1. 2. 3. - ddtwo.org · Standard: 8.EEI.7 Extend concepts of linear equations and inequalities in one variable to more complex multi-step equations and inequalities in real-world

Day 1 – Surface Area of Prisms Name: ______________________________

Standard: 7.GM.6 Apply the concepts of three-dimensional figures to real-world and mathematical situations.

Objective: I can solve for surface area of a prism using the examples provided.

Warm – up: Find the area of the following 2D shapes.

1. 2. 3.

Example and Formulas:

5 cm

Practice:

1. 2.

3. 4.

12 cm

3 m

8 m

7.G.6 - Surface Area of Three-Dimensional Objects 80 © www.mathfunbook.com

280 in2 200 in2 544 in2 210 in2 174 in2 216 in2 324 in2 528 in2 396 in2 790 in2 290 in2

What Makes Music on Your Hair?

Find the surface area of the following shapes.

6 in

6 in

6 in

D

17 in

11 in 16 in

15 i

n

N

4 i

n

5 in

10 in 6 in

E

24 in

25 in

2 in 7 in

A

9 in

5 in 3 in

A

H

16 in 16 in

15 in 9 in

12 in 5 in

5 in

D

10 in

12 in 16 in

B 6 in

B = 72 in2

7 in

A 6 in

6 in

6 in

6 in

6 in 6 in

5 in

Day 2 – Surface Area of Cylinders Name: ______________________________

Standard: 8.GM.9 Solve real-world and mathematical problems the surface area of cylinders.

Objective: I can solve for surface area of a cylinder using the example that is worked out.

Warm – up: Practice these math problems without using a calculator, show work.

1. 2. 1

4+

3

7= 3. 3𝑥 + 2 = 11

Example and Formula:

Practice

1. 2.

3. ERROR ANALYSIS Describe and correct the error in finding the surface area of the cylinder.

4. CRITICAL THINKING The lateral surface area of a cylinder is 184 square centimeters. The radius is 9 centimeters.

What is the surface area of the cylinder? Explain how you found your answer

Solve in terms of π then at the end use

3.14 for π

Day 3 – Equations Name: ______________________________

Standard: 8.EEI.6 Apply concepts of slope and 𝑦-intercept to graphs, equations, and proportional relationships.

8.EEI.7 Extend concepts of linear equations and inequalities in one variable to more complex multi-step equations and inequalities in real-world and mathematical situations.

Objective: I can solve equations for linear functions. I can identify the number of solutions to an equation.

Warm – up: Solve these expressions using NO calculator. Show work.

Example – Variables on Both Sides Practice – Variables on Both Sides

1. 7b − 15 = 5b − 3

2. −7 + 4m + 10 = 15 − 2m

3. 12c − 4 = 14c − 10

Examples – Multiple Solutions

Practice – Multiple Solutions Solve the following equations and say how many solutions it has.

4. 3x + 15 = 3(x + 5) 5. x + 8 − x = 9 6. 5x − 7 = 4x − 1

Examples – Slope and Y-intercept

Practice – Slope and Y-intercept Match 7 - 9 with the corresponding graph; Graph 10 given the equation.

7. 8. 9.

.

10.

.

Solving Equations Maze Name: _______________________________________ Dodge the monsters. Make it home. Solve problems along the way to reveal the right path.

If a correct answer takes you to a monster, you made a wrong turn earlier on!

Created by ChalkDoc | Creative Commons BY-NC 4.0 | Icons by Freepik and Madebyoliver

2

-2 1 4 = -4 - 9x

1 4

- 6

4

-5

3

5

-2

7

- 1

1

1 2

5

2

1 1

- 1 1

24

9

- 4

1 0 1 0

-5

- 1 5

5

0

8

3

-6 (n - 7) + n= 82 -(v- 1 ) =-6v + 1 6 3 (-6 + 5v)=-39 - 6v

-4 + x2

= 8 1 - 4p -7 = 1 0 86 = 2n- 4 (-4 - 3n)

6 + 9x = 5 1 -3 =x6

- 2 5n + 7(n + 4) = 88 108 = -12n - 4 (-5n+ 7)

-1 2 = p + 2p - 3

2- v = 5 (v + 4) 8(v - 6)=-20 + v

Finish

Start 4 = 8n - 2 + 6

Day 4 Inequalities Name: ___________________________

Standard: 8.EEI.7 Extend concepts of linear equations and inequalities in one variable to more complex multi-step equations and inequalities in real-world and mathematical situations.

Objective: I can write and solve inequalities.

Warm – up: Solve these expressions using NO calculator. Show work.

1. 1

3∗ 1

4

5= 2.

1

5−

2

7= 3.

What is an Inequality?

An inequality is a mathematical sentence that compares expressions. It contains the symbols <, >, ≤ , or ≥. To write an inequality, look for the following phrases to determine where to place the inequality symbol.

Examples: Practices:

1. A number b is fewer than 30.4.

Tell whether -6 is a solution

2. c + 4 < −1

3. 5 − m ≤ 10

Graph the inequality

4. b > −8

Mary needs to order pizza for 18 students. Each

student should get ¼ of a pizza. How many

pizzas should Mary order? How much pizza will

be left over?

NAME: _____________________________________ DATE: ___________________________ BLOCK: ______

Two-Step Inequality Scramble Directions: Find an inequality and color in the rectangle. Then, find the rectangle with the first step to solve the inequality and color it in. Then, find the rectangle with the second step to solve the inequality and color it in. Finish solving the inequality and find the answer and color it in. When you are done, graph each answer.

1. 2.

3. 4.

5. 6.

1. 5x – 7 < 13 Add 5 to both sides x ≥ 8 Subtract 8 from

both sides

2. x

7 – 6 ≥ -5 Multiply by 8 x > -3 Divide by 5

Subtract 8 from both sides

x < 4 5. x

2 – 5 ≤ -9

Add 11 to both sides

x ≤ -8 4. -7x + 8 > 29 Multiply by 2 6. -4x + 8 > -4

3. x

4 – 11 ≥ -9 Divide by -7 Add 7 to both sides x ≥ 7

Multiply by 7 Add 6 to both sides x > 3 Divide by -4

Day 5 – Parallel Lines and Transversals Name: ______________________________

Standard: 8.GM.5 Extend and apply previous knowledge of angles to properties of triangles, similar figures, and

parallel lines cut by a transversal.

Objective: I can match definitions to terms for each type of angle. I can solve for missing angles.

Warm – up: Solve these expressions using NO calculator. Show work.

1. 11 + (−7)2 – 9 2. 8 ÷ 22 + 1 3. 4 + 32

Definitions - Matching: Draw a line to connect each of the definitions to the correct term,

1. Corresponding 2. Alternate Exterior 3. Alternate Interior 4. Vertical

a. a pair of angles on the inner side of the parallel lines but on opposite sides of the transversal

b. the angles which occupy the same relative position at each intersection where a straight line crosses two others

c. each of the pairs of opposite angles made by two intersecting lines d. a pair of angles on the outer side of the parallel lines but on opposite

sides of the transversal

5. Supplementary 6. Complimentary 7. Transversal 8. Perpendicular Lines 9. Parallel Lines

e. two straight lines in a plane that do not intersect at any point f. two angles that add up to 180 degrees g. two lines which meet at a right angle h. two angles that add up to 90 degrees i. a line that passes through two lines in the same plane at two distinct points

List ALL angle pairs for each type of angle using the diagram to the right:

Example: Corresponding angles <1 and <4

10. Corresponding Angles

11. Alternate Exterior Angles

12. Alternate Interior Angles

13. Vertical Angles

Solve for the missing angle in each problem

14. 15. 16. The painted lines that separate

parking spaces are parallel. The

measure of ∠1 is 60°. What is

the measure of ∠2?

17. OPEN-ENDED Describe two real-life situations that use parallel lines.

Day 6 Triangles Name: ________________________ Standard: 8.GM.5 Extend and apply previous knowledge of angles to properties of triangles, similar figures, and parallel lines cut by a transversal.

Objective: I can solve for the interior and exterior angles in a triangle.

Warm – up:

1. Joel is looking at costs for using a gym. He could pay $50 per month for unlimited use or he could pay $12 per

month plus $4 per visit. How many visits would he have to make each month to make the $50 per month

unlimited use option the cheapest one?

Triangle Examples:

Triangle Practice:

4. The ratio of the interior angle measures of a triangle is 2 : 3 : 5. What are the angle measures?

Day 7 Rotations Name: __________________________

Standard: 8.GM.4 Apply the properties of transformations (rotations, reflections, translations, dilations).

Objective: I can rotate a shape about the origin on a coordinate plane.

Warm-up:

1. During the winter, you charge people $12 for going to their house to shovel, then $9 for every hour you

shovel. If you make $57 one day, how many hours did you spend shoveling?

Rotation Rules:

90° Counterclockwise (x,y) (-y,x)

180° (x,y) (-y, -x)

270° Counterclockwise (x,y) (y,-x)

Practice:

1. 2. A triangle has vertices Q(4, 5), R(4, 0), and S(1, 0).

a. Rotate the triangle 90° counterclockwise about

the origin. List the new vertices.

b. Rotate the triangle 180° about vertex S. List the

new vertices

Graph triangle ABC with coordinates

A(1,1) B(4,-3) C(-2,-3)

Rotate this triangle 270°

Day 8 & 9 Reflections and Translations Name: ___________________________

Standard: 8.GM.4 Apply the properties of transformations (rotations, reflections, translations, dilations).

Objective: I can reflect a shape across x- and y- axis. I can translate a shape on a coordinate plane.

Reflections:

Translations:

Practice:

1. 2. The vertices of a triangle are A(−2, −2), B(0, 2),

and C(3, 0). Draw the figure and its image after

a translation 1 unit left and 2 units up.

The vertices of a rectangle are A(−4, −3), B(−4, −1),

C(−1, −1), and D(−1, −3). a. Draw the rectangle and

its reflection in the x-axis. b. Draw the rectangle

and its reflection in the y-axis.

Day 10 Dilations Name: ___________________________

Standard: 8.GM.4 Apply the properties of transformations (rotations, reflections, translations, dilations).

Objective: I can dilate a figure using a scale factor.

Warm-up:

1. Triangle DEF with vertices D(-2,4) E(5,7) and F(4,-2) is reflected across the x-axis. What are the new vertices?

Dilations:

Practice:

1. 2. 3.

4. A(− 5, 3), B(− 2, 3), C(− 2, 1), D(− 5, 1) Reflect in the y-axis.

Then dilate with respect to the origin using a scale factor of 2.

The blue figure is a dilation of the red figure. Identify the type of dilation and find the scale factor.

Choice Board: Pick 3 items from this tic-tac-toe board to complete. You must pick one assignment from each column (transformations, triangles, & transversals) and one assignment from each row (easy, medium, hard).

Transformations Easy Design a poster showing the definitions of a translations, reflection, dilation, and rotation. Include the word, definition (in a complete sentence, in your own words), and a picture.

Triangles Easy B

A x – 22 3x+19 x - 17 C Find the measure of ∠A. Show all your work.

Transversals Easy Use colored pencils to follow the directions below: -Draw 2 parallel lines in red. Label the lines b and a. -Draw a transversal in orange through the parallel lines. Label the transversal d. -Label the angles formed 1 through 8 in yellow. -Label ONE pair of alternate interior angles with green dots(•). -Label ONE pair of consecutive interior angles with blue dots(•). -Label ONE pair of alternate exterior angles with purple dots(•). -Label ONE pair of corresponding angles with pink dots(•).

Transformations Medium Graph triangle ABC with the coordinates 𝐴(3, 7), 𝐵(7, 3), and 𝐶(3, 3). Dilate triangle 𝐴𝐵𝐶 on the coordinate plane using the origin as the center of dilation and a scale factor of 3 to form triangle 𝐴’𝐵’𝐶.

1) What are the coordinates of A’B’C’?

2) Are these triangles similar or congruent?

Triangles Medium Solve for x.

Transversals Medium 1. Which lines are parallel lines? 2. If angle 6 measures 113⁰, what are the measures of angle 3, 4, 5, 11, 12, 13, 14? 3. If the measure of angle 2 is 3x, and the measure of 1 is 5x – 12, what is the measure of angle 9? --Show all your work for each problem and explain in words how you got the answers.

Tranformations Hard Given the pentagon:

𝑃 (1, 4) 𝐸 (4, 4) 𝑁 (4, 1) 𝑇 (2.5, 2)

𝐴 (1, 1) First (x, y) (x, ­y). Then use the image you just made and do (x, y) Rotate 90⁰ clockwise. Last, use the image you just made and (x, y) (x + 3, y - 2). Color the final image blue.

Triangles Hard Create ten triangle problems like the one in the Triangles Easy Box. Solve all the problems, showing your work. Circle your answer for each problems.

Transversals Hard You are to design your own city. Your city must have a name and population written at the top of your project. Your city must have the following and be correct to receive full credit. -5 parallel streets (each street must be named) -2 transversal streets (each street must be named) -A gas station and a restaurant (alternate exterior angles) -Your house and a school (same side interior angles) -a dollar store and a movie theater (corresponding angles) -a library and a park (alternate interior angles) Each building must be labeled. All names must be school appropriate.