AISL Grade 5 Benchmarks in Mathematics

(Revised June, 2010)

• AISL.MAT.01 Number Sense: Students will understand and apply numbers, ways of representing numbers, relationships among numbers, and number systems.
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• AISL.MAT.01.G5.01 Model, read, write, compare, order, and identify the place value of 1) decimals to the ten thousandths; 2) whole numbers up to one billion and; 3) fractions.
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• AISL.MAT.01.G5.02 Recognize and describe equivalent representation for the same number.
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• AISL.MAT.01.G5.03 Read, write, compare, and order all whole numbers, fractions, and mixed numbers, using multiple strategies (e.g. symbols, manipulatives, number line, place value concept).
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• AISL.MAT.01.G5.04 Read, order, and compare whole numbers to the millions and decimals to the ten thousandths.
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• AISL.MAT.01.G5.05 Express numerals in standard and expanded notation.
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• AISL.MAT.01.G5.06 Identify and apply number theory concepts, such as prime, multiple, composites.
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• AISL.MAT.01.G5.07 Develop an understanding of fraction as parts of a whole, as parts of a collection, as locations on number lines, and as divisions of whole numbers.
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• AISL.MAT.01.G5.08 Compare and order fractions, decimals, improper numbers, and mixed numbers.
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• AISL.MAT.01.G5.09 Use, model, and identify place value and describe its relationship to magnitude.
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• AISL.MAT.02 Computation : Students will estimate, compute, and assess reasonableness of solutions.
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• AISL.MAT.02.G5.01 Multiply and divide multi-digit numbers by two-digit numbers.
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• AISL.MAT.02.G5.02 Add, subtract, multiply, and divide with decimals.
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• AISL.MAT.02.G5.03 Add and subtract fractions and mixed numbers with like and unlike denominators, with and without regrouping.
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• AISL.MAT.02.G5.04 Multiply and divide a fraction by a whole number.
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• AISL.MAT.02.G5.05 Demonstrate proficiency with and memorize basic multiplication and division facts through the 12s.
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• AISL.MAT.02.G5.06 Select and use the most efficient computational methods (concrete materials, paper and pencil, estimation, mental computation, calculators).
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• AISL.MAT.02.G5.07 Use order of operations to solve equations.
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• AISL.MAT.02.G5.08 Identify all whole number factors and pairs of factors for a given whole number through 144.
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• AISL.MAT.02.G5.09 Solve multi-step word problems that may contain whole numbers, fractions, decimals, and all four operations.
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• AISL.MAT.02.G5.10 Use estimation to predict and judge the reasonableness of an answer.
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• AISL.MAT.03 Algebra: Students will use algebraic methods to represent, analyze, and solve problems
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• AISL.MAT.03.G5.01 Use a variable to represent an unknown quantity using a letter or symbol.
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• AISL.MAT.03.G5.02 Solve equations and open sentences with an unknown variable.
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• AISL.MAT.03.G5.03 Write and solve equations or word problems using variables.
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• AISL.MAT.03.G5.04 Describe, extend, and make generalizations about geometric and numeric patterns.
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• AISL.MAT.03.G5.05 Represent and analyze patterns and functions, using words, tables, and graphs.
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• AISL.MAT.03.G5.06 Use the commutative, associative, and distributive properties to compute with whole numbers.
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• AISL.MAT.03.G5.07 Express mathematical relationships using equations.
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• AISL.MAT.03.G5.08 Model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions.
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• AISL.MAT.03.G5.09 Investigate how a change in one variable relates to a change in a second variable.
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• AISL.MAT.04 Measurement: Students will estimate and measure accurately by using appropriate units, tools, and technologies.
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• AISL.MAT.04.G5.01 Select and use appropriate tools and units to measure length, area, weight, volume, time, and temperature.
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• AISL.MAT.04.G5.02 Understand the need for measuring with standard units and become familiar with standard units in the customary and metric systems.
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• AISL.MAT.04.G5.03 Understand that measurement can be approximate and uses estimation to obtain reasonable approximations.
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• AISL.MAT.04.G5.04 Determine an amount of elapsed time in hours, minutes, and seconds within a 24-hour period using both an AM/PM and 24-hour clock.
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• AISL.MAT.04.G5.05 Identify and use equivalent measurements as required by the situation (60 minutes = 1 hour, 7 days = 1 week)
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• AISL.MAT.04.G5.06 Carry out simple conversion within a system of measurement, such as from centimeters to meters.
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• AISL.MAT.05 Geometry: Students will apply the properties and relationships of geometric figures to represent, analyze and solve problems.
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• AISL.MAT.05.G5.01 Identify and describe triangles (right, isosceles, equilateral) and quadrilaterals (square, rectangle, parallelogram, rhombus, trapezoid).
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• AISL.MAT.05.G5.02 Identify, describe, and compare solid figures (e.g. sphere, cylinder, prism, cube, cone, pyramid).
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• AISL.MAT.05.G5.03 Sketch and identify lines segments, intersections, and parallel and perpendicular lines.
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• AISL.MAT.05.G5.04 Use a compass, protractor, and ruler to construct and measure shapes, designs, and angles.
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• AISL.MAT.05.G5.05 Identify coordinates of any point on a coordinate grid.
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• AISL.MAT.05.G5.06 Plot ordered pairs of coordinates on a coordinate grid.
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• AISL.MAT.05.G5.07 Identify simple geometric transformations: translations (slides), reflections (flips), and rotations (turns).
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• AISL.MAT.05.G5.08 Identify the diameter, radius, chord, and circumference of a circle.
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• AISL.MAT.06 Data Analysis and Probability: Students will collect, organize, analyze, represent and interpret date in order to make decisions and predictions.
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• AISL.MAT.06.G5.01 Design investigations to address a question and consider how data collection methods affect the data set.
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• AISL.MAT.06.G5.02 Collect data using observations, surveys, and experiments.
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• AISL.MAT.06.G5.03 Represent data using tables and graphs, such as line plots, bar graphs, line graphs, histograms, and stem and leaf plots.
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• AISL.MAT.06.G5.04 Find the median, mean, mode, and range for a given set of data.
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• AISL.MAT.06.G5.05 Express the probability of an even in words (certain, equally likely, impossible), and as fractions, decimals, and percents.
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• AISL.MAT.06.G5.06 Predict the probability of outcomes of simple experiments (e.g. tossing a coin, rolling dice) and test the predictions.
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• AISL.MAT.07 Problem Solving: Students will apply a wide variety of mathematical concepts, processes, and skills to solve a broad range of problems.
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• AISL.MAT.07.G5.01 Apply a variety of problem solving strategies to solve problems and justify the choice of strategy (e.g. guess and check, work backwards, look for a pattern, use a picture or diagram, use a table or organized list, use logical reasoning).
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• AISL.MAT.07.G5.02 Differentiate between relevant and irrelevant information.
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• AISL.MAT.07.G5.03 Evaluate the reasonableness of the solution in the context of the original problem.