Number Sense, Estimation, Computation:

1.      Demonstrate an understanding and application of place value from billions to thousandths, adding/subtracting integers and fractions with and without the use of number lines, and zero and one as the additive and multiplicative identities.

2.      Mentally add/subtract two-digit numbers.

3.      Select and use appropriate operations to solve problems involving addition, subtraction, multiplication, division, and positive integer exponents with whole numbers, and with positive fractions, mixed numbers, decimals, and percents.

4.      Demonstrate an understanding of fractions as a ratio of whole numbers, as parts of unit wholes, as parts of a collection, and as locations on the number line.

5.      Identify and determine common equivalent fractions, mixed numbers, decimals, and percents.  

6.      Demonstrate an understanding of positive integer exponents, in particular, when used in powers of ten, e.g., 10², 10⁵. Extend multiplication/division by powers of ten, expanded notation without exponents, factors, and prime factors.

7.      Use a calculator to: multiply/divide large numbers develop order of operations.

8.      Use long division to one decimal place.

9.      State basic multiplication and division facts 0-144. 

10. Round decimals to the nearest thousandth    

11. Accurately and efficiently add, subtract, multiply, and divide (with double-digit divisors) whole numbers and positive decimals.

12. Find, compare, and position integers, fractions, mixed numbers, decimals, and percents (both positive and negative), on the number line. 

13. Apply number theory concepts to the solution of problems.  These include prime and composite numbers, prime factorization, greatest common factor, least common multiple, and divisibility rules for 2, 3, 4, 5, 6, 9, and 10.

Patterns, Relations, & Algebra:

1.      Locate missing terms in a sequence using powers of ten.

2.      Use patterns and calculators to explain the rules of divisibility.

3.      Analyze and determine the rules for extending symbolic, arithmetic, and geometric patterns and progressions, e.g., ABBCCC; 1, 5, 9, 13 …; 3, 9, 27, ….

4.      Demonstrate an understanding of variables to discover arithmetic processes, patterns when converting fractions to decimals.

5.      Use the property of equality to solve problems, e.g., if c + 7 = 13, then c = 13 – 7, therefore c = 6; if 3 x c = 15, then ¹/₃ x 3 x c = ¹/₃ x 15, therefore c = 5.

6.      Represent real situations and mathematical relationships with concrete models, tables, graphs, and rules in words and with symbols, e.g., input-output tables.

Geometry:

1.      Identify polygons based on their properties, including types of interior angles, perpendicular or parallel sides, and congruence of sides, e.g., squares, rectangles, rhombuses, parallelograms, trapezoids, and isosceles, equilateral, and right triangles.

2.      Identify the relationship between radius, diameter, and circumference through concrete examples.

3.      Use a protractor to draw and compare angles.

4.      Graph points and identify coordinates of points on the Cartesian coordinate plane (all four quadrants).

5.      Find the distance between two points on horizontal or vertical number lines.

6.      Predict, describe and perform transformations on two-dimensional shapes, e.g., translations, rotations, and reflections.  

Measurement:

1.      Measure and apply the concepts of perimeter and area to the solution of problems.     Apply formulas where appropriate.

2.      Demonstrate an understanding of common units of measurement within the same measurement system.

3.      Estimate weight, length, and capacity.

4.      Find areas of triangles and parallelograms. Recognize that shapes with the same number of sides but different appearances can have the same area. Develop strategies to find the area of more complex shapes.

Statistics & Probability:

1.      Determine validity of statements based on data.

2.      Make predictions based on experimental and theoretical probabilities, and calculate averages.

3.      Describe and compare data sets using the concepts of median, mean, mode, maximum and minimum, and range.