Math Gr4 Ch3

Chapter 3Algebra: Use Addition and Subtraction

Click the mouse or press the space bar to continue.

Chapter 3Algebra: Use Addition and Subtraction

Click the mouse or press the space bar to continue.

http://ca.gr4math.com/

Lesson 3-1 Addition and Subtraction Expressions

Lesson 3-2 Solve Equations Mentally

Lesson 3-3 Problem-Solving Strategy: Missing and Extra Information

Lesson 3-4 Algebra: Find a Rule

Lesson 3-5 Problem-Solving Investigation: Choose a Strategy

Lesson 3-6 Balanced Equations

33Algebra: Use Addition and Subtraction



Five-Minute Check (over Chapter 2)

Main Idea and Vocabulary

California Standards

Example 1

Example 2

Example 3

3-13-1 Addition and Subtraction Expressions



• I will write and find the value of expressions.

• expression

• variable

• parentheses



Standard 4AF1.1 Use letters, boxes, or other symbols to stand for any number in simple expressions or equations (e.g., demonstrate an understanding and the use of the concept of a variable).


You need to find the value of 2 + n when n = 3.

Mr. and Mrs. Presley and some of their children eat apples in their lunches. Today, 3 of their children are eating apples. What is the value of 2 + n if n = 3?


2 + n Write the expression.



2 + 3 Replace n with 3.

5 Add 2 and 3.



A. 7

B. 4

C. 11

D. 12

What is the value of 4 + n if n = 7?


Find the value of 15 + (h – 3) if h = 4.

15 + (h – 3)

15 + (4 – 3)

15 + 1

16

Write the expression.

Repleace h with 4.

Find (4 – 3) first.

Next, find 15 + 1.




A. 6

B. 2

C. 1

D. 7

Find the value of (k + 2) – 1 if k = 6.


Danielle ran 6 fewer miles than Martha last week. Write an expression for the number of miles Danielle ran.


Answer: So Danielle ran m – 6 miles.

Words

Expression

Variable

Ran 6 fewer miles than Martha

m – 6

Define a variable. Let m represent the miles that Martha ran.



A. a – 10

B. 10 – a

C. a + 10

D. a + 2b

Sven earned $10 more than Erin last month. Write an expression for the amount of money Sven earned.



Five-Minute Check (over Lesson 3-1)



Example 1

Example 2

Example 3

3-23-2 Solve Equations Mentally

Addition and Subtraction Equations



• I will solve addition and subtraction equations mentally.

• equation

• variable

• solve





Misae baby-sat for 2 hours on Friday, and by the end of the day on Saturday she had baby-sat 6 hours total. How many hour did she baby-sit on Saturday?


In the previous Explore activity, you solved equations using models. Equations can also be solved mentally.



Step 1 Model the equation.

One Way: Use Models

2 + x = 6



Step 2 Find the value of x.

One Way: Use Models



2 + x = 6

Another Way: Mental Math

Answer: So, x = 4.

2 + 4 = 6



A. 3

B. 8

C. 5

D. 11

Adelina worked for 3 hours on Tuesday, and by the end of Wednesday she had worked a total of 8 hours. How many hours did she work on Wednesday?


Solve 19 – n = 12 mentally.

Answer: So, the value of n is 7.


19 – n = 12

19 – 7 = 12

n = 7

19 minus what number equals 12?

You know that 19 – 7 = 12.



A. 16

B. 5

C. 11

D. 6

Solve 16 – y = 11 mentally.


Big Red had 7 puppies last spring. This spring she had some more puppies and now has a total of 13 puppies. How many puppies did she have this spring?

Write and solve an equation.


Words

Expression

Variable

7 puppies plus some more equals 13.

7 + p = 13

Let p represent the additional puppies.



Answer: So, Big Red had 6 more puppies this spring.

7 + p = 13

7 + 6 = 13

p = 6

7 plus what number equals 13?

You know that 7 + 6 = 13.



A. 9 + x = 13; 4

B. 9 + x = 13; 3

C. 9 – x = 13; 3

D. 9 – x – 13; 4

Write and solve an equation for the following situation: 9 plus a number is 13.




Main Idea


Example 1: Problem-Solving Strategy

3-33-3 Problem-Solving Strategy: Missing and Extra Information



• I will identify extra and missing information when solving problems.



Standard 4MR1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.





Trina is making friendship bracelets to sell for $2 each. Last week, she sold 63 bracelets. Two weeks ago, she sold 21 bracelets. How many more bracelets did Trina sell last week than two weeks ago?



Understand

What facts do you know?

• Trina sells friendship bracelets for $2 each.

• She sold 63 bracelets last week.

• She sold 21 bracelets two weeks ago.

What do you need to find?

• Find how many more bracelets Trina sold last week than two weeks ago.



Plan

Once you identify the information needed to solve the problem you can write a number sentence. Look for any extra information.



Solve

Subtract 21 from 63. You do not need to know how much the bracelets cost. This is extra information.

Answer: So, Trina sold 42 more bracelets last week than the week before.

last week two weeks ago

63 – 21 = n

63 – 21 = 42



Check

Look back at the problem. You can check subtraction with addition. 21 + 42 = 63. So, you know the answer is correct.





Main Idea


Example 1

3-43-4 Algebra: Find a Rule



• I will find a rule and use the rule to write an equation.



Standard 4AF1.5 Understand that an equation such as y = 3x + 5 is a prescription for determining a second number when a first number is given.


Write an equation that describes the pattern in the table.


Pattern: 1 + 4 = 5

Rule: Add 4.

Equation: x + 4 = y

3 + 4 = 7



A. x + 1 = y

B. x + 9 = y

C. x + 10 = y

D. x + 8 = y

Write an equation that describes the pattern in the table.


Use the equation to find the next three numbers.


Find the next three numbers when the input (x) is 5, 7, and 9.

x + 4 = y x + 4 = y x + 4 = y

5 + 4 = 9 7 + 4 = 11 9 + 4 = 13

Answer: So, the next three numbers in the pattern are 9, 11, and 13.

9 11 13



A. 10, 13

B. 15, 18

C. 17, 22

D. 9, 12

Use the equation, x + 5 = y, to find the last 2 numbers.


The uniform store is offering a $5 discount for any purchase of $20 or more. Use a rule to write an equation to describe the pattern. Then use the equation to find the next three prices.




Identify the rule and write it as an equation.

Rule: Subtract 5.

Equation: x – $5 = y



x – 5 = y x – 5 = y x – 5 = y

22 – 5 = 17 23 – 5 = 18 24 – 5 = 19

Answer: So, the next three amounts are $17, $18, and $19.

Find the next three numbers when the input (x) is 22, 23, and 24.

17 18 19



A. x + y = 7; 11, 12

B. x + 7 = y; 18, 19

C. x + y = 8; 8, 9

D. x + 7 = y; 11, 12

A shoe store is offering a discount of $7 for any purchase of $15 or more. Use a rule to write an equation to describe the pattern. Then use the equation to find the next 2 prices.




Main Idea


Example 1: Problem-Solving Investigation

3-53-5 Problem-Solving Investigation: Choose a Strategy



• I will choose the best strategy to solve a problem.



Standard 4MR2.3 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.



Standard 4NS3.0 Students solve problems involving addition, subtraction, multiplication, and division of whole numbers and understand the relationships among the operations.



KAMILAH: My soccer team is raising money by having a car wash. We earn $36 each hour of washing cars.

YOUR MISSION: Find how much money Kamilah’s soccer team will make in 5 hours.



Understand

What facts do you know?

• The soccer team earns $36 each hour.

What do you need to find?

• You need to find how much money the team will make in 5 hours.



Plan

You can make a table that shows how much the team will earn in 1, 2, 3, 4, and 5 hours.



Solve

Answer: So, Kamilah’s soccer team will make $180.

The table shows how much money the team earns in 1, 2, 3, 4, and 5 hours.



Check

Look back at the problem. Start with $180. Subtract $36 5 times.

$180 – $36 = $144$144 – $36 = $108$108 – $36 = $72$72 – $36 = $36$36 – $36 = $0

So, you know that the answer is correct.






Example 1

Example 2

Example 3

3-63-6 Balanced Equations



• I will balance addition and subtraction equations.

• balance



Standard 4FS2.1 Know and understand that equals added to equals are equal.


Show that the equality of 7 + 9 = 16 does not change when 3 is added to each side of the equation.


7 + 9 = 16 Write the equation.

7 + 9 + 3 = 16 + 3 Add 3 to each side.

19 = 19 19 = 19

So, when you add 3 to each side, the equality does not change.



A. 1 + 2 + 6 = 3 + 6; 9 = 9

B. 1 + 2 + 3 = 3 + 6 = 6 = 9

C. 1 + 2 = 3 + 6; 3 = 9

D. 1 + 2 + 6 = 3 + 6; 6 = 6

Show that they equality 1 + 2 = 3 does not change when 6 is added to each side of the equation.


Show that the equality of 12 + 5 = 17 does not change when 6 is subtracted from each side of the equation.

12 + 5 = 17 Write the equation.

12 + 5 – 6 = 17 – 6 Subtract 6 from each side.

11 = 11 11 = 11

So, when you subtract 6 from each side, the equality does not change.




A. 10 + 9 = 19 – 4; 19 = 15

B. 10 + 9 = 19; 15 = 15

C. 10 + 9 – 4 = 19 – 4; 15 = 15

D. 10 + 9 – 4 = 19 – 4; 15 = 19

Show that the equality of 10 + 9 = 19 does not change when 4 is subtracted from each side of the equation.


Write the equation.

You know that 27– 11 = 16.

To keep the equation balanced, a number must be added to 9 + 3 that will give the result of 16. 9 + 3 + 4 = 16.

Find the missing number in 27 – 11 = 9 + 3 + ___ .

27 – 11 = 9 + 3 +

27 – 11 = 9 + 3 +

Answer: So, the missing number is 4.




A. 12

B. 2

C. 24

D. 10

Find the missing number in 24 + 2 = 12 + 12 + ___.




Five-Minute Checks

Addition and Subtraction Equations


Lesson 3-1 (over Chapter 2)

Lesson 3-2 (over Lesson 3-1)






A. 10

B. 121

C. 11

D. 21

(over Chapter 2)

Find each difference.

200 – 189


A. $2.43

B. $1.33

C. $4.67

D. $1.43

(over Chapter 2)


$3.00 – $1.67


A. 4,356

B. 6,754

C. 3,256

D. 4,246

(over Chapter 2)


5,500 – 1,254


A. 546

B. 1,546

C. 456

D. 1,656

(over Chapter 2)


6,000 – 5,454


A. $57.83

B. $58.93

C. $47.83

D. $37.83

(over Chapter 2)


$70.00 – $22.17


A. 13

B. 12

C. 6

D. 11

(over Lesson 3-1)

Find the value of each expression if x = 3 and a = 4.

(9 – a) + 7


A. 4

B. 5

C. 9

D. 8

(over Lesson 3-1)


x + (3 – 2)


A. 19

B. 18

C. 11

D. 20

(over Lesson 3-1)


8 + (15 – x)


A. 12

B. 13

C. 5

D. 4

(over Lesson 3-1)


4 + (a + 5)


(over Lesson 3-1)

A. 4

B. 11

C. 5

D. 6


(a + 4) – 3


C. n = 7

(over Lesson 3-2)

A. n = 8

Solve each equation mentally.

6 + n = 13

B. n = 6

D. n = 5


A. k = 9

(over Lesson 3-2)

C. k = 10


k – 2 = 7

B. k = 8

D. k = 5


B. g = 5

(over Lesson 3-2)

C. g = 6

A. g = 3


8 – g = 3

D. g = 4


D. x = 11

(over Lesson 3-2)

C. x = 12

A. x = 10


x + 4 = 15

B. x = 9


(over Lesson 3-3)

Identify any missing or extra information. Then solve if possible. An express train leaves Grand Terminal at 5:05 P.M. The train arrives at the first stop at 5:21 P.M., the second stop at 5:46 P.M., and the last stop at 6:04 P.M. How long is the train ride?

A. missing information: what time the train arrives at the last stop; can not solve the problem

B. extra information: the times of the first and second stops; 59 minutes


(over Lesson 3-3)


C. extra information: the time of the first stop: 41 minutes

D. extra information: the times of the first and second stop; 1 hour


(over Lesson 3-3)

B. extra information: the times of the first and second stops; 59 minutes



(over Lesson 3-4)

Use a rule to write an equation to describe the pattern. Then use the equation to find the next three numbers in the pattern.

D. 5 + x = y; 13, 16, 19

C. x + 4 = y; 12, 15, 18

A. x + 3 = y; 11, 14, 17

B. 3x = y; 24, 33, 42


(over Lesson 3-5)

Identify any missing or extra information. Use the Four-Step Plan in this problem; solve if possible. Viviana is taking a late train from home to visit her cousins. The train leaves Savannah at 11 A.M. and arrives in Charleston at 1:30 P.M. on July 13. How long is Viviana’s trip?

A. 2 hours and 30 minutes; extra information: July 13, visiting her cousins, late train

B. 10 hours and 10 minutes; no extra information


(over Lesson 3-5)


C. 1 hour and 30 minutes; extra information: July 13, visiting her cousins, late train

D. 2 hours and 30 minutes; missing information: why she is visiting her cousins


(over Lesson 3-5)


A. 2 hours and 30 minutes; extra information: July 13, visiting her cousins, late train

This slide is intentionally blank.

Education

Math Gr4 Ch3