IAR Grades 6-8 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

Illinois Learning Standards incorporating the Common Core State Standards (CCSS-M) — Illinois

How the IAR reports it

IAR is Illinois’ state assessment built on the Illinois Learning Standards incorporating the Common Core, and its math design follows the PARCC-style blueprinting approach used for grades 3–8. ISBE’s resources page points to the PARCC mathematics model content frameworks, and the IAR page says the math evidence statements are aligned directly to the Common Core State Standards.

Blueprint & weighting

IAR uses the PARCC-derived / Illinois Assessment of Readiness (IAR) framework (by grade domains structure).

Official sources

Illinois State Board of Education – Illinois Assessment of Readiness
Illinois State Board of Education – Resources

Practice by skill

Topics mapped to this domain

Try it now

8 free questions · 0/0 correct

Practice playeasy

What is $3.35 + 6.75$ ?

$3.35 + 6.75 = 10.1$ .

Practice playeasy

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

Multiply across: $\dfrac{3 \times 6}{6 \times 7} = \dfrac{18}{42} = \dfrac{3}{7}$ .

Practice playeasy

What is $|-3|$ ?

Absolute value gives the non-negative distance from $0$ , so $|-3| = 3$ .

Practice playeasy

Which of the following values lies strictly between $-\dfrac{19}{4}$ and $\dfrac{11}{2}$ on the real number line?

The interval is open: $-\dfrac{19}{4} = -4.75$ and $\dfrac{11}{2} = 5.5$ , so values must satisfy $-4.75 < x < 5.5$ . Check each choice: $-5 < -4.75$ (outside), $-4$ is between the bounds, $\dfrac{11}{2}$ equals the upper endpoint (not strict), and $-\dfrac{19}{4}$ equals the lower endpoint (not strict).

Practice playeasy

What is $28.7 \div 7$ ?

Result: $4.1$ .

Practice playeasy

What is $\dfrac{3}{7} \div \dfrac{3}{7}$ ?

Multiply by the reciprocal: $\dfrac{3}{7} \times \dfrac{7}{3} = \dfrac{21}{21} = \dfrac{1}{1}$ .

Practice playeasy

What is $|17|$ ?

The absolute value of a non-negative number is itself: $|17| = 17$ .

Practice playeasy

Which value is greatest on the real number line?

Compare positions: $\dfrac{9}{5} = 1.8$ , $-\dfrac{2}{3} \approx -0.67$ , $\dfrac{5}{8} = 0.625$ , and $-\dfrac{7}{12} \approx -0.58$ . The greatest is $\dfrac{9}{5}$ .