M4:1: Demonstrates conceptual understanding of rational numbers with respect to:

M4:1.1: whole numbers from 0 to 999,999 through equivalency, composition, decomposition, or place value using models, explanations, or other representations; and

Modeling Whole Numbers and Decimals (Base-10 Blocks)

M4:1.2: positive fractional numbers (benchmark fractions: a/2, a/3, a/4, a/5, a/6, a/8, or a/10, where a is a whole number greater than 0 and less than or equal to the denominator) as a part to whole relationship in area, set, or linear models where the number of parts in the whole are equal to, and a multiple or factor of the denominator; and decimals as hundredths within the context of money, or tenths within the context of metric measurements (e.g., 2.3 cm) using models, explanations, or other representations.

Equivalent Fractions (Fraction Tiles)
Fraction Garden (Comparing Fractions)
Modeling Decimals (Area and Grid Models)
Modeling Fractions (Area Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Toy Factory (Set Models of Fractions)

M4:2: Demonstrates understanding of the relative magnitude of numbers from 0 to 999,999 by ordering or comparing whole numbers; and ordering, comparing, or identifying equivalent proper positive fractional numbers; or decimals using models, number lines, or explanations.

Adding Whole Numbers and Decimals (Base-10 Blocks)
Equivalent Fractions (Fraction Tiles)
Fraction Garden (Comparing Fractions)
Fractions Greater than One (Fraction Tiles)
Modeling Decimals (Area and Grid Models)
Modeling Fractions (Area Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Toy Factory (Set Models of Fractions)

M4:3: Demonstrates conceptual understanding of mathematical operations by describing or illustrating the relationship between repeated subtraction and division (no remainders); the inverse relationship between multiplication and division of whole numbers; or the addition or subtraction of positive fractional numbers with like denominators using models, number lines, or explanations.

Factor Trees (Factoring Numbers)
Fractions Greater than One (Fraction Tiles)
Modeling Fractions (Area Models)
No Alien Left Behind (Division with Remainders)
Number Line Frog Hop (Addition and Subtraction)

M4:4: Accurately solves problems involving multiple operations on whole numbers or the use of the properties of factors and multiples; and addition or subtraction of decimals and positive proper fractions with like denominators. (Multiplication limited to 2 digits by 2 digits, and division limited to 1 digit divisors.)

Adding Fractions (Fraction Tiles)
Adding Whole Numbers and Decimals (Base-10 Blocks)
Chocomatic (Multiplication, Arrays, and Area)
Fractions Greater than One (Fraction Tiles)
Modeling Fractions (Area Models)
No Alien Left Behind (Division with Remainders)
Pattern Flip (Patterns)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)

M4:7: Estimates and evaluates the reasonableness of solutions appropriate to grade level.

Cannonball Clowns (Number Line Estimation)
Critter Count (Modeling Multiplication)
Multiplying Decimals (Area Model)

M4:8: Applies properties of numbers (odd, even, factor, multiple, remainders, composition/decomposition) to solve problems and to simplify computations.

Chocomatic (Multiplication, Arrays, and Area)
Pattern Flip (Patterns)

M4:9: Uses properties or attributes of angles (number of angles) or sides (number of sides, length of sides, parallelism, or perpendicularity) to identify, describe, or distinguish among triangles, squares, rectangles, rhombi, trapezoids, hexagons, or octagons; or classify angles relative to 90° as more than, less than, or equal to. Recognizes symmetrical figures and uses symmetry to identify and classify figures.

Classifying Quadrilaterals

M4:14: Demonstrates conceptual understanding of perimeter of polygons, and the area of rectangles, polygons, or irregular shapes on grids using a variety of models, manipulatives, or formulas. Expresses all measures using appropriate units.

Balancing Blocks (Volume)
Fido's Flower Bed (Perimeter and Area)

M4:16: Determines elapsed and accrued time to the 1/4 hour.

Elapsed Time

M4:18: Solves problems using the Cartesian coordinate system (Quadrant 1) to locate coordinates and to represent data from tables.

Graphing Skills

M4:23: Interprets a given representation (line plots, tables, bar graphs, pictographs, or circle graphs) to answer questions related to the data, to analyze the data to formulate or justify conclusions, to make predictions, or to solve problems. And (tally charts, frequency charts, line graphs, Venn diagrams).

Elevator Operator (Line Graphs)
Forest Ecosystem
Graphing Skills
Reaction Time 1 (Graphs and Statistics)

M4:24: Analyzes patterns, trends, or distributions in data in a variety of contexts by determining or using measures of central tendency (median or mode), or range.

Movie Reviewer (Mean and Median)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

M4:25: Organizes and displays data using line plots, bar graphs, tally charts and frequency charts, or tables to answer question related to the data, to analyze the data to formulate or justify conclusions, or to make predictions.

Graphing Skills
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

M4:27: For a probability event in which the sample space may or may not contain equally likely outcomes, determines the theoretical probability of an event and expresses the result as part to whole (e.g., two out of five).

Spin the Big Wheel! (Probability)

M4:28: In response to a teacher- or student-generated question or hypothesis, collects appropriate data, organizes the data, displays/ represents the data, analyzes the data to draw conclusions about the questions or hypothesis being tested.

Graphing Skills