# VGLA COE Organizer Mathematics 4

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1 4.1 The Student will identify the place value for each digit in a whole number expressed through millions a) orally and in writing; b) compare two whole numbers expressed through millions, using symbols (>, <, or =); and round whole numbers expressed through millions to the nearest thousand, c) ten thousand, and hundred thousand.

2 4.2 The student will identify, model, and compare rational numbers (fractions and mixed numbers), using a) concrete objects and pictures; b) represent equivalent fractions; and c) relate fractions to decimals, using concrete objects.

3 4.3 The student will compare the numerical value of fractions (with like and unlike denominators) having denominators of 12 or less, using concrete materials.

4 4.4 The student will read decimals expressed through thousandths, write decimals expressed through thousandths, a) represent decimals expressed through thousandths, and identify decimals expressed through thousandths; round to the nearest whole number, b) tenth, and hundredth; and compare the value of two decimals, using symbols (<, >, or =), c) concrete materials, drawings, and calculators.

5 4.5 The student will estimate whole-number sums and differences and describe the method of estimation. Students will refine estimates, using terms such as closer to, between, and a little more than.

6 4.6 The student will add and subtract whole numbers written in vertical form and horizontal form, choosing appropriately between paper and pencil methods and calculators.

7 4.7 The student will find the product of two whole numbers when one factor has two digits or fewer and the other factor has three digits or fewer, using estimation and paper and pencil. For larger products (a two-digit numeral times a three-digit numeral), estimation and calculators will be used.

8 4.8 The student will estimate and find the quotient of two whole numbers, given a one-digit divisor.

9 4.9 The student will add and subtract with fractions having like and unlike denominators of 12 or less, using concrete materials, a) pictorial representations, and paper and pencil; add and subtract with decimals through thousandths, using concrete materials, b) pictorial representations, and paper and pencil; and solve problems involving addition and subtraction with fractions having like and unlike denominators of 12 or less and with decimals expressed through thousandths, using various computational methods, including c) calculators, paper and pencil, mental computation, and estimation.

10 4.10 The student will estimate and measure weight/mass, using actual measuring devices, and describe the results in U.S. Customary/metric units as appropriate, including ounces, a) pounds, grams, and b) c) kilograms; identify equivalent measurements between units within the U.S. Customary system (ounces and pounds) and metric system (grams and kilograms); and estimate the conversion of ounces and grams and pounds and kilograms, using approximate comparison e.g. 1oz. is about 28g., 1 g. is about the weight of a paper clip; 1 km. is a little more than 2lbs. The intent of this standard is for students to make ballpark comparisons and not to memorize conversion factors between U.S. Customary and metric units.

11 4.11 The student will estimate and measure length, using actual measuring devices, and describe the results in both metric and U.S. Customary units, including part of an inch (1/2, 1/4, and 1/8), inches, a) feet, yards, millimeters, centimeters, and meters; identify equivalent measurements between units within the U.S. Customary system inches and feet; feet and yards; b) inches and yards and metric system millimeters and centimeters; centimeters and meters; and millimeters and meters; and estimate the conversion of inches and centimeters, using approximate comparisons e.g. 1 in. is about 2.5 cm *, yards and meters using approximate comparisons e.g. 1 m is a little longer than 1 yd *, c) miles and kilometers, using approximate comparisons e.g. 1 mile is slightly farther than 1.5 km, or 1 km is slightly farther than half a mile.* *The intent of this standard is for students to make ballpark comparisons and not to memorize conversion factors between U.S. Customary and metric units.

12 4.12 The student will estimate and measure liquid volume, using actual measuring devices and using metric and U.S. Customary units, including cups, pints, a) quarts, gallons, milliliters, and liters; identify equivalent measurements between units within the b) U.S. Customary system (cups, pints, quarts, and gallons) and metric system (milliliters and liters); and estimate the conversion of quarts and liters, using approximate comparisons (1 quart is a little less than 1 liter, 1 liter is a little more than 1 quart).* c) * The intent of this standard is for students to make ballpark comparisons and not to memorize conversion factors between U.S. Customary and metric units.

13 4.13 The student will identify and describe situations representing the use of a) perimeter and area; and use measuring devices to find perimeter in both b) standard units of measure and nonstandard units of measure.

14 4.14 The student will investigate and describe the relationships between and among points, lines, line segments, and rays.

15 4.15 The student will identify and draw (using a straightedge or ruler) representations of points, lines, a) line segments, rays, and angles; and b) describe the path of shortest distance between two points on a flat surface.

16 4.16 The student will identify and draw representations of lines that illustrate intersection, parallelism, and perpendicularity.

17 4.17 The student will analyze and compare the properties of two-dimensional (plane) geometric figures circle, square, rectangle, triangle, a) parallelogram, and rhombus and three-dimensional (solid) geometric figures sphere, cube, and rectangular solid [prism]; identify b) congruent shapes and noncongruent shapes; and investigate congruence of plane figures after geometric transformations such as reflection (flip), translation (slide) and rotation (turn), using c) mirrors, paper folding, and tracing.

18 4.18 The student will identify the order pair for a point and locate the point for an ordered pair in the first quadrant of a coordinate plane.

19 4.19 The student will predict the likelihood of outcomes of a simple event, using the terms certain, a) likely, unlikely, impossible; and b) determine the probability of a given simple event, using concrete materials.

20 4.20 The student will collect, organize, and display data in Line graphs with scale increments of one or greater than one and bar graphs with scale increments of one or greater than one and use the display to interpret the results, draw conclusions, and make predictions.

21 4.21 The student will recognize, create, and extend numerical and geometric patterns, using concrete materials, number lines, symbols, tables and words.

22 4.22 The student will recognize and demonstrate the meaning of equality, using symbols representing numbers, operations, and relations [e.g., 3 + 5=5 + 3 and 15 + ( ) = ( ) + 16].

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