Unit 4: Algebraic Reasoning
Topics 10 & 11 in enVision; see Pearson app on webdesk.pisd.edu
Students will understand that…
U1 Geometry and spatial sense provide a way to describe our environment.
U2 Algebraic representations are used to communicate and generalize patterns and relationships.
U3 Patterns and relationships can be represented physically, graphically, numerically, symbolically or verbally.
U4 Patterns of change can be used to predict outcomes and solve problems.
Students will know …
K1 brackets indicate a second level of grouping.
K2 the order of operations in order to simplify expressions.
K3 ordered pairs are used to identify locations on the coordinate plane.
K4 key attributes of the coordinate plane.
K5 letters can represent an unknown quantity, which can be any part of an equation.
K6 additive patterns follow the form y=x+a.
K7 multiplicative patterns follow the form y=ax.
K8 x represents the input and y represents the output.
K9 parentheses can represent multiplication.
Critical Vocabulary
Students will be skilled at …
S1 graphing relationships found in input/output tables (limited to first quadrant.)
S2 describing the process of graphing.
S3 using order of operations to simplify numerical expressions which may include all four operations for whole numbers and decimals.
S4 using order of operations to simplify numerical expressions using addition and subtraction, for fractions.
S5 simplifying numerical expressions with two levels of grouping, ex. [(3 + 7) ÷ 2]
S6 describing relationships between numbers and operations involving parentheses and brackets, 4(14+5) is 4 times as large and (14 + 5)
S7 identifying, generating, and graphing additive and multiplicative patterns.
S8 representing and solving multi-step problems using an equation with a variable.
S9 graphing fractional and decimal values in the first quadrant of the coordinate plane on or between grid lines.
S10 using models to represent the known and unknown quantities in a multi-step problem.
S11 applying the mathematical process standards.
TEKS
5.1 (A-G) The student uses mathematical processes to acquire and demonstrate mathematical understanding.
5.4 The student applies mathematical process standards to develop concepts of expressions and equations.
(B) represent and solve multi-step problems involving the four operations with whole numbers using equations with a letter standing for the unknown quantity
(C) generate a numerical pattern when given a rule in the form y = ax or y = x + a and graph
(D) recognize the difference between additive and multiplicative numerical patterns given in a table or graph
(E) describe the meaning of parentheses and brackets in a numeric expression
(F) simplify numerical expressions that do not involve exponents, including up to two levels of grouping
5.8 The student applies mathematical process standards to identify locations on a coordinate plane.
(A) describe the key attributes of the coordinate plane, including perpendicular number lines (axes) where the intersection (origin) of the two lines coincides with zero on each number line and the given point (0, 0); the x-coordinate, the first number in an ordered pair, indicates movement parallel to the x-axis starting at the origin; and the y-coordinate, the second number, indicates movement parallel to the y-axis starting at the origin
(B) describe the process for graphing ordered pairs of numbers in the first quadrant of the coordinate plane
(C) graph in the first quadrant of the coordinate plane ordered pairs of numbers arising from mathematical and real-world problems, including those generated by number patterns or found in an input-output table
Texas Focal Point 2: Understanding and generating expressions and equations to solve problems
Texas Focal Point 4: Organizing, representing, and interpreting sets of data
Bold = Readiness Standard