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# Mathematics Entry Points of Grade 7

 Grade 7 Learning Standards as written Essential and Prioritized Skill Number Sense and Operations 7NSO-N1 Compare, order, estimate, and translate among integers, fractions, mixed numbers (i.e., rational numbers), decimals, and percents. ♦ Compare, order, estimate and translate integers, fractions, mixed numbers, decimals, and percents. Less Complex Possible Entry Points More Complex The student will: ♦ Define integers, fractions, mixed numbers, decimals and percents. ♦ Classify integers, fractions, mixed numbers, decimals and percents. The student will: Using a number line: ♦ Order fractions and/or mixed numbers. ♦ Order integers ♦ Order decimals and/or percents The student will: ♦ Compare and/or order integers, fractions (mixed numbers) and decimals ♦ Compare and order percents and decimals ♦ Estimate using fractions, decimals, and/or percents ♦ Translate (convert) between decimals and percents; decimals and fractions; and/or fractions and percents Grade 7 Learning Standards as written Essential and Prioritized Skill Number Sense and Operations 7NSO-N7 Apply number theory concepts, including prime factorization and relatively prime numbers, to the solution of problems (e.g., find the prime factorization of whole numbers, and write the results using exponents: 24 = 2 x 2 x 2 x 3 = 23 x 3). ♦ Use prime or composite numbers, factorization, greatest and least common multiples, or divisibility rules to solve problems. Less Complex Possible Entry Points More Complex The student will: ♦ Use models and/or manipulatives to identify factors of one and/or two-digit numbers ♦ Identify prime numbers ♦ Sort objects into even groups The student will: ♦ Use a model to identify factors of two-digit numbers ♦ Convert from one number form to another (expanded form to exponent form to standard form.) ♦ List prime numbers up to 29 The student will: ♦ Complete a factorization tree for two or three-digit numbers ♦ Use a model to illustrate prime factorization ♦ Determine which numbers are divisible by another number (e.g., sort a group of 6 and a group of 8 by 3 to determine which is divisible by 3) General Education Examples Grade 7 Learning Standards as written Essential and Prioritized Skills Patterns, Relations, and Algebra 7PRA1 Extend, represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic expressions. Include arithmetic and geometric progressions (e.g., compounding) ♦ Identify and extend a variety of grade-level patterns Less Complex Possible Entry Points More Complex The student will: ♦ Identify sets as patterns or non-patterns ♦ Recognize the sequence of a pattern The student will: ♦ Match a pattern to its mathematical expression ♦ Explain a geometrical pattern and an arithmetic pattern The student will: ♦ Extend a compounding pattern (e.g., 3, 5, 7, __) ♦ Translate and extend an arithmetic pattern into a visual representation ♦ Translate and extend geometric pattern General Education Example Grade 7 Learning Standards as written Essential and Prioritized Skills Patterns, Relations, and Algebra 7PRA3 Use the correct order of operations to evaluate expressions (e.g., 3(2x) = 5). ♦ Use order of operations to solve an equation Less Complex Possible Entry Points More Complex The student will: ♦ List the sequence of the order of operations ♦ Identify the operations (e.g. 3(2) = 3 · 2 this means multiplication) The student will: ♦ Solve a simple equation involving two or three operations ♦ Identify the correct order of operations for a given expression The student will: ♦ Use order of operations to solve an equation ♦ Use task analysis to follow order of operations and solve an equation General Education Example Grade 7 Learning Standards as written Essential and Prioritized Skills Patterns, Relations, and Algebra 7PRA4 Create and use symbolic expressions for linear relationships, and relate them to verbal and graphical representations. ♦ Use symbolic expressions for linear relationships and relate them to graphic or verbal expressions. Less Complex Possible Entry Points More Complex The student will: ♦ Identify numbers in an ordered pair (x, y) ♦ Graph a point The student will: ♦ Given verbal data represent the data in a table, as a graph, or as an equation. ♦ Interpret (explain) the graph The student will: ♦ Graph a set of ordered pairs ♦ Use manipulative to show data on a graph ♦ Use information in a T-table to create a graph