Mathematics

Grade 6

Unit 3

SKILLS

EquationsDay Lesson Name

1 Translating and Evaluating Expressions and Equations

2 One-Step Addition and Subtraction Equations & Check

3 One-Step Addition and Subtraction Equations & Check

4 One-Step Multiplication and Division Equations and Check

5 One-Step Multiplication and Division Equations and Check

6 Mix of all four operations7 Translate & Solve Word Problems (real world)8 Translate & Solve Word Problems (real world)9 Performance Task & Review10 Review for Test11 Test

Name: _____________________________

Period: _____________________________

Lesson 1: Translating and Evaluating Expressions and Equations

What is the difference between an expression and an equation?

_______________________________________________________________________

_________________________________________________________________________Lesson:

Algebraic expression- ________________________________________

Numerical expression- _______________________________________

Algebraic equation- _________________________________________

Numerical equation- _________________________________________

Guided Class Practice: Translate the expressions and equations.

1.) 7 more than a number b is 8 _______________________

2.) 2 less than the product of 6 and a number y _______________________

3.) The quotient of 2 and a number g, minus 8 _______________________

4.) A number b times twelve is forty-two _______________________

5) Kristen read a number of books, k. Eric read 3 books fewer than Kristen. Write an

expression that can be used to find the number of books Eric read.

6.) Josh ate a number of popsicles, p. Eric ate 3 popsicles more than Josh.

Write an expression that you can use to find the number of popsicles Eric ate.

7.) Farrah scored three times as many points in her basketball game as her teammate

Cheyenne. If (k) represents Cheyenne’s points, write an expression that can be used to

show how many points Farrah’s scored.

Try these: Express each phrase as an algebraic expression or equation.

8.) 12 more than the product of a number z and 11 _______________________

9.) subtract a number y from 5 _______________________

10.) quotient of a number j and 15 _______________________

11) 5 plus a number w minus 19 _______________________

12.) a number u multiplied by 46 _______________________

Try these: Evaluate each expression for y= 4 and z= 7.

13.) 15 + z 14.) 4 + (z + 10)

15.) 25 – 2y 16.) 8 + yz

17) Circle the expression below that is a numerical expression.

a.) 19x + 16 b.) 4c c.) 16 – 3 d.) x – 10

Explain. ___________________________________________________________________________

___________________________________________________________________________________

Try these: Write an equation to model the real-world scenarios. Then solve the equations.

1.) Marcus had 34 pictures on his digital camera. After he took some pictures of a sunset, he had 53

pictures on his camera. How many pictures did he take of the sunset? Let p= the pictures of the

sunset.

2.) Antonio bought several bags of marbles. Each bag has 14 marbles. In total, Antonio bought 56

marbles. How many bags did he buy? Let m= the bags.

3.) Gail jogged around the track 4 times. She jogged a total of 600 meters. What is the length of the track? Let t= the length of the track.

Homework- Finish today’s problems for homework. Lesson 2: One Step Addition and Subtraction Equations & Check

Vocabulary:

variable- _____________________________________________________________________________

inverse operation- ______________________________________________________________________

Lesson: How can you get the variable alone in an addition or subtraction equation?

ADDITION AND SUBTRACTION are inverse operations because what one operation does to the other one can undo.

Examples:

x + 3 = 7 CHECKx + 3 = 7

- 3 = -3 x= 4

O: x + 3 = 7P: 4 +3 =7S: 7 =7

x – 6 = 4 CHECK

x – 6 = 4 O:

P:

S:

Guided Class Practice: Solve the equation. Show your steps.

Check1) x – 5 = 16

2.) b + 9 = 28

3.) y – 38 = 6

4.) 22 = a + 7

5.) y – 16 = 24

CHECK6.) 49 = w + 23

7.) 19 = y – 2

8.) x – 36 = 21

9.) d + 2.5 = 8.5

CHECK:

10.) f + 7.3 = 19.2

11.) 2.5 = h – 3.7

12.) 7.8 = r – 3.9

13.) z + 6.5 = 20

Try These: Show all work.

1.) Lacy scored 6 points lower on her test than her friend Steve. Steve scored an 83 on her

test. Write an equation you would use to find what Lacy scored on her test.

2.) Ms. Alexander planted 11 bushes in her yard when she first moved in. Then she

planted some more (c) bushes in her yard a year later. Now she has 32 bushes in her

yard. Write an algebraic equation to show how many more trees were planted a

year later. Then solve.

3.) Lila would like to take a ceramics class. The class costs $120. She has saved $80 so

far. Solve the equation 80 + d = 120 to find the amount that Lila still needs.

Homework: Finish today’s practice problems.

Lesson 3: Addition and Subtraction Equations and Check (continued)

Try these: Complete the following solution sets.

4.) Which of the following sets contain a solution to c + 5 = 21?

a.) {1,2,7} b.) {2,10,20} c.) {14, 16, 21} d.) {9, 10, 21}

5.) Which of the following sets contain a solution to b - 2 = 4?

a.) {1,2,7} b.) {4 ,10, 20} c.) {14, 16, 21} d.) { 6, 10, 21}

6.) Which of the following sets contain a solution to 9 + x = 13?

a.) {1,2,6} b.) {2,10,11} c.) {4, 12, 21} d.) { 8, 10, 21}

7.) Which of the following sets contain a solution to c + 15 = 21?

a.) {1,6,7} b.) {2,10,20} c.) {14, 16, 21} d.) {9, 10, 21}

8) Which of the following sets contain a solution x+ 9 = 20?

a) {2,13,12} b) {29, 20, 9} c) {10,11,19}

9) Which of the following sets contain a solution v – 30 = 20

a) { 20,30,40} b) {50,60,70} c) { 10,15,16}

10) Which of the following sets contain a solution 25= n + 6

a) { 30,31,32} b) { 15,16,17} c) { 18,19,20}

Homework- Complete problems that we didn’t finish in class

Lesson 4: Multiplication and Division Equations and Check

Vocabulary:

reciprocal-

________________________________________________________________________

Lesson: How can you get the variable alone in a multiplication or division equation?

MULTIPLICATION AND DIVISION are inverse operations because what one operation

does to the other one can undo.

Examples:

3x = 45 CHECK

3x = 45

3 3

x= 15

O: 3x =45

P: 3 (15) = 45

S: 45 = 45

x2.5

=40 O:

P:

S:

Guided Class Practice: Solve the equation. Show your steps. Division (division sign and

with fraction.)

Check 1.) u14= 2

2.) 8= s ÷3

3.) 3= c2

4.) 6f = 54

5.) 4d = 16

6.) 8b = 48

7.) 28= 4a

8.) 7 = h35

9.) 2v = 8

10.) q ÷3= 9

11) 10= 5t

12.) 8 = x7

13.) m ÷ 7 = 6

14.) 10 = 5 q

Try These: Show all work.

1.) A female whale shark is 35 feet long. An average 12 year old is 5 feet tall. How

many times longer is this fish than an average 12 year old? Solve the equation 35 =

5x.

2.) Mrs. Alexander throws a birthday party for her daughter and invites 19 children

to take part in a balloon toss (20 kids in all). She divides the 20 children up so that

each child has 15 balloons. How many balloons will Ms. Alexander have to fill in

order to play the game? Use the equation r20=15

5b) Write and solve an equation to determine how many balloons each child will

get if there were now 30 children to divide the same number of balloons up.

Homework- Finish problems from today’s lesson.

Lesson 5: Multiplication and Division Equations and Check (continued)

Try these: Complete the following solution sets.

1.) Which of the following sets contain a solution to c5= 20?

a.) {1, 20, 100} b.) {20 , 160 ,200} c.) {14, 16, 21}

2.) Which of the following sets contain a solution to 8x = 32?

a.) {1,2,7} b.) {4 ,10, 20} c.) {14, 16, 21}

3.) Which of the following sets contain a solution to x ÷7 = 3?

a.) {1,2,6} b.) {2,10,11} c.) {4, 12, 21}

Lesson 6: Solving Equations for all four operations

Try These: Translate and solve.

1.) The Washington Monument is 555 feet tall. It is 75 feet shorter than the Gateway to

the West Arch. Find the height of the Gateway to the West Arch.

2.) A killer whale, which can grow to a length of 9 meters, is 4 meters longer than the

bottle-nosed dolphin. Find the length of the dolphin.

3.) The Smiths sold a valuable painting for $55,000. This price is $18,000 more than

they originally paid for it. Find the original cost of the painting.

Homework- Worksheet Practice

Lesson 7: Translate and Solve Word Problems

Lesson: Drawing a picture can always help you solve a math word problem.

Ex. Joseph and her 4 friends had a garage sale to help pay for their choir trip. They

divided their total earnings so that each person had $37. How much was the total

earnings from the garage sale?

Equation _________________________

Ex. Ryan made a CD of his favorite songs. There are 42 minutes of time on the CD. He

records 14 songs. What is the average length of each song?

Equation _________________________

Ex. David saves $15 each week that he earns babysitting. After 8 weeks, how much

money will he have saved? Draw a picture and write an equation to solve.

Equation _________________________

1.) The Technology Club pools their money to buy robot parts. They divide the parts

among the 13 members. Each gets 24 parts. Write an equation to find the total

number of parts.

Equation _________________________

2.) A charity group divides donated items among 19 families. Each family receives 14

items. How many items were donated in total?

Equation _________________________

3.) Vicki hands out stickers to 23 preschool students. If each child gets 9 stickers, how

many stickers were there to begin with? Solve the equation s÷23 =9

Equation _________________________

4.) Darby rents in-line skates for 4.5 hours. His total bill is $27. How much did he pay

per hour to rent the skates? Write an equation and solve.

Equation _________________________

5.) In an orchestra, there are 5 times as many string instruments as percussion

instruments. If there are 45 string instruments, how many percussion instruments

are there?

Equation _________________________

Homework- Finish today’s practice problems.