Chapter 2
Family Letter (English) ... 51
Family Letter (Spanish) ... 53
Lesson 2.1 ... 55
Lesson 2.2 ... 61
Lesson 2.3 ... 67
Lesson 2.4 ... 73
Chapter
2
Numerical Expressions
Name _________________________________________
Dear Family,
In this chapter, your student is learning about number properties and order of operations. Your student will learn about the Commutative Property,
Associative Property, Addition Property of Zero, Multiplication Properties of Zero and One, and Distributive Property. These properties are helpful in
writing equivalent numerical expressions. The vocabulary terms for the chapter are: evaluate, numerical expression, and order of operations.
Numerical expressions can be evaluated using a set of rules known as the order of operations. These rules are:
1. Perform operations in grouping symbols. 2. Multiply and divide from left to right. 3. Add and subtract from left to right.
Your student will write verbal statements as numerical expressions. Your student will also interpret the meaning of numerical expressions.
Help your student practice these skills using real-life situations.
Have your student find ticket prices for different events in your area. The ticket prices should have multiple prices (e.g., adult/child prices, sections with different pricing). Have your student write an expression to represent the cost for your family to attend the different events. Create additional scenarios by having your student invite different numbers of friends or by changing the prices.
By the end of this chapter, your student should feel confident with number properties. Your student will also have an understanding of evaluating numerical expressions using the order of operations and writing numerical expressions. Have a great time working with numerical expressions!
Chapter
2
Numerical Expressions
(continued)Lesson Learning
Target
Success Criteria
2.1 Number Properties
Use number properties. I can identify number properties in equations. I can use number properties to write equivalent
expressions. 2.2 Order of
Operations
Use order of operations to evaluate numerical
expressions.
I can identify the operations in a numerical expression.
I can determine the order to perform the operations in a numerical expression. I can evaluate a numerical expression. 2.3 Write Numerical
Expressions Write numerical expressions. I can write a verbal statement as a numerical expression. I can use parentheses in an expression
appropriately.
I can interpret an expression. 2.4 Evaluate
Expressions with Grouping Symbols
Use order of operations to evaluate expressions with grouping symbols.
I can identify different types of grouping symbols.
I can evaluate an expression with multiple pairs of grouping symbols.
Capítulo
2
Expresiones numéricas
Nombre _______________________________________
Querida familia:
En este capítulo, su estudiante está aprendiendo sobre propiedades de números y orden de operaciones. Su estudiante aprenderá acerca de la Propiedad
Conmutativa, Propiedad Asociativa, Propiedad Aditiva del Cero, Propiedades de Multiplicación del Cero y Uno y Propiedad Distributiva. Estas propiedades son útiles para escribir expresiones numéricas equivalentes. Palabras de vocabulario asociadas con este capítulo son: evaluar, expresión numérica y orden de
operaciones.
Las expresiones numéricas pueden ser evaluadas usando un conjunto de reglas conocidas como el orden de operaciones. Estas reglas son:
1. Ejecutar operaciones agrupando símbolos. 2. Multiplicar y dividir de izquierda a derecha. 3. Sumar y restar de izquierda a derecha.
Su estudiante escribirá enunciados verbales como expresiones numéricas. Su estudiante también interpretará el significado de expresiones numéricas. Ayude a su estudiante a practicar estas habilidades usando situaciones de la vida real.
Haga que su estudiante encuentre los precios de tickets para diferentes eventos en su área. El precio de los tickets deberían tener múltiples valores (por ejemplo, precio para adulto/niño, secciones con diferentes precios). Haga que su estudiante escriba una expresión para representar el costo de su familia para asistir a los diferentes eventos. Planteé escenarios adicionales haciendo que su estudiante invite a números diferentes de amigos, o cambiando los precios.
Al finalizar este capítulo, su estudiante se sentirá seguro de sí mismo aplicando propiedades de los números. Su estudiante también tendrá conocimientos para evaluar expresiones numéricas usando el orden de operaciones y escribiendo expresiones numéricas.
Capítulo
2
Expresiones numéricas
(continuación)Lección Objetivo de
aprendizaje
Criterios de éxito
2.1 Propiedades de números
Usar propiedades de números. Sé identificar propiedades de números en ecuaciones.
Sé usar propiedades de números para escribir expresiones equivalentes. 2.2 Orden de
operaciones
Usar el orden de operaciones para evaluar expresiones numéricas.
Sé identificar las operaciones en una expresión numérica.
Sé determinar el orden para resolver las operaciones en una expresión numérica. Sé evaluar una expresión numérica. 2.3 Escribir expresiones
numéricas
Escribir expresiones numéricas. Sé escribir un enunciado verbal como una expresión numérica.
Sé usar apropiadamente paréntesis en una expresión.
Sé interpretar una expresión. 2.4 Evaluar expresiones
con símbolos agrupados
Usar el orden de operaciones para evaluar expresiones con símbolos agrupados.
Sé identificar diferentes tipos de símbolos agrupados.
Sé evaluar una expresión con múltiples pares de símbolos agrupados.
Lesson
2.1
Daily Skills Practice
For use before Lesson 2.1Lesson
2.1
Vocabulary Practice
For use before Lesson 2.1 1. Write the decimal as a fraction.0.777 = _____
1. Write what you know about this word. Give an example. exponent
Lesson
2.1
Lesson
2.1
Prerequisite Skills Practice
For use before Lesson 2.1 Lesson2.1
Prerequisite Skills Practice
For use before Lesson 2.1 Find each product. Use patterns to help.1. 3 × 10 = _____ 3 × 100 = _____ 3 × 1,000 = _____ 3 × 10,000 = _____ 2. 7 × 10 = _____ 7 × 100 = _____ 7 × 1,000 = _____ 7 × 10,000 = _____
Extra Practice
Lesson
2.1
Name ________________________________________________________
Complete the equation. Identify the property shown.
1. 353 + _____ = 353 2. _____ × 141 = 0 3. 3 + 8 + 10 = 3 + _____ + 8 4. 16 + _____ = 12 + 16 5. _____ × 25 = 25 × 18 6. 3 (8 – 4) = (3 × _____) – (3 × 4) 7. 6 × (9 × 3) = (_____ × 3) × 9 8. _____ × 1 = 24
Use the Distributive Property to find the product.
9. 9 × 16 10. 37 × 7 11. 45 × 8 12. 41 × 5 13. 84 × 6 14. 3 × 91 15. 4 × 73 16. 2 × 83
Use a property to find the sum or product. Identify the property used.
17. 48 × 0 × 3 18. (34 × 5) × 2 19. 305 + 83 + 0
20. (49 + 65) + 75 21. 9 × (15 – 8) 22. 148 × 1
23. 173 + 241 + 127 24. 5 × 43 25. (9 × 5) × 4
30. A section of a stadium has 52 rows with 14 seats in each row.
400 of the seats have cup holders. How many seats do not have cup holders? How can you use the Distributive Property to help solve this problem mentally?
26. To find 20 × (15 × 14),
your friend multiplies 20 and 15 first. Then he multiplies the product by 14. Which property did he use and why?
27. Explain how using the
Distributive Property can help you find answers to problems.
28. Descartes uses two properties to
evaluate the expression (16 + 22) + 44. Identify the properties he uses. Why would Descartes use these properties?
29. Students were asked which type
of ice cream is their favorite. How many students responded? Identify the property you used.
= 6 students
(16 + 22) + 44 = 22 + (16 + 44)
Reteach
Lesson
2.1
Name ________________________________________________________
Here are several number properties.
Commutative Properties: Changing the
order of addends or factors does not change the sum or product.
4 + 8 = 8 + 4 4 × 8 = 8 × 4
Associative Properties: Changing the
grouping of addends or factors does not change the sum or product.
(4 + 8) + 3 = 4 + (8 + 3) (4 × 8) × 3 = 4 × (8 × 3)
Addition Property of Zero: The sum of any
number and 0 is that number. 9 + 0 = 9
Multiplication Properties of Zero and One:
The product of any number and 0 is 0. The product of any number and 1 is that number.
8 × 0 = 0 8 × 1 = 8
Distributive Property: Multiplying a sum (or
difference) by a number is the same as multiplying each number in the sum (or difference) by the number and adding (or subtracting) the products.
5 × (2 + 4) = (5 × 2) + (5 × 4) 5 × (2 – 1) = (5 × 2) – (5 × 1)
Example Complete the equation. Identify the property shown.
6 × 7 × 8 = 6 × 8 × 7 Commutative Property of Multiplication
Example Use the Distributive Property to
find 4 × 62.
4 × 62 = 4 × (60 + 2) Write 62 as a sum. = (4 × 60) + (4 × 2) Distributive Property
= 240 + 8 Multiply.
= 248 Add.
1. Complete the equation. Identify
the property shown. 23 × ____ = 0
2. Use the Distributive Property
to find 34 × 7.
You can also write 62 as a difference. 4 × 62 = 4 × (70 – 8).
Enrichment and Extension
Lesson
2.1
Name ________________________________________________________
1. A public library receives a shipment of 40 boxes with 125 books in each
box. 2,500 of these books will be sent to schools. How many of the books will be left at the library after the other books are delivered to schools? How can you use the Distributive Property to help solve this problem mentally?
2. A company ships 16 bags of coffee in each box. They ship a total of
24 boxes. 200 of the bags weigh 1 pound each, and the rest of the bags weigh 1 pounds each. What is the total weight of the 1 pound bags of coffee?
3. A music venue is hosting a summer concert series. There will be
30 shows with 150 people attending each show. 3,000 of the tickets will be sold at regular price, and the rest will be offered at a discounted price of $25. What will be the total amount of money collected for the
discounted tickets? How can you use the Distributive Property to help solve this problem mentally?
Lesson
2.2
Daily Skills Practice
For use before Lesson 2.2Lesson
2.2
Vocabulary Practice
For use before Lesson 2.2 1. Write the number in two other forms.Word form: seven and four hundred eighteen thousandths Standard form: ___________
Expanded form: ___________
1. Write what you know about this phrase. Give an example. thousandths place
Lesson
X.X
Lesson
2.2
Prerequisite Skills Practice
For use before Lesson 2.2 Use the Distributive Property to find the product.Extra Practice
Lesson
2.2
Name ________________________________________________________
Evaluate the expression.
1. (7 + 5) × 3 2. 9 – (8 ÷ 4) 3. 6 × (4 + 9)
4. 8 ÷ (9 – 8) 5. 6 × 3 + 15 6. 72 – 18 ÷ 3
7. 7 × 5 + 25 8. 24 + (8 – 5) × 3 9. (7 + 5) ÷ 4 + 20
10. 40 – (20 + 10) ÷ 5 11. (16 – 9) × 7 – 8 12. (18 + 12) ÷ 3 + 42
Evaluate the expression.
16. 40 + 8 × 9 + 16 17. 35 – 63 ÷ 7 – 18 18. (414 – 227 + 13) ÷ 10
Insert parentheses to make the statement true.
19. 28 + 7 ÷ 7 = 5 20. 20 × 2 + 3 = 100 21. 10 + 7 × 5 + 2 = 59
22. 20 – 8 ÷ 4 + 4 = 19 23. 24 – 18 × 3 + 14 = 32 24. 45 – 10 ÷ 5 – 4 = 3
25. Your friend says that because of
the order of operations, the
expressions are equivalent. Is your friend correct? Explain.
16 – (20 ÷ 4) + 3 16 – 20 ÷ 4 + 3
26. Which expressions have a value
of 8?
6 × 3 – 8 24 ÷ 4 + 2 18 – 50 ÷ 10 – 5 24 – 8 ÷ 2 + 4 (14 – 8 – 5) × 8 4 × 4 – 18 ÷ 2
27. At a school, there are 6 classes of 22 students and 2 classes of
24 students for the fifth grade. Use the expression 6 × 22 + 2 × 24 to find the number of fifth grade students.
28. At a fundraising event, there are 18 groups with 5 volunteers and
3 groups with 4 volunteers. Use the expression 18 × 5 + 3 × 4 to find the number of volunteers.
Reteach
Lesson
2.2
Name ________________________________________________________
A numerical expression is an expression that contains numbers and
operations. When you evaluate a numerical expression, you find the
value of that expression.
When evaluating a numerical expression, use a set of rules called the
order of operations. These rules tell you the order
in which to perform the operations.
Order of Operations
1. Perform the operation in parentheses. 2. Multiply and divide from left to right. 3. Add and subtract from left to right. Example Evaluate 24 + 20 × 4.
Using the order of operations, multiply first. Then add. 24 + 20 × 4 = 24 + 80 Multiply 20 and 4.
= 104 Add 24 and 80.
So, 24 + 20 × 4 = 104.
Example Evaluate 27 ÷ (9 – 6) + 10.
Using the order of operations, perform the subtraction in the parentheses first. Then divide. Then add.
27 ÷ (9 – 6) + 10 = 27 ÷ 3 + 10 Perform the operation in parentheses. = 9 + 10 Divide 27 by 3.
= 19 Add 9 and 10.
So, 27 ÷ (9 – 6) + 10 = 19. Evaluate the expression.
1. 20 + 18 ÷ 6 2. 22 – (14 – 2) ÷ 2
The four basic operations are addition, subtraction,
multiplication, and division.
Enrichment and Extension
Lesson
2.2
Name ________________________________________________________
Evaluate the expression.
1. (2 × 24) + 3 × 15 + 1
2. 6 + 8 ÷ 2 ÷ 1 × 10
3. (10 – 8) ÷ 2 + 1 × 3
4. 44 11 + 3 × 3 – 5
5. 3 × (1 + 4) – 20 ÷ 4
6. Descartes buys 9 bouquets of flowers. There are 12 flowers in 7 of
the bouquets and 13 flowers in 2 of the bouquets. He divides the flowers into 10 vases with an equal amount of flowers in each vase. How many flowers are in each vase?
Lesson
2.3
Daily Skills Practice
For use before Lesson 2.3Lesson
2.3
Vocabulary Practice
For use before Lesson 2.3 1. Write the fraction as a decimal.
, = _____
1. Write what you know about this phrase. Give an example.
Lesson
X.X
Lesson
2.3
Prerequisite Skills Practice
For use before Lesson 2.3 Evaluate the expression.Extra Practice
Lesson
2.3
Name _______________________________________________
Write the words as an expression. 1. Subtract 24 from the product
of 12 and 8. 2. Add 62 to the difference of 90 and 36.
3. Multiply 8 by the difference of
40 and 28. 4. Divide 48 by 6, then add 50.
Write the words as an expression. Then interpret the expression.
5. Subtract 48 from 72, then multiply
by 5. 6. Add 38 and 29, then multiply by 2.
7. Subtract 55 from 69, then divide
by 2. 8. Add 58 and 42, then divide by 10.
Write the words as an expression. Then evaluate the expression.
9. Subtract 18 from the quotient of
80 and 2. 10. Add the product of 6 and 4 to the product of 3 and 5.
11. Add 35 to the product of
Write the expression in words.
13. 45 – (16 + 8) 14. (60 + 20) ÷ 8
15. (36 – 24) × 4 16. 9 × (55 ÷ 5)
17. You work 8 hours and earn $9
each hour. You have $30 saved in a bank account. Write an expression to represent the situation.
18. Write a real-life problem that can
be represented by the phrase “10 less than the sum of 16 and 18.”
19. Write two different expressions that each represent the combined area
of the rectangles. Then evaluate the expressions.
20. A family of four adds 6, 9,
5, and 8 apps to their cell phones. Each app costs $2. What is the total cost for the apps?
21. The price of a family ticket for an
amusement park is $89. The price of one adult ticket is $35, and the price of one child’s ticket is $18. What is the savings for a family of 2 adults and 2 children?
15 in.
14 in. 14 in. 14 in. 14 in.
Reteach
Lesson
2.3
Name ________________________________________________________
Example Write the words as an expression.
Multiply 8 by the difference of 10 and 6. 8 × (10 − 6)
The numerical expression is 8 × (10 − 6).
Example Write the words as an expression. Then interpret
the expression.
Add 58 and 74, then divide by 11. (58 + 74) ÷ 11
The numerical expression is (58 + 74) ÷ 11.
The value of the expression is the sum of 58 + 74 divided by 11. Write the words as an expression.
1. Add 16 and 27, then subtract
18. 2. Divide the difference of 35 and 8 by 9.
Write the words as an expression. Then interpret the expression.
3. Add 20 and 40, then multiply
by 5. 4. Divide 6 by the difference of 65 and 41. Remember to include the parentheses.
Enrichment and Extension
Lesson
2.3
Name
1. Newton and 9 of his friends use 5 sets of 52 cards to play a
game. The cards are divided equally among the players. How many cards does each player get?
2. Descartes and 4 of his friends pick apples. They collect
6 baskets of 20 apples. They divide the apples equally among themselves. How many apples does each friend get?
3. You and your friend have 102 tokens to play arcade games.
You play the first five games together and use 22 tokens. The remaining tokens are divided equally between you and your friend. How many of the remaining tokens do each of you get?
4. Descartes and Newton are recycling. There are 84 items that
need to be sorted and put into bins. 12 glass items are placed in a bin. The rest of the items are cardboard and need to be
divided equally into three different bins. How many cardboard items will go in each bin?
5. Write a real-life problem that can be represented by the
expression 21 + (12 × 2).
6. Write a real-life problem that can be represented by the
Lesson
2.4
Daily Skills Practice
For use before Lesson 2.4Lesson
2.4
Vocabulary Practice
For use before Lesson 2.4 Lesson2.4
1. Complete the statements.
_____ is 10 times as great as 7,000. _____ is of 7,000.
1. Write what you know about this phrase. Give an example. order of operations
Lesson
X.X
Lesson
2.4
Prerequisite Skills Practice
For use before Lesson 2.4 Complete the equation. Identify the property shown.1. 4 × (15 + 10) = (4 × 15) + (4 × _____)
Extra Practice
Lesson
2.4
Name ________________________________________________________
Evaluate the expression.
1. 16 ÷ (2 × 2) + (3 × 4) 2. 5 × (3 + 8) – (7 + 4) 3. (8 × 5) ÷ (3 + 9 + 8) 4. (21 – 14) × (16 ÷ 8) 5. [(10 – 8) + (12 – 4)] × 2 6. [(13 – 5) ÷ (8 – 6)] × 9 7. [(14 – 9) × (12 – 6)] ÷ 10 8. 5 × [(7 + 8) – 10] 9. 75 ÷ [(105 + 20) ÷ 5] 10. 20 ÷ [(24 – 20) × 5] 11. 4 + {[16 ÷ 8 + (7 – 3)] + 3} 12. 8 × [(20 – 9 ÷ 3 – 9) + 2]
Write the words as an expression. Then evaluate the expression.
13. Divide the sum of 25 and 41 by
the difference of 17 and 11. 14. Multiply the difference of 24 and 17 by the difference of 12 and 9.
15. Subtract 24 from 49, then divide
by 5. 16. Add 17, 20, and 33, then multiply by 8.
17. Explain how to evaluate the
expression.
45 ÷ [(30 + 15) ÷ 5]
18. Explain how to evaluate the
expression.
10 × [4 × (12 – 8)]
19. Explain how to evaluate the
expression. [(24 – 8) × 3] ÷ 2
20. Write and evaluate two equivalent
numerical expressions that show the Distributive Property.
21. Four laps around a track is a mile.
Your friend runs 20, 18, and 14 laps over the course of 3 days. She completes this pattern twice a week. How many miles does she run?
22. You have 12 blue sticky notes,
8 purple sticky notes, 5 green sticky notes, and 5 red sticky notes. You keep 2 sticky notes, and then divide the rest equally between 4 friends. How many sticky notes does each friend receive?
Reteach
Lesson
2.4
Name ________________________________________________________
Parentheses ( ), brackets [ ], and braces { } are called grouping symbols. You can write and evaluate numerical expressions that have more than one pair of grouping symbols.
Order of Operations (with Grouping Symbols) 1. Perform operations in grouping symbols. 2. Multiply and divide from left to right. 3. Add and subtract from left to right. Example Evaluate (14 – 10) × (6 + 5).
(14 – 10) × (6 + 5) = 4 × 11 Perform operations inside parentheses. = 44 Multiply 4 and 11.
Example Evaluate [40 + (20 – 5)] ÷ 5.
[40 + (20 – 5)] ÷ 5 = [40 + 15] ÷ 5
= 55 ÷ 5 Perform operations inside brackets.
= 11 Divide 55 by 5.
Evaluate the expression.
1. (9 + 21) ÷ (10 – 5) 2. 18 + [20 ÷ (3 + 2)]
3. (28 – 7) × (9 ÷ 3) 4. 57 – [8 × (9 – 3)]
Perform operations inside parentheses. Perform the
operation inside the innermost grouping
Enrichment and Extension
Lesson
2.4
Name ________________________________________________________
Insert parentheses, brackets, and/or braces to make the statement true.
1. 40 – 8 ÷ 2 × 3 = 108 2. 43 + 17 – 8 × 6 ÷ 2 = 70 3. 9 – 6 ÷ 3 + 15 = 16 4. 14 – 2 × 5 + 4 = 108 5. 3 × 60 – 10 ÷ 10 = 15 6. 7 × 8 ÷ 4 + 6 ÷ 10 = 2 7. 20 × 4 ÷ 4 + 16 – 15 = 40 8. 17 – 15 × 41 – 11 ÷ 6 + 7 = 24
Chapter Self-Assessment
Chapter
2
Name _______________________________________________
Use the scale below to rate your understanding of the learning target and the success criteria.
1
2
3
4
I can teach someone else.
I do not understand. I can do it
with help.
I can do it on my own.
Rating 2.1 Number Properties
Learning Target: Use number properties. 1 2 3 4 I can identify number properties in equations. 1 2 3 4 I can use number properties to write equivalent expressions. 1 2 3 4
2.2 Order of Operations
Learning Target: Use order of operations to evaluate
numerical expressions. 1 2 3 4
I can identify the operations in a numerical expression. 1 2 3 4 I can determine the order to perform the operations in a
numerical expression. 1 2 3 4
I can evaluate a numerical expression. 1 2 3 4
2.3 Write Numerical Expressions
Learning Target: Write numerical expressions. 1 2 3 4 I can write a verbal statement as a numerical expression. 1 2 3 4 I can use parentheses in an expression appropriately. 1 2 3 4 I can interpret an expression. 1 2 3 4
2.4 Evaluate Expressions with Grouping Symbols Learning Target: Use order of operations to evaluate
expressions with grouping symbols. 1 2 3 4 I can identify different types of grouping symbols. 1 2 3 4 I can evaluate an expression with multiple pairs of grouping