TCAP Grade 6 The Number System Practice

What the test measures

The Number System skills

6.NS.A.1 Interpret and compute quotients of fractions
6.NS.B.2 Fluently divide multi-digit numbers using the standard algorithm
6.NS.B.3 Fluently add, subtract, multiply, and divide multi-digit decimals
6.NS.B.4 Find common factors and multiples
6.NS.B.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values
6.NS.C.6 Understand a rational number as a point on the number line
6.NS.C.7 Understand ordering and absolute value of rational numbers
6.NS.C.8 Solve real-world and mathematical problems by graphing points in all four quadrants

Standards basis

Tennessee Academic Standards for Mathematics — Tennessee

How the TCAP reports it

TCAP math is Tennessee’s state assessment program and its blueprints are aligned to Tennessee Academic Standards, which closely mirror the Common Core content structure in grades 3-8 and the CCSS-style high school conceptual categories. The blueprint page lists the current 2025-26 assessment overviews, including Math Grade 2, Grades 3-5, Grades 6-8, and Math EOC. [Tennessee Department of Education](https://www.tn.gov/education/districts/lea-operations/assessment/tcap-blueprints.html)

Blueprint & weighting

Published TCAP math blueprints assign content emphasis by grade/course, but the exact percentage table was not recoverable from the accessible blueprint page in this session. The state blueprint landing page confirms the math overviews but did not expose the PDF links in the fetched page content. [Tennessee Department of Education](https://www.tn.gov/education/districts/lea-operations/assessment/tcap-blueprints.html)

Official sources

Tennessee Department of Education TCAP Blueprints
Tennessee Education Glossary (academic standards entry)

Practice by skill

Topics mapped to this domain

Try it now

8 free questions · 0/0 correct

Practice playeasy

What is $|0|$ ?

$0$ is its own distance from $0$ , so $|0| = 0$ .

Practice playeasy

What is $6.60 \times 6$ ?

$6.60 \times 6 = 39.6$ .

Practice playeasy

What is $\dfrac{3}{6} \times \dfrac{3}{7}$ ?

Multiply across: $\dfrac{3 \times 3}{6 \times 7} = \dfrac{9}{42} = \dfrac{3}{14}$ .

Practice playmedium

Which integer is closest to $-\dfrac{29}{6}$ on the real number line?

$-\dfrac{29}{6} \approx -4.83$ . Compare distances: $|{-5} - (-4.83)| \approx 0.17$ and $|{-4} - (-4.83)| \approx 0.83$ . The closest integer is $-5$ .

Practice playeasy

What is $|5 - 4|$ ?

First compute the difference: $5 - 4 = 1$ . Then take the absolute value: $|1| = 1$ .

Practice playeasy

What is $6.07 - 4.71$ ?

$6.07 - 4.71 = 1.36$ .

Practice playeasy

What is $\dfrac{3}{4} \div \dfrac{2}{3}$ ?

Multiply by the reciprocal: $\dfrac{3}{4} \times \dfrac{3}{2} = \dfrac{9}{8} = \dfrac{9}{8}$ .

Practice playhard

How many integers satisfy $-\dfrac{11}{2} < x \leq 4$ ?

$-\dfrac{11}{2} = -5.5$ , so integers greater than $-5.5$ start at $-5$ ; the closed upper bound includes $4$ . Integers: $-5, -4, \ldots, 0, \ldots, 4$ ; $0$ is an integer and must be counted. Total: $4 - (-5) + 1 = 10$ ; the $+1$ counts both $-5$ and $4$ inclusive.