LAUSD Division of Instruction:
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Graduate Level
Upon graduation from LAUSD, students will be able to:1. Use operations (addition, subtraction, multiplication, and division), estimation, mental arithmetic, and number sense to solve problems using whole numbers, integers, fractions, decimals, rational numbers, and scientific notation. S
2. Use both the U.S. customary and the metric systems of measurement to determine geometric and nongeometric measures of length, weight, mass, monetary value, time, and temperature. S
3. Solve problems based on algebraic relationships and functions; explore the relationship between the symbolic mathematical form of a function (expressed in equalities or inequalities) and a two- or three- dimensional graph of that function. S
4. Analyze and represent solutions using geometric relationships (for example, congruency and similarity), geometric measurement (perimeter, area, angle measures, volume and capacity, and proportions), and spatial dimensions. S
5. Represent problem situations using discrete structures (combinations and permutations) such as patterns, series, sequences, recurrence relationships, and finite graphs to determine possible combinations and arrangements. LA, S, H
6. Apply theoretical or experimental probability to represent data effectively to make valid, appropriate, and useful decisions. S, H
7. Summarize data from real-world situations by collecting, organizing, and analyzing data; draw statistical inferences from charts, tables, and graphs. S, H
8. Investigate the relationship between mathematical models and real-life problems by using hands-on materials and/or current technology such as calculators and computer modeling. LA, S, H
9. Make and test conjectures (inductive and deductive), construct simple arguments, validate solutions, and apply conclusions to various real-world situations. LA, S, H
10. Make connections among related mathematical concepts and apply these concepts to other content areas and the world of work. S, H
11. Analyze how inventions, discoveries, and events influence the development of mathematical theories and how mathematics continues to respond to changing societal, cultural, and technological forces. LA, S, H
12. Use mathematical language and concepts to validate and communicate the solutions of given problems in oral, written, and graphic forms. LA
Grade Nine
Upon completing grade nine in LAUSD, students will be able to:13. Add, subtract, multiply, and divide using whole numbers, integers, primes, factors, multiples, fractions, decimals, rational numbers, and scientific notation; use estimation to solve problems and check for reasonableness of results in real-life situations to increase number sense. S
14. Use both the U.S. customary and the metric systems of measurement, including basic geometric and nongeometric measures, to measure length, weight, mass, monetary value, time, and temperature. S
15. Identify patterns, functions, and other algebraic relationships including inequalities; use tables, graphs, and equations to model functional relationships in real-life situations; apply knowledge of functions to analyze and interpret problems, predict solutions, and create algebraic algorithms to solve problems. S
16. Use inductive and deductive reasoning and concepts of coordinate and transformational geometry to analyze geometric relationships, validate formal and informal proofs, and solve problems in geometric relationships such as congruency and similarity. S
17. Use a variety of discrete structures such as series, sequences, recurrences, matrices, tree diagrams, and networks to find possible combinations and arrangements, make conjectures, validate solutions, analyze the logic of arguments, and apply the conclusions to mathematical situations. S, H
18. Develop and apply probability simulations to evaluate information, to predict possible outcomes, and to make valid, appropriate, and useful decisions. LA, S, H
19. Use various statistical methods to describe, analyze, and evaluate data to make valid, appropriate, and useful decisions. H
20. Employ appropriate technology (for example, calculators, graphing calculators, and computers) and hands-on materials in mathematical investigations and in real-life situations. LA, S, H
21. Apply inductive and deductive reasoning and problem-solving strategies such as analysis of patterns, properties, relations of number systems, to validate solutions and apply conclusions to various real-world situations. LA, S, H
22. Make connections among mathematical concepts and apply these concepts to other content areas and to real-life situations. S, H
23. Analyze the influences that historical events, scientific discoveries, and social changes have had and continue to have on the development of mathematical theories. LA, S, H
24. Communicate by using mathematical reasoning orally, in writing, and graphically and by using mathematical language and concepts (terms and symbols) to support ideas and conclusions. LA
Grade Seven
Upon completing grade seven in LAUSD, students will be able to:25. Add, subtract, multiply, and divide using whole numbers, integers, primes, factors, multiples, fractions, decimals, rational numbers, exponents, and scientific notation; estimate and check the reasonableness of results. S
26. Analyze the structure and use of both the U.S. customary and metric measurement systems; select and apply relevant measurement systems to solve real-world problems. S
27. Identify and apply mathematical relationships and functions, algebraic algorithms (step-by-step problem-solving processes), variables, constants, mathematical expressions, coordinates, and scale for solving problems. S
28. Identify, describe, compare, and classify geometric figures; apply geometric properties and relationships to solve problems; and use geometric concepts as a means to describe the physical world. S
29. Apply a variety of discrete structures (series, sequences, matrices, and tree diagrams) to find possible combinations and arrangements in a problem situation. LA, S, H
30. Apply concepts of probability such as chance, fairness, odds, and expected values to determine probable outcomes and make informed decisions. S, H
31. Develop, use, and interpret tables and graphs that describe everyday situations; collect, organize, and display data graphically; draw conclusions supported by given data. LA, S, H
32. Select and apply appropriate problem-solving methods from among mental arithmetic, pencil-and-paper computation, and calculators; model mathematical situations using hands-on materials and appropriate software such as spreadsheets, sketchpads, or graphing calculators. H
33. Use deductive and inductive reasoning to solve mathematical problems; apply proportional reasoning to examine the relationships among fractions, decimals, and percents through examples involving rates, ratios, proportions, and scales. LA, S, H
34. Make and apply connections among mathematical concepts to other content areas and to daily life (such as using measurement in construction). S, H
35. Compare and describe the number systems and mathematical concepts, for example, the Pythagorean Theorem, developed in different civilizations, historical periods, and cultures. LA, S, H
36. Use mathematical symbols, terms, and concepts to communicate mathematical reasoning orally, in writing, and graphically. LA
Grade Three
Upon completing grade three in LAUSD, students will be able to:37. Apply the basic operations (addition, subtraction, multiplication, and division) using whole numbers and simple fractions (halves, fourths); use rounding to the tens, hundreds, and thousands as an estimation strategy to check the reasonableness of results. S
38. Use appropriate non-standard and standard measurement systems and measurement tools (rulers, scales, thermometers, clocks, money, etc.) to estimate or directly measure length, capacity, weight, mass, area, volume, time, temperature, and monetary value. S
39. Express the appropriate operation symbols ( +, -, x, ÷, =, >, < ) and find missing numbers to make a true mathematical sentence; show how the basic arithmetic operations are related. S
40. Use the geometric concepts of space and form to construct, describe, and compare the properties of one-, two-, and three-dimensional figures such as line segments, circles, simple polygons, and solids. S
41. Create and use discrete structures such as sets, graphs, tables, and diagrams to find possible combinations and arrangements of countable items (for example, how many combinations of outfits are possible given three different shirts and three pairs of pants?) LA, S, H
42. Predict outcomes and perform simple experiments (such as with dice and spinners) to check if predicted outcomes are reasonable; identify possible strategies to increase or decrease the likelihood of a predicted outcome (such as a raffle drawing). S, H
43. Collect, organize, and interpret statistical data in charts, tables, and bar graphs; formulate and solve problems using data to make appropriate and useful decisions. LA, S, H
44. Select and use appropriate technology, such as calculators and computers with software models to solve problems; develop and apply strategies to solve problems and explain solutions using hands-on materials, trial and error, analysis of patterns and sequences, and arithmetic reasoning. H
45. Interpret and use logical statements that contain expressions such as "and," "or," "if... then," "all," "some," "none," "not," and "out of," to make reasonable inferences. LA, S, H
46. Make connections among mathematical concepts and relate them to concepts in other content areas and in daily life. S, H
47. Compare the use of various number systems (for example, Hindu-Arabic, Roman, tally, etc.) from different historical periods. LA, S, H
48. Use oral and written language, drawings, and mathematical symbols and terms to communicate understanding of mathematics. LA