JAVA

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Mathematical Topics

COURSE: MATH CONCEPTS AND APPLICATIONS

TOPIC: Arithmetic Review

STAGE 1: IDENTIFY DESIRED RESULTS
Content Standard(s) Generalizations about what students should know and be able to do
Established Goals: CT Framework: a) Properties of numbers are used to develop strategies for computation and estimation. b) Percents can be used to make comparisons between groups of unequal size because each group is based on a ratio of parts per hundred. NCTM Standards: a) Understand numbers, ways of representing numbers and relationships among numbers. b) Understand the meanings of operations and how they relate to one another. c) Compute fluently and make reasonable estimates.
Enduring Understandings Insights earned from exploring generalizations via the essential questions (Students will understand THAT…)	Essential Questions Inquiry used to explore generalizations
The student will understand that: Whole numbers, fractions, and decimals can be read, written, and rounded. Whole numbers, fractions, and decimals can be added, subtracted, multiplied, and divided. There are divisibility rules. There are prime and composite numbers. Relationships between fractions exist Operations with whole numbers, fractions and decimals can be used to solve word problems. Percents are a ratio.	What are the ways whole numbers, fractions, and decimals can be read, written, and rounded? How are whole numbers, fractions, and decimals added, subtracted, multiplied, and divided? What are the divisibility rules? What is a prime number and what is a composite number? What relationships exist between fractions? What four operations can be used to solve everyday word problems? How are percents written as a ratio?
Knowledge and Skills What students are expected to know and be able to do
Students will know… How to read, write, and round whole numbers, fractions, and decimals. How to do the four basic operations with whole numbers, fractions, and decimals. What numbers are divisible by. Which numbers are prime and which numbers are composite. The relationship of ratio and proportion. How to do word problems with whole numbers, fractions, and decimals. How to solve all types of percent problems.	Students will be able to… Given examples of whole numbers, fractions, and decimals, students will read, write and round them. Given problems with whole numbers, fractions, and decimals, students will add, subtract, multiply, and divide. Using the divisibility rules for two, three, five, and ten, students will tell whether a number is divisible by 2,3,5,or 10. Identify a number as prime or composite. Set up and do problems using ratios and proportions. Set up and solve word problems by adding, subtracting, multiplying, and dividing whole numbers, fractions, and decimals. Set up and find the missing rate, percentage, or base for a percent problem.
STAGE 2: DETERMINE ACCEPTABLE EVIDENCE
Performance Task(s) Authentic application in new context to evaluate student achievement of desired results designed according to GRASPS (Goal, Role, Audience, Setting Performance, Standards)	Other Evidence Application that is functional in a classroom context only to evaluate student achievement of desired results
Jeremy and his 4 friends go to the Burger Shack for lunch. Jeremy decides he will treat with the $25 he has in his pocket. If plain burgers cost $1.95 and cheeseburgers cost $2.55, fries cost $.99 and onion rings cost $1.49, small drinks cost $1.50 and large drinks cost $1.99, what is the least amount he will spend on lunch if everyone has some sort of burger, side order and a drink? What is the most he might have to spend? Does he have enough to treat to lunch? What would you have ordered and how much would it cost?	In addition to quizzes and/or tests, one or more of the following will be used: Cooperative learning Scientific calculator activities Informal and formal checks: homework checks, problem of the day and review sheets.
STAGE 3: DEVELOP LEARNING PLAN
Learning Activities: 1. Cooperative learning activities 2. Scientific calculator activities 3. Homework and review worksheets.

COURSE: MATH CONCEPTS AND APPLICATIONS

TOPIC: Geometric Relationships

STAGE 1: IDENTIFY DESIRED RESULTS
Content Standard(s) Generalizations about what students should know and be able to do
Established Goals: CT Framework: a) Relationships exist among sides, angles, perimeters, and areas of two-dimensional figures. b) The Pythagorean Theorem can be used to find an unknown length. NCTM Standards: a) Use Cartesian coordinates to analyze geometric situations. b) Use geometric ideas to solve problems, and gain insights into, other disciplines and other areas of interest such as art and architecture.
Enduring Understandings Insights earned from exploring generalizations via the essential questions (Students will understand THAT…)	Essential Questions Inquiry used to explore generalizations
The student will understand that: Points and lines have many properties. Segments have distance. Angles have many properties. There are formulas for finding perimeter, area and volume. The Pythagorean Theorem can be used to solve geometric problems. Graphing in two-dimensions can be used to create pictures of objects and designs.	What are the properties associated with points and lines? How can we find out how long a segment is? What are the relationships that exist between different types of angles? What are the formulas for finding perimeter, area and volume? How is the Pythagorean Theorem used to solve geometric problems? How can a graph using Cartesian coordinates create a picture or design?
Knowledge and Skills What students are expected to know and be able to do
Students will know… 1. The properties of points and lines. 2. How to find the lengths of segments. 3. The properties and relationships of angles. 4. The formulas used to find perimeter, area and volume. 5. The Pythagorean Theorem can be used to find the missing side of a right triangle. 6. The properties of the x-y coordinate graphing system	Students will be able to… 1. Draw parallel and perpendicular lines. 2. Measure the length of a segment using a ruler. 3. Give the measure of angles that form a linear pair, vertical angles and perpendicular lines. 4. Find perimeter, area and volume using the correct formulas. 5. Determine the hypotenuse of a right triangle given the two legs using the Pythagorean Theorem. 6. Define and locate the four quadrants, define and locate ordered pairs on the plane and create a picture or design by graphing ordered pairs.
STAGE 2: DETERMINE ACCEPTABLE EVIDENCE
Performance Task(s) Authentic application in new context to evaluate student achievement of desired results designed according to GRASPS (Goal, Role, Audience, Setting Performance, Standards)	Other Evidence Application that is functional in a classroom context only to evaluate student achievement of desired results
A landscaper used a 120 foot rope to lay out a square flower bed. He then used it to lay out a rectangular flower bed with a side of 20 feet, so that the perimeters are the same. Are the areas the same? If they are different, which is has the larger area, the square or the rectangle? If you decide to redo the flower beds and put in grass and a box of grass seed covers 400 sq. ft., how many boxes would you need to buy to cover the square garden? The rectangular garden?	In addition to quizzes and/or tests, one or more of the following will be used: Cooperative learning activities Scientific calculator activities Informal and formal checks: homework checks, problem of the day and review sheets.
STAGE 3: DEVELOP LEARNING PLAN
Learning Activities: 1. Cooperative learning sessions 2. Scientific calculator activities 3. Homework and review worksheets.