IAR Grades 3-5 Operations and Algebraic Thinking. Practice it free.

Apply and extend multiplication and division concepts and use them to solve problems. This Grades 3-5 reporting domain maps to 3 practice skills and 8 representative questions from the playable bank.

Grades 3-53 mapped skills

What the test measures

Operations and Algebraic Thinking skills

represent and solve problems involving multiplication and division
understand properties of multiplication and the relationship between multiplication and division
multiply and divide within 100
solve problems involving the four operations, and identify and explain patterns in arithmetic

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 $132 \div 12$ ?

$12 \times 11 = 132$ , so $132 \div 12 = 11$ .

Practice playeasy

What is $4 \times 2$ ?

$4 \times 2 = 8$ .

Practice playeasy

Which property is $6 \times 1 = 6$ ?

$6 \times 1 = 6$ shows multiplying by $1$ does not change the answer, so the expressions are equal in value. This is the identity property.

Practice playeasy

What is $0 \div 1$ ?

$1 \times 0 = 0$ , so $0 \div 1 = 0$ .

Practice playeasy

What is $1 \times 1$ ?

$1 \times 1 = 1$ .

Practice playeasy

Which property is $(2 \times 3) \times 4 = 2 \times (3 \times 4)$ ?

$(2 \times 3) \times 4 = 2 \times (3 \times 4)$ shows the grouping of the multiplication does not change the answer, so the expressions are equal in value. This is the associative property.