ACOS+Math


 * ** Mathematics, Grade 2, 2009 **

1.) Demonstrate the concept of number sense by comparing, ordering, and expanding whole numbers up to 1000; determining the place value of a digit in a number through 999; and determining a number when given the value of ones, tens, and hundreds.

Example: expanding--recognizing 251 as being represented by two hundred fifty-one, by 2 hundreds + 5 tens + 1 one, and by 200 + 50 + 1

• Identifying a number that is 100 more or 100 less than a given number

• Counting forward in multiples from a given number

Examples:3, 6, 9, 12; 4, 8, 12, 16

• Identifying zero as a placeholder in two- and three-digit numbers

• Comparing numbers using the symbols >, <, and =

• Using estimation to compare sets of objects when the quantity of one set is known

Example: estimating the quantity of set B when compared to set A that contains 20 items ||
 * 2.) Solve two-digit addition and subtraction problems, with and without regrouping, using multiple strategies.

Example: strategies--using concrete objects, mental calculations, paper-and-pencil activities

• Solving multistep addition and subtraction problems using authentic situations

• Justifying the strategy used to solve addition and subtraction problems

• Using estimation to determine if an answer is reasonable ||
 * 3.) Demonstrating computational fluency, including quick recall, of addition and subtraction facts with sums through 20 and differences with minuends through 20. ||
 * 4.) Demonstrate conceptual understanding of multiplication and division by solving authentic problems.

Examples: //There are 3 trees in the orchard. On each tree there are 4 peaches. What is the total number of peaches on the trees? Answer: There are 12 peaches on the trees.//

- //The teacher has 12 sheets of paper. There are 6 students in the classroom. The teacher wants to give each student the same number of sheets of paper. How many sheets of paper will each student get? Answer: Each student will get 2 sheets of paper.// ||
 * 5.) Illustrate fractions with multiple representations, including manipulatives, drawings, and verbal descriptions.

• Using the terms //numerator// and //denominator// to label parts of a fraction

• Recognizing that one-half of an object is not always the same as one-half of a different object

Example: recognizing that one-half of a baseball is not equal to one-half of a basketball ||
 * 6.) Determine the monetary value of like and unlike sets of coins and bills up to $2.00.

• Identifying sets of coins of equivalent value

• Selecting coins to make equivalent sets

• Applying monetary symbols, including dollar ($), cent (¢), and decimal point (.)

• Recognizing decimal numbers .10, .25, .50, and .75 as related to money ||
 * 7.) Describe a pattern in a number sequence. ||
 * 8.) Recognize the associative property of addition.

Example: (3 + 4) + 2 = 3 + (4 + 2) ||
 * 9.) Describe change over time in observable (qualitative) and measurable (quantitative) terms.

Examples: observable--recognizing that a plant grew taller

- measurable--determining that a plant grew three inches ||
 * 10.) Describe attributes of three-dimensional (solid) figures, including cubes, cylinders, cones, pyramids, spheres, and rectangular prisms according to faces, sides, vertices, surfaces, edges, and angles.

• Identifying lines of symmetry in triangles, quadrilaterals, pentagons, hexagons, heptagons, and octagons

• Recognizing results of changing the position (transformation) of objects or shapes by sliding (translating), turning (rotating), and flipping (reflecting) ||
 * 11.) Describe the route from one location to another by applying concepts of direction and distance.

Examples: direction--left, right, north, south, east, west

- nonstandard distance--twenty-five steps from the library

- standard distance--ten feet from the walkway

• Following multistep directions to locate objects

• Using grids for determining movement between points ||
 * 12.) Measure length in standard units, including inches, feet, and yards.

• Measuring length using metric units, including centimeter and meter

• Measuring temperature in degrees Fahrenheit

• Using measurement tools, including rulers, yardsticks, metersticks, tape measures, or thermometers

• Estimating length to the nearest unit ||
 * 13.) Measure weight and volume of familiar objects with nonstandard units.

• Estimating weight and volume using nonstandard units

Example: estimating how many buckets of sand it will take to fill a tub ||
 * 14.) Determine time to the minute using digital and analog clocks.

• Interpreting time to the minute as part of an hour

Examples: 6:30 a.m. as half past six in the morning, 6:45 p.m. as a quarter to seven in the evening, 6:15 a.m. as a quarter past six in the morning ||
 * 15.) Interpret data using graphs, including bar, line, and circle graphs and Venn diagrams.

• Using labels and a title to complete a graph ||
 * 16.) Determine if one event related to everyday life is more likely or less likely to occur than another event.

Example: determining if it is more likely to rain or snow on July 4th in Alabama ||


 * ** Mathematics, Grade 3, 2009 **

1.) Demonstrate concepts of number sense by comparing, ordering, and expanding whole numbers through 9,999.

• Determining the place value of a digit in a whole number through 9,999

• Writing a four-digit number in words

• Locating a positive integer through the thousands place and a negative integer between -21 and 0 on a number line

• Converting a number written in expanded notation to standard form

Example: 5,000 + 600 + 70 + 3 = 5,673

• Rounding whole numbers to the nearest tens or hundreds place ||
 * 2.) Solve addition and subtraction problems, including word problems, involving two- and three-digit numbers with and without regrouping.

• Estimating sums and differences using multiple methods, including compatible numbers and rounding, to judge the reasonableness of an answer

• Demonstrating computational fluency in addition and subtraction of two-digit whole numbers without regrouping

• Using mental computation strategies to solve addition and subtraction problems of two-digit numbers with and without regrouping

• Explaining problems and their solutions using diagrams, numbers, and symbolic expressions ||
 * 3.) Demonstrate computational fluency, including quick recall, of multiplication facts through 12 x 12 and division facts with divisors and quotients through 12. ||
 * 4.) Multiply one-, two-, and three-digit multiplicands, with and without regrouping, using single-digit multipliers.

• Applying concepts of multiplication through the use of manipulatives, number stories, skip-counting arrays, area of a rectangle, or repeated addition

• Applying basic multiplication facts through 9 x 9 using manipulatives, solving problems, and writing number stories

• Identifying product, multiplier, and multiplicand when given a completed problem

• Using the terms //product// or //factor// to label multiplication problems

• Naming the first 10 multiples of each one-digit natural number

Example: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70 ||
 * 5.) Divide whole numbers using two-digit dividends and one-digit divisors.

• Recognizing division as either repeated subtraction, parts of a set, parts of a whole, or the inverse of multiplication

• Applying divisibility rules for 2, 5, and 10

Example: recognizing that 32 is divisible by 2 because the digit in the ones place is even

• Recognizing fractions as numerals that may represent division problems

• Identifying quotient, divisor, and dividend when given a completed problem

• Using the terms //quotient, divisor//, and //dividend// to label division problems ||
 * 6.) Demonstrate equivalent fractions using concrete objects or pictorial representations.

• Recognizing different interpretations of fractions, including parts of a set or a collection, points on a number line, numbers that lie between two consecutive whole numbers, and lengths of segments on a ruler

• Locating proper fractions with common denominators 2 through 10 on a number line with fractional parts of the whole indicated on the number line

• Solving problems that involve addition or subtraction of fractions with common denominators

• Comparing fractions with common denominators using the symbols <, >, and = ||
 * 7.) Use coins to make change up to $1.00.

• Determining the monetary value of a set of unlike coins and bills up to $20

• Rounding money values to the nearest dollar

• Using coins and bills to make change up to $20.00

• Using addition and subtraction to find money values up to $20.00 ||
 * 8.) Complete a given geometric or numeric pattern.

• Analyzing patterns on a graph to determine change

Example: observing plant growth over a period of time

• Describing mathematical relationships in context ||
 * 9.) Recognize commutative, associative, and identity properties of multiplication.

Examples: commutative--4 x 3 = 3 x 4

- associative--(6 x 2) x 3 = 6 x (2 x 3)

- identity--450 x 1 = 450

• Using parentheses to signify grouping

Example: 4 x (6 x 5) ||
 * 10.) Identify geometric representations for points, lines, line segments, parallel and perpendicular lines, angles, and rays.

• Recognizing real-life examples of points, lines segments, parallel and perpendicular lines, and angles

• Drawing points, lines, line segments, and parallel and perpendicular lines

• Identifying angles as right, obtuse, or acute

• Drawing lines of symmetry in triangles, quadrilaterals, pentagons, hexagons, and octagons ||
 * 11.) Specify locations on a coordinate grid by using horizontal and vertical movements.

• Demonstrating translations, reflections, and rotations using two-dimensional shapes ||
 * 12.) Measure length in metric units.

• Converting linear measures in meters to centimeters

• Estimating lengths to the nearest metric unit

• Measuring weight, mass, volume, and capacity using metric and customary units

• Measuring temperature in Celsius

• Relating Celsius temperatures to Fahrenheit temperatures

Example: describing 30° as being hot, 20° as being pleasing, 10° as being cool, and 0° as being freezing

• Calculating perimeter and area of rectangular shapes ||
 * 13.) Determine elapsed time to the day with calendars and to the hour with a clock.

• Calculating elapsed time to the minute within the same hour ||
 * 14.) Recognize data as either categorical or numerical.

Examples: categorical--month, color, food, name

- numerical--time, age, length, weight

• Comparing related data sets from Venn diagrams, bar graphs, line graphs, and line plots

• Interpreting data from displays, including Venn diagrams, bar graphs, and line plots

• Locating the mode of a data set represented on a bar graph or a line plot ||
 * 15.) Determine the likelihood of different outcomes in a simple experiment.

Example: determining that the letter "//z//" is most likely to be drawn from a bag containing all letters of the word, //pizza//

• Defending predictions of outcomes of simple experiments ||

//Alabama Course of Study objectives from: http://alex.state.al.us/browseMath.php//