tens, Hundreds, and Thousands CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Also CC.4.NBT.1 Divide tens, hundreds, and thousand by whole numbers through 10. Cómo puedes dividir números hasta los millares entre números naturales hasta 10? Animated Math Models 0 min. activity is for students to use basic facts and place value to divide whole numbers. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction. division to develop sound mathematical practices by asking these questions. Qué hiciste primero? Por qué? Has resuelto algún problema parecido al planteado? Describe las semejanzas. Qué propiedades aplicaste para calcular la respuesta? Funcionará siempre el método que usaste? once they understand these division Exercises 16, 18, 1 or 3 5 Cómo puedes dividir números hasta los millares entre números naturales hasta 10? Primero, identifico la operación básica y luego uso el valor posicional para dividir. Explain how your knowledge of place value helps you divide a number in the thousands by whole numbers through 10. Give an example to support your explanation. Chapter 4 63 New York City Implementation Guide NYC67

32 Lesson 4.5 Estimate Quotients Using Compatible Numbers CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Use compatible numbers to estimate quotients. Cómo puedes usar números compatibles para estimar cocientes? Animated Math Models itools: Number Charts 0 min. activity is for students to use compatible numbers to estimate quotients. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction. estimation and division to develop sound mathematical practices by asking these questions. Has resuelto algún problema parecido al planteado? Describe las semejanzas. Qué hiciste primero? Por qué? Qué operación usaste para representar la situación? Cómo sabes que la respuesta es razonable? once they understand these division The exercises below require higher order thinking skills and critical reasoning, making them especially rich. Exercises or 17 0 Cómo puedes usar números compatibles para estimar cocientes? Puedo elegir un número cercano al dividendo y fácil de dividir entre el divisor. 64 Chapter 4 NYC68 New York City Implementation Guide

33 Lesson 4.6 Investigate Division and the Distributive Property CC.4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Use the Distributive Property to find quotients. Cómo puedes aplicar la propiedad distributiva para calcular cocientes? color pencils grid paper base-ten blocks itools: Base-Ten Blocks 0 min. Investigate Activity to Build Conceptual Understanding activity is for students to make division easier by using the Distributive Property. As students work through Unlock the Problem, gauge their level of understanding to make better decisions about how to progress through instruction. division to develop sound mathematical practices by asking these questions. Por qué es un rectángulo un buen modelo para este problema? Qué conclusiones puedes sacar de tu modelo? Qué propiedades aplicaste para calcular la respuesta? Funcionará siempre este método? Problem Solving Approximately 10 min. once they understand these division The exercise below requires higher order making it especially rich. Exercise 15 Cómo puedes aplicar la propiedad distributiva para calcular cocientes? Puedo delinear un rectángulo sobre una cuadrícula para representar el problema de división. Luego, puedo descomponer el modelo en dos rectángulos más pequeños para mostrar cómo se puede descomponer el dividendo en dos sumandos; la suma de las dos partes es igual al dividendo y cada parte se puede dividir entre el divisor. Después puedo resolver los dos problemas de división más pequeños y sumar los cocientes. Chapter 4 65 New York City Implementation Guide NYC69