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## Concepts tested in 4th Grade TAKS Math Assessment
- describe independent and dependent quantities in functional relationships
- gather and record data and use data sets to determine functional relationships between quantities
- describe functional relationships for given problem situations and write equations or inequalities to answer questions arising from the situations
- represent relationships among quantities using [concrete] models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities
- interpret and make decisions, predictions, and critical judgments from functional relationships
- identify [and sketch] the general forms of linear ( y = x) and quadratic ( y = x 2 ) parent functions
- identify mathematical domains and ranges and determine reasonable domain and range values for given situations, both continuous and discrete
- interpret situations in terms of given graphs or create situations that fit given graphs
- collect and organize data, make and interpret scatterplots (including recognizing positive, negative, or no correlation for data approximating linear situations), and model, predict, and make decisions and critical judgments in problem situations
- use symbols to represent unknowns and variables
- look for patterns and represent generalizations algebraically
- find specific function values, simplify polynomial expressions, transform and solve equations, and factor as necessary in problem situations
- use the commutative, associative, and distributive properties to simplify algebraic expressions
- connect equation notation with function notation, such as y = x + 1 and f(x) = x + 1.
- determine whether or not given situations can be represented by linear functions
- use, translate, and make connections among algebraic, tabular, graphical, or verbal descriptions of linear functions
- develop the concept of slope as rate of change and determine slopes from graphs, tables, and algebraic representations
- interpret the meaning of slope and intercepts in situations using data, symbolic representations, or graphs
- investigate, describe, and predict the effects of changes in m and b on the graph of y = mx + b
- graph and write equations of lines given characteristics such as two points, a point and a slope, or a slope and y-intercept
- determine the intercepts of the graphs of linear functions and zeros of linear functions from graphs, tables, and algebraic representations
- interpret and predict the effects of changing slope and y-intercept in applied situations
- relate direct variation to linear functions and solve problems involving proportional change
- analyze situations involving linear functions and formulate linear equations or inequalities to solve problems
- investigate methods for solving linear equations and inequalities using [concrete] models, graphs, and the properties of equality, select a method, and solve the equations and inequalities
- interpret and determine the reasonableness of solutions to linear equations and inequalities
- analyze situations and formulate systems of linear equations in two unknowns to solve problems
- solve systems of linear equations using [concrete] models, graphs, tables, and algebraic methods;
- interpret and determine the reasonableness of solutions to systems of linear equations.
- investigate, describe, and predict the effects of changes in a on the graph of y = ax2 + c
- investigate, describe, and predict the effects of changes in c on the graph of y = ax 2 + c
- analyze graphs of quadratic functions and draw conclusions
- solve quadratic equations using [concrete] models, tables, graphs, and algebraic methods
- make connections among the solutions (roots) of quadratic equations, the zeros of their related functions, and the horizontal intercepts (x-intercepts) of the graph of the function
- use patterns to generate the laws of exponents and apply them in problem-solving situations
- generate similar figures using dilations including enlargements and reductions
- graph dilations, reflections, and translations on a coordinate plane.
- locate and name points on a coordinate plane using ordered pairs of rational numbers
- draw three-dimensional figures from different perspectives;
- use geometric concepts and properties to solve problems in fields such as art and architecture
- use pictures or models to demonstrate the Pythagorean Theorem
- find lateral and total surface area of prisms, pyramids, and cylinders using [concrete] models and nets (two-dimensional models);
- connect models of prisms, cylinders, pyramids, spheres, and cones to formulas for volume of these objects
- estimate measurements and use formulas to solve application problems involving lateral and total surface area and volume
- use the Pythagorean Theorem to solve real-life problems
- use proportional relationships in similar two-dimensional figures or similar three-dimensional figures to find missing measurements
- describe the resulting effects on perimeter and area when dimensions of a shape are changed proportionally
- describe the resulting effect on volume when dimensions of a solid are changed proportionally
- estimate and find solutions to application problems involving percents and other proportional relationships, such as similarity and rates
- find the probabilities of dependent and independent events
- use theoretical probabilities and experimental results to make predictions and decisions
- select the appropriate measure of central tendency or range to describe a set of data and justify the choice for a particular situation
- select and use an appropriate representation for presenting and displaying relationships among collected data, including line plots, line graphs, [stem and leaf plots,] circle graphs, bar graphs, box and whisker plots, histograms, and Venn diagrams, with and without the use of technology
- recognize misuses of graphical or numerical information and evaluate predictions and conclusions based on data analysis
- identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics
- use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness
- select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem
- communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models.
- make conjectures from patterns or sets of examples and nonexamples
- validate his/her conclusions using mathematical properties and relationships
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