Using the Needs Assessment results and the student achievement results, the following offerings for middle school mathematics teachers are prioritized as follows:

Professional Development Course Requirements for all Mathematics and Science Courses

• the science and/or mathematics content must be one of the identified areas of critical need;
• inquiry-based pedagogy must form the basis of the instruction;
• content must be aligned with both the TEKS and Project CLEAR; and
• a minimum of 30 contact hours.

Content: 6^th, 7^th, and 8^th Grades

• Proportion and Proportional Reasoning
• Fractions
• Measurement
• Integers

• Fractions

Fractions and Proportion—the links

Place value fractions and decimals operation

• Integers and their operations
• Measurement
• Probability
• Similarity (with different orientation of figures) and its connection to proportion and ratio
• Perimeter and area
• Linear inequalities in one dimension—on the number line
• Ratio
• Equations—writing equations, translating numeric and verbal information into equations

1. Fractions: how to develop the concept and connections to ratio, proportion, similarity, and probability
2. Integers: operations and their use in solving linear inequalities and equations
3. Measurement: area & perimeter

After examining student achievement data, there is a need for further work in the area problem solving that addresses solution strategies, mathematical representation and reasonableness in grades 6 –8. Proportional reasoning is one of the focuses of the middle school curriculum. This concept is integrated into the teaching of rational numbers, geometry, measurement and probability units. The understanding of the concepts and their vertical connections need to be emphasized. Students are expected to use operations at the application level, not at the computation level. Therefore, teachers must be given staff development opportunities that address problem solving strategies especially in estimation, solution strategies, mathematical representation, reasonableness, measurement, probability and statistics. Also, training for teachers is needed in the use of manipulatives as a tool that helps in the development of student understanding of mathematical concepts.

Mathematical Process Skills:

The student use higher order thinking skills and critical skills to make informed and relevant decisions. The student is expected to:

1. Use concepts, algorithms and properties of rational numbers to explore mathematical relationships and to describe increasingly complex situations.
2. Use algebraic thinking to describe how a change in one quantity in a relationship results in a change in the other; and connect verbal, numeric, graphic, and symbolic representations of relationships.
3. Use geometric properties and relationships, as well as spatial reasoning, to model and analyze situations by quantifying attributes, generalize procedures from measurement experiences, and use the procedures to solve problems.
4. Use appropriate statistics, representations of data, reasoning, and concepts of probability to draw conclusions, evaluate arguments, and make recommendations.

Problem solving language and communication, connections within and outside mathematics and formal and informal reasoning underlie all content areas in mathematics. The student is expected to:

1. Use these processes together with technology (at least four function calculators for whole numbers, decimals, and fractions) and other mathematical tools such as manipulative materials to develop conceptual understanding and solve problems as they do mathematics.

Mathematics concept: The student knows how to develop the concept and connections of fractions to ratio, proportion, similarity, and probability. The student is expected to:

1. Compare and order non-negative rational numbers(TEKS 6.1a; )
2. Generate equivalent forms of rational numbers including whole numbers, fractions, and decimals(TEKS 6.1b)
3. model addition and subtraction situations involving fractions with objects, pictures, words, and numbers(TEKS 6.2a)
4. use addition and subtraction to solve problems involving fractions and decimals(TEKS 6.2b)
5. Use ratios to describe proportional situations(TEKS 6.3a)
6. Represent ratios and percents with concrete models, fractions, and decimals

(TEKS 6.3b)

7. Use ratios to make predictions in proportional situations (TEKS 6.3c)

Mathematics concept: The student understand the operations (involving integers) and their use in solving linear inequalities and equations. The student is expected to:

1. Use integers to represent real-life situations (TEKS 6.1c)
2. Use multiplication and division of whole numbers to solve problems including situations involving ratios and rate (TEKS 6.2c)
3. Formulate an equation from a problem situation(TEKS 6.5)

Mathematics concept: The student will know the difference between area and perimeter and generate formulas from data. The student is expected to:

1. Use tables and symbols to represent and describe proportional and other relationships

Involving conversions, sequences, perimeter, area, etc. (TEKS 6.4a)

2. Generate formulas to represent relationships involving perimeter, area…from a table of data.(TEKS 6.4b)

To the maximum extent possible and where appropriate, course offering should include experiences that prepare teachers to help students acquire knowledge, skills and experiences that will help students to:

1. Identify and apply mathematics to everyday experiences, to activities in and outside

of school, with other disciplines, and with other mathematical topics.

2. Use a problem-solving model that incorporates understanding the problem, making a

plan, and evaluating the solution for reasonableness

3. Select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem
4. Select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems.
5. Communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models
6. Make conjectures from patterns or sets of examples and non-examples
7. Validate his/her conclusions using mathematical properties and relationships

Mathematics concept: The student knows how to develop the concept and connections of fractions to ratio, proportion, similarity, and probability. The student is expected to:

1. Compare and order integers and positive rational numbers(TEKS 7.1a; )
2. Convert between fractions, decimals, whole numbers, and percents mentally, on paper, or with a calculator(TEKS 7.1b)
3. Represent multiplication and division situations involving fractions and decimals with concrete models, picture, words, and number(TEKS 7.2a)
4. Use addition, subtraction, multiplication, and division to solve problems involving fractions and decimals(TEKS 7.2b)
5. Use division to find unit rates and ratios in proportional relationships such as speed, density, price, recipes, and student-teacher ratio (TEKS 7.2d)
6. Estimate and find solutions to application problems involving proportional relationships such as similarity, scaling, unit costs, and related measurement units.(TEKS 7.3b)

Mathematics concept: The student understand the operations (involving integers) and their use in solving linear inequalities and equations. The student is expected to:

1. Compare and order integers and positive rational numbers (TEKS 7.1c)
2. Use models to add, subtract, multiply, and divide integers and connect the actions to algorithms (TEKS 7.2c)
3. Simplify numerical expressions involving order of operations and exponents (TEKS 7,2e)
4. Select and use appropriate operations to solve problems and justify the selections (TEKS 7.2f)
5. Determine the reasonableness of a solution to a problem (TEKS 7.2g)

Mathematics concept: The student will know the difference between area and perimeter and generate formulas from data. The student is expected to:

1. Estimate measurements and solve application problems involving length (including perimeter and circumference), area, and volume(TEKS 7.9)

To the maximum extent possible and where appropriate, course offering should include experiences that prepare teachers to help students acquire knowledge, skills and experiences that will help students to:

1. Identify and apply mathematics to everyday experiences, to activities in and outside

of school, with other disciplines, and with other mathematical topics.

2. Use a problem-solving model that incorporates understanding the problem, making a

plan, and evaluating the solution for reasonableness

3. Select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem
4. Select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems.
5. Communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models
6. Make conjectures from patterns or sets of examples and non-examples
7. Validate his/her conclusions using mathematical properties and relationships

Mathematics concept: The student knows how to develop the concept and connections of fractions to ratio, proportion, similarity, and probability. The student is expected to:

1. Compare and order rational numbers in various forms including integers, percents, and positive and negative fractions and decimals (TEKS 8.1a; )
2. Select and use appropriate forms of rational numbers to solve real-life problems including those involving (TEKS 8.1b)
3. add, subtract, multiply, and divide rational numbers in problem situations (TEKS 8.2b)
4. Estimate and find solutions to application problems involving proportional relationships such as similarity, scaling, unit costs, and related measurement units.(TEKS 8.3b)

Mathematics concept: The student understand the operations (involving integers) and their use in solving linear inequalities and equations. The student is expected to:

1. Compare and order irrational numbers in various forms including integers, percents, and positive and negative fractions and decimals(TEKS 8.1c)
2. Approximate (mentally and with calculators) the value of irrational numbers as they arise from problem situation (TEKS 8.1c)
3. Express numbers in scientific notation, including negative exponents, in appropriate problem situations using a calculator. (TEKS 8.1d)
4. Select and use appropriate operations to solve problems and justify the selections (TEKS 8.2)
5. Evaluate a solution for reasonableness (TEKS 8.2c)
6. Use multiplication by a constant factor (unit rate) to represent proportional relationships; for example, the arm span of a gibbon is about 1.4 times its height, a=1.4h (TEKS 8.2d)
7. Generate a different representation given one representation of data such as a table, graph, equation, or verbal description. (TEKS 8.4)
8. Estimate, find, and justify solutions to application problems using appropriate tables, graphs, and algebraic equations (TEKS 8.5a)
9. Use an algebraic expression to find any term in a sequence (TEKS 8.5b)
10. Locate and name points on a coordinate plane using ordered pairs of rational numbers (TEKS 8.7d)

Mathematics concept: The student will know the difference between area and perimeter and generate formulas from data. The student is expected to:

1. Find surface area of prisms and cylinders using concrete models and nets (two-dimensional models) (TEKS 8.8a)
2. Estimate answers and use formulas to solve application problems involving surface area and volume (TEKS 8.8c)
3. Describe the resulting effects on perimeter and area when dimensions of a shape are changed proportionally (TEKS 8.10a)

To the maximum extent possible and where appropriate, course offering should include experiences that prepare teachers to help students acquire knowledge, skills and experiences that will help students to:

1. Identify and apply mathematics to everyday experiences, to activities in and outside

of school, with other disciplines, and with other mathematical topics.

2. Use a problem-solving model that incorporates understanding the problem, making a

plan, and evaluating the solution for reasonableness

3. Select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem
4. Select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems.
5. Communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models
6. Make conjectures from patterns or sets of examples and non-examples

Validate his/her conclusions using mathematical properties and relationships

The offering should include TEKS strands, content correlated with Project CLEAR and the NCTM Standards (STANDARDS 2000), project-based learning, hands-on experiences, ways to address diverse learners, integration of technology in a one computer classroom, using graphing calculators, and other mathematical manipulative materials. The offerings should include transfer of knowledge from concept to application, integration of math concepts across the curriculum, math/science integration mathematics content and mathematics processes connections, and mathematics/science vocabulary links. Teachers should produce units with specific lessons based upon the Project CLEAR instructional planning tool for teachers.

Content materials that the district can provide include:

• Project CLEAR Curriculum
• Sample TAAS released tests so that the lessons can incorporate the vocabulary, skills, concepts, style of questioning, level of thinking, transfer of knowledge
• Item analysis of objectives
• Lesson plan format for the entire unit
• Dana Center (http://www.utdanacenter.org/) materials focused on mathematics