Number Sense, Estimation & Computation:

1.      Demonstrate an understanding and application of numbers to 100,000, including place value.

·        Represent, order, and compare large numbers (to at least 100,000) using various forms, including expanded notation, e.g., 853 = 8 x 100 + 5 x 10 + 3.

2.      Demonstrate number sense through calculator problem solving activities.

3.      Multiply/ divide 3 digit numbers without remainders, and relate to each other.

·        Select, use, and explain various meanings and models of multiplication and division of whole numbers. Understand and use the inverse relationship between the two operations.

·        Select, use, and explain the commutative, associative, and identity properties of operations on whole numbers in problem situations, e.g., 37 x 46 = 46 x 37, (5 x 7) x 2 = 5 x (7 x 2).

·        Know multiplication facts through 12 x 12 and related division facts. Use these facts to solve related multiplication problems and compute related problems, e.g., 3 x 5 is related to 30 x 50, 300 x 5, and 30 x 500.

·        Demonstrate in the classroom an understanding of and the ability to use the conventional algorithm for division of up to a three-digit whole number with a single-digit divisor (with or without remainders).

4.      Add, subtract, and order fractions & decimals using symbols and manipulatives.

·        Use concrete objects and visual models to add and subtract common fractions.

5.      Demonstrate numerator and denominator, numbers greater than 1 with manipulatives.

·        Select, use, and explain models to relate common fractions and mixed numbers (1/2, 1/3, 1/4, 1/5, 1/6, 1/8, 1/10, 1/12, and 1¹/2), find equivalent fractions, mixed numbers, and decimals, and order fractions.

6.      Demonstrate rounding to tens, hundreds, etc.

·        Round whole numbers through 100,000 to the nearest 10, 100, 1000, 10,000, and 100,000.

7.      Estimate for reasonableness in problem solving solutions.

8.      Estimate products and quotients; compare with calculator products and quotients.

9.      Exhibit an understanding of the base ten number system by reading, naming, and writing decimals between 0 and 1 up to the hundredths.

10. Recognize classes (in particular, odds, evens; factors or multiples of a given number; and squares) to which a number may belong, and identify the numbers in those classes. Use these in the solution of problems.

11. Divide up to a three-digit whole number with a single-digit divisor (with or without remainders) accurately and efficiently. Interpret any remainders.

12. Demonstrate in the classroom an understanding of and the ability to use the conventional algorithms for addition and subtraction (up to five-digit numbers), and multiplication (up to three digits by two digits).

Patterns, Relations, & Algebra:

1.      Demonstrate an understanding of variables.

·        Use symbol and letter variables (e.g., D, x) to represent unknowns or quantities that vary in expressions and in equations or inequalities (mathematical sentences that use =, <, >).

·        Determine values of variables in simple equations, e.g., 4106 – Ñ = 37; c – m = 3 and 4 + 5 = m + 3.

·        Determine how change in one variable relates to a change in a second variable, e.g., input-output tables.

2.      Use calculator sequencing to extend patterns and relationships.

3.      Use pictures, models, tables, charts, graphs, words, number sentences, and mathematical notations to interpret mathematical relationships.

4.      Demonstrate an understanding and application of sequence: rules and missing numbers etc.

5.      Solve problems involving proportional relationships, including unit pricing (e.g., four apples cost 80¢, so one apple costs 20¢) and map interpretation (e.g., one inch represents five miles, so two inches represent ten miles).

Geometry:

1.      Identify geometric concepts such as points, parallel, perpendicular lines, and right angles in everyday surroundings.

·        Describe and draw intersecting, parallel, and perpendicular lines.

2.      Describe, model, draw, compare, and classify two- and three-dimensional shapes, e.g., circles, polygons—especially triangles and quadrilaterals—cubes, spheres, and pyramids.

3.      Identify angles as acute, right, or obtuse.

4.      Using ordered pairs of numbers and/or letters, graph, locate, identify points, and describe paths (first quadrant).

Measurement:

1.      Demonstrate an understanding of such attributes as length, area, weight, and volume, and select the appropriate type of unit for measuring each attribute. 

·        Estimate and find area and perimeter of a rectangle, triangle, or irregular shape using diagrams, models, and grids or by measuring.

·        Identify and use appropriate metric and English units and tools (e.g., ruler, angle ruler, graduated cylinder, thermometer) to estimate, measure, and solve problems involving length, area, volume, weight, time, angle size, and temperature.

2.      Identify time, time lapsed, leap years

·        Identify time to the minute on analog and digital clocks using a.m. and p.m. Compute elapsed time using a clock (e.g., hours and minutes since…) and using a calendar (e.g., days since…).

3.      Identify key benchmarks on Fahrenheit and Celsius scales.

Statistics & Probability:

1.      Graph simple coordinates.

2.      Demonstrate an understanding and application of tables, charts, graphs and timelines.

·        Construct, draw conclusions, and make predictions from various representations of data sets, including tables, bar graphs, circle graphs, pictographs, line graphs, line plots, and tallies.

3.      Make predictions based on chance given events.

·        Represent the possible outcomes for a simple probability situation, e.g., the probability of drawing a red marble from a bag containing three red marbles and four green marbles.