## MATHEMATICS FOURTH GRADE - GRADE LEVEL EXPECTATIONS

__ALGEBRAIC RELATIONSHIPS__

**UNDERSTAND PATTERNS, RELATIONS AND FUNCTIONS**Describe geometric and numeric patterns

Analyze patterns using words, tables and graphs

*REPRESENT AND ANALYZE MATHEMATICAL SITUATIONS AND STRUCTURES USING ALGEBRAIC SYMBOL*Using all operations, represent a mathematical situation as an expression or number sentence

Use the commutative, distributive and associative properties of addition and multiplication for multidigit numbers

*USE MATHEMATICAL MODELS TO REPRESENT AND UNDERSTAND QUANTITATIVE RELATIONSHIPS*Model problem situations, using representations such as graphs, tables or number sentences

*ANALYZE CHANGE IN VARIOUS CONTEXTS*Describe mathematical relationships in terms of constant rates of change

__DATA AND PROBABILITY__**Collect data using observations, surveys and experiments**

*FORMULATE QUESTIONS THAT CAN BE ADDRESSED WITH DATA AND COLLECT, ORGANIZE AND DISPLAY RELEVANT DATA TO ANSWER THEM*

Create tables or graphs to represent categorical and numerical data (including line plots)

*SELECT AND USE APPROPRIATE STATISTICAL METHODS TO ANALYZE DATA*Describe important features of the data set

*DEVELOP AND EVALUATE INFERENCES AND PREDICTIONS THAT ARE BASED ON DATA*Given a set of data, propose and justify conclusions that are based on the data

__GEOMETRIC AND SPATIAL RELATIONSHIPS__

*ANALYZE CHARACTERISTICS AND PROPERTIES OF TWO-AND THREE-DIMENSIONAL GEOMETRIC SHAPES AND DEVELOP MATHEMATICAL ARGUMENTS ABOUT GEOMETRIC RELATIONSHIPS*Name and identify properties of 1-, 2-, and 3-dimensional shapes and describe the attributes of 2- and 3-dimensional shapes using appropriate geometric vocabulary (rectangular prism, cylinder, pyramid, sphere, cone, parallelism, perpendicularity)

Describe the results of subdividing, combining and transforming shapes

*SPECIFY LOCATIONS AND DESCRIBE SPATIAL RELATIONSHIPS USING COORDINATE GEOMETRY AND OTHER REPRESENTATIONAL SYSTEMS*Describe movement using common language and geometric vocabulary (forward, back, left, right, north, south, east, west)

*APPLY TRANSFORMATIONS AND USE SYMMETRY TO ANALYZE MATHEMATICAL SITUATIONS*Predict the results of sliding/translating, flipping/reflecting or turning/rotating around the center point of a polygon

Create a figure with multiple lines of symmetry and identify the lines of symmetry

*USE VISUALIZATION, SPATIAL REASONING AND GEOMETRIC MODELING TO SOLVE PROBLEMS*Given the picture of a prism, identify the shapes of the faces

__MEASUREMENT__**Identify and justify the unit of linear measure including perimeter and (customary metric)**

*UNDERSTAND MEASURABLE ATTRIBUTES OF OBJECTS AND THE UNITS, SYSTEMS AND PROCESSES OF MEASUREMENT*Identify equivalent linear measures within a system of measurement

Tell time to the nearest minute

Determine change from $10.00 and add and subtract money values to $10.00

**S**

*APPLY APPROPRIATE TECHNIQUES, TOOLS AND FORMULAS TO DETERMINE MEASUREMENT*Select and use benchmarks to estimate measurements (linear, capacity, weight)

Select and use benchmarks to estimate measurements of 0-, 45- (acute), 90- (right) greater than 90 (obtuse) degree angles

Determine and justify areas of polygons and non-polygonal regions imposed on a rectangular grid

__NUMBER AND OPERATIONS__

**UNDERSTAND NUMBERS, WAYS OF REPRESENTING NUMBERS, RELATIONSHIPS AMONG NUMBERS AND NUMBER SYSTEMS**Read, write and compare whole numbers less than 100,000 Use models, benchmarks (0, 1/2 and 1) and equivalent forms to judge the size of fractions

Recognize equivalent representations for the same number and generate them by decomposing and composing numbers

Classify and describe numbers by their characteristics, including odd, even, multiples and factors

*UNDERSTAND MEANINGS OF OPERATIONS AND HOW THEY RELATE TO ONE ANOTHER*Represent and recognize multiplication and related division using various models, including equal intervals on the number line, equal size groups, distributive property, etc.

Describe the effects of multiplying and dividing whole numbers as well as the relationship between the two operations

*COMPUTE FLUENTLY AND MAKE REASONABLE ESTIMATES*Represent a mental strategy used to compute a given multiplication problem (up to 2-digit by 2-digit multiple of)

Demonstrate fluency with basic number relationships (12 x 12) of multiplication and related division facts

Apply and describe the strategy used to compute a given multiplication of 2-digit by 2-digit numbers and related division facts

Estimate and justify products of whole numbers