• ## GLE-Math3

STANDARDS FOR MATHEMATICS

Standard 1:
Students develop number sense and use numbers and number relationships in problem-solving situations and communicate the reasoning used in solving these problems.
1.1 Demonstrating meanings for whole numbers, commonly-used fractions and decimals (for example, 1/3, 3/4, 0.5, 0.75), and representing equivalent forms of the same number through the use of physical models, drawings, calculators, and computers.
1.1.1 using objects and pictures, represent whole numbers including odds and evens from 0 to 10,000
1.1.2 apply equalities and inequalities with whole numbers from 0 to 10,000 using the symbols =, •, <, >
1.1.3 using concrete materials (for example, fraction strips), compare and order fractions with like denominators, such as halves, thirds, fourths, eighths, and tenths
1.1.4 demonstrate different combinations of coins for change (for example, 52¢ = 2 quarters and 2 pennies)
1.1.5 using concrete materials, make change up to \$1.00

1.2 Reading and writing whole numbers and knowing place-value concepts and numeration through their relationships to counting, ordering, and grouping.
1.2.1 read and write numerals from 0 to 10,000 in meaningful contexts
1.2.2 read and write the number words for selected numbers from zero to one thousand
1.2.3 order according to place value (for example, given 9 ones, 5 tens, 4 hundreds, and 7 thousands, the student can write the number 7,459; given the number 7,459, the student can show 7 thousands, 4 hundreds, 5 tens, and 9 ones)
1.2.4 identify place value through ten thousands (for example, in 86,243, ‘6’ is in the thousands place)
1.2.5 write four-digit numbers in expanded form (for example, 7,459 = 7,000 + 400 + 50 +9

1.3 Using numbers to count, to measure, to label, and to indicate location.
1.3.1 count forward from any even number by 2’s; and from any number by 10’s and 100’s (for example, 216, 316, 416, 516, ...)
1.3.2 use ordinal positions for selected whole numbers greater than thirty-first
1.3.3 sequence selected whole numbers form 0 to 10,000
1.3.4 locate and label 1/2’s and multiples of 1/4’s between whole numbers on the number line
1.3.5 locate and label a point in the first quadrant of the coordinate plane (for example, locates the point (11,15))

1.4 Developing, testing and explaining conjectures about properties of whole numbers, and commonly used fractions and decimals (for example, 1/3, 3/4, 0.5, 0.75).
1.4.1 verify the commutative and associative properties of addition and multiplication of whole numbers
1.4.2 verify the multiplication properties of zero and one with whole numbers

1.5 Using number sense to estimate and justify the reasonableness of solutions to problems involving whole numbers, and commonly used fractions and decimals (for example, 1/3, 3/4, 0.5, 0.75).
1.5.1 estimate sums and differences first by rounding to the nearest ten and hundred prior to performing the operation and, then, using the estimate to determine the reasonableness of the solution
1.5.2 estimate products first by rounding to the nearest ten prior to performing the operation, and then using the estimate to determine the reasonableness of the solution

Standard 2:
Students use algebraic methods to explore, model and describe patterns and functions involving numbers, shapes, data, and graphs in problem-solving situations and communicate the reasoning used in solving these problems.
2.1 Reproducing, extending, creating, and describing patterns and sequences using a variety of materials (for example, beans, toothpicks, pattern blocks, calculators, unifix cubes, colored tiles).
2.1.1 reproduce, extend, create, and describe patterns, such as in common fractions, geometric shapes, money, measurement, addition, subtraction, and multiplication facts
2.1.2 find missing elements of patterns of multiples

2.2 Describing patterns and other relationships using tables, graphs, and open sentences.
2.2.1 given data, extend a table and plot points on a coordinate plane

2.3 Recognizing when a pattern exists and using that information to solve a problem.
2.3.1 identify a rule using addition or subtraction and solve a problem using the rule

2.4 Observing and explaining how a change in one quantity can produce a change in another (for example, the relationship between the number of bicycles and the numbers of wheels).
2.4.1 determine how the change in one variable affects the change in the other by addition or subtraction

Standard 3:
Students use data collection and analysis, statistics, and probability in
problem-solving situations and communicate the reasoning and processes used in solving these problems.
3.1 Constructing, reading, and interpreting displays of data including tables, charts,
pictographs, and bar graphs.
3.1.1 select the appropriate type of graph to use in various problem-solving situations
3.1.2 collect and display data using surveys, tallies, bar graphs, dot plots, pictographs, or tables
3.1.3 use a computer to create bar and circle graphs
3.1.4d use a timeline to display a sequence of events

3.2 Interpreting data using the concepts of largest, smallest, most often, and middle.
3.2.1 determine the median and mode from a data set
3.2.2 using various displays of data, interpret and draw conclusions

3.3 Generating, analyzing, and making predictions based on data obtained from surveys and chance devices.
3.3.1 use survey data to make a prediction from various displays of data
3.3.2 analyze the results of rolling a number cube
3.3.3 predict the most likely outcome from spinners
3.3.4 analyze the fairness of different spinners

3.4 Solving problems using various strategies for making combinations (for example,
determining the number of different outfits that can be made using two blouses and three skirts).
3.4.1 determine the number of outcomes when rolling a number cube
3.4.2 using manipulatives or pictures, determine the possible combinations of matching a set containing two elements with a set containing three elements

Standard 4:
Students use geometric concepts, properties, and relationships in problemsolving situations and communicate the reasoning used in solving these problems.
4.1 Recognizing shapes and their relationships (for example, symmetry and congruence) using a variety of materials (for example, pasta, boxes, pattern blocks).
4.1.1 compare similarities and differences between the concepts of similarity and congruence
4.1.2 make a pattern by rotating, flipping, and sliding a two-dimensional figure
4.1.3 identify lines of symmetry of regular hexagons, pentagons, and octagons

4.2 Identifying, describing, drawing, comparing, classifying, and building physical models of geometric figures.
4.2.1 identify points, lines, line segments, and rays
4.2.2 recognize and identify hexagons, pentagons, and octagons
4.2.3 classify angles as obtuse, acute, or right
4.2.4 draw obtuse, acute, and right angles
4.2.5 compare what is the same and what is different between two-dimensional figures and three-dimensional figures
4.2.6 draw rectangles and squares on a coordinate plane and identify the vertices with coordinates
4.2.7 identify cubes, spheres, cylinders, cones, and pyramids
4.2.8 build cubes (for example, with marshmallows and toothpicks) and spheres (for example, soap bubbles)

4.3 Relating geometric ideas to measurement and number sense.
4.3.1 measure the sides and perimeters of geometric shapes to the nearest half inch and centimeter
4.3.2 measure the area of geometric figures using nonstandard units

4.4 Solving problems using geometric relationships and spatial reasoning (for example, using rectangular coordinates to locate objects, constructing models of three-dimensional objects).
4.4.1 draw a picture or diagram to solve a problem (for example, use a number line to locate one half)
4.4.2 investigate and predict geometric shapes by combining and subdividing groups of pattern blocks
4.4.3 investigate and predict the result of changing the lengths of sides of polygons
4.4.4 investigate and predict the geometric figures that result from cutting along a line of symmetry

Standard 5:
Students use a variety of tools and techniques to measure, apply the results in problem-solving situations, and communicate the reasoning used in solving these problems.
5.1 Knowing, using, describing, and estimating measures of length, perimeter, capacity, weight, time, and temperature; and 5.3 Demonstrating the process of measuring and explaining the concepts related to units of measurement.
5.1.1 tell time to the nearest five minutes, using an analog and digital clock
5.1.2 estimate how long a minute is
5.1.3 estimate and measure the length of objects
5.1.4 estimate and measure the perimeter of an object with a string measured in U.S. customary and metric units
5.1.5 estimate and measure areas using non-standard units
5.1.6 estimate and measure the capacity of a container in cups, pints, quarts, gallons, and liters
5.1.7 estimate and weigh an object on a balance or scale to the nearest ounce
5.1.8 measure temperatures in both Fahrenheit and Celsius
5.1.9 describe the units for measuring time, length, area, capacity, and temperature
5.1.10 know the number of seconds in a minute, hours in a day, days in a month, days in a year, pints in a quart, quarts in a gallon, and centimeters in a meter

5.2 Comparing and ordering objects according to measurable attributes (for example, longest to shortest, lightest to heaviest).
5.2.1 compare objects according to the measurable attributes of length, area, capacity, weight, and temperature
5.2.2 order objects according to the measurable attributes of length, area, capacity, weight and temperature
5.2.3 compare and order various times

5.4 Using the approximate measures of familiar objects (for example, the width of your finger, the temperature of a room, the weight of a gallon of milk) to develop a sense of measurement.
5.4.1 use familiar objects as referents for measurement (for example, the width of the index fingernail equals approximately one centimeter; ten pennies weigh approximately an ounce)

5.5 Selecting and using appropriate standard and non-standard units of measurement in problem-solving situations.
5.5.1 select the appropriate units of measurement of time, length, area, capacity, weight, and temperature

Standard 6:
Students link concepts and procedures as they develop and use computational techniques, including estimation, mental arithmetic, paper-and-pencil, calculators, and computers, in problem-solving situations and communicate the reasoning used in solving these problems.

6.1 Demonstrating conceptual meanings for the four basic arithmetic operations of addition, subtraction, multiplication, and division.
6.1.1 using concrete materials, demonstrate and verbally explain addition and subtraction of whole numbers with regrouping for up to four-digit numbers
6.1.2 using concrete materials or pictures, demonstrate multiplication with regrouping of whole numbers
6.1.3 using concrete materials, demonstrate division of whole numbers with remainders as partitioning of sets
6.1.4 using paper-and-pencil, demonstrate the inverse relationship of addition and subtraction of whole numbers
6.1.5 using paper-and-pencil, demonstrate multiplication of whole numbers as repeated addition

6.2 Adding and subtracting commonly used fractions and decimals using physical models (for example, 1/3, 3/4, 0.5, 0.75).
6.2.1 using concrete materials, demonstrate addition and subtraction of proper fractions with common denominators of ten or less
6.2.2 using coins as models, add and subtract decimals in which sums and differences may exceed \$1.00

6.3 Demonstrating understanding of and proficiency with basic addition, subtraction,
multiplication, and division facts without the use of a calculator.
6.3.1 demonstrate understanding of basic multiplication and division facts of 1’s, 2’s, 3’s, 5’s, and 10’s
6.3.2 demonstrate automatic recall of basic multiplication facts of 1’s, 2’s, 3’s, 5’s, and 10’s
6.3.3 continue automatic recall of basic addition and subtraction facts
6.3.4 use a multiplication facts table to locate all factors for a particular product (for example, 6 = 1 x 6, 6 = 2 x 3, . . . )

6.4 Constructing, using, and explaining procedures to compute and estimate with whole numbers.