Primary Type: Lesson Plan
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 48313
Déjà Vu Addition, 2 plus 2 plus 2
This lesson illustrates that when you have a rectangular array of items with the same number of items in each row or each column, you can
determine the sum of the items by adding the group in column 1 to the group in column 2, etc. This is the foundation of repeated addition and
multiplication in 3rd grade.
Subject(s): Mathematics
Grade Level(s): 2
Intended Audience: Educators
Instructional Time: 1 Hour(s)
Freely Available: Yes
Keywords: addition, array, repeated addition
Instructional Design Framework(s): Guided Inquiry (Level 3)
Resource Collection: CPALMS Lesson Plan Development Initiative
LESSON CONTENT
Lesson Plan Template: General Lesson Plan
Learning Objectives: What should students know and be able to do as a result of this lesson?
Students will be able to add a number of objects that are arranged in a rectangular array that does not exceed 5 columns and 5 rows.
Students will be able to express the array in an equation that shows the total as the sum of addends.
Prior Knowledge: What prior knowledge should students have for this lesson?
Students should be able to solve real world problems that involve addition of 3 whole numbers that equal up to 20 (1st grade).
Students should be able to fluently add within 20 (2nd grade).
Students should be able to use equations to solve real world problems with addition to 100 (2nd grade).
Guiding Questions: What are the guiding questions for this lesson?
In what situations do we add numbers?
What strategies will help me add numbers quickly when I have the same addends?
What is an array? What does it look like? What must an arrangement have in order to be an array?
What pattern do you see?
Teaching Phase: How will the teacher present the concept or skill to students?
1. After assessing prior knowledge, the teacher will put students in pairs or groups of no more than four.
2. Explain to the students that each group will be given a piece of paper with situations on it. Your expectation is that you want them to come up with at least two
different ways to express the sum of the items in each situation.
3. Groups are to write their two ways and explanations on the paper (provide extra paper if needed).
4. Pass out group assignment and provide groups 5-10 minutes (adjust time as needed) for them to justify, solve and write their responses.
5. Ask students to share one of the ways they got a sum (have students write it on the board (or you can write it for them). Inevitably one of the ways they will give is
to simply count the items. This is not wrong, but after students get other strategies like 2+2+2 = 6 or 3+3= 6 you may want to ask the class if counting one by one
is the best/quickest/most efficient way.
6. Give students 2 minutes to discuss with their partner/group why 2+2+2 = 6 or 3+3= 6 is a better way to express the sum.
7. The teacher should use the terminology 1 group of 3 + 1 group of 3 = 6, or 1 group of 2 + 1 group of 2 + 1 group of 2 = 6.
page 1 of 3 8. Guide students to say that this is a good strategy for adding same size groups to each other. Ask them if it would work if you had a group with a different number
(addend) in it? You may have a student say yes but you would have some left over. Let them know that is correct, but for now we are only going to worry about
groups with the same number in each column or row.
9. Define the rectangular arrangement of equal amounts in rows and columns as an array.
Group Assignment
Guided Practice: What activities or exercises will the students complete with teacher guidance?
Embedded in Teaching Phase and includes Independent Practice.
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the
lesson?
Students may still work with their partner(s), if the teacher prefers. See attached Independent Practice sheet.
Independent Practice
Independent Practice - Answer Key
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
Teacher asks: What are some situations that we need to add numbers?
Teacher asks: What are some situations that we need to add groups with the same addends?
Teacher can ask: Are there strategies that will help me add or subtract numbers quickly?
Teacher can ask: What is an array? Why is it useful?
Review of the Independent Practice sheet is also part of the closure.
Summative Assessment
Students will demonstrate their learning by writing equations and solving addition situations through 25 with equal addends. Students will write their own problem for an
array with the same addends, not to exceed a 5 x 5 array. Then on the following day, the student generated problems will be shuffled and given to a different student.
They will solve the new problem, generating an equation and answer. Then the teacher will randomly ask students to read their problem and explain their answer and
equation. These can continue to be used in a center for practice. If this is too challenging for the students to create, the teacher can create a one or two question
assessment to gauge understanding.
Formative Assessment
To assess prior knowledge, the teacher can ask students to solve various addition equations (e.g. 7+13=?, ?+11=24, 5+?=14). You can also ask students to write
and solve an equation for a situation such as: Billy had some comic books. For his birthday, his Dad gave him 8 more comic books. Now he has 16 comic books.
How many comic books did he have before his birthday? Have students explain their answer/equation.
Teacher would visually spot check to see when students are ready to move on to the lesson.
Feedback to Students
Students will be provided with feedback throughout the lesson through observation and sharing of partnered work. They will be working with their partner to solve
addition problems. Partners will provide feedback as justifications are made.
Feedback will also be provided by the teacher in the guided practice phase as the teacher monitors and facilitates partner critiques of answers, as well as spot
checking student responses.
Feedback will also be provided with the completion of the attached independent practice sheet.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations:
Provide manipulatives
Put them in a group of three.
Allow them to only provide one way to determine the sum of the group of items.
Provide the student with a hundreds chart.
Provide them with a calculator to check their answer.
Extensions:
Challenge students to come up with more than 2 ways to determine the sum.
Challenge the students to write their own problem situations that you can perhaps use later.
Special Materials Needed:
Teacher Materials:
Group Assignment sheet
Independent Practice Sheet (and answer key)
Board or display to write/draw responses/equations/explanations
Writing utensils
Student Materials:
Extra paper to write responses/equations/explanations on (if needed)
Group Assignment Sheet to record responses on
Independent Practice Sheet
Writing utensils
Further Recommendations: The concept of repeated addition is the foundation of multiplication and is an important benchmark to understand for the successful
transition into multiplication in third grade. If students struggle with this concept, you should spend more time with it either in whole group, small group, or in a center,
whichever meets your students' needs.
page 2 of 3 Additional Information/Instructions
By Author/Submitter
This lesson aligns to the Mathematical Practice Standard MAFS.K12.MP.7.1: Look for and make use of structure, because the students will be trying to see a pattern in the
numbers and what is the same about the solution strategies. It also aligns to MAFS.K12.MP.8.1: Look for and express regularity in repeated reasoning, because students are
finding the pattern and reason to express an addition problem as repeated addition.
SOURCE AND ACCESS INFORMATION
Contributed by: Gary Elkins
Name of Author/Source: Gary Elkins
District/Organization of Contributor(s): Volusia
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.2.OA.3.4:
Description
Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns;
write an equation to express the total as a sum of equal addends.
page 3 of 3