Smarter Balanced Assessment (SBAC) Mathematics: Concepts and Procedures Syllabus

Mathematics: Concepts and Procedures syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Mathematics: Concepts and Procedures in Smarter Balanced Assessment (SBAC), not a summary of it.

1. 1

   Number Sense and Operations

   4 topics

   • Place Value and Whole Numbers
     • Reading, writing, and comparing numbers
     • Multi-digit addition and subtraction
   • Multiplication and Division
     • Strategies and standard algorithms
     • Factors, multiples, and prime numbers
   • Fractions
     • Equivalence and comparison
     • Operations with fractions
   • Decimals and Percentages
     • Decimal operations and rounding
     • Percent of a quantity
2. 2

   Ratios, Proportional Relationships, and the Number System

   4 topics

   • Ratios and Unit Rates
     • Equivalent ratios and tables
     • Unit rate and price comparison
   • Proportional Reasoning
     • Constant of proportionality
     • Proportions in scale and maps
   • Rational Numbers and Integers
     • Operations with negative numbers
     • Absolute value and the number line
   • Exponents and Roots
     • Properties of exponents
     • Square and cube roots
3. 3

   Expressions, Equations, and Functions

   4 topics

   • Algebraic Expressions
     • Writing and evaluating expressions
     • Combining like terms and distributing
   • Linear Equations and Inequalities
     • Solving one- and two-step equations
     • Graphing inequalities on a number line
   • Systems of Equations
     • Solving by substitution and elimination
     • Interpreting solutions graphically
   • Functions
     • Defining and evaluating functions
     • Linear versus nonlinear functions
4. 4

   Geometry and Measurement

   4 topics

   • Shapes and Their Properties
     • Classifying polygons and angles
     • Lines, rays, and segments
   • Area, Surface Area, and Volume
     • Area of triangles and quadrilaterals
     • Volume of prisms and cylinders
   • The Coordinate Plane
     • Plotting points and distance
     • Transformations and reflections
   • The Pythagorean Theorem
     • Finding missing side lengths
     • Applications and distance
5. 5

   Statistics and Probability

   3 topics

   • Representing and Interpreting Data
     • Bar graphs, line plots, and histograms
     • Box plots and scatter plots
   • Measures of Center and Spread
     • Mean, median, and mode
     • Range and variability
   • Probability of Events
     • Simple and compound probability
     • Theoretical versus experimental

Mathematics: Concepts and Procedures flashcards for Smarter Balanced Assessment (SBAC)

20 of 50 cards from the Mathematics: Concepts and Procedures deck — real questions with worked answers.

1. What is the value of the digit 7 in the number 4,7 placed as 4,729 — specifically the 7?

   700 (the 7 is in the hundreds place, so it represents 7 × 100 = 700).

2. In a multi-digit whole number, how does the value of a digit change as it moves one place to the left?

   It becomes 10 times greater; each place to the left is worth 10 times the place to its right.

3. What is the standard process for multiplying a multi-digit number using the standard algorithm?

   Multiply each digit of one factor by each digit of the other, recording partial products shifted by place value, then add the partial products.

4. In the division statement 84 ÷ 5 = 16 R4, name the dividend, divisor, quotient, and remainder.

   Dividend = 84, divisor = 5, quotient = 16, remainder = 4.

5. What is a fraction, and what do its numerator and denominator represent?

   A fraction a/b represents a parts of a whole divided into b equal parts; the numerator (a) is the count of parts, the denominator (b) is the total equal parts.

6. How do you add or subtract fractions with unlike denominators?

   Rewrite them with a common denominator (often the LCD), then add or subtract the numerators and keep the common denominator.

7. How do you multiply two fractions, and how do you divide them?

   Multiply: multiply numerators and multiply denominators (a/b × c/d = ac/bd). Divide: multiply by the reciprocal of the divisor (a/b ÷ c/d = a/b × d/c).

8. What is an equivalent fraction, and how do you create one?

   A fraction representing the same value; create it by multiplying or dividing both numerator and denominator by the same nonzero number.

9. How do you convert a fraction to a decimal?

   Divide the numerator by the denominator.

10. How do you convert a decimal to a percent, and a percent to a decimal?

    Decimal to percent: multiply by 100 and add the % sign. Percent to decimal: divide by 100 (move the decimal point two places left).

11. What is the formula for finding a percent of a number?

    Part = percent (as a decimal) × whole. For example, 20% of 50 = 0.20 × 50 = 10.

12. How do you compare and order decimals such as 0.7, 0.07, and 0.75?

    Align by place value (compare tenths, then hundredths). 0.07 < 0.7 < 0.75.

13. What is a ratio, and what are the common ways to write one?

    A ratio compares two quantities; it can be written as a:b, a to b, or as the fraction a/b.

14. What is a unit rate, and how do you find it?

    A rate with a denominator of 1; find it by dividing the first quantity by the second (e.g., 120 miles in 2 hours = 60 miles per hour).

15. What does it mean for two quantities to be in a proportional relationship?

    Their ratio is constant; y = kx, where k is the constant of proportionality, and the graph is a straight line through the origin.

16. How do you solve a proportion such as a/b = c/d for an unknown?

    Use cross-multiplication: a × d = b × c, then solve the resulting equation.

17. What are rational numbers?

    Numbers that can be written as a fraction a/b where a and b are integers and b ≠ 0; includes integers, terminating decimals, and repeating decimals.

18. What is the rule for adding two integers with different signs?

    Subtract the smaller absolute value from the larger, and give the result the sign of the number with the larger absolute value.

19. What is the result of multiplying or dividing two integers with the same sign versus different signs?

    Same signs give a positive result; different signs give a negative result.

20. What is the absolute value of a number?

    Its distance from zero on the number line, always nonnegative (e.g., |−6| = 6 and |6| = 6).

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