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Utah Algebra I Standards Correlation
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Utah Core - Algebra 1
| Standard I: Students will
expand number sense to understand, perform operations, |
| and solve problems with real numbers. |
| Objective 1.1: Represent real numbers as points on the number
line and distinguish rational numbers from irrational numbers. |
|
| a. |
Define a rational number as
a point on the number line that can be expressed as the ratio of two
integers, and points that cannot be so expressed as irrational. |
Chapter 2: Unit 1:
2.01, 2.03, 2.04 Chapter 12: Unit 1: 12.01, 12.05 |
| b. |
Classify
numbers as rational or irrational, knowing that rational numbers can be
expressed as terminating or repeating decimals and irrational numbers can be
expressed as non-terminating, non-repeating decimals. |
Chapter 2: Unit 1:
2.03 |
| c. |
Classify pi and square roots of
non-perfect square numbers as irrational. |
Chapter 2: Unit 1: 2.01, 2.03, 2.04
Chapter 12: Unit 1: 12.01, 12.02, 12.03,
12.05 |
| d. |
Place rational and
irrational numbers on a number line between two integers. |
Chapter 2: Unit 1:
2.04 |
| Objective 1.2: Compute fluently and make reasonable estimates
with rational and irrational numbers. |
|
| a. |
Simplify, add, subtract, multiply, and divide expressions with
square roots. |
Chapter 12: Unit 1: 12.01, 12.02, 12.03, 12.04, 12.07, 12.08 |
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Chapter 12: Unit 2: 12.09, 12.10,
12.11, 12.12, 12.13, 12.14, 12.15, 12.16 |
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Chapter 12: Unit 3: 12.17, 12.18,
12.19, 12.20, 12.21, 12.22, 12.23, 12.24 |
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Chapter 12: Unit 4: 12.25, 12.26,
12.27, 12.28, 12.29, 12.30, 12.31, 12.32 |
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Chapter 12: Unit 6: 12.37,
12.38, 12.39, 12.40, 12.41, 12.42, 12.43, 12.44 |
| b. |
Evaluate and simplify numerical expressions containing rational numbers and square roots using the
order of operations. |
Chapter 12: Unit 1: 12.01, 12.02, 12.03, 12.04, 12.07, 12.08 |
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Chapter 12: Unit 2: 12.09, 12.10,
12.11, 12.12, 12.14, 12.15, 12.16 |
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Chapter 12: Unit 3: 12.17, 12.18,
12.19, 12.20, 12.21, 12.22, 12.23, 12.24 |
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Chapter 12: Unit 4: 12.25, 12.26,
12.28, 12.29, 12.30, 12.31, 12.32 |
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Chapter 12: Unit 5: 12.33, 12.34,
12.35, 12.36 |
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Chapter 12: Unit 10: 12.65, 12.66 |
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Chapter 13: Unit 1: 13.10 |
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Chapter 13: Unit 4: 13.31,
13.32 |
| c. |
Compute
solutions to problems, represent answers in exact form, and determine the
reasonableness of answers. |
NOTE: Throughout the program students compute solutions to
problems, represent answers in exact form, and check to determine
reasonableness of solutions. See
sample lessons below: |
| |
Chapter 3: Unit 1: 3.01 |
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Chapter 3: Unit 6: 3.34, 3.35 |
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Chapter 8: Unit 1: 8.07 |
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Chapter 11: Unit 7: 11.40 |
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Chapter 12: Unit 8: 12.47 |
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Chapter 13: Unit 1: 13.06 |
| d. |
Calculate the measures of
the sides of a right triangle using the Pythagorean Theorem. |
Chapter 12: Unit 6: 12.38, 12.39,
12.40, 12.41, 12.42, 12.43, 12.44 |
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Chapter 12: Unit 11: 12.69, 12.70 |
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Chapter 12: Unit 12: 12.71
Chapter 13: Unit 1: 13.08 |
| Standard
II: Students will extend concepts of
proportion to represent and analyze linear relations. |
| Objective 2.1: Represent
and analyze the slope of a line. |
|
| a. |
Identify
the slope of a line when given points, a graph, or an equation. |
Chapter 5: Unit 4: 5.23, 5.24, 5.25,
5.26 |
| |
Chapter 5: Unit 5: 5.27,
5.28, 5.29, 5.30, 5.31, 5.33, 5.34, 5.35, 5.36, 5.37, 5.39, 5.40 |
| b. |
Identify
horizontal and vertical lines given the equations or slopes. |
Chapter 5: Unit 5: 5.31,
5.37, 5.39 |
| c. |
Determine
the effect of changes in slope or y-intercept tin y = mx + b . |
Chapter 5: Unit 5:
5.27, 5.28, 5.29 |
| d. |
Determine
and explain the meaning of slopes and intercepts using real-world examples. |
Chapter 5: Unit 4: 5.26
Chapter 5: Unit 5: 5.32, 5.35, 5.36, 5.38, 5.40 |
| Objective 2.2 Model and interpret problems having a constant
rate of change using linear functions. |
|
| a. |
Write
algebraic expressions or equations to generalize visual patterns, numerical
patterns, relations, data sets, or scatter plots. |
Chapter 5: Unit 5: 5.31,
5.32, 5.33, 5.34, 5.35, 5.36, 5.37, 5.39, 5.40
Chapter 5: Unit 6: 5.42, 5.43, 5.44, 5.45, 5.46, 5.47, 5.48
Chapter 5: Unit 8: 5.50, 5.51, 5.52, 5.53, 5.54, 5.55, 5.56, 5.57
Chapter 5: Unit 9: 5.58, 5.59, 5.60, 5.61, 5.64 |
| b. |
Represent linear equations
in slope-intercept form, y = mx + b, and standard form, Ax+ By =C. |
Chapter 5: Unit 5: 5.27, 5.28, 5.29,
5.30, 5.31, 5.32 , 5.33, 5.34, 5.36, 5.37, 5.39, 5.40 |
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Chapter 5: Unit 6: 5.41 |
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Chapter 6: Unit 1:
6.08 |
| c. |
Distinguish
between linear and non-linear functions by examining a table, equation, or
graph. |
Chapter 6: Unit 1:
6.00, 6.01, 6.02, 6.03, 6.04, 6.05, 6.06, 6.07, 6.08, 6.09, 6.11, 6.13, 6.14 |
| d. |
Interpret
the slope of a linear function as a rate of change in real-world situations. |
Chapter 5: Unit 8: 5.50,
5.51, 5.52, 5.53, 5.54, 5.55, 5.56, 5.57 |
| Objective 2.3: Represent
and analyze linear relationships using algebraic equations, expressions, and
graphs. |
|
| a. |
Write the
equation of a line when given two points or the slope and a point on the
line. |
Chapter 5: Unit 5: 5.33,
5.34, 5.35, 5.36, 5.39, 5.40 |
| b. |
Approximate the equation of
a line given the graph of a line. |
Chapter 5: Unit 5: 5.27, 5.28, 5.29,
5.30, 5.31, 5.33, 5.34, 5.35, 5.36, 5.39, 5.40 |
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Chapter 5: Unit 6: 5.41, 5.42, 5.43,
5.44, 5.45, 5.46, 5.47, 5.48 |
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Chapter 5: Unit 9: 5.62,
5.63, 5.64 |
| c. |
Identify the x- and y-intercepts from an
equation or graph of a line or a table
of values. |
Chapter 5: Unit 5:.29, 5.29, 5.30
Chapter 5: Unit 6: 5.41
Chapter 5: Unit 10: 10.79 |
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Chapter 5: Unit 13: 13.48 |
| d. |
Graph
linear relations and inequalities by plotting points, by finding x- and y
intercepts, or by using the slope and any point of the line. |
Chapter 5: Unit 5: 5.33,
5.34, 5.35
Chapter 5: Unit 8: 8.27, 8.28, 8.29, 8.30, 8.31, 8.32, 8.33, 8.34, 8.35 |
| Standard
III: Students will develop fluency with the language and operations of
algebra to analyze and represent relationships. |
| Objective 3.1: Simplify
polynomials and the quotient of monomials. |
|
| a. |
Simplify and evaluate monomial expressions and formulas. |
Chapter 1:
Unit 2: 1.12, 1.13, 1.14, 1.15, 1.16, 1.17, 1.18,
1.20, 1.21, 1.22 |
| Chapter
1: Unit 5: 1.30, 1.31, 1.32, 1.33, 1.34, 1.35, 1.36,
1.37 |
| Chapter
2: Unit 4: 2.31, 2.32, 2.33, 2.34, 2.35, 2.36, 2.37 |
| Chapter
9: Unit 1: 9.01, 9.02, 9.03, 9.04, 9.05, 9.06, 9.07,
9.08, 9.09, 9.10, 9.11 |
| Chapter
9: Unit 2: 9.12, 9.13, 9.14, 9.15, 9.16, 9.17, 9.18,
9.19, 9.20, 9.21, 9.22, 9.23 |
| Chapter
9: Unit 3: 9.24, 9.25, 9.26, 9.27, 9.28, 9.29, 9.30,
9.31, 9.32 |
| b. |
Add and subtract polynomials. |
Chapter 10: Unit 2: 10.14, 10.15,
10.16, 10.17, 10.18, 10.19 |
| c. |
Multiply monomials by a polynomial. |
Chapter 10: Unit 3: 10.20, 10.21,
10.22, 10.23, 10.24, 10.25, 10.26, 10.27, 10.28, 10.29 |
| d. |
Multiply binomials. |
Chapter 10:
Unit 3: 10.21, 10.22, 10.23, 10.24, 10.25, 10.26,
10.27, 10.28, 10.29 |
| Chapter
10: Unit 4: 10.29, 10.30, 10.31, 10.32, 10.33, 10.34 |
| e. |
Simplify the quotient of monomials using
positive exponents. |
Chapter 10: Unit 5: 10.35, 10.36,
10.37, 10.38, 10.39, 10.40, 10.41, 10.42 |
| Objective 3.2: Solve and
interpret linear equations and inequalities in various situations including
real-world problems. |
|
| a. |
Solve single-variable linear equations and
inequalities algebraically and graphically. |
Chapter 3:
Unit 8: 3.45, 3.46, 3.47, 3.48, 3.49, 3.50 |
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Chapter 3: Unit 10: 3.56, 3.57, 3.58, 3.59 |
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Chapter 5: Unit 5: 5.27, 5.28, 5.29, 5.30, 5.31, 5.33, 5.34, 5.35, 5.36,
5.39, 5.40 |
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Chapter 8: Unit 1: 8.01, 8.01, 8.02, 8.03, 8.04, 8.05, 8.06, 8.07, 8.08,
8.09, 8.10, 8.11, 8.12 |
| b. |
Solve real-world problems involving constant
rates of change. |
Chapter 5: Unit 8: 5.50, 5.51, 5.52,
5.53, 5.54, 5.55, 5.56, 5.57 |
| c. |
Solve equations for a specified variable. |
Chapter 5: Unit 8: 5.56, 5.57, 5.58,
5.59 |
| d. |
Solve proportions that include
algebraic first-degree expressions. |
Chapter 4:
Unit 1: 4.07 |
| Chapter
5: Unit 8: 5.50, 5.51, 5.52, 5.53, 5.54, 5.55, 5.56,
5.57 |
| Chapter
13: Unit 4: 13.35 |
| Objective 3.3: Solve and
interpret pairs of linear equations and inequalities. |
|
| a. |
Solve systems of two linear equations graphically and
algebraically with and without technology. |
Chapter 7: Unit 1: 7.00, 7.01, 7.02, 7.03, 7.04 |
|
Chapter 7: Unit 2: 7.05, 7.08, 7.09 |
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Chapter 7: Unit 3: 7.10 |
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Chapter 7: Unit 4: 7.11, 7.12, 7.13, 7.14, 7.15, 7.16, 7.17, 7.18, 7.20, 7.21 |
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Chapter 7: Unit 5: 7.22, 7.23, 7.24, 7.25, 7.26, 7.27, 7.28, 7.29, 7.30, 7.31 |
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Chapter 7: Unit 6: 7.32, 7.33, 7.34, 7.35, 7.36 |
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Chapter 7:
Unit 7: 7.37, 7.38, 7.39, 7.40, 7.41, 7.42, 7.43,
7.44, 7.45, 7.46 |
| b. |
Determine the number of possible solutions for
a system of two linear eqauations. |
Chapter 7: Unit 2: 7.05, 7.06, 7.07,
7.08, 7.09 |
| c. |
Graph a system of linear inequalities and
identify the solution. |
Chapter 8: Unit 4: 8.27, 8.28, 8.29,
8.30, 8.31, 8.32, 8.33, 8.34, 8.35 |
| Objective 3.4: Factor polynomials with common monomial factors
and factor simple quadratic expressions. |
|
| a. |
Find the greatest common monomial factor of a polynomial. |
Chapter 10: Unit 7: 10.51, 10.60 |
|
Chapter 10: Unit 8: 10.64 |
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Chapter
11: Unit 4: 11.26 |
| b. |
Factor trinomials with integer coefficients of the form x2 + bx + c . |
Chapter 10: Unit 7: 10.51, 10.52, 10.53, 10.54, 10.55, 10.56, 10.57, 10.58,
10.59, 10.60, 10.61, 10.62, 10.63 |
|
Chapter 10: Unit 8: 10.64, 10.65, 10.66, 10.67, 10.68, 10.69, 10.70 |
|
Chapter 11: Unit 1: 11.04 |
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Chapter
13: Unit 1: 13.04 |
| c. |
Factor the difference of two squares and
perfect square trinomials. |
Chapter 10: Unit 9: 10.71, 10.72 |
| Objective 3.5: Solve quadratic equations using factoring or by taking square roots. |
|
| a. |
Solve quadratic equations that can be
simplified to the form x2 = a where a ≥ 0 by taking square
roots. |
Chapter 13: Unit 2: 13.13, 13.14,
13.15, 13.16, 13.17, 13.18, 13.19, 13.20 |
| b. |
Solve quadratic equations using
factoring. |
Chapter 13: Unit 1: 13.00, 13.01, 13.02, 13.03, 13.04, 13.05, 13.06, 13.07,
13.08, 13.09, 13.10, 13.11, 13.12 |
| Chapter
13: Unit 3: 13.21, 13.22, 13.23, 13.24, 13.25, 13.26 |
| Chapter 13: Unit 4: 13.27, 13.28,
13.29, 13.30, 13.31, 13.32, 13.33, 13.34, 13.35, 13.36, 13.37 |
| c. |
Write a quadratic equation when
given the solutions. |
Chapter 13: Unit 1: 13.01, 13.02, 13.07 |
| Chapter 13: Unit 6: 13.45, 13.46,
13.47, 13.48, 13.49, 13.50, 13.51, 13.52, 13.53, 13.54 |
| Standard
IV: Students will understand concepts from statistics and apply statistical
methods to solve problems. |
| Objective 4.1: Objective 1: Summarize, display, and analyze
bivariate data. |
|
| a. |
Collect,
record, organize, and display a set of data with at least two variables. |
Chapter 4: Unit 1: 4.00, 4.01, 4.02,
4.03, 4.04, 4.05, 4.06, 4.07, 4.08, 4.09, 4.10, 4.11 |
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Chapter 4: Unit 2: 4.12, 4.13, 4.14,
4.15 |
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Chapter 4: Unit 3: 4.16, 4.17, 4.18,
4.19, 4.20, 4.21 |
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Chapter 4: Unit 4: 4.22, 4.23 |
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Chapter 4: Unit 5: 4.24 |
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Chapter 5: Unit 9: 5.58,
5.59, 5.60, 5.61 |
| b. |
Determine
whether the relationship between two variables is approximately linear or
non-linear by examination of a scatter plot. |
Chapter 5: Unit 9: 5.58,
5.59, 5.60, 5.61, 5.62, 5.64 |
| c. |
Characterize
the relationship between two linear related variables as having positive,
negative, or approximately zero correlation. |
Chapter 5: Unit 9: 5.62,
5.64 |
| Objective 4.2: Estimate,
interpret, and use lines fit to bivariate data. |
|
| a. |
Estimate the equation of a
line of best fit to make and test conjectures. |
Chapter 5: Unit 5: 5.27, 5.28, 5.29,
5.30, 5.31, 5.33, 5.34, 5.35, 5.36, 5.39, 5.40 |
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Chapter 5: Unit 9: 5.62,
5.63, 5.64 |
| b. |
Interpret the slope and y-intercept of a line through data. |
Chapter 5: Unit 4: 5.23, 5.24, 5.25,
5.26 |
| Chapter 5: Unit 5: 5.27,
5.28, 5.29, 5.30, 5.31, 5.33, 5.34, 5.35, 5.36, 5.39, 5.40 |
| Chapter 5: Unit 9: 5.62,
5.63, 5.64 |
| c. |
Predict y-values for given x-values when appropriate
using a line fitted to bivariate numerical data. |
Chapter 5: Unit 9: 5.62, 5.63, 5.64 |
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