© 21st Century Math Projects - Amazon S3 · construct simple equations and inequalities to solve problems by reasoning about the quantities. Quantities N-Q 2. Define appropriate

© 21st Century Math Projects


Title: Equation Boot Camp

Standard Focus: Patterns, Functions, and Algebra Time Range: 3-5 Days

Supplies: Calculator

Topics of Focus:

- Solving Equations of Varying Complexity

- Word Problems

Benchmarks:

Expressions and

Equations 6.EE

5. Understand solving an equation or inequality as a process of answering a question: which

values from a specified set, if any, make the equation or inequality true? Use substitution to

determine whether a given number in a specified set makes an equation or inequality true.

Expressions and

Equations 6.EE

6. Use variables to represent numbers and write expressions when solving a real-world or

mathematical problem; understand that a variable can represent an unknown number, or,

depending on the purpose at hand, any number in a specified set.

Expressions and

Equations 7.EE

4. Use variables to represent quantities in a real-world or mathematical problem, and

construct simple equations and inequalities to solve problems by reasoning about the

quantities.

Quantities N-Q 2. Define appropriate quantities for the purpose of descriptive modeling.

Seeing Structure

in Expressions A-SSE 1. Interpret expressions that represent a quantity in terms of its context.★

Creating

Equations A-CED

1. Create equations and inequalities in one variable and use them to solve problems. Include

equations arising from linear and quadratic functions, and simple rational and exponential

functions.

Creating

Equations A-CED

2. Create equations in two or more variables to represent relationships between quantities;

graph equations on coordinate axes with labels and scales.

Creating

Equations A-CED

3. Represent constraints by equations or inequalities, and by systems of equations and/or

inequalities, and interpret solutions as viable or nonviable options in a modeling context.

Reasoning with

Equations and

Inequalities

A-REI 3. Solve linear equations and inequalities in one variable, including equations with

coefficients represented by letters.


Procedures:

A. To start, give the Pre-Assessment to students. The rows of problems correspond to the Levels. The first row is Level

1, the second row is Level 2 and so on ending with the sixth row Level 6.

If students miss questions on a level, that is where I have them start. If they finish the entire thing without making a

mistake they will start on Level 7.

I like to use stickers or stamps to sign off on their mastery of a level. Regardless the age of students, they like this too.

In my experience, it works well to have students on similar levels work through problems together.

B. Once they complete a Practice assignment, they can take the Mastery Test. There are two versions of each test

provided. If they pass the mastery test (you set the threshold – I like to use 90%) then they can move onto the next level.

If they do not then they can repeat that Practice Assignment.

I like to let students take a Practice Assignment home so they can walk in and take a Mastery Test the next day.

C. Once a student completes all the levels, they become a teacher. A tutor for a student or a small group instructor

generally works well.

The goal is that the students get differentiated practice on perhaps the most important math skill of all.


Equation

Boot Camp

Name_____________________

Insignia Rank Mastery

Private

Specialist

Corporal

Sergeant

Staff Sergeant

Lieutenant

Captain

Major

Colonel

General


Basic Training

(Pre-Assessment)

Equation Boot Camp

Placement Test

Name:

𝒙

𝟔

𝟒𝒙+𝟏

𝟑

𝟐𝒚

𝟓

𝟐𝒈−𝟔

𝟓


Private

(One-Step)

Equation Boot Camp

Level 1 Practice

Name:

𝒙

𝟓

𝟏

𝟓

𝟐

𝟓

𝟕

𝟖

𝒙

𝟔

𝟔𝟏𝟐


Private

(One-Step)

Equation Boot Camp

Level 1 Mastery A

Name:

𝒙

𝟔

Private

(One-Step)

Equation Boot Camp

Level 1 Mastery B

Name:

𝒙

𝟐


Specialist

(Two-Step)

Equation Boot Camp

Level 2 Practice

Name:

𝟓

𝟖

𝟑

𝟓

𝟏

𝟐

𝟑

𝟏𝟎


Specialist

(Two-Step)

Equation Boot Camp

Level 2 Mastery A

Name:

𝟒

𝟑

𝟗

𝟏𝟎

𝟓

𝟔

Specialist

(Two-Step)

Equation Boot Camp

Level 2 Mastery B

Name:

𝟔

𝟓

𝟑

𝟒

𝟑

𝟏𝟎


Corporal

(Multi-Step)

Equation Boot Camp

Level 3 Practice

Name:

𝟐𝒙−𝟏

𝟑

𝟒𝒅+𝟐

𝟑

𝟑−𝟓𝒂

𝟔

−𝟖𝒃+𝟏

𝟑

𝒚−𝟏

𝟑

𝟔𝒅−𝟏

𝟓

𝒒

𝟑

𝒑

𝟐

𝟒𝒕

𝟓


Corporal

(Multi-Step)

Equation Boot Camp

Level 3 Mastery A

Name:

𝟐𝒙+𝟔

𝟓

𝒛

𝟑

−𝟐𝒅+𝟏

𝟑

𝒕

𝟕

Corporal

(Multi-Step)

Equation Boot Camp

Level 3 Mastery B

Name:

𝟐𝒘−𝟖

𝟑

𝒙

𝟓

𝟕−𝟒𝒑

𝟑

𝒉

𝟗


Sergeant

(Like Terms)

Equation Boot Camp

Level 4 Practice

Name:

𝟑

𝟖

𝟑

𝟓

𝟕

𝟐𝟎

𝟓

𝟖

𝟓

𝟗

𝟏

𝟑

𝟐

𝟗


Sergeant

(Like Terms)

Equation Boot Camp

Level 4 Mastery A

Name:

𝟕

𝟓

𝟗

𝟏𝟎

𝟏

𝟏𝟎

𝟓

𝟖

Sergeant

(Like Terms)

Equation Boot Camp

Level 4 Mastery B

Name:

𝟓

𝟕

𝟓

𝟐

𝟏

𝟏𝟒

𝟒

𝟕


Staff

Sergeant

(VariaBles on

Both Sides)

Equation Boot Camp

Level 5 Practice

Name:


Staff

Sergeant

(VariaBles on

Both Sides)

Equation Boot Camp

Level 5 Mastery A

Name:

Staff

Sergeant

(VariaBles on

Both Sides)

Equation Boot Camp

Level 5 Mastery B

Name:


Lieutenant

(DistriBution)

Equation Boot Camp

Level 6 Practice

Name:

½

𝟐

𝟑

𝟑

𝟓


Lieutenant

(DistriBution)

Equation Boot Camp

Level 6 Mastery A

Name:

𝟑

𝟒

Lieutenant

(DistriBution)

Equation Boot Camp

Level 6 Mastery B

Name:

𝟒

𝟓


Captain

(Mixed-Up)

Equation Boot Camp

Level 7 Practice

Name:

5

2x

𝒙−𝟑

𝟐

𝟑𝒙−𝟏

𝟐


Captain

(Mixed-Up)

Equation Boot Camp

Level 7 Mastery A

Name:

𝟑𝒙−𝟔

𝟒

Captain

(Mixed-Up)

Equation Boot Camp

Level 7 Mastery B

Name:

𝒙−𝟓

𝟒


Major

(Advanced)

Equation Boot Camp

Level 8 Practice

Name:

𝟑𝒕+𝟏

𝟒

𝟑

𝟒

𝟓𝒎−𝟑

𝟒

𝟓𝒎+𝟑

𝟔

𝟔𝒑−𝟐

𝟕

𝟓𝒑+𝟕

𝟖

𝟏

𝒚−𝟑

𝟑

𝒚−𝟓


Major

(Advanced)

Equation Boot Camp

Level 8 Mastery A

Name:

𝟐𝒅−𝟓

𝟐

𝟓𝒅+𝟐

𝟗

Major

(Advanced)

Equation Boot Camp

Level 8 Mastery B

Name:

𝒂−𝟒

𝟔

𝟐𝒂+𝟒

𝟑


Colonel

(Word)

Equation Boot Camp

Level 9 Practice

Name:


Equation Bank

𝒅

𝒕

𝟏

𝟐

2/ sm


Colonel

(Word)

Equation Boot Camp

Level 9 Mastery A

Name:

Equation Bank

𝒅

𝒕

𝟏

𝟐


Colonel

(Word)

Equation Boot Camp

Level 9 Mastery B

Name:

Equation Bank

𝒅

𝒕

𝟏

𝟐

2/ sm


General

(Teacher)

Equation Boot

Camp Level 10


Equation

Boot Camp

ANSWER GUIDE

Pre-

Test

1.) T= 4.667 7.) X = 5 13.) K = 6 2.) W = 14 8.) Y =20 14.) M = 7 3.) X = -36 9.) G = -7 15.) V=0 4.) D = 3 10.) Q = 11 16.) Z=0 5.) C = 12 11.) N = 3 17.) Q=10 6.) W = 7 12.) Y = 3 18.) H = -3

Level Practice Mastery A Mastery B

1

1 X = -15

2 Y = 2

3 Z = 0

4 P = -2

5 Q = 6/5

6 T = -4.5

7 M = -5

8 N = 7

9 W = 19/40

10 X = 42

11 V = -4

12 X = 1

13 2 ½

14 6 1/3

1 T = 0

2 Y = -1

3 W = -2

4 X = -6

5 -21

1 N = 11

2 M = -10

3 X = 10

4 P = 1

5 25

2

1 X = 3

2 Y = 11 2/3

3 Z = -4

4 X = 44/25

5 W = 5

6 V = -5.05

7 X = 10

8 D = 0

9 X = -15

10 2.5

1 G = -3

2 D = -4

3 Q = 4.67

4 X = -1/20

5 8

1 D = -3

2 V = -5

3 K = 3.62

4 X = -3/8

5 5.1


3

1 X = -11/2

2 D = 19/4

3 A = 63/5

4 B = 5

5 Y = 1

6 D = -4

7 Q=66

8 P=20

9 T = 35/4

10 12

11 60

12 37.5%

1 X = -13

2 Z = 9

3 D=8

4 T = 42

5 18

1 W=19

2 X=65

3 P= -17/4

4 H = 72

5 40%

4

1 -6k+15

2 13y-4

3 9.9x+16.1

4 B = -2

5 D = 1

6 X = 4/5

7 X = 7/3

8 N = -0.7

9 M = -1

10 X = 16/11

11 K = -10

12 Y = 3/2

1 Q=23/13

2 A= 4 1/6

3 B = 7/10

4 X= -11/60

5 D= -1/3

6 F= 8.97

1 N = 4 1/3

2 T = -13

3 W = 12/ 25

4 X = -43/11

5 Y = 1

6 Z = 10

5

1 D = -2

2 T = 7

3 P = 10

4 N = -11

5 Z = 7

6 Y = 2

7 X = 1

8 W = 9

9 V = -9

10 X = 4

11 Y = 1

1 D = -6

2 G = 9

3 M = 9

4 Z = -12

5 Z = -1.23

1 Y = 6

2 Z = 4

3 X = -3

4 A = -10

5 Q = -2

6

1 5x + 25

2 -6x – 3

3 3x + 5/2

4 A = -1/2

5 D = 6

6 Y = ½

7 X = 7

8 B= -17/3

9 P = 2

10 W = -6

11 K= -53/9

12 N = -1/4

1 J = 4

2 V = -3

3 X = 5

4 D = 4

5 W = -2

6 B = -22/7

1 Q = 21/5

2 T = -4

3 Z = 85/24

4 K = 3

5 W = 5

6 D = -3


7

1 D = -4

2 N = -4

3 M = 4

4 H = -4

5 X = -10

6 Q = 11.85

7 X = 11

8 X = 9 2/3

9 T = 6

10 G = -6.14

11 P = -1

12 K = 9

13 Z = -5

14 Y = 8

15 E = 1

16 W = 11

17 X = -4

18 V = 7

1 K = 3

2 M = 0

3 N = 0

4 T = 7

5 Y = 9

6 X = -6

1 B = -11

2 D = 10

3 H = 1

4 M = 7

5 N = 0

6 X = -7

8

1 W = 2

2 Infinite

3 X = 0

4 T = -6

5 No Solution

6 M = 3

7 P = 5

8 Y = 2

9 X = -4/3

10 34, 35, 36

1 X = 23/2

2 D = 49/8

3 P = 1/3

4 17 & 19

1 X= 39/8

2 A = -4

3 N = 11/4

4 26, 28, 30

9

1 28,800

2 5

3 1338.09

4

8 hr,

Denisse is

cheaper at

9 hours

5 2 m/s2

6 4.52 s

7

21.27 m/s

Jason

19.05 m/s

Angel;

Jason’s was

faster

1

3hrs same

5 hours,

Ciara is

cheaper

2 11%

3

20.16 m/s

Jason

15.48 m/s

Angel;

Jason was

faster

1 He lost 5

2 6.67 lbs of

Cans

3 10.1 s

Documents

© 21st Century Math Projects - Amazon S3 · construct simple equations and inequalities to solve problems by reasoning about the quantities. Quantities N-Q 2. Define appropriate