Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
List of important publications in mathematics wikipedia , lookup
Mechanical calculator wikipedia , lookup
Positional notation wikipedia , lookup
Mathematics of radio engineering wikipedia , lookup
Location arithmetic wikipedia , lookup
Proofs of Fermat's little theorem wikipedia , lookup
Large numbers wikipedia , lookup
Hempfield School District Curriculum: Unit Template Course Title: Pre-Algebra Grade 8 Unit Title: Numbers and Operations Names of Teachers who Developed Unit: Ringler Dates Developed: May – July 2010 Approximate Dates when Taught During School Year: August –September Approximate Number of Periods: 13 Class Periods Summary: In this unit students will begin to build the foundational number sense necessary for the remainder of the course. They will investigate number patterns and properties as well as discuss rounding answers appropriately. Students will learn how to do integer, fraction, and decimal operations with and without calculators and apply these skills to simplify expressions using order of operations. These expressions can be numeric or algebraic if given values to substitute for the variables. Print Materials Needed: Resources: McDougal Littell’s Pre-Algebra Textbook (sections 1.1 – 1.7, 2.1, 2.7, 5.2 – 5.5) McDougal Littell’s Middle School Math Course 3 Textbook (sections 1.2 – 1.4, 2.1 – 2.6, 4.3, 5.1 – 5.7) Internet Resource Links: classzone.com Essential Questions (Include PA Standards, Anchors & Eligible Content) Big Ideas: The set of real numbers has infinite subsets including the sets of whole numbers, integers, rational, and irrational numbers. There are some mathematical relationships that are always true and these relationships are used as the rules of arithmetic and algebra and are useful for writing equivalent forms of expressions and solving equations and inequalities. Essential Questions: How can numbers and operations be used to represent and solve problems? When are integers appropriate to represent problems? Assessment Anchors: M8.A.1 Demonstrate an understanding of numbers, ways of representing numbers, relationships among numbers and number systems M8.A.2 Understand the meaning of operations, use operations and understand how they relate to each other M8.A.3 Compute accurately and fluently and make reasonable estimates M8.D.1 Demonstrate an understanding of patterns, relations and functions 1 Hempfield School District Curriculum: Unit Template Eligible Content: M8.A.1.1.2 Find the square or cube of a whole number (single digit) M8.A.2.1.1 Simplify numeric expressions involving integers, using the order of operations. (May include grouping symbols. No combining negatives with exponents or compound exponents) M8.A.3.1.1 Identify, use and/or explain when it is appropriate to round up or round down. M8.A.3.1.2 Identify, apply and/or explain when an exact answer is needed or when estimation is appropriate M8.A.3.3.1 Add, subtract, multiply and/or divide integers, fractions, and/or decimals with and without a calculator (straight computation or word problems) M8.D.1.1.1 Continue a numeric or algebraic pattern (pattern must show 3 repetitions – may include up to 2 operations, squares and square roots) Know Vocabulary: exponent, power, base, order of operations, numerical expression, variable, variable expression, evaluate, substitute, integer, negative integer, positive integer, absolute value, opposite, sum, difference, product, quotient, numerator, denominator, common denominator, least common denominator, equivalent fractions, reciprocal, commutative property, associative property, identity property Facts: order of operations, addition rules, subtraction rule, multiplication and division rules Understand Do Students will understand: The students will be able to: Numbers and Complete a number pattern operations can be Read and write exponents in used to represent equivalent forms (exponent and solve real form and multiplication of world problems factors) There are some Simplify numeric expressions mathematical using order of operations relationships that Simplify algebraic expressions are always true and by substituting values for all these relationships variables and then using order are used as the rules of operations of arithmetic and Write expressions by algebra translating sentences What type of Write expressions from word answer is problems appropriate for a Use rounding rules to given problem and approximate answers if their answer Locate points on a number makes sense line Compare and order numbers Find opposites and absolute values of numbers Add, subtract, multiply, and divide integers without a calculator Add, subtract, multiply, and divide fractions and decimals with and without a calculator Identify what property is 2 Hempfield School District Curriculum: Unit Template being shown (commutative, associative, identity) Determine if the answer they obtain is a valid solution to the problem at hand Determine what type of answer is appropriate or inappropriate for a given problem (rounding up or down, estimation or exact) Stage 2: Assessment Evidence Assessments/Performance Tasks Rubric Titles Benchmark(s) for Course: Unit’s key Assessments Self-Assessments Other Evidence, Summarized Stage 3: Learning Activities Differentiation: Readiness Profile: Learning Styles / Multiple Intelligences Interest 3 Hempfield School District Curriculum: Unit Template . Accommodations for ELLs: 4