Unit at a Glance – Long Range Planning
Grade 3, Unit 1: Understanding Multiplication and Division
3.OA.A.1 / Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 x 7.Level 4 / More complex learning goal
Evidence shows students are able to transfer learning above and beyond level three expectations (products and performances)
Authentic problem /task[SMP 1, 2, 3, 4, 5, 6, 7, 8]
Level 3 / Target learning goal
Evidence shows students are able to demonstrate what you want them to know and be able to do as dictated by the RIGOR of the standards
- Describe a word problem or a situation where the total can be represented with multiplication. [SMP 1, 2, 4, 7, 8]
- Show or explain how a multiplication problem can be solved with both repeated addition and multiplication.
[SMP 2, 3, 4, 5, 7, 8]
Level 2 / Simpler learning goal
Evidence shows the students demonstrate an understanding of the knowledge and reasoning targets but are not at the level to have mastered the standards and/or apply the understanding as the standard dictates.
- Solve a multiplication word problem by modeling equal groups and arrays. [SMP 1, 2, 4, 5, 6, 7, 8 ]
Level 1 / Foundational knowledge, prerequisite
Evidence shows students have demonstrated basic foundational knowledge as related to the standards
- Write repeated addition equations that are represented by arrays. [SMP 3, 4, 5, 7, 8]
3.OA.A.2 / Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.
Level 4 / More complex learning goal
Evidence shows students are able to transfer learning above and beyond level three expectations (products and performances)
Authentic problem /task[SMP 1, 2, 3, 4, 5, 6, 7, 8]
Level 3 / Target learning goal
Evidence shows students are able to demonstrate what you want them to know and be able to do as dictated by the RIGOR of the standards
- Select and use models to solve word problems involving division as sharing. [SMP 1, 2, 4, 5, 6, 8]
- Solve word problems involving division as repeated subtraction by using models. [SMP 1, 2, 4, 5, 6, 7, 8]
- Solve and create basic division word problems or describe division situations. [SMP 1, 2, 3, 4, 5, 6, 7, 8]
Level 2 / Simpler learning goal
Evidence shows the students demonstrate an understanding of the knowledge and reasoning targets but are not at the level to have mastered the standards and/or apply the understanding as the standard dictates.
- Recognize division situations. [SMP 1, 2, 4, 5, 6, 7, 8]
Level 1 / Foundational knowledge, prerequisite
Evidence shows students have demonstrated basic foundational knowledge as related to the standards
- Represents a set of concrete objects being shared equally and identifies the quantity in each share.[SMP 1, 2, 7]
3.OA.A.3 / Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
Level 4 / More complex learning goal
Evidence shows students are able to transfer learning above and beyond level three expectations (products and performances)
Authentic problem /task[SMP 1, 2, 3, 4, 5, 6, 7, 8]
Level 3 / Target learning goal
Evidence shows students are able to demonstrate what you want them to know and be able to do as dictated by the RIGOR of the standards
- Solve and represent multiplication word problems within 100 by using equations, arrays, and equal groups.
[SMP 1, 2, 4, 5, 6, 7, 8] - Solve and representdivisionword problems within 100by using equations, arrays, and equal groups. [SMP 1, 2, 4, 5, 6, 7, 8]
Level 2 / Simpler learning goal
Evidence shows the students demonstrate an understanding of the knowledge and reasoning targets but are not at the level to have mastered the standards and/or apply the understanding as the standard dictates.
- Solve and represent multiplication word problems with factors of 2, 5, and 10 by using models. [SMP 1, 2, 4, 5, 6, 8]
- Represent division word problems involving equal groups and arrays by using manipulatives. [SMP 1, 2, 4, 5, 6, 7, 8]
Level 1 / Foundational knowledge, prerequisite
Evidence shows students have demonstrated basic foundational knowledge as related to the standards
- Represent multiplication problems involving equal groups and arrays by using manipulatives. [SMP 1, 4, 5, 6, 7, 8]
3.OA.B.5 / Apply properties of operations as strategies to multiply and divide. Examples: If 6 x 4 = 24 is known, then 4 x 6 = 24 is also known. (Commutative property of multiplication.) 3 x 5 x 2 can be found by 3 x 5 = 15, then 15 x 2 = 30, or by 5 x 2 = 10, then 3 x 10 = 30. (Associative property of multiplication.) Knowing that 8 x 5 = 40 and 8 x 2 = 16, one can find 8 x 7 as 8 x (5 + 2) = (8 x 5) + (8 x 2) = 40 + 16 = 56. (Distributive property.)
Level 4 / More complex learning goal
Evidence shows students are able to transfer learning above and beyond level three expectations (products and performances)
Authentic problem /task[SMP 1, 2, 3, 4, 5, 6, 7, 8]
Level 3 / Target learning goal
Evidence shows students are able to demonstrate what you want them to know and be able to do as dictated by the RIGOR of the standards
- Apply various properties of multiplication to solve multiplication problems. [SMP 2, 4, 5, 6, 7, 8]
- Explain or show how to apply the Distributive Property to find products within 100, by using words, models, or equations.
[SMP 2, 3, 4, 5, 6, 7, 8]
Level 2 / Simpler learning goal
Evidence shows the students demonstrate an understanding of the knowledge and reasoning targets but are not at the level to have mastered the standards and/or apply the understanding as the standard dictates.
- Explain why I can multiply factors in any order to solve problems. [SMP 3, 4, 6, 7]
- Multiply by zero and one by using properties of operations. [SMP 3, 4, 6, 7]
- Break apart unknown facts into known facts to solve multiplication problems supported by concrete or visual models. [SMP 2, 4, 6, 7, 8]
Level 1 / Foundational knowledge, prerequisite
Evidence shows students have demonstrated basic foundational knowledge as related to the standards
- Multiply factors in any order to solve problems. [SMP 4, 6, 7]
- Decompose numbers and arrays in a variety of ways. [SMP 2, 6, 7]
- Represent multiplication using an array. [SMP 4, 5, 7]
3.OA.C.7 / Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
Level 4 / More complex learning goal
Evidence shows students are able to transfer learning above and beyond level three expectations (products and performances)
Authentic problem /task[SMP 1, 2, 3, 4, 5, 6, 7, 8]
Level 3 / Target learning goal
Evidence shows students are able to demonstrate what you want them to know and be able to do as dictated by the RIGOR of the standards
- Apply the various properties of Multiplication to solve multiplication problems. [SMP 1, 2, 4, 7, 8]
- Explain or show how to apply the Distributive Property to find products within 100, by using words, models, or equations.
- Solve problems involving division as repeated subtraction by using models. [SMP 1, 4, 5, 6, 8]
Level 2 / Simpler learning goal
Evidence shows the students demonstrate an understanding of the knowledge and reasoning targets but are not at the level to have mastered the standards and/or apply the understanding as the standard dictates.
- Explain why changing the order of the factors in a multiplication problem results in the same product by using words, models, or equations. [SMP 3, 4, 5, 6, 7]
- Explain the Zero and Identity Properties of Multiplication. [SMP 2, 3, 4, 5, 6, 7]
- Apply patterns in products within 100 when 0, 1, 2, 5, 9, and 10 are factors to solve multiplication problems by using words, models, or equations. [SMP 5, 7, 8]
- Solve multiplication problems using arrays and number lines. [SMP 2, 4, 5, 6, 7, 8]
- Solve problems involving division as sharing by using models. [SMP 2, 4, 5, 6, 7, 8]
Level 1 / Foundational knowledge, prerequisite
Evidence shows students have demonstrated basic foundational knowledge as related to the standards
- Identify patterns in products within 100 when 0, 1, 2, 5, 9, and 10 are factors. [SMP 3, 5, 7, 8]
- Write repeated addition equations that are represented by arrays. [SMP 3, 4, 5, 7, 8]
3.OA.D.9 / Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.
Level 4 / More complex learning goal
Evidence shows students are able to transfer learning above and beyond level three expectations (products and performances)
Authentic problem /task[SMP 1, 2, 3, 4, 5, 6, 7, 8]
Level 3 / Target learning goal
Evidence shows students are able to demonstrate what you want them to know and be able to do as dictated by the RIGOR of the standards
- Explain how to use patterns in products to solve multiplication problems.[SMP 3, 5, 7, 8]
Level 2 / Simpler learning goal
Evidence shows the students demonstrate an understanding of the knowledge and reasoning targets but are not at the level to have mastered the standards and/or apply the understanding as the standard dictates.
- Solve problems using patterns in products.[SMP 5, 7, 8]
Level 1 / Foundational knowledge, prerequisite
Evidence shows students have demonstrated basic foundational knowledge as related to the standards
- Identify number patterns in products. [SMP 5, 7, 8]
- Skip count. [SMP 7, 8]
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Unit at a Glance – Long Range Planning
Grade 3, Unit 1: Understanding Multiplication and Division
21 lessons, 29 days allotted / Suggested Unit Completion Date:Start Date: / End Date:
Lesson, Objective, and Materials / Pre-Planning Notes – Reflection
Lesson 1: Multiplication as Repeated Addition (3.OA.A.1, 3.OA.A.3)
Represent multiplication facts by writing addition and multiplication number sentences.
- enVisionmath 1-1
- SR, Naming Things That Come in Groups
- SR, Circles and X’s Game
- SR, Relate Addition and Multiplication
Refer to 3.OA.A.3.PL1.U1 for a digital asset.
Represent Multiplication Problems Involving Equal Groups and Arrays by Using Manipulatives
- Materials:
- two-color counters
- A way to record thinking (paper, dry-erase board, etc.)
Repeated Addition and Arrays
- Materials:
- two-color counters
- number cube
- Rolling Arrays Recording Sheet
- A way to record thinking (math notebook, paper and pencil, dry-erase board, etc.)
Lesson 2: Multiplication on a Number Line (3.OA.A.1, 3.OA.A.3)
Represent multiplication facts by using a number line.
- enVisionmath 1-2
- Investigations, Unit 5, Equal Groups, pp. 28-33
- Investigations, M6, Pictures of Things That Come in Groups
Lesson 3: Arrays and Multiplication (3.OA.A.1, 3.OA.A.3)
Find a total represented by an array by using words and number sentences.
- enVisionmath 1-3
- Investigations, Unit 5, Equal Groups, “Arranging Chairs,” pp. 83-84
- two-color counters
- inch tiles
- Investigations,M14, Half-Inch Grid Paper
- Investigations, M15-M16, Arranging Chairs
- SR, Be an Array Detective
Explain and Describe Word Problems Using Repeated Addition and MultiplicationMaterials:
- A way to record thinking (math notebook, paper and pencil, dry-erase board, etc.)
- Manipulatives for solving multiplication problems should be available (counters, tiles, etc.)
Solving Multiplication Word Problems by Modeling Equal Groups and Arrays
- Materials:
- ‘Pictures of Things that Come in Groups’ recording sheet
- Manipulatives for solving multiplication problems should be available (counters, tiles, etc.)
Lesson 4: Arrays and the Commutative Property of Multiplication (3.OA.A.1, 3.OA.A.3, 3.OA.B.5)
Demonstrate understanding of the Commutative Property of Multiplication by writing two related multiplication sentences represented by an array.
- enVisionmath 1-4
- Investigations Digit Cards
- Investigations, M14, Half-Inch Grid Paper
Lesson 5: Division Story Problems – Number in Each Group (3.OA.A.2, 3.OA.A.3)
Solve division story problems by finding the number in each group.
- enVisionmath 1-5
- cubes and/or counters
- Investigations, M14, Half-Inch Grid Paper
Representing Division Word Problems Involving Equal Groups and Arrays
- Materials:
- Landmark Tic Tac Toe Resources
- two-color counters
- A way to record thinking (math notebook, paper and pencil, dry-erase board, etc.)
Sharing Objects Equally and Identifying the Quantity in Each Share
- Materials:
- number cubes
- Gumball Game Board
- two-color counters
- a way to record thinking (math notebook, paper and pencil, dry-erase board, etc.)
Lesson 6: Division Story Problems – Number of Groups (3.OA.A.2, 3.OA.A.3)
Solve division story problems by finding the number of groups.
- enVisionmath 1-6
- cubes and/or counters
- Investigations, M14, Half-Inch Grid Paper
Solving Word Problems Involving Division as Repeated Subtraction by Using Models
- Materials:
- A way to record thinking (math notebook, paper and pencil, dry-erase board, etc.)
- Manipulatives for solving division problems should be available (counters, tiles, etc.)
- Paper and crayons or markers for creating a comic
Lesson 7: Use Appropriate Tools (3.OA.A.1, 3.OA.A.2, 3.OA.A.3)
Select and use appropriate tools to solve real-world problems.
- enVisionmath 1-7
- cubes
- counters
- grid paper
Refer to 3.OA.A.2.PL2.U1 for a digital asset.
Recognize Division Situations
- No materials needed
Lesson 8: 2 as a Factor (3.OA.A.1, 3.OA.A.3, 3.OA.B.5, 3.OA.D.9)
Solve problems with two as a factor by using addition doubles facts and skip counting by two to find a total.
- enVisionmath 2-1
- Investigations, M12, 100 Chart with Skip Counting Circles
Recognize Numerical Patterns
- Materials:
- A way to record thinking (math notebook, paper and pencil, dry-erase board, etc.)
Recognize Numerical Patterns
- Materials:
- A way to record thinking (math notebook, paper and pencil, dry-erase board, etc.)
- ‘Solve with Numerical Patterns’ recording sheet.
Lesson 9:5 as a Factor (3.OA.A.1, 3.OA.A.3, 3.OA.B.5, 3.OA.D.9)
Solve problems with five as a factor by skip counting by five to find a total.
- enVisionmath 2-1
- Investigations, M12, 100 Chart with Skip Counting Circles
Lesson 10: 9 as a Factor (3.OA.A.1, 3.OA.A.3, 3.OA.B.5, 3.OA.C.7, 3.OA.D.9)
Represent and solve problems with nine as a factor by using patterns and skip counting strategies.
- enVisionmath 2-2
- SR, Skip Counting by Nine
Recognize Numerical Patterns
- Materials:
- A way to record thinking (math notebook, paper and pencil, dry-erase board, etc.)
Lesson 11:Multiplying with 0 and 1 (3.OA.A.1, 3.OA.A.3, 3.OA.B.5, 3.OA.D.9)
Solve problems with 0 and 1 as factors by identifying and using the Identity and Zero Properties for Multiplication.
- enVisionmath 2-3
Lesson 12:10 as a Factor (3.OA.A.1, 3.OA.A.3, 3.OA.B.5, 3.OA.D.9)
Solve problems with ten as a factor by skip counting by ten to find a total.
- enVisionmath 2-4
- Investigations, M12, 100 Chart with Skip Counting Circles
Lesson 13:Multiplication Facts (3.OA.A.1, 3.OA.A.3, 3.OA.D.9)
Solve problems by using basic multiplication facts.
- enVisionmath 2-5
Solve and Represent Multiplication Word Problems Within 100 by Using Equations, Arrays, and Equal Groups
- Materials:
- 'Representing Multiplication Word Problems' recording sheet
- two-color counters
- a way to record thinking (math notebook, paper and pencil, dry-erase board, etc.)
Lesson 14:Modeling Mathematics (3.OA.A.3, 3.OA.C.7)
Solve real-world problems by using models.
- enVisionmath 2-6
Refer to 3.OA.C.7.PL2.U1 for a digital asset.
Solving Multiplication Problems Using Arrays and Number Lines
- Materials:
- two-color counters
- A way to record thinking (math notebook, paper and pencil, dry-erase board, etc.)
Solving Multiplication Problems Using Arrays and Number Lines
- Materials:
- two-color counters
- Investigations Array Cards
- A way to record thinking (math notebook, paper and pencil, dry-erase board, etc.)
Lesson 15:The Distributive Property (3.OA.B.5)
Solve multiplication problems by decomposing unknown facts into known facts.
- enVisionmath 3-1
Explain or Show How to Apply the Distributive Property to Find Products Within 100,
- Materials:
- a way to record voice or video
- a way to record a written response (math notebook, paper and pencil)
- two-color counters
Break Apart Unknown Facts into Known Facts to Solve Multiplication Problems
- Materials
- 'Solving Decomposed Arrays' recording sheet
- two-color counters
Decomposing Numbers and Arrays in a Variety of Ways
- Materials
- 'Decomposing Arrays' recording sheet
- Investigations Array Cards
- two-color counters
- a way to record thinking (math notebook, paper and pencil, dry-erase board, etc.)
Lesson 16: 3 as a Factor (3.OA.A.1, 3.OA.A.3, 3.OA.B.5, 3.OA.C.7, 3.OA.D.9)
Represent and solve problems with three as a factor by using skip-counting, models, words, and number sentences.
- enVisionmath 3-2
- Investigations, M12, 100 Chart with Skip Counting Circles
- two-color counters for representing arrays
- grid paper for drawing arrays
Lesson 17: 4 as a Factor (3.OA.A.1, 3.OA.A.3, 3.OA.B.5, 3.OA.C.7, 3.OA.D.9)
Represent and solve problems with four as a factor by using mathematical properties, skip-counting, models, words, and number sentences.
- enVisionmath 3-3
- SR, Multiples on a Hundred Chart
- two-color counters for representing arrays
- grid paper for drawing arrays
- Investigations Array Cards
Lesson 18: 6 and 7 as a Factor (3.OA.A.1, 3.OA.A.3, 3.OA.B.5, 3.OA.C.7, 3.OA.D.9)
Represent and solve problems with six or seven as a factor by using mathematical properties, skip-counting, models, words, and number sentences.
- enVisionmath 3-4
- two-color counters for representing arrays
- grid paper for drawing arrays
- Investigations Array Cards
Lesson 19: 8 as a Factor (3.OA.A.1, 3.OA.A.3, 3.OA.B.5, 3.OA.C.7, 3.OA.D.9)
Represent and solve problems with eight as a factor by using mathematical properties, skip-counting, models, words, and number sentences.
- enVisionmath 3-5
- two-color counters for representing arrays
- grid paper for drawing arrays
- Investigations Array Cards
Lesson 20: The Associative Property: Multiply with 3 Factors (3.OA.A.3, 3.OA.B.5)
Represent and solve problems with eight as a factor by using mathematical properties, skip-counting, models, words, and number sentences.
- enVisionmath 3-7
Lesson 21: Repeated Reasoning (3.OA.B.5)
Apply repeated reasoning to find general strategies for finding products.
- enVisionmath 3-8
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