Teaching operations and algebraic thinking (O&AT) in 3rd, 4th, and 5th grade is essential for building a strong mathematical foundation. Understanding how these standards connect across grade levels helps teachers scaffold instruction effectively.
However, the thing with operations and algebraic thinking standards in 3rd-5th grade is that they aren’t very linear. This domain is kind of all over the place.
In 3rd grade, operations and algebraic thinking standards focus on multiplication and division. However, most of those standards move over to the place value domain in 4th and 5th grade because we want students to use their knowledge of place value to compute more significant numbers.
So while the standards in this domain aren’t as vertical as other domains in 3rd,4th, and 5th grade common core math standards, there are still benefits to looking at each grade level’s standards to see how they connect to the overall math picture.
This guide explores key concepts and their progression for seamless transitions between grades. Each standard is linked to a grade-level standards-based activity that will help students practice the skill.
Operations and Algebraic Thinking Goals
3rd Grade: MULTIPLICATION and DIVISION! Operations and algebraic thinking standards are a huge focus in 3rd grade, and almost all standards focus on learning and understanding multiplication and division. Students need to represent and solve problems with multiplication and division, understand how math rules apply to multiplication and division, and master multiplication and division math facts within 100.
There also are standards that involve solving arithmetic problems with the four operations and understanding arithmetic patterns.
4th grade: In 4th grade, the goal is to solve a whole number of math problems using the four operations. This goal has continued since 3rd grade operations and algebraic thinking standards. Students also work towards familiarity with factors and multiples and analyzing patterns.
5th grade: All operations and algebraic thinking standards in 5th grade are additional clusters. They are meant to teach needed skills but aren’t tied to the significant skills learned in 5th-grade math. Students are working to understand numerical expressions and analyze patterns.
Operations and algebraic thinking standards are unique in that they don’t vertically align very much between the three grades. Overall, the only vertically aligned standards involve patterns. However, the standards in grade 3 are essential in providing students with a basis for skills in multiple other math domains in 4th and 5th grade.
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Operations and Algebraic Thinking: Multiplication and Division
Multiplication and division standards are major clusters in 3rd and 4th grade operations and algebraic thinking standards. Seven 3rd-grade multiplication standards vertically align to three 4th-grade standards. So, let’s start with the 4th-grade standards first.
4th Grade:
The first two 4th grade operations and algebraic thinking standards focus on multiplicative comparisons. What is a multiplicative comparison? A multiplicative comparison compares two numbers by showing how many times one number is larger or smaller than the other. For example, “6 is 3 times as many as 2″ can be written as 6 = 3 × 2.
4.OA.A.1: The first 4th grade OA standard requires students to interpret a multiplication problem as a multiplicative comparison and to be able to write comparisons as a multiplication equation.
4.OA.A.2: This standard requires students to use multiplication or division to solve word problems about comparing quantities, with strategies like drawing pictures or writing equations to find the unknown number and recognizing when the problem is about multiplication comparison rather than additive comparison. For example, students may use a tape diagram to display the multiplicative comparison of 3 times as many as 2 to solve a word problem.
4.OA.B.4: The other 4th grade operations and algebraic thinking standard involving multiplication require students to find all the factor pairs of numbers between 1 and 100, and know that a number is a multiple of each factor. Students must also recognize whether a whole number between 1 and 100 is prime or composite.
3rd Grade:
3rd grade operations and algebraic thinking standards focus on multiplication and division. So let’s go through each one and then connect it to the 4th-grade standard it supports.
3.OA.A.1: Understand products of whole numbers means finding the total when you have a certain number of equal groups. For example, 4 × 5 is four groups of five objects. This vertically aligns with 4.OA.A.1.
3.OA.A.2: Understand division as splitting a number into equal groups or finding how many are in each group. For example, 35 ÷ 7 is 36 items split evenly between 7 groups. There is no 4th or 5th grade vertically aligned standard for this 3rd grade standard.
3.OA.A.3: Use multiplication and division up to 100 to solve word problems with equal groups, arrays, or measurements. The goal is for students to use tools (tape diagrams, drawings, ect.) to solve these word problems. This vertically aligns with 4.OA.A.1 and 4.OA.A.2 in support of multiplicative comparisons.
3.OA.A.4: Find the missing number in a multiplication or division equation with three numbers. For example… fact families! This standard vertically aligns to 4th grade OA.A.1, OA.A.2, and OA.B.4 (factors).
3.OA.B.5: Use properties of operations to multiply and divide numbers. For example, multiply and divide numbers using the commutative, associative, distributive, and identity properties of multiplication. This does not vertically align to a 4th or 5th grade operations and algebraic thinking standard.
3.OA.B.6: Understand division as finding the missing number in a multiplication problem. For example, n × 8 = 24 is finding what number, multiplied by 8, equals 24. This standard vertically aligns with 4th grade OA.A.1 and 2.
3.OA.B.7: Quickly and accurately multiply and divide numbers up to 100, using strategies like knowing how multiplication and division are related. What does this mean? Learn your facts! This standard vertically aligns with 4.OA.B.4 (it will help them learn their factors and multiples).
It is important to note that this is the FINAL multiplication and division standard addressed in this domain. Most of our time needs to be spent building the conceptual understanding of multiplication and division BEFORE students work to learn their facts.
Operations and Algebraic Thinking: Word Problems
In 3rd grade, students work to solve word problems that need two steps using addition, subtraction, multiplication, or division. They use equations with a letter for the unknown number and check if answers make sense by estimating or rounding.
In 4th grade students work to solve multi-step word problems with whole numbers using addition, subtraction, multiplication, or division, including those with remainders. Use equations with a letter for the unknown number and check if answers make sense by estimating or rounding.
The 4th grade standard builds on the 3rd grade standard by opening the problem up to multiple steps and includes division with remainders. There is no 5th grade standard that vertically aligns to these 3rd and 4th grade standards. If your students are struggling with any of these concepts, look at this post to discover a tool that could help support their learning.
Operations and Algebraic Thinking: Patterns
These are the only operations and algebraic thinking standards that vertically align in 3rd, 4th, and 5th grade.
In 3rd grade, students recognize computation patterns, such as addition and multiplication tables, and explain them using math rules.
In 4th grade students create a number or shape pattern by following a rule, notice new features in the pattern, and explain why it repeats or changes in a certain way.
In 5th grade, students create two number patterns by following given rules, finding relationships between the numbers, and plotting them as ordered pairs on a coordinate plane.
These standards build on what students can do with patterns. In 3rd grade, they are working on recognizing them; in 4th grade, they are creating patterns; and in 5th grade, they are creating patterns and applying them. In all grades, students are expected to explain the pattern.
Operations and Algebraic Thinking: 5th Grade
All the 5th grade operations and algebraic thinking standards are additional clusters. That means they are extra work in the grade, but not the overall math focus.
5.OA.A.1: Use parentheses, brackets, or braces in math expressions to show the order of operations and solve them correctly. For example, solve 4 + (34 – 10).
5.OA.A.2: Write math expressions to show calculations and understand their meaning without solving them. For example, write an expression for add 10 and 8, then multiply by 2.
These two 5th grade standards will lay a foundation for major 6th grade math clusters.
Understanding how operations and algebraic thinking progress across 3rd, 4th, and 5th grade ensures teachers can effectively support student learning. Although these standards don’t often vertically align through all three grade levels, the skills learned and practiced are applied in every other math domain.
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