Partnership for Assessment of Readiness for College and Careers (PARCC) Mathematics: Grades 3-8 Content Syllabus

Mathematics: Grades 3-8 Content syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Mathematics: Grades 3-8 Content in Partnership for Assessment of Readiness for College and Careers (PARCC), not a summary of it.

1. 1

   Operations and Algebraic Thinking

   3 topics

   • Multiplication and Division Concepts
     • Interpreting products and quotients
     • Properties of operations as strategies
   • Patterns and Expressions
     • Generating and analyzing numerical patterns
     • Writing and interpreting expressions
   • Solving Word Problems
     • Multi-step problems with the four operations
     • Assessing reasonableness of answers
2. 2

   Number and Operations

   3 topics

   • Base-Ten Operations
     • Place value understanding
     • Multi-digit arithmetic algorithms
   • Fractions
     • Equivalence and comparison
     • Addition, subtraction, multiplication, and division of fractions
   • The Number System
     • Rational numbers and the coordinate plane
     • Operations with positive and negative numbers
     • Irrational numbers and approximations
3. 3

   Ratios, Proportions, and Expressions/Equations

   3 topics

   • Ratios and Proportional Relationships
     • Unit rates and equivalent ratios
     • Percent problems
     • Proportional relationships in graphs and tables
   • Expressions and Equations
     • Equivalent expressions and properties
     • One- and two-step equations and inequalities
     • Linear equations and systems
   • Functions
     • Defining and comparing functions
     • Linear function models
4. 4

   Geometry and Measurement

   3 topics

   • Geometric Measurement
     • Area, surface area, and volume
     • Perimeter and circumference
   • Geometric Properties and Reasoning
     • Angle relationships
     • Scale drawings and constructions
   • Transformations and the Pythagorean Theorem
     • Congruence and similarity via transformations
     • Applying the Pythagorean Theorem
5. 5

   Statistics and Probability

   3 topics

   • Data Representation and Interpretation
     • Line plots, histograms, and box plots
     • Measures of center and variability
   • Statistical Variability
     • Distribution shape and spread
     • Sampling and inference
   • Probability Models
     • Simple and compound events
     • Approximating probabilities from data

Mathematics: Grades 3-8 Content flashcards for Partnership for Assessment of Readiness for College and Careers (PARCC)

23 of 51 cards from the Mathematics: Grades 3-8 Content deck — real questions with worked answers.

1. What is the result of a multiplication called, and what are the two numbers being multiplied called?

   The result is the product; the numbers being multiplied are factors.

2. What is the inverse operation of multiplication, and how can a division fact be checked?

   Division is the inverse of multiplication. Check 24 / 6 = 4 by confirming 4 x 6 = 24.

3. State the Commutative, Associative, and Distributive properties of multiplication.

   Commutative: a x b = b x a. Associative: (a x b) x c = a x (b x c). Distributive: a x (b + c) = a x b + a x c.

4. In a division problem, what are the dividend, divisor, quotient, and remainder?

   Dividend is the number being divided, divisor is the number you divide by, quotient is the result, and remainder is what is left over.

5. What is the difference between an arithmetic pattern and a geometric pattern?

   An arithmetic pattern adds/subtracts a constant each term (e.g., 2,5,8,11); a geometric pattern multiplies/divides by a constant each term (e.g., 3,6,12,24).

6. What is the order of operations (PEMDAS)?

   Parentheses, Exponents, Multiplication and Division (left to right), then Addition and Subtraction (left to right).

7. What is the difference between an expression and an equation?

   An expression is a combination of numbers, variables, and operations with no equals sign; an equation states that two expressions are equal using an equals sign.

8. In word problems, what operations do the key phrases 'in all', 'difference', 'each', and 'shared equally' typically signal?

   'In all' signals addition, 'difference' signals subtraction, 'each' often signals multiplication, and 'shared equally' signals division.

9. What does place value mean in the base-ten system, and how do adjacent places relate?

   Each digit's value depends on its position; each place is 10 times the value of the place to its right (and 1/10 of the place to its left).

10. How do you round a number to a given place value?

    Look at the digit to the right of the rounding place; if it is 5 or more round up, if 4 or less round down, then replace digits to the right with zeros.

11. What is the standard algorithm for multiplying multi-digit numbers based on?

    Place value and the distributive property—multiplying each place and adding partial products.

12. What is a fraction, and what do the numerator and denominator represent?

    A fraction represents part of a whole; the numerator (top) is the number of parts taken, and the denominator (bottom) is the total number of equal parts.

13. What are equivalent fractions and how do you create one?

    Equivalent fractions name the same value; create one by multiplying or dividing the numerator and denominator by the same nonzero number, e.g., 1/2 = 2/4.

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

    Find a common denominator, rewrite each fraction as an equivalent fraction with that denominator, then add or subtract the numerators.

15. How do you multiply two fractions?

    Multiply the numerators together and the denominators together: (a/b) x (c/d) = ac/bd.

16. How do you divide by a fraction?

    Multiply by its reciprocal: (a/b) / (c/d) = (a/b) x (d/c).

17. What is the reciprocal of a number?

    The reciprocal of a/b is b/a; a number times its reciprocal equals 1.

18. How do you convert an improper fraction to a mixed number?

    Divide the numerator by the denominator; the quotient is the whole number and the remainder over the denominator is the fraction part.

19. What is a rational number?

    Any number that can be written as a fraction a/b where a and b are integers and b is not zero, including terminating and repeating decimals.

20. What are integers, and what is the absolute value of a number?

    Integers are whole numbers and their opposites (...,-2,-1,0,1,2,...). Absolute value is a number's distance from zero, always nonnegative, e.g., |-5| = 5.

21. State the rules for the sign of a product or quotient of two nonzero numbers.

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

22. How do you add two integers with different signs?

    Subtract the smaller absolute value from the larger and keep the sign of the number with the larger absolute value.

23. What is a ratio, and how does it differ from a rate?

    A ratio compares two quantities (a:b); a rate is a ratio comparing quantities with different units, and a unit rate has a denominator of 1.

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