8th Grade Mathematics Summer School Curriculum - ic...

8th Grade Mathematics Summer School Curriculum Course Summary: In Grade 8, instructional time will focus on four critical areas: (1) formulating and reasoning about expressions and equations, and solving linear equations (2) analyzing two- and three-dimensional space and figures using perimeter and area. (3) graphing proportional relationships on the coordinate plane and using the graph to solve problems (4) analyzing two-dimensional space and figures using properties of angles to write equations and solve problems. Scope and Sequence:

Time Frame Unit

5 days Expressions and Equations

5 days Perimeter and Area

5 days Proportional Relationships and Linear Equations

7 days Angles

DRAFT—January, 2016 1 | P a g e

Unit 1: Algebraic Expressions and Equations

Subject: Math Grade: 8th grade Name of Unit: Algebraic Expressions and Equations Length of Unit: 5 days Overview of Unit: Students will understand the difference between an expression and an equation. Students will translate words to expressions and words to equations. Students will apply these skills to real-world problems. Priority Standards for unit:

● 7.EE.4 Use variables to represent quantities in real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

a. Solve word problems leading to equations of the form px + q = r and p(x +q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54cm. Its length is 6cm. What is its width?

● 6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers. a. Write expressions that record operations with numbers and with letters standing

for numbers. For example, express the calculation “Subtract y from 5” as 5 - y. Supporting Standards for unit:

● 7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

d. Apply properties of operations as strategies to add and subtract rational numbers. ● 7.NS.2 Apply and extend previous understandings of multiplication and division and of

fractions to multiply and divide rational numbers. c. Apply properties of operations as strategies to multiply and divide rational numbers.


Standard

Unwrapped Concepts (Students

need to know)

Unwrapped Skills (Students need to be able to

do) Bloom’s Taxonomy

Levels Webb's DOK

7.EE.4a expressions and

equations. Solve Apply 2

7.EE.4a

an algebraic solution to an arithmetic

solution, identifying the sequence of

operations used in each approach. Compare Understand 3

6.EE.2a

expressions that record operations with numbers and

with letters standing for numbers. Write Understand 1

Essential Questions:

1. For what are algebraic expressions and equations are used? Enduring Understanding/Big Ideas:

1. To help us solve real-world problems we can use algebraic expressions and equations to represent and describe situations.

Unit Vocabulary:

Academic Cross-Curricular Words Content/Domain Specific

variable expression equation

Resources for Vocabulary Development: CI Tools


8th grade Cluster 23: Numerical and Algebraic Expressions

Section Class Structure Suggested # of Days

Resources

i23-2

7.EE.4a 6.EE.2a

● Pretest: Writing Expressions and Equations (15 minutes)

● Skill #1(Integers--add, subtract, multiply, divide)-10 questions, grade, and chart progress (15-20 minutes)

● Lesson i23-2: Variables and Expressions (15-20 minutes)

● Practice i23-2 (5-10 minutes)

1 day Resources: Pretest (copies), Skill Sheet (copies), Tracking Sheet (copies), i23-2 Guided Notes (copies), i23-2 Practice (on computers-Digits), pencils, computers

Activity/Skill Practice

7.EE.4a 6.EE.2a

● Skill (Integers--add, subtract, multiply, divide)-10 questions, grade, and chart progress (15-20 minutes)

● Activity (10 minutes)-“Who Wants to be a Hundredaire?” http://www.math-play.com/Algebraic-Expressions-Millionaire/algebraic-expressions-game.html

● Language of Algebra Matching (20 minutes)


1 day Resources: Skill Sheet (copies), pencils, computers, Language of Algebra Lesson Plan, Language of Algebra cards on cardstock (copies-1 deck per group of 4)


http://www.math-play.com/Algebraic-Expressions-Millionaire/algebraic-expressions-game.html





8th grade Cluster 25: Solving Equations


Resources

i25-1

7.EE.4a 6.EE.2a

● Skill #1 (Integers--add, subtract, multiply, divide)-10 questions, grade, and chart progress (15-20 minutes)

● Lesson i25-1: Writing Equations (15-20 minutes)


1 day Resources: Skill Practice Sheet (copies), i25-1 Guided Notes (copies), i25-1 Practice (on computers-Digits), pencils, computers


7.EE.4a 6.EE.2a

● Skill #1 (Integers--add, subtract, multiply, divide)-10 questions, grade, and chart progress (15-20 minutes)

● Mobile Math (30 minutes) http://solveme.edc.org/mobiles/

● Alternate option: “By the Shapes” Activity

● Finish Practice i25-1 (5-10 minutes)

1 day Resources: Skill Sheet (copies), pencils, computers “By the Shapes” recording sheet (copies), 4 clue cards on cardstock (groups of 4 per class), counters (optional)

Engaging Scenario

● “Sweet Algebra” (45 minutes) ● Post Test (15 min)

1 day Resources: Sweet Algebra handouts, 11 brown paper bags, 151 individually wrapped candies, Post Test (copies)


http://solveme.edc.org/mobiles/

http://solveme.edc.org/mobiles/

Engaging Scenario

Engaging Scenario Students will use work cooperatively to write expressions and equations based on teacher-given scenarios. The teacher will use manipulatives to set up situations involving paper bags and candy. The number of candies in each bag is represented by the variable x and students are given clues to determine each bag. See attachment for “Sweet Algebra.”

Rubric for Engaging Scenario: See attachment-- “Sweet Algebra”


Unit 2: Perimeter and Area

Subject: Math Grade: 8th grade Name of Unit: Perimeter and Area Length of Unit: 5 days Overview of Unit: Students will understand how to use formulas to find perimeter and area of rectangles and squares. Priority Standards for unit:

● 7.G.6 Solve real-world and mathematical problems involving area, volume, and surface area of two-and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

Supporting Standards for unit: ● 8.NS.2 Use rational approximations of irrational numbers to compare the size of

irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., 𝜋𝜋2). For example, by truncating the decimal expansion of √2, show that √2is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

Standard


need to know)

Unwrapped Skills (Students need to be able

to do) Bloom’s Taxonomy

Levels Webb's DOK

7.G.6

real-world and mathematical

problems involving perimeter, area, and surface area of two-

and three-dimensional objects

composed circles and quadrilaterals. Solve Apply 2


1. What is the difference between perimeter and area? 2. How can you use perimeter and area to help you find the surface area of a 3-dimensional

shape?


Enduring Understanding/Big Ideas: 1. Perimeter is the distance around an object. Area is the space inside of an object. 2. You can use the perimeter and area formulas to break down the parts of a 3-dimensional

figure in order to find the surface area. Unit Vocabulary:


perimeter area surface area face



7th grade Cluster 20: Measuring 2- and 3- Dimensional Objects


Notes

i20-1

7.EE.4a

● Pretest: Perimeter and Area (15 minutes)

● Skill #2 (Comparing and Ordering Rational/Irrational Numbers)-10 questions, grade, and chart progress (15-20 minutes)

● Lesson i20-1: Perimeter (15-20 minutes)


1 day Resources: Pretest (copies), Skill Sheet #2(c opies), i20-1 Guided Notes (copies), i20-1 Practice (on computers-Digits), pencils, computers


7.EE.4a


● Interactive Perimeter (10 minutes) http://www.shodor.org/interactivate/activities/PerimeterExplorer/

● Gallery Walk--perimeter problems (20 minutes)

● Alternate Resource: http://www.mathplayground.com/manipulatives/AreaandPerimeter_secure.swf

● Finish Practice i20-1 (5-10 minutes)

1 day Resources: Skill Sheet #2 (copies), Perimeter Gallery Walk questions/printouts, pencils, computers

i20-2

7.G.6


1 day

Resources: Skill Sheet #2(copies), i20-2 Guided Notes (copies), i20-2 Practice (on computers-Digits), pencils, computers


http://www.shodor.org/interactivate/activities/PerimeterExplorer/



http://www.mathplayground.com/manipulatives/AreaandPerimeter_secure.swf



● Lesson i20-2: Area of Rectangles and Squares (15-20 minutes)



7.G.6

● Skill-Comparing and Ordering Rational/Irrational Numbers-10 questions, grade, and chart progress (15-20 minutes)

● Activity (30 minutes) ● Finish Practice i20-2 (5-10

minutes)

1 day

Resources: Skill Sheet (copies), pencils, computers

Engaging Scenario

“Polly Gone” Problem Level C (30 minutes), share out on chart paper (15 minutes) Post Test (15 minutes)

1 day Resources: “Polly Gone” handouts (copies), chart paper, markers, Post Test (copies)


Engaging Scenario

Engaging Scenario Students will work together in groups to solve the “Polly Gone” problem. They will put their steps and process on chart paper to share out with the class.

Rubric for Engaging Scenario: See attachment-- “Polly Gone”


Unit 3: Proportional Relationships and Linear Equations

Subject: Math Grade: 8th grade Name of Unit: Linear Equations Length of Unit: 5 days Overview of Unit: Students will graph proportional relationships on the coordinate plane, and use the graph to solve problems. Priority Standards for unit:

● 8.EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.

● 8.F.4 Describe qualitatively the functional relationship between two quantities by analyzing a graph. Sketch a graph that exhibits the qualitative features of a function that has been described verbally

Supporting Standards for unit: ● 7.RP.2.c Represent proportional relationships by equations. ● 7.RP.2.b Identify the constant of proportionality (unit rate) in tables, graphs, equations,

diagrams, and verbal descriptions of proportional relationships.

Standard


need to know)



Levels Webb's DOK

8.EE.5 proportional relationships Graph Apply 2

8.EE.5 unit rate as the slope Interpret Understand 3

8.F.4

two different proportional relationships

represented in different ways Compare Analyze 3

8.F.4

qualitatively the functional

relationship between two quantities by

analyzing a graph Describe Understand 1


Essential Questions: 1. What role do rate of change and initial value in a function play in how a graph looks?

Enduring Understanding/Big Ideas:

1. Rate of change represents the slope of the graphed line. Initial value represents the y-intercept of the graphed line.

Unit Vocabulary:


slope y-intercept rate of change coordinate plane function proportional relationship



Cluster 8: Linear Functions


Resources

8-2

8.F.4 8.EE.5

● Pretest: Linear Equations (15 minutes)

● Skill #3 (Fractions--add, subtract, multiply, divide)-10 questions, grade, and chart progress (15-20 minutes)

● Lesson 8-2: Rate of Change (15-20 minutes)

● Practice 8-2 (5-10 minutes)

1 day Resources: Pretest (copies), Skill Sheet (copies), 8-2 Guided Notes (copies), 8-2 Practice (on computers-Digits), pencils, computers


8.F.4

8.EE.5


● Activity (30 minutes) ● Practice 8-2 (5-10 minutes)

1 day Resources: Skill Sheet (copies), pencils, computers

8-3

8.F.4


● Lesson 8-3: Initial Value (15-20 minutes)

● Practice 8-3 (5-10 minutes)




● Activity (30 minutes) ● Practice 8-3 (5-10 minutes)


Engaging Scenario

● Domino Effect (45 minutes) http://www.mathalicious.com/lessons/domino-effect/teach

● Post Test (15 minutes)

1 day Resources: Domino Effect handouts (copies), computers, Post Test (copies)


http://www.mathalicious.com/lessons/domino-effect/teach

http://www.mathalicious.com/lessons/domino-effect/teach

Engaging Scenario

Engaging Scenario Students will understand the ideas of slope and y-intercept within the context of Domino’s pizza pricing, write and graph a linear equation given two points on the line, and understand what it means for a function to be linear (constant rate of change).

Rubric for Engaging Scenario: See attached: “Domino Effect”


Unit 4: Angles

Subject: Math Grade: 8th grade Name of Unit: Angles and Angle Relationships Length of Unit: 5 days Overview of Unit: Students will write equations and solve problems using their understanding of angle relationships. Priority Standards for unit:

● 7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure..

Supporting Standards for unit: ● 7.EE.3.a Solve multi-step real-life and mathematical problems posed with positive and

negative rational numbers in any form, using tools strategically.

Standard


need to know)



Levels Webb's DOK

7.G.5

simple equations for an unknown angle

in a figure. Write Understand 2

7.G.5

simple equations for an unknown angle

in a figure. Solve Apply 2

7.EE.3.a

multi-step real-life and mathematical problems posed

with positive and negative rational numbers in any

form, using tools strategically Solve Apply 3


1. Why are angle relationships important? Enduring Understanding/Big Ideas:

1. Angle relationships can help us solve real-world problems.


Unit Vocabulary:


adjacent perpendicular vertical complementary supplementary



Supplemental Materials


Resources


7.G.5

● Pretest: Angle Relationships (15 min)

● Skill#4- (Measuring Angles)-10 questions, grade, and chart progress (15 minutes)

● Lesson 1: Complementary and Supplementary Angles (30-35 minutes)

1 day Resources: Pretest (copies), Skill Sheet (copies), Lesson Notes (copies), Practice (on computers-Digits), computers, pencils, protractors


7.G.5

● Skill#4- (Measuring Angles)-10 questions, grade, and chart progress (15 min)

● Lesson 2 Activity-Stations (45 min)

1 day Resources:


7.G.5


● Lesson 3: Solving for Unknown Angles using Equations (45-50 min)

1 day Resources: Skill Sheet (copies), Lesson Notes (copies), Practice (on computers-Digits), computers, pencils, protractors


7.G.5


● Lesson 4 Activity (45 min)

● http://www.hoodamath.com/mobile/games/minigolf.html

● http://www.puttingedge.com/online-game/

1 day Resources:


http://www.hoodamath.com/mobile/games/minigolf.html



http://www.puttingedge.com/online-game/

http://www.puttingedge.com/online-game/

Engaging Scenario

7.G.5

● Engaging Scenario: Mini Golf!

1 day Resources: money for mini-golf, transportation to Parkville (mini-golf), device to take pictures (BYOD?)

Engaging Scenario

7.G.1 7.G.5 7.G.6

● Engaging Scenario: Mini-Golf Course Creation (Mini Golf Final)

2 days Resources: Mini Golf Final handout (copies), chart graph paper, graph paper, rulers, pencils, markers, colored pencils


Engaging Scenario

Engaging Scenario Students will go miniature golfing as a class to gain perspective of angles and ideas for their final project. Students will create their own mini-golf hole using their knowledge of properties of angles, as well as perimeter and area from previous unit. Students will present their personally designed hole in class and we will vote on which one will be included in the mini-golf course.

Rubric for Engaging Scenario: See attachment: “Mini Golf Final”


Unit of Study Terminology

Big Ideas/Enduring Understandings: Foundational understandings teachers want students to be able to discover and state in their own words by the end of the unit of study. These are answers to the essential questions. Engaging Experience: Each topic is broken into a list of engaging experiences for students. These experiences are aligned to priority and supporting standards, thus stating what students should be able to do. An example of an engaging experience is provided in the description, but a teacher has the autonomy to substitute one of their own that aligns to the level of rigor stated in the standards. Engaging Scenario: This is a culminating activity in which students are given a role, situation, challenge, audience, and a product or performance is specified. Each unit contains an example of an engaging scenario, but a teacher has the ability to substitute with the same intent in mind. Essential Questions: Engaging, open-ended questions that teachers can use to engage students in the learning. Priority Standards: What every student should know and be able to do. These were chosen because of their necessity for success in the next course, the state assessment, and life. Supporting Standards: Additional standards that support the learning within the unit. Topic: These are the main teaching points for the unit. Units can have anywhere from one topic to many, depending on the depth of the unit. Unit of Study: Series of learning experiences/related assessments based on designated priority standards and related supporting standards. Unit Vocabulary: Words students will encounter within the unit that are essential to understanding. Academic Cross-Curricular words (also called Tier 2 words) are those that can be found in multiple content areas, not just this one. Content/Domain Specific vocabulary words are those found specifically within the content. Symbols: This symbol depicts an experience that can be used to assess a student’s 21st Century Skills using the rubric provided by the district. This symbol depicts an experience that integrates professional skills, the development of professional communication, and/or the use of professional mentorships in authentic classroom learning activities.


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