VTCAP Grade 6 The Number System Practice

What the test measures

The Number System skills

Apply and extend previous understandings of multiplication and division to divide fractions by fractions
Compute fluently with multi-digit numbers and find common factors and multiples
Apply and extend previous understandings of numbers to the system of rational numbers

Standards basis

Common Core State Standards for Mathematics (CCSS-M) — Vermont

How the VTCAP reports it

Vermont administered the Smarter Balanced summative through spring 2022, then replaced it with the Cognia-developed Vermont Comprehensive Assessment Program (VTCAP) beginning spring 2023 — this landing slug predates the switch. VTCAP mathematics is an adaptive, CCSS-M-aligned assessment in grades 3-9. It is NOT a Smarter Balanced administration: its reporting categories are groupings of the CCSS grade-level domains (e.g. 'The Number System, Expressions and Equations'), not SBAC claims, though two cross-grade Mathematical Practices indicators ('Problem Solving, Reasoning, and Argument'; 'Modeling, Patterns, and Structure') echo the old claim structure. Per the test specifications, the grades 3-8 test may assess any CCSS-M standard at the grade; the grade 9 test assesses a prioritized subset of the high school CCSS-M within the conceptual categories of Number and Quantity, Algebra, Functions, Geometry, and Statistics and Probability (the assessed focus areas are published in the grade 9 Performance Level Descriptors).

Blueprint & weighting

VTCAP Test Specifications (Spring 2026) operational test blueprint, target percent of points per grade — Grade 3: OA 24-35%, NBT 10-14%, NF 16-20%, MD 22-29%, G 6-10%, constructed-response Mathematical Practices 12%. Grade 4: OA 20-31%, NBT 16-20%, NF 20-31%, MD 12-20%, G 6-10%, practices 12%. Grade 5: OA 14-22%, NBT 14-25%, NF 22-29%, MD 20-27%, G 8-16%, practices 12%. Grade 6: RP 15-22%, NS 15-22%, EE 15-22%, G 11-19%, SP 11-19%, practices 11%. Grade 7: RP 15-22%, NS 11%, EE 15-30%, G 11-19%, SP 19-22%, practices 11%. Grade 8: F 18-29%, NS 7%, EE 20-31%, G 18-29%, SP 18-22%, practices 11%. Grade 9 (all machine-scored): Number and Quantity/Algebra 18-27%, Algebra/Functions 31-40%, Geometry 20-29%, Statistics and Probability 13-20%; the two practices indicators are dual-aligned targets of >18% of points each. Identical figures appear in the Spring 2025 specifications.

Official sources

VTCAP Test Specifications, Spring 2026 (Vermont AOE / Cognia)
VTCAP Test Specifications, Spring 2025 (Vermont AOE / Cognia)
VTCAP Performance Level Descriptors: Mathematics, Grades 3-9 (Vermont AOE)

Practice by skill

Topics mapped to this domain

Try it now

8 free questions · 0/0 correct

Practice playeasy

What is $7.00 + 1.62$ ?

$7.00 + 1.62 = 8.62$ .

Practice playeasy

What is $\dfrac{3}{6} \times \dfrac{5}{8}$ ?

Multiply across: $\dfrac{3 \times 5}{6 \times 8} = \dfrac{15}{48} = \dfrac{5}{16}$ .

Practice playeasy

What is $|-2|$ ?

Absolute value gives the non-negative distance from $0$ , so $|-2| = 2$ .

Practice playmedium

On the real number line, how many integers are strictly between $-\dfrac{91}{5}$ and $-\dfrac{12}{4}$ ?

Convert: $-\dfrac{91}{5} = -18.2$ and $-\dfrac{12}{4} = -3$ . Integers $n$ with $-18.2 < n < -3$ are $-18, -17, \ldots, -4$ . Count with $-4 - (-18) + 1$ : subtracting endpoints gives the gap between them; the $+1$ counts both $-18$ and $-4$ inclusive.

Practice playeasy

What is $9.6 \div 6$ ?

Result: $1.6$ .

Practice playeasy

What is $\dfrac{3}{9} \div \dfrac{5}{8}$ ?

Multiply by the reciprocal: $\dfrac{3}{9} \times \dfrac{8}{5} = \dfrac{24}{45} = \dfrac{8}{15}$ .

Practice playeasy

What is $|8|$ ?

The absolute value of a non-negative number is itself: $|8| = 8$ .

Practice playmedium

On the real number line, how many integers are strictly between $\dfrac{7}{3}$ and $\dfrac{47}{5}$ ?

Convert: $\dfrac{7}{3} \approx 2.33$ and $\dfrac{47}{5} = 9.4$ . Integers $n$ with $2.33 < n < 9.4$ are $3, 4, 5, 6, 7, 8, 9$ . Count with $9 - 3 + 1$ : subtracting endpoints gives the gap between them; the $+1$ counts both $3$ and $9$ inclusive.