OREGON MATH STANDARDS (2021): [3.OA]
Overview
The intent of clarifying statements is to provide additional guidance for educators to communicate the intent of the standard to support the future development of curricular resources and assessments aligned to the 2021 math standards.
Clarifying statements can be in the form of succinct sentences or paragraphs that attend to one of four types of clarifications: (1) Student Experiences; (2) Examples; (3) Boundaries; and (4) Connection to Math Practices.
2021 Oregon Math Guidance: 3.OA.A.1
Cluster: 3.OA.A - Represent and solve problems involving multiplication and division.
STANDARD: 3.OA.A.1
Standards Statement (2021):
Represent and interpret multiplication of two factors as repeated addition of equal groups.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
2.OA.C.3, 2.OA.C.4 | 3.OA.B.5, 3.OA.A.3, 3.OA.B.6, 3.OA.A.2, 5.NF.B.4 | 5.NF.B.5, 5.NF.B.6 | 3.OA.A.1 3.OA.A Crosswalk |
Standards Guidance:
Boundaries:
- Interpret the factors as representing the number of equal groups and the number of objects in each group. Describe a context in which a total number of objects can be expressed as __ x __.
- This standard does not include calculating products. It is about understanding the meaning of each of the factors in 5 x 7, not the product of 5 x 7.
Progressions
- The equation 3 x 6 = ? means how many are in 3 groups of 6 things each: three sixes. But in many other countries the equation 3 x 6 = ? means how many are 3 things taken 6 times (6 groups of 3 things each): six threes. Some students bring this interpretation of multiplication equations into the classroom. So it is useful to discuss the different interpretations and allow students to use whichever is used in their home. (Please reference page 25 in the Progression document).
Examples
- Student Achievement Partners:
2021 Oregon Math Guidance: 3.OA.A.2
Cluster: 3.OA.A - Represent and solve problems involving multiplication and division.
STANDARD: 3.OA.A.2
Standards Statement (2021):
Represent and interpret whole-number quotients as dividing an amount into equal sized groups.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
3.OA.A.1, 3.OA.A.3, 3.OA.B.6 | 3.OA.B.5 | 5.NF.B.3, 5.NF.B.5, 5.NF.B.6 | 3.OA.A.2 3.OA.A Crosswalk |
Standards Guidance:
Clarifications
- Students should solve multiplication problems including single-digit factors and division problems including single- digit divisors and quotients.
Terminology
- This standard focuses on two models of division: partition models and measurement (repeated subtraction) models.
- Partition models focus on "How many in each equal-sized group?"
- Measurement (repeated subtraction) models focus on "How many groups can you make?".
- This standard does not include calculating. It is about understanding the meaning of what does 56 ÷ 8 mean, not the quotient of what does 56 ÷ 8 equal.
Boundaries
- Students should be able to use numerical reasoning to learn multiplication and division facts through playing games and solving contextual, mathematical problems.
- Fluency does not lend itself to timed tests or speed. Students should be given opportunities to choose flexibly among strategies to solve mathematical problems accurately and efficiently.
Teaching Strategies
- Multiplication strategies may include repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Multiplication tables may be used to help students discover patterns and relationships.
- Division strategies may include repeated subtraction, equal sharing, and forming equal groups.
Progressions
- In Equal Groups, the roles of the factors differ. One factor is the number of objects in a group (like any quantity in addition and subtraction situations), and the other is a multiplier that indicates the number of groups. So, for example, 4 groups of 3 objects is arranged differently than 3 groups of 4 objects. Thus there are two kinds of division situations depending on which factor is the unknown (the number of objects in each group or the number of groups). (Please reference page 24 in the Progression document).
Examples
- Illustrative Mathematics:
2021 Oregon Math Guidance: 3.OA.A.3
Cluster: 3.OA.A - Represent and solve problems involving multiplication and division.
STANDARD: 3.OA.A.3
Standards Statement (2021):
Use multiplication and division within 100 to solve problems in authentic contexts involving equal groups, arrays, and/or measurement quantities.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
3.OA.A.1, 3.OA.A.2 | 3.OA.A.4, 3.OA.D.8, 4.OA.A.1, 4.OA.A.2 | 3.OA.A.3 3.OA.A Crosswalk |
Standards Guidance:
Clarifications
- Students should be able to solve practical, real-life division problems including “how many in each group” and “how many groups” using efficient and flexible strategies.
- 7 x 3 is known, then 3 x 7 is also known (Commutative Property)
- 3 x 5 x 2 can be found by 3 x 5 = 15, then 15 x 2 = 30, or 5 x 2 = 10, then 3 x 10 = 30 (Associative Property)
- Knowing 8 x 5 = 40 and 8 x 2 = 16, 8 x 7 can be found as the sum of these partial products: 8 x (5 + 2) = (8 x 5) + (8 x 2) = 40 + 16 = 56 (Distributive Property)
Boundaries
- Solve multiplication word problems with factors up to and including 10.
- Solve division word problems with a divisor and quotient up to and including 10.
- Students at this grade level are not expected to formally name or identify the specific properties (e.g. commutative, associative, and distributive).
Teaching Strategies
- Students should use a variety of representations for creating and solving one-step word problems, including using drawings and equations with a symbol for the unknown number.
- Some problems should include reading bar graphs, pictographs, and dot plots, as well as measurements in grams, kilograms, liters. Dot plots and line plots can be used interchangeably.
Progressions
- Relating Equal Group situations to Arrays, and indicating rows or columns within arrays, can help students see that a corner object in an array (or a corner square in an area model) is not double counted: at a given time, it is counted as part of a row or as a part of a column but not both.
- Problems in terms of “rows” and “columns,” e.g., “The apples in the grocery window are in 3 rows and 6 columns,” are difficult because of the distinction between the number of things in a row and the number of rows. There are 3 rows but the number of columns (6) tells how many are in each row. There are 6 columns but the number of rows (3) tells how many are in each column. (Please reference page 24 in the Progression document).
Examples
- Illustrative Mathematics:
- Student Achievement Partners:
2021 Oregon Math Guidance: 3.OA.A.4
Cluster: 3.OA.A - Represent and solve problems involving multiplication and division.
STANDARD: 3.OA.A.4
Standards Statement (2021):
Determine the unknown number in a multiplication or division equation relating three whole numbers by applying the understanding of the inverse relationship of multiplication and division.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
3.OA.A.3 | N/A | 4.NBT.B.6, 4.GM.B.6 | 3.OA.A.4 3.OA.A Crosswalk |
Standards Guidance:
Boundaries
- The focus of 3.OA.4 goes beyond the traditional notion of fact families by having students explore the inverse relationship of multiplication and division.
Examples
- Determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = __÷ 3, 6 × 6 = ?.
- Illustrative Mathematics:
- Student Achievement Partners:
2021 Oregon Math Guidance: 3.OA.B.5
Cluster: 3.OA.B - Understand properties of multiplication and the relationship between multiplication and division.
STANDARD: 3.OA.B.5
Standards Statement (2021):
Apply properties of operations as strategies to multiply and divide.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
3.OA.A.1, 3.OA.A.2 | 3.OA.C.7, 3.OA.D.9 | 4.NBT.B.5, 4.NBT.B.6 | 3.OA.B.5 3.OA.B Crosswalk |
Standards Guidance:
Boundaries
- Students need not use formal terms for these properties.
Progressions
- In the Array situations, the roles of the factors do not differ. One factor tells the number of rows in the array, and the other factor tells the number of columns in the situation. But rows and columns depend on the orientation of the array. If an array is rotated 90º, the rows become columns and the columns become rows. This is useful for seeing the commutative property for multiplication in rectangular arrays and areas. (Please reference page 24 in the Progression document).
Examples
- If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.)
- If 3 × 5 × 2 can be found by 3 × 5 = 15 then 15 × 2 = 30, or by 5 × 2 = 10 then 3 × 10 = 30. (Associative property of multiplication.)
- Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)
- Illustrative Mathematics:
- Student Achievement Partners:
2021 Oregon Math Guidance: 3.OA.B.6
Cluster: 3.OA.B - Understand properties of multiplication and the relationship between multiplication and division.
STANDARD: 3.OA.B.6
Standards Statement (2021):
Understand division as an unknown-factor in a multiplication problem.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
3.OA.A.1 | 3.OA.C.7, 3.OA.A.2 | 4.NBT.B.6, 5.NF.B.3, 5.NF.B.7 | 3.OA.B.6 3.OA.B Crosswalk |
Standards Guidance:
Boundaries
- Solve an unknown factor problem, by using division strategies or changing the division problem to an equivalent multiplication problem.
- Since multiplication and division are inverse operations, students are expected to solve problems and explain their processes of solving division problems that can also be represented as unknown factor multiplication problems.
Examples
- Divide 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. (8 x ? = 32)
- Student Achievement Partners:
2021 Oregon Math Guidance: 3.OA.C.7
Cluster: 3.OA.C - Multiply and divide within 100.
STANDARD: 3.OA.C.7
Standards Statement (2021):
Fluently multiply and divide within 100 using accurate, efficient, and flexible strategies and algorithms based on place value and properties of operations.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
3.OA.B.5, 3.OA.B.6 | 4.OA.B.4 | 4.NBT.B.5, 4.NBT.B.6, 4.GM.B.4 | 3.OA.C.7 3.OA.C Crosswalk |
Standards Guidance:
Terminology
- This standard uses the word fluently, which means accuracy, efficiency (using a reasonable amount of steps and time), and flexibility (using strategies such as the distributive property).
- Fluently/Fluency – To achieve fluency, students should be able to choose flexibly among methods and strategies to solve mathematical problems accurately and efficiently.
Boundaries
- By the end of Grade 3, know from memory all products of one-digit numbers. “Know from memory” should not focus only on timed tests and repetitive practice.
- This standard does not require timed assessments. Ample opportunity to develop efficient, accurate, and flexible strategies is essential.
- Students should be allowed to choose an appropriate strategy to demonstrate fluency.
- Finding and using key words is not an appropriate strategy.
Teaching Strategies
- Ample experiences working with manipulatives, pictures, arrays, word problems, and numbers to internalize the basic facts (up to 9 x 9).
- Some problems should include reading bar graphs, pictographs, and dot plots. Some problems should involve grams, kilograms, and liters. Dot plots and line plots can be used interchangeably.
Progressions
- All of the understandings of multiplication and division situations, of the levels of representation and solving, and of patterns need to culminate by the end of Grade 3 in fluent multiplying and dividing of all single-digit numbers and 10.
- Organizing practice so that it focuses most heavily on understood but not yet fluent products and unknown factors can speed learning. To achieve this by the end of Grade 3, students must begin working toward fluency for the easy numbers as early as possible. (Please reference pages 26 & 27 in the Progression document)
Examples
- Student Achievement Partners:
2021 Oregon Math Guidance: 3.OA.D.8
Cluster: 3.OA.D - Solve problems involving the four operations, and identify and explain patterns in arithmetic.
STANDARD: 3.OA.D.8
Standards Statement (2021):
Solve two-step problems in authentic contexts that use addition, subtraction, multiplication, and division in equations with a letter standing for the unknown quantity.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
2.OA.A.1, 3.OA.A.3 | 4.OA.A.3 | 3.GM.B.4 | 3.OA.D.8 3.OA.D Crosswalk |
Standards Guidance:
Clarifications
- Students should represent problems using equations with a variable standing for the unknown quantity and justify their answers.
Boundaries
- This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).
- This is limited to problems posed with whole numbers and having whole-number answers. Situations involving money should not include decimal numbers.
Teaching Strategies
- Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
- Some problems should include reading bar graphs, pictographs, and dot plots, as well as measurements in grams, kilograms, liters. Dot plots and line plots can be used interchangeably.
- Represent these problems using equations with a letter standing for the unknown quantity.
- Students should use numerical reasoning to assess the reasonableness of answers.
Progressions
- Use of two-step problems involving easy or middle difficulty adding and subtracting within 1,000 or one such adding or subtracting with one step of multiplication or division can help to maintain fluency with addition and subtraction while giving the needed time to the major Grade 3 multiplication and division standards. (Please reference page 28 in the Progression document).
Examples
- At the movies, tickets cost $11 each, popcorn costs $7 each, and drinks costs $4 each. If I have $25, do I have enough to purchase 1 ticket, 1 popcorn, and 2 drinks?
- Illustrative Mathematics:
- Student Achievement Partners:
2021 Oregon Math Guidance: 3.OA.D.9
Cluster: 3.OA.D - Solve problems involving the four operations, and identify and explain patterns in arithmetic.
STANDARD: 3.OA.D.9
Standards Statement (2021):
Identify and explain arithmetic patterns using properties of operations, including patterns in the addition table or multiplication table.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
2.OA.C.3, 3.OA.B.5 | 4.OA.C.5 | N/A | 3.OA.D.9 3.OA.D Crosswalk |
Standards Guidance:
Boundaries
- Identifying patterns can help students derive and automatize multiplication facts.
- Multiplication tables may be used to help students discover patterns and relationships.
- A student looking at a multiplication table may discover that multiples of even numbers (2, 4, 6, and 8) are always even; the products in each row and column increase by the same amount (skip counting); the multiples of 6 are double the multiples of 3; the multiples of any number fall on a horizontal and a vertical line due to the commutative property, etc.
- Patterns may include exposure to even and odd extending from previous work in 2nd grade.
Teaching Strategies
- Opportunities for students to examine numerical patterns.
- The ability to recognize and explain patterns in mathematics leads students to developing the ability to make generalizations, a foundational concept in algebraic thinking.
- Students investigate multiplication tables in search of patterns and explain why these patterns make sense mathematically.
- The multiples of 4, 6, 8, and 10 are all even because they can all be decomposed into two equal groups.
- The doubles (multiples of 2) in a multiplication table fall on horizontal and vertical lines.
- On a multiplication chart, the products in each row and column increase by the same amount (skip counting).
- All the multiples of 5 end in a 0 or 5 while all the multiples of 10 end with 0. Every other multiple of 5 is a multiple of 10.
Examples
- Observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.
- A student highlighting the multiples of 9 on a hundreds chart might notice 2 x 9 is 2 away from 20, 3 x 9 is 3 away from 30, and so forth.
- Illustrative Mathematics: