Content Topics

 

Unit 1

Whole Number Concepts - Place Value, Standard and Exponential Form, Rounding, Comparing and Ordering Decimals, and Integers

 

Unit 2

Whole Number Math Operations (add, subtract, multiply, divide), Integer Math Operations  (add, subtract, multiply, divide), and Decimal Math Operations  (add, subtract, multiply, divide)

 

Unit 3

Measurement Concepts - Length, Volume, Width, Time, and Money

 

Unit 4

Data, Statistics and Probability and Ratio and Percent

 

Unit 5

Geometry, Pre-Algebra Concepts

 

 

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Key Skills

 

• Be able to complete all four math operations with and without a calculator
• Complete times tables through 12
• Be able to use a calculator
• Analyze data to answer questions or make predictions
• Create graphs, tables and/or charts to demonstrate understanding of data
• Use a ruler, protractor, compass and other measuring tools

 

 

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Assessments

 

• Student created projects
• Tests
• Quizzes
• Homework & Notebook
• Attendance
• Participation

 

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Standards Alignment:

 

PA State Standards:

2.1.5.A. Apply number patterns to count and compare values of whole numbers, fractions and decimals.

2.1.5.B. Use number theory concepts and models to represent or rename whole numbers, fractions and decimals.

2.1.5.C. Use models to represent the concept of an integer, fraction, decimal or percent.

2.1.5.D. Apply place-value concepts to order and compare decimals and to express whole numbers and decimals in expanded notation.

2.1.5.E. Develop and apply number theory concepts (e.g., primes, factors, multiples, composites) to represent numbers in various ways.

2.1.5.F. Understand the concepts of multiplication and division and use the inverse relationships between multiplication and division, to determine unknown quantities in equations.

2.2.5.B. Multiply and divide single- and double-digit numbers; add and subtract fractions and mixed numbers; add, subtract, multiply and divide decimals.

2.2.5.D. Estimate results from calculations with basic operations of whole numbers and decimals and check the reasonableness of those estimates.

2.3.5.A. Use concrete objects to demonstrate the meaning of measurement quantities (e.g., perimeter, area, weight, capacity).

2.3.5.B. Select and use appropriate instruments and units for measuring quantities to a specified level of accuracy.

2.3.5.C. Calculate perimeter and area, and sums and differences of measurements.

2.3.5.D. Perform basic conversions within a system.

2.3.5.F. Estimate and verify measurements of length, perimeter, area, volume, capacity, temperature, time, weight, and angles.

2.4.5.A. Use models, number facts, properties and relationships to draw conclusions and explain reasons for conclusions.

2.4.5.B. Use if…then statements to express conditional relationships.

2.5.5.A. Develop a plan to analyze a problem, identify the information needed to solve the problem, carry out the plan, check whether an answer makes sense and explain how the problem was solved in grade appropriate contexts.

2.5.5.B. Use appropriate mathematical terms, vocabulary, language, symbols and graphs to explain clearly and logically solutions to problems.

2.6.5.A. Gather data from surveys and observations from sources outside the classroom or home.

2.6.5.B. Use pictures, tallies, tables, charts, bar graphs, line graphs, diagrams, and graphs to organize, display, and analyze data.

2.6.5.C. Calculate mean and range, identify the median and the mode of a set of data, and use these quantities to describe the data.

2.6.5.D. Compare data using multiple categories displayed in a graph.

2.6.5.E. Determine the reasonableness of a statement based on a comparison to data displayed in a graph and summarized by numerical measures.

2.7.5.A. Predict and calculate the likelihood of simple events.

2.7.5.B. Predict and determine why some outcomes of a particular event are certain, more likely, less likely, equally likely or impossible.

2.7.5.C. Express probabilities as fractions and/or decimals.

2.7.5.D. List all possible combinations and arrangements of outcomes of an experiment (i.e. tree diagrams, matrices, etc.)

2.7.5.E. Compare predictions based on theoretical probability and experimental results.

2.8.5.A. Use the concept of equality to demonstrate understanding of the distributive property.

2.8.5.B. Select and use strategies, including concrete objects, to solve number sentences (equations and inequalities) and explain the method of solution.

2.8.5.C. Recognize, describe, extend, create, replicate, and form a rule for a variety of patterns, sequences, and relationships verbally, numerically, symbolically, and graphically.

2.8.5.D. Determine a functional rule from a table or graph.

2.8.5.E. Use concrete objects and combinations of symbols and numbers to create expressions, equations, and inequalities that model mathematical situations.

2.8.5.F. Describe data represented in equations, inequalities, tables, or graphs and/or create a story that matches that data.

2.9.5.A. Identify, describe, and define 1-, 2-, and 3-dimensional shapes and their related parts, and classify and compare 2- and 3- dimensional shapes on the basis of their properties.

2.9.5.B. Predict and describe the result of a translation (slide), rotation (turn), or reflection (flip) of a 2- dimensional shape.

2.9.5.C. Identify location of points with fractional or decimal coordinates on a number line or on a 2- dimensional coordinate system.

2.10.5.A. Identify and compare parts of right triangles, including right angles, acute angles, hypotenuses, and legs.

2.11.5.A. Make comparisons of numbers (e.g., more, less, same, least, most, greater than, less than).

2.11.5.B. Describe the relationship between rates of change and another variable (e.g., time, temperature).

2.11.5.C. Estimate areas and volumes of shapes and solids as the sums of areas of tiles and volumes of cubes.

 

National Standards:

• Understand numbers, ways of representing numbers, relationships among numbers, and number systems
• Understand meanings of operations and how they relate to one another
• Compute fluently and make reasonable estimates
• Understand patterns, relations, and functions
• Represent and analyze mathematical situations and structures using algebraic symbols
• Use mathematical models to represent and understand quantitative relationships
• Analyze change in various contexts
• Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships
• Specify locations and describe spatial relationships using coordinate geometry and other representational systems
• Apply transformations and use symmetry to analyze mathematical situations
• Use visualization, spatial reasoning, and geometric modeling to solve problem
• Understand measurable attributes of objects and the units, systems, and processes of measurement
• Apply appropriate techniques, tools, and formulas to determine measurements
• Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them
• Select and use appropriate statistical methods to analyze data
• Develop and evaluate inferences and predictions that are based on data
• Understand and apply basic concepts of probability