Patterns, Relations, and Algebra  

1)         Create, describe, extend and explain symbolic (geometric) and numeric patterns, including multiplication patterns like 3, 30,300,3000…

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

3)         Determine values of variables in simple equations (e.g. 4106 – Δ =37, 5 = μ + 3).

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

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).

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

Geometry

1)         Compare and analyze attributes and other features (e.g., number of sides, faces, corners, right angles, diagonals, and symmetry) of two- and three-dimensional geometric shapes.

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)         Recognize similar figures.

4)         Identify angles as acute, right, or obtuse.

5)         Describe and draw intersecting, parallel, and perpendicular lines.

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

7)         Describe and apply techniques such as reflections (flips), rotations (turns), and translations (slides) for determining if two shapes are congruent.

8)         Identify and describe line symmetry in two-dimensional shapes.

9)         Predict and validate the results of partitioning, folding, and combining two- and three-dimensional shapes.

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.

2)         Carry out simple unit conversions within a system of measurement (e.g., hours to minutes, cents to dollars, yards to feet or inches, etc.).

3)         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…).

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

5)         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.

Data Analysis, Statistics, and Probability

1)         Collect and organize data using observations, measurements, surveys, or experiments, and identify appropriate ways to display the data.

2)         Match representations of a data set such as lists, tables, or graphs (including circle graphs) with the actual set of data

3)         Construct, draw conclusions, and make predictions of data sets, including tables, bar graphs, pictographs, line graphs, line plots, and tallies.

4)         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).

5)         List and count the number of possible combinations of objects from three sets (e.g., how many different outfits can one make from a set of three shirts, a set of two skirts, and a set of two hats?).

6)         Classify outcomes as certain, likely, unlikely, or impossible by designing and conducting experiments using concrete objects such as counters, number cubes, spinners or coins.

Patterns, Relations, and Algebra  

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

2)         Replace variables with given values and evaluate/simplify (e.g., 2μ + 3 when μ =4).

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

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

5)         Solve linear equations using concrete models, tables, graphs, and paper-pencil methods.

6)         Produce and interpret graphs that represent the relationship between two variables in everyday situations.

7)         Identify and describe relationships between two variables with a constant rate of change. Contrast these with relationships where the rate of change is not constant.

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 three-dimensional shapes (e.g., cubes, prisms, spheres, cones, and pyramids) based on their properties such as edges and faces.

3)         Identify relationships among points, lines, and planes (e.g., intersecting, parallel, perpendicular).

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).

7)         Identify types of symmetry, including line and rotational.

8)         Determine if two shapes are congruent by measuring sides or a combination of sides and angles, as necessary; or by motions or series of motions (e.g., translations, rotations, and reflections).

9)         Match three-dimensional objects and their two-dimensional representations (e.g. nets, projections, and perspective drawings).

Measurement

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

2)         Identify, measure, describe, classify, and construct various angles, triangles, and quadrilaterals.

3)         Solve problems involving proportional relationships and units of measurement (e.g., same system unit conversions, scale models, maps, and speed).

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.

5)         Identify, measure, and describe circles and the relationships of the radius, diameter, circumference, and area (e.g., d=2r, p=C/d), and use the concepts to solve problems.

6)         Find volumes and surface areas of rectangular prisms.

7)         Find the sum of the angles in simple polygons (up to eight sides) with and without measuring the angles.

Data Analysis, Statistics, and Probability

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

2)         Construct and interpret stem-and-leaf plots, line plots, and circle graphs.

3)         Use tree diagrams and other models (e.g., lists and tables) to represent possible or actual outcomes of trials.

4)         Predict the probability of outcomes of simple experiments (e.g., tossing a coin, rolling a die) and test the predictions. Use appropriate ratios between 0 and 1 to represent the probability of the outcome and associate the probability with the likelihood of the event.