This lesson is designed for students in grades 3-5 but includes standards for grades 1-5 because it focuses on building students’ foundational and conceptual knowledge of addition, subtraction, multiplication, and division. During this lesson, students will collaborate with a small group of their peers to explore a mathematical operation, considering any related strategies, connections to other mathematical operations and concepts, and examples of the operation in the real world. Students will reflect on and respond to their peers’ writing about the opposite operation. This will not only strengthen students’ conceptual understanding of relationships between operations, but will also help foster a reflective and respectful classroom community. Finally, students will apply their conceptual understanding of operations by demonstrating how to think critically about story situations before determining operations and strategies that can be used to efficiently find a correct solution.
This lesson is designed to be flexible in nature. Consider your students’ learning abilities and needs when deciding which operations and portions of this lesson to use. It is suggested to choose one of the following, but use your best judgement to support your students:
CCSS.Math.Practice.MP4 | Model with mathematics. |
CCSS.Math.Practice.MP6 | Attend to precision. |
CCSS.Math.Practice.MP7 | Look for and make use of structure. |
CCSS.Math.Practice.MP8 | Look for an express regularity in repeated reasoning. |
CCSS.Math.Content.1.OA.A.1 – Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. |
CCSS.Math.Content.1.OA.A.2 – Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. |
CCSS.Math.Content.1.NBT.C.4 - Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. |
CCSS.Math.Content.2.OA.A.1 - Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. |
CCSS.Math.Content.2.NBT.B.5 - Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. |
CCSS.Math.Content.2.NBT.B.7 - Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. |
CCSS.Math.Content.2.NBT.B.9 - Explain why addition and subtraction strategies work, using place value and the properties of operations. |
CCSS.Math.Content.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. |
CCSS.Math.Content.3.OA.B.5 - Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 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.) |
CCSS.Math.Content.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. |
CCSS.Math.Content.3.NBT.A.2 - Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. |
CCSS.Math.Content.3.NBT.A.3 - Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. |
CCSS.Math.Content.4.OA.A.2 - Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. |
CCSS.Math.Content.4.OA.A.3 - Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. 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. |
CCSS.Math.Content.4.NBT.B.5 - Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. |
CCSS.Math.Content.4.NBT.B.6 - Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. |
CCSS.Math.Content.5.OA.A.1 - a Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. |
CCSS.Math.Content.5.OA.A.2 - a Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation "add 8 and 7, then multiply by 2" as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. |
CCSS.Math.Content.5.NBT.B.5 - Fluently multiply multi-digit whole numbers using the standard algorithm. |
CCSS.Math.Content.5.NBT.B.6 - a Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. |
Students will be able to collaborate with peers to discuss and write about such mathematical operations as addition, subtraction, multiplication, and division.
Students will be able to make connections between operations as well as to real world situations.
Students will be able to apply their conceptual understanding of the four basic mathematical operations to demonstrate their procedural knowledge.
• The Building Blocks of Math series, specifically the Addition, Subtraction, Multiplication, and Division texts
• Scratch paper
• Pencils
• Chart Paper (1 per group of 3-4 students)
It is suggested to set up the chart paper prior to the lesson. In the center of each sheet of chart paper, draw a large rectangle and partition it into four boxes. Students will respond to four questions, placing their answers into the four boxes accordingly. Leave enough room around the edges of the inner rectangle as margins because students will also be asked to reflect in writing here.
• Markers
• Guiding Questions (1 per group)
• Operations Articles (1 matching article per group)
• Addition and Subtraction Assignments:
Lowest cognitive demand: Snorkeling in the Swamp and Bubble Trouble
Average cognitive demand: Ticket Sale and Sports Runs in the Family
Highest cognitive demand: Dazzling Dives and Turtle Hurdles
• Multiplication and Division Assignments:
Lowest cognitive demand: How Many Jumps? and Numbers from the Sky
Average cognitive demand: Meet the Athletes and Hula Hoop Questions
Highest cognitive demand: Tasty Problems and The Big Race
Approximately 70-80 minutes.
Prior to engaging in this lesson, students should have a working knowledge of the operations addressed. This lesson does not serve as an introduction, rather students will rely on and build upon their knowledge of these operations.
Students should be familiar with collaborating as a team. Consider reviewing any group work expectations you have before engaging in the task.
Because this lesson involves writing about mathematics, it would be beneficial to review any expectations you have prior to students engaging in the writing task. For example, consider whether students can use bullet points or if they should write using complete sentences, how students should highlight their use of academic language, and what visuals they can use to support and extend their writing.
Addition – the adding of one number or quantity to another
Subtraction – the act or process of taking one number or quantity from another; finding the difference between two numbers or quantities
Multiplication – the operation of finding a product by adding a number or quantity (the multiplicand) as many times as there are units in another (the multiplier)
Division – the process of dividing one number by another into equal parts
This lesson includes two major opportunities for differentiation. First, consider using strategic grouping during this lesson. Students will work in teams of 3-4 throughout this lesson. It might be beneficial to ensure each group has a strong reader/writer. In addition, it may be helpful to assign students roles such as reader, scribe, timekeeper, etc. to hold students accountable to their team during work time. When grouping students, you can also consider assigning different operations, depending on students’ skills and needs.
The Independent Application and Demonstration of Learning section of this lesson plan provides another opportunity for differentiation: assign any of the three leveled sets of independent practice to students with different learning needs (see Materials for information about the cognitive demand of each assignment).
Time Guidelines:
Approximately 10 minutes
Teacher Actions
Determine whether your focus is on addition and subtraction or on multiplication and division prior to beginning the lesson.
Begin by presenting the appropriate mathematical story situation and questions (see below) to students. Provide students 2-3 minutes to discuss the situation and determine which operations they might need to use in order to solve these problems with a neighbor. Have 2-3 students share their responses with the class.
Next, provide students time to solve the problem on scratch paper independently. Review the solutions with students and explain that today they will do a deep dive into one of the two operations they just used. They will consider strategies, relationships to other mathematical operations and concepts, and connections to the real world to help them better understand their operation.
Addition and Subtraction: Susan grows beautiful flowers! She picked 15 flowers from her garden for her brother and 23 more flowers for her mother. How many flowers did she pick in all? How many more flowers did she pick for her mother than for her brother?
Answers: 15 + 23 = 38, so she picked 38 flowers in all. 23 – 15 = 8, so she picked 8 more flowers for her mother than for her brother.
Multiplication and Division: Marco baked 3 trays of cookies. Each tray contained 8 cookies. How many cookies did Marco bake? Once the cookies cooled, Marco decided to share them with three of his friends (while keeping an equal share for himself!). How many cookies will each person get?
Answers: 3 trays of 8 cookies can be represented as 3 x 8 = 24, so Marco baked 24 total cookies. Marco wanted to share the cookies with his three friends and himself, so we must divide the total number of cookies into 4 groups. 24 ÷ 4 = 6, so each person will get 6 cookies.
Time Guidelines:
Approximately 5-7 minutes
Teacher Actions
Because today’s lesson is largely reflective in nature and student driven, use this time to introduce the task to students. Explain that students will work in groups of 3-4 to reflect on and respond to guiding questions about specific mathematical operations (addition, subtraction, multiplication, or division).
First, students will consider and discuss their assigned operation. As a team, they will respond to 4 prompts, writing each answer in one of the 4 inner-most boxes on their chart paper.
Next, students will switch chart paper with a group that focused on the opposite operation (i.e., addition and subtraction will switch, and multiplication and division will switch). Students will then use a provided set of guiding questions to review what the other team wrote on their chart paper. Again, students will collaborate as a team to respond to what their peers wrote about the opposite operation. Students should record their questions, connections, answers, and additional ideas in the margins of the chart paper.
Finally, students will wrap up the collaborative portion of this lesson by returning to their original chart paper to review the notes their peers left in the margins. Students will again use a set of guiding questions to structure their discussion.
Pause to address any student questions, create groups of 3-4, and pass out needed materials. Before beginning the task, review with students where to answer each of the four prompts on their chart paper (each answer should go inside one of the four inner-most boxes, the margins should be left blank until groups swap chart paper).
Time Guidelines:
Part A: 10-13 minutes
Part B: 10 minutes
Part C: 10 minutes
Teacher Actions
Part A: Students will collaborate to read a short article about their operation. Next, they will read and respond to four prompts about their operation, writing each answer in a separate box on their chart paper.
Encourage students to respond in full to all four prompts. Students should aim to have at least 2-3 answers/ideas written in each of the four boxes on their chart paper.
Part B: Students will transition and switch chart paper with a group focused on the opposite operation (addition will switch with subtraction and multiplication will switch with division). They will read and discuss the following guiding questions, pausing after each question to respond in the margins of the chart paper. Students do not need a response for every single guiding question, rather they should use these to aid their discussion and inform their writing.
Part C: Students will swap chart papers once more so they are back to their original work. Students will read and discuss the following guiding questions to reflect on their peers’ comments about their operation.
Return to the whole group setting and discuss any aha! moments, interesting facts, stand out real-world examples, and questions students may still have.
Time Guidelines:
Approximately 15-20 minutes
Teacher Actions
Have students transition to the independent work setting where they will apply their conceptual knowledge of operations to answer story problems involving a variety of operations. Consider your students’ needs and assign independent work accordingly:
• Addition and Subtraction Assignments:
o Lowest cognitive demand: Snorkeling in the Swamp and Bubble Trouble
o Average cognitive demand: Ticket Sale and Sports Runs in the Family
o Highest cognitive demand: Dazzling Dives and Turtle Hurdles
• Multiplication and Division Assignments:
o Lowest cognitive demand: How Many Jumps? and Numbers from the Sky
o Average cognitive demand: Meet the Athletes and Hula Hoop Questions
o Highest cognitive demand: Tasty Problems and The Big Race
Time Guidelines:
Approximately 10 minutes
Teacher Actions
Revisit the story situation from the hook. Discuss how you originally tackled this problem. Consider using the following prompts: After reflecting, what can be said about how we solved that problem originally? What other strategies could you use to help you solve this problem? In the future, what would you change about how you solve those types of story problems?
Review today’s learning objectives by explaining to students that they spent time today collaborating to better understand mathematical operations. They considered specific strategies, how operations relate to one another, and connections to mathematics in the real-world. Students also applied that conceptual understanding to solve story problems related to those operations. Doing this deep dive into operations helped students develop strong foundations upon which great mathematical knowledge can be built.
What went well?
What changes might be beneficial?
Reteaching Needs
Extension Needs