GRADE 5 - Mathematics 5.OA.1/5.OA.2/5.OA.3 Practice Items

Oct 10, 2026

Uploaded by hdkawk

GRADE 5 mathematics sample items outline proficiency expectations aligned to Illinois Assessment of Readiness (IAR) and classroom instruction. The tasks emphasize evaluating numerical expressions with multiple grouping symbols, writing and interpreting expressions with parentheses, and completing patterns using given rules. Items include reasoning-focused questions where students must explain thinking, translate situations into algebraic expressions, and identify values from multi-step computations. Additional sections address base-ten concepts and decimal understanding using place value.

LanguageEnglish

CategoryExam

FormatPDF

Pages23

Reading Time58 min

AccessFree to download

Operations & Algebraic Thinking

5.OA.1 Evaluate numerical expressions with grouping symbols

5.OA.2 Write and interpret expressions involving parentheses

5.OA.3 Generate and complete patterns

Number & Operations in Base Ten

5.NBT.1 Place value in multi-digit numbers

5.NBT.3a Read and write decimals to thousandths

Samples to Success Sample items provide valuable insight into how students engage with different texts, tasks, and contexts, highlighting the types of opportunities they need for success in the classroom. These items offer a shared reference point for understanding proficiency expectations, complementing the assessment's role in measuring learning. By analyzing items alongside performance data, educators can gain a deeper understanding of students' strengths and areas for growth. Students thrive in environments rich with diverse materials, challenges that vary in task type, and multiple avenues for demonstrating understanding. High-quality instruction, aligned with the learning goals, is the most effective way to support students' growth and prepare them for success. GRADE 5 The items featured in this rubric are a mix of items representative of those found on the Illinois Assessment of Readiness (IAR) and items appropriate for classroom instruction to support and build the skills measured on the IAR. The distinction between a student scoring proficient and above proficient on the IAR is primarily determined by the total points earned on items that require modeling and/or reasoning. Students who can effectively explain and demonstrate their thinking are most likely to earn these points. MATHEMATICS 5.OA.1 Expectation at Proficient: Evaluate numerical expressions with multiple grouping symbols. Operations & Algebraic Thinking Below Proficient Approaching Proficient Proficient Above Proficient Which operation should be done first to determine the value of the following expression? 12 − (3 × 2) + 5 A. 12 − 3 B. 3 × 2 C. 2 + 5 D. 12 − 5 What is the value of the expression shown? 12 − (3 × 2) + 5 A. 1 B. 11 C. 12 D. 23 What is the value of the expression shown? 12 − ((3 × 2) + 5) Answer: 1 A farmer has 12 apples in a basket. He gives 2 apples to each of his 3 children. Then, he adds 5 more apples to the basket. Write an expression to determine the resulting number of apples in the basket. Answer: 12−(3×2)+5 How many apples are in the basket? Answer: 11 Operations & Algebraic Thinking Expectation at Proficient: Write and interpret expressions involving parentheses. Which expression represents“the product of 5 and 3?” A. 5 + 3 B. 5 − 3 C. 5 × 3 D. 5 ÷ 3 Which expression represents “7 more than the product of 5 and 3?” A. (7 + 5) × 3 B. ( × 3) + 7 C. 5 + (3 × 7) D. 3 + (5 × 7) Write an expression that represents “7 more than the product of 5 and 3.” Answer: ( × 3) + 7 Mabel solves a problem by adding 7 to the product of 5 and 3. Write an expression Mabel could use to solve the problem. Answer: (5×3)+7 What is the answer to the problem? Answer: 22 5.OA.3 Below Proficient Approaching Proficient Proficient Above Proficient Compete the pattern given the rule “add 2.” 9, 11 , 13, 15 Complete the pattern given the rule “multiply by 3.” 4, 12 , 36 , 108 Complete the table of values given the two patterns shown. Pattern A: add 2 Pattern B: add 6 Complete the table of values given the two patterns shown. Pattern A: add 2 Pattern B: add 6 | Pattern A | 9 | 11 | 13 | 15 | | --- | --- | --- | --- | --- | | Pattern B | 27 | 33 | 39 | 45 | | Pattern A | 9 | 11 | 13 | 15 | | --- | --- | --- | --- | --- | | Pattern B | 27 | 33 | 39 | 45 | Complete the statement comparing corresponding values in Pattern A the and Pattern B. Each term in Pattern B is 3 times the corresponding term in Pattern A. 5.OA.2 Below Proficient Approaching Proficient Proficient Above Proficient 5 5 Operations & Algebraic Operations Expectation at Proficient: Generate two numerical patterns using two given rules. Plot ordered pairs on a coordinate plane and identify apparent patterns or relationships between the two given rules. Number & Operations in Base Ten 5.NBT.1 Below Proficient Approaching Proficient Proficien

FAQs

How does the rubric determine a student’s proficiency on IAR math items?

The distinction between proficient and above proficient is primarily determined by the total points earned on items that require modeling and/or reasoning.

What skills are students expected to demonstrate in 5.OA.1?

Students evaluate numerical expressions with multiple grouping symbols and determine which operations occur first to find the value.

What types of patterns do Grade 5 students complete in 5.OA.3?

Students complete sequences using rules such as adding a constant or multiplying by a factor, and they fill tables comparing corresponding values across two patterns.

Oct 10, 2026

Uploaded by hdkawk